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2/24/2008 ELF 1

Professional DevelopmentShort Course on

Tactical Missile Design

Professional DevelopmentShort Course on

Tactical Missile Design

Eugene L. FleemanTactical Missi le DesignE-mail: [email protected]

Web Site: http://genefleeman.home.mindspring.com



2/24/2008 ELF 2

Outline Outline

Introduction / Key Drivers in the Design Process

Aerodynamic Considerations in Tactical Missile Design

Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design

Flight Performance Considerations in Tactical Missile Design

Measures of Merit and Launch Platform Integration Sizing Examples

Development Process

Summary and Lessons Learned References and Communication

Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )



2/24/2008 ELF 3

Emphasis Is on Physics-Based, Analytical Sizing

of Aerodynamic Configuration

Emphasis Is on Physics-Based, Analytical Sizing

of Aerodynamic Configuration

Safe, Arm, and Fuzing

Power Supply

Seeker, Sensors, and Electronics

Launch Platform Integration

Additional Measures of Merit

Cost

Miss Distance

WarheadWeight

Structure

Propulsion

Aero Flight Performance

Aero Stability & Control

Aero Configuration Sizing

Emphasis Area

Primary Emphasis

Secondary Emphasis

Tertiary EmphasisNot Addressed- -



2/24/2008 ELF 4

Superior Better Comparable Inferior

Axial Acceleration AGM-88

Maneuverability AA-11Speed / altitude SM-3

Dynamic pressure PAC-3

Size Javelin

Weight FIM-92

Production cost GBU-31

Observables AGM-129

Range AGM-86Kills per use Storm Shadow

Target acquisition LOCAAS

Tactical MissileCharacteristics

Comparison WithFighter Aircraft

– –

–

–

Tactical Missiles Are Different from Fighter Aircraft Tactical Missiles Are Different from Fighter Aircraft

Example of State-of-the-Art



2/24/2008 ELF 5

Aero Configuration Sizing Parameters Emphasized in This Course

Aero Configuration Sizing Parameters Emphasized in This Course

Nose FinenessDiameter

Propulsion Sizing /Propellant or Fuel

Wing Geometry / Size

Stabilizer

Geometry / Size

Flight Control

Geometry / Size

Length

ThrustProfile

Flight Conditions ( α, M, h )



2/24/2008 ELF 6

Conceptual Design Process Requires Evaluation

of Alternatives and Iteration

Conceptual Design Process Requires Evaluation


• Mission / ScenarioDefinition

• WeaponRequirements,Trade Studiesand Sensitivity

Analysis

• Launch PlatformIntegration

• Weapon ConceptDesign Synthesis

• Technology Assessment andDev Roadmap

InitialTech

InitialReqs

BaselineSelected

Al tConcepts

Initial Carriage /Launch

Iteration

RefineWeapons

Req

Initial Revised

Trades / Eval Effectiveness / Eval

TechTrades

InitialRoadmap

RevisedRoadmap

Al ternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine

Update

Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirementsto engineering characteris tics . DOE may be used to efficiently evaluate the broad range of design solut ions.



2/24/2008 ELF 7

Missile Concept Synthesis Requires Evaluation




Yes

Define Mission Requirements

Establish Baseline

Aerodynamics

Propulsion

Weight

Trajectory

Meet

Performance?

Measures of Merit and ConstraintsNo

No

Yes

Resize / Alt Conf ig / Subsystems / Tech

Al t Mission

Al t Baseline



2/24/2008 ELF 8

Examples of Air-Launched Missile Missions /

Types

Examples of Air-Launched Missile Missions /

Types

Air-to-air Example SOTA

• Short range ATA. AA-11. Maneuverability

• Medium range ATA. AIM-120. Performance / weight

• Long range ATA. Meteor. Range

Air-to-surface

• Short range ATS. AGM-114. Versatility

• Medium range ATS. AGM-88. Speed

• Long range ATS. Storm Shadow. Modularity

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved

10 feet



2/24/2008 ELF 9

Surface-to-surface Example SOTA

• Short range STS. Javelin. Size

• Medium range STS. MGM-140. Modularity

• Long range STS. BGM-109. Range

Surface-to-air

• Short range STA. FIM-92. Weight

• Medium range STA. PAC-3. Accuracy

• Long range STA. SM-3. High altitude

Examples of Surface-Launched Missile Missions /

Types

Examples of Surface-Launched Missile Missions /

Types

Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved

10 feet



2/24/2008 ELF 10

Aero Conf iguration Range / Time to Robust- Miss Observ- LaunchSizing Parameter Weight Maneuver Target ness Lethality Distance ables Survivability Cost Platform

Nose Fineness

Diameter

Length

Wing Geometry / Size

Stabilizer Geometry / Size

Flight ControlGeometry / Size

Propellant / Fuel

Thrust Profile

Flight Conditions( α, M, h )

Aero Configuration Sizing Has High Impact on Mission Requirements

Aero Configuration Sizing Has High Impact on Mission Requirements

Impact on Weapon Requirement

Aero Measures of Meri t Other Measures of Meri t Const raint

–Very Strong Strong Moderate Relatively Low



2/24/2008 ELF 11

–

Alternatives for Precision Str ikeCost per

ShotFuture Systems

Standoff platforms / hypersonic missiles

Overhead loitering UCAVs / hypersonic missiles

Overhead lo itering UCAVs / light weight PGMs

Current Systems

Penetrating aircraft / subsonic PGMs

Standoff platforms / subsonic missiles

Note: Superior Good Average Poor

Number of Launch Platforms

Required

TCT

Effectiveness

– –

–

Example of Assessment of Alternatives to Establish Future Mission Requirements

Example of Assessment of Alternatives to Establish Future Mission Requirements

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity

time of less than 2 m and target location error ( TLE ) of less than 1 m for mot ion suspended target.

Measures of Merit



2/24/2008 ELF 12

C4ISR Tactical Satellites and UAVs Have High

Impact on Mission Capability

C4ISR Tactical Satellites and UAVs Have High

Impact on Mission Capability Launch Platforms

•Fighter Aircraft

•Bomber

•Ship / Submarine

•UCAV

Precision Strike Weapons•Hypersonic SOW

•Subsonic PGM

•Subsonic CM

Launch Platforms

•Fighter Aircraft

•Bomber

•Ship / Submarine

•UCAV

Precision Strike Weapons

•Hypersonic SOW

•Subsonic PGM

•Subsonic CM

Off-board Sensors•Tactical Satellite

•UAV

Off-board Sensors

•Tactical Satellite

•UAV

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivitytime of less than 2 m and target location error ( TLE ) of less than 1 m for mot ion suspended target.

Time Critical Targets

•TBM / TEL

•SAM

•C3

•Other Strategic

Time Critical Targets•TBM / TEL

•SAM

•C3

•Other Strategic



2/24/2008 ELF 13

Example of System-o -Systems Analysis to

Develop Future Mission Requirements

Example of System-o -Systems Analysis to

Develop Future Mission Requirements 1. Compare Targeting of Subsonic Cruise Missile

Versus Hypersonic Missile

t0 t1

TBM

Launch

Launch

Pt Rcvd

t2 t3

Cruise Missile Launch

HM Intercept

at XXX nm

Range 3 > R2

Range 2 > R1

Range 1

1000 2000 3000 4000 5000

Average Speed, fps

T i m e

, M i n

120

0

20

4060

80

100

20

4060

80

100

020000 4000 6000

Average Speed to Survive, fps

A l t i t u d e –

1 0 0 0 f t

L e t h a l i t y / C o n c r e t e

P e n e t r a t i o n ( f t )50

40

30

20

10

01000 2000 3000 40000Impact Velocity, fps

W/H W3 > W2

W/H W2 > W1

Warhead W1

0

2. Time To Target

3. Alt / Speed / RCS RequiredFor Survivability

4. Lethality

Selected For All :• Value of Speed /

Range• Time Urgent Targets• High Threat

Environments

• Buried Targets• Launch Platform Al ternat ives

• Operating and At tri ti on Cost inCampaign

• Weapon Cost inCampaign• Mix of Weapons in

Campaign• Cost Per Target Ki ll• C4ISR Interface

5. Campaign Model WeaponsMix ( CM, Hypersonic

Missi le ) Resul ts( eg., Korean Scenario )

Hypersonic

Missile Launch

RCS1 RCS2 > RCS1

1 - 2

3 - 4 2

- 3

4 - 5



2/24/2008 ELF 14

Example of Technological Surprise Driving

Immediate Mission Requirements

Example of Technological Surprise Driving

Immediate Mission Requirements

Archer AA-11 / R-73 ( IOC 1987 )

Performance

•> +/- 60 deg off boresight

•20 nm range

New Technologies

•TVC

•Split canard

•Near-neutral static margin

•+/- 90 deg gimbal seeker

•Helmet mounted sight

Sidewinder AIM-9L ( IOC 1977 )Performance

•+/- 25 deg off boresight

•6.5 nm range

Note: AIM-9L maneuverability shortfall compared to Archer drove sudden development of AIM-9X.



2/24/2008 ELF 15





Yes

Establish Baseline

Aerodynamics

Propulsion

Weight

Trajectory

Meet

Performance?


No

Yes


Al t Mission

Al t Baseline




2/24/2008 ELF 16

Baseline Design Benefits and Guidelines Baseline Design Benefits and Guidelines

Benefits of Baseline Design Allows simple, conceptual design methods to be used with good

accuracy

Well documented benchmark / configuration control / traceabili tybetween cause and effect

Balanced subsystems

Gives fast startup / default values for design effort

Provides sensitivity trends for changing design Baselines can cover reasonable range of starting points

Baselines can normally be extrapolated to ±50% with good accuracy

Guidelines

Don’t get locked-in by baseline Be creative

Project state-of-the-art ( SOTA ) if baseline has obsolete subsystems Sensors and electronics almost always need to be updated



2/24/2008 ELF 18

Baseline Design Data Allows Correction of Computed Parameters in Conceptual Design Baseline Design Data Allows Correction of Computed Parameters in Conceptual Design

PCD, C Parameter of conceptual design, corrected

PB, C Parameter of baseline, corrected ( actual data )

PB, U Parameter of baseline, uncorrected ( computed ) PCD, U Parameter of conceptual design, uncorrected (computed )

Example• Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm )

• Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide =18,500,000 ft-lbf / lbm )

• Flight condi tions: Mach 3.5 cruise, 60k ft altitude, combustion temperature4,000 R

• Calculate specific impulse ( ISP )CD,C for conceptual design, based on correctedbaseline data – ( ISP )B, C = 1,120 s

– ( ISP )B, U = 1387 s

– ( ISP )CD, U = 2,271 s

– ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 )

= 1,834 s

PCD, C = ( PB, C / PB, U ) PCD, U



2/24/2008 ELF 19

Summary of This Chapter Summary of This Chapter

Overview of Missile Design Process

Examples Tactical missile characteristics

Conceptual design process

SOTA of tactical missiles

Aerodynamic configuration sizing parameters Processes that establish mission requirements

Process for correcting design predictions

Discussion / Questions?

Classroom Exercise



2/24/2008 ELF 20

Introduction Problems Introduction Problems

1. The missile design team should address the areas of mission / scenariodefinition, weapon requirements, launch platform integration, design, andt_______ a_________.

2. The steps to evaluate missile flight performance require computingaerodynamics, propulsion, weight, and flight t_________.

3. Air-to-air missile characteristics include light weight, high speed, and highm______________.

4. Air-to-surface missiles are often versatile and m______.5. Four aeromechanics measures of merit are weight, range, maneuverability,

and t___ to target.

6. The launch platform often constrains the missile span, length, and w_____.

7. An enabling capability for hypersonic strike missiles is fast and accurateC____.

8. An enabling capability for large off boresight air-to-air missiles is a h_____m______ sight.

9. A baseline design improves the accuracy and s____ of the design process.



2/24/2008 ELF 21

Outline Outline



Propulsion Considerations in Tactical Missile Design

Weight Considerations in Tactical Missile Design


Measures of Merit and Launch Platform Integration

Sizing Examples

Development Process

Summary and Lessons Learned

References and Communication

Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,

Conversion Factors, Syllabus )



2/24/2008 ELF 22





Yes

Establish Baseline

Propulsion

Weight

Trajectory

Meet

Performance?


No

Yes


Al t Mission

Al t Baseline


Aerodynamics



2/24/2008 ELF 23

Missile Diameter Tradeoff Missile Diameter Tradeoff

Drivers toward Small Diameter • Decrease drag

• Launch platform diameter constraint Drivers toward Large Diameter

• Increase seeker range and signal-to-noise, better resolut ion and tracking

• Increase blast frag and shaped charge warhead effectiveness ( larger diameter

⇒ higher velocity fragments or higher velocity jet )• Increase body bending frequency

• Subsystem diameter packaging

• Launch platform length constraint

Typical Range in Body Fineness Ratio 5 < l / d < 25• Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 )

• Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 )



2/24/2008 ELF 24

Small Diameter Missiles Have Low Drag Small Diameter Missiles Have Low Drag

10

100

1000

10000

100000

4 8 12 16 20

d, Diameter, in

D / C D ,

D r a g

/ D r a g C o e f f i c

i e n t , l b

Dynamic Pressure =1,000 psf



Example for Rocket Baseline:

d = 8 in = 0.667 ft

Mach 2, h = 20k ft, ( CD0 )Powered = 0.95q = 1/2 ρ V2 = 1/2 ρ ( M a )2

= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )] 2 = 2,725 psf

D0 / CD0= 0.785 ( 2725 ) ( 0.667 )2 = 952

D0 = 0.95 ( 952 ) = 900 lb

D = CD q SRef = 0.785 CD q d2

Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf,d = diameter ( reference length ) in ft

L Di R d S k P id LL Di t R d S k P id L



2/24/2008 ELF 25

Large Diameter Radar Seeker Provides Longer

Detection Range and Better Resolution

Large Diameter Radar Seeker Provides Longer


1

10

100

0 5 10 15 20

d, Diameter, Inches

Example Seeker Range for Transmitted Power Pt = 100 W, nm

Example Seeker Range for Transmitted Power Pt = 1,000 W, nm

Example Seeker Range for Transmitted Power Pt = 10,000 W, nm

Example Seeker Beam Width, deg

RD = { π σ n3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 Pt1/4 d

θ3dB = 1.02 λ / d, θ3dB in rad

Assumptions: Negl ig ib le clut ter , interference, andatmospheric attenuation; non-coherent radar ( onlysignal amplitude integrated ); uniformly ill uminatedcircular aperture; receiver sensitivi ty limited bythermal noise

Symbols:

σ = Target radar cross section, m2

n = Number of pu lses integratedλ = Wavelength, mK = Boltzman’s constant = 1.38 x 10-23 J / KT = Receiver temperature, KB = Receiver bandwidth, HzF = Receiver noise factor L = Transmitter loss factor S / N = Signal-to-noise ratio for target detectionPt = Transmitted power, Wd = Antenna diameter

Example: Rocket Baselined = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz )RD = Target detection range = { π ( 10 ) ( 100 )3/4 / [ 64 (

0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 (1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm

θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507

rad or 8.6 deg

Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmi tter frequency = 10 x 109 Hz ), T = 290 K, B = 106 Hz ( 10-6 s pulse ), F

= 5, L = 5, S / N = 10

L Di t IR S k P id LL Di t IR S k P id L



2/24/2008 ELF 26

Large Diameter IR Seeker Provides Longer


Large Diameter IR Seeker Provides Longer


1

10

100

0 2 4 6 8 10

do, Optics Diameter, Inches

Example Seeker Range for Exo-atmospheric, km

Example Seeker Range for Humidity at 7.5 g / m3, km

Example Seeker Range for Rain at 4 mm / hr, km

Example Seeker IFOV, 10-5 rad

RD = { ( IT )Δλ ηa Ao { D* / [( Δf p )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2

IFOV= dp / [ ( f-number ) do ]

Example: do = 5 in = 0.127 m, exo-atmosphericLλ = 3.74 x 104 / { 45 { e{ 1.44 x 104 / [ 4 ( 300 ) ]} – 1 }} = 0.000224 W cm -2 sr -2

μm-1, ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad =256 x 256 x ( 20 μm )2 = 0.262 cm2, f-number = 20 / [ 2.44 ( 4 ) ] = 2.05

RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 1011 / [( 250 )1/2 ( 0.262 )1/2 ]} ( 1 )-1

}1/2 = 12, 740 m

IFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad

Figure: dT = 2 ft ( 60.96 cm ), TT = 300 K, λ1 = 3.8 μm,λ

2= 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm

), D* = 8 x 1011 cm Hz1/2 / W, ( S / N )D = 1, Δf p = 250 Hz.

RD = Target detection range, m

( IT )Δλ = Target radiant intensity between λ1 and λ2= εLλ ( λ2 - λ1 ) AT, W / sr

ηa = Atmospheric transmission Ao = Optics aperture area, m2

D* = Specif ic detectivity, cm Hz1/2 / WΔf p = Pixel bandwidth, Hz Ad = Detectors total area, cm2

( S / N )D = Signal-to-noise ratio required for detection

ε = Emissivity coefficient

Lλ = Spectral radiance ( Planck’s Law ) = 3.74 x 104 / {

λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }} , W cm-2 sr -2 μm-1

λ2 = Upper cutoff wavelength for detection, μm

λ1 = Lower cutoff wavelength for detection, μm AT = Target planform area, cm2

λ = Average wavelength, μm

TT = Target temperature, K

IFOV = Instantaneous f ield-of-view of pixel, radf-number = dspot / ( 2.44 λ )

dp = Pixel diameter, either μm

dspot = Spot resolution i f diff raction limi ted = dp, μm

Mi il Fi R ti M B Li it d bMissile Fineness Ratio Ma Be Limited b



2/24/2008 ELF 27

Missile Fineness Ratio May Be Limited by

Impact of Body Bending on Flight Control

Missile Fineness Ratio May Be Limited by

Impact of Body Bending on Flight Control

100

1000

10000

0 10 20 30

l / d, length / diameter

F i r s t M o d e B o d y B e

n d i n g F r e q u e n c

y , r a d / s

E t / W = 1,000 per in

E t / W = 10,0000 per in

E t / W = 100,000 per in

Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.

ωBB = 18.75 { E t / [ W ( l / d ) ]}1/2


l / d = 18E AVG = 19.5 x 106 psit AVG = 0.12 in

W = 500 lbE t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per inωBB = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 Hzω Ac tuator = 100 rad / sec = 16 HzωBB / ω Ac tuator = 302 / 100 = 3.02 > 2

Assumes body cylinder st ructure, th in skin, h ighfineness ratio, uniform weight dist ribution, free-freemotion. Neglects bulkhead, wing / tail s tiffness.

ωBB = First mode body bending frequency, rad / s

E = Modulus of elasticity in ps i

t = Thickness in inchesW = Weight in lb

l / d = Fineness ratio



2/24/2008 ELF 28

Nose Fineness Tradeoff Nose Fineness Tradeoff

d

Example: lN / d = 5 tangent ogive

Example: lN / d = 0.5 ( hemisphere )

High Nose Fineness Superior Aerodynamically, Low Observables

Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume

Moderate Nose Fineness Compromise Dome

d

Examples: lN / d = 2 tangent ogive lN / d = 2 faceted lN / d = 2 window lN / d = 2 mult i-lens

d

W i n d o w

Faceted and Flat Window Domes Can Have LowFaceted and Flat Window Domes Can Have Low



2/24/2008 ELF 29

Firestreak

Mistral

SLAM-ER

JASSM

THAAD

Faceted and Flat Window Domes Can Have Low

Dome Error Slope, Low Drag, and Low RCS

Faceted and Flat Window Domes Can Have Low

Dome Error Slope, Low Drag, and Low RCS

Faceted Dome ( Mistral ) Video

Supersonic Body Drag Driven by Nose FinenessSupersonic Body Drag Driven by Nose Fineness



2/24/2008 ELF 30

Supersonic Body Drag Driven by Nose Fineness

while Subsonic Drag Driven by Wetted Area

Supersonic Body Drag Driven by Nose Fineness

while Subsonic Drag Driven by Wetted Area

0.01

0.1

1

10

0 1 2 3 4 5

M, Mach Number

(CD0)Body,Wave;lN / d = 0.5

(CD0)Body,Wave;lN / d = 1



(CD)Base,Coast


( CD0 )Body, Wave ( CD0 )Body, Friction ( CD )Base

lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M =2, h = 20k ft , q = 2725 psf, l / d = 18, l = 12 ft

( CD0)Body, Friction = 0.053 ( 18 ) { ( 2 ) / [( 2725 )

( 12 ) ]}0.2

= 0.14( CD )Base Coast = 0.25 / 2 = 0.13

( CD )Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10

( CD0)Body, Wave = 0.14

( CD0)Body, Coast = 0.14 + 0.13 + 0.14 = 0.41

( CD0 )Body, Powered = 0.14 + 0.10 + 0.14 = 0.38

( CD0)Body = (CD0

)Body,Friction + ( CD0)Base + ( CD0

)Body, Wave

(CD0)Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.

( CD0)Base,Coast = 0.25 / M, if M > 1 and (CD0

)Base,Coast = ( 0.12 + 0.13 M2 ), if M < 1

( CD0)Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0

)Base,Powered = ( 1 – Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1

( CD0)Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad.

Note: ( CD0)Body,Wave = body zero-lif t wave drag coefficient, ( CD0

)Base = body base drag coefficient, ( CD0)Body, Friction = body skin

friction drag coefficient, ( CD0)Body = body zero-lift drag coefficient, lN = nose length, d = missi le diameter, l = missile body

length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad.

Moderate Nose Tip Bluntness Causes aModerate Nose Tip Bluntness Causes a



2/24/2008 ELF 31

Moderate Nose Tip Bluntness Causes a

Negligible Change in Supersonic Drag

Moderate Nose Tip Bluntness Causes a

Negligible Change in Supersonic Drag

Steps to Calculate Wave Drag of a Blunted Nose1. Relate blunted nose tip geometry to pointed nose tip geometry

2. Compute (CD0)Wave,SharpNose for sharp nose, based on the body reference area

( CD0)Wave,SharpNose = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69

3. Compute ( CD0)Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the

nose tip area

( CD0)Wave,Hemi = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 )

4. Final ly, compute ( CD0)Wave,BluntNose of the blunt nose, based on the body reference area

( CD0)Wave,BluntNose = ( CD0

)Wave,SharpNose ( SRef - SNoseTip ) / SRef + ( CD0)Wave,Hemi SNoseTipi / SRef

Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2

• ( CD0)Wave,SharpNose = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14

• dNoseTip = 0.10 ( 8 ) = 0.8 in

• SNoseTip = π dNoseTip2 / 4 = 3.1416 ( 0.8 )2 / 4 = 0.503 in2 = 0.00349 ft2

• ( CD0)Wave,Hemi = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36

• ( CD0 )Wave,BluntNose = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15

dRef dNoseTip

lN



2/24/2008 ELF 32

Boattail Decreases Base Pressure Drag Area Boattail Decreases Base Pressure Drag Area

Without Boattail

With Boattail

During Motor Burn After Motor Burnout

Base Pressure Drag Area

θBT

Note: Boattail angle θBT and boattail diameter dBT limi ted by propuls ion nozzle packaging, tail flightcontrol packaging, and flow separation

dRef

dBT

Reference: Chin, S. S., Missile Configuration Design , McGraw-Hill Book Company, New York, 1961



2/24/2008 ELF 33

Boattailing Reduces Drag for Subsonic Missiles Boattailing Reduces Drag for Subsonic Missiles

0.45

0.40

0.05

0.10

0.15

0.20

0.25

0.30

0.35

C

D O ,

E x a m p l e Z e r o - L i f t D r a g C o e f f i c i e n t

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5M∞

Note: Boatail half angle should be less than 10 deg, to avoid flow separattion.Source: Mason, L.A., Devan, L. and Moore, F.G., “ Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July1981

3.00 6.00 1.50

Center bodyNose

10.50

dBT / dRef = 1.0dBT / dRef = 0.9dBT / dRef = 0.8dBT / dRef = 0.6

dBT / dRef = 0.4

Boattail

Note:d

BT

= Boattail Diameter dRef = Body Reference Diameter



2/24/2008 ELF 34

Note:If α negative, CN negativeBased on slender body theory ( Pitts, et al ) and cross f low theory ( Jorgensen ) references

Valid for l / d > 5Example l / d = length / diameter = 20d = 2 ( a b )1/2

φ = 0°

Lifting Body Has Higher Normal Force Lifting Body Has Higher Normal Force

CN,ExampleNormalForce

Coefficientfor l / d = 20

150

100

50

00 20 40 60 80 100

α, Angle of Attack, Deg

φ2a

2b

a / b = 3

a / b = 2

a / b = 1

⏐ CN ⏐ = [⏐( a / b ) cos2 φ + ( b / a ) sin2 φ ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

CN

L / D Is Impacted by C Body Fineness andL / D Is Impacted by CD Body Fineness and



2/24/2008 ELF 35

L / D Is Impacted by C D 0 , Body Fineness, and Lifting Body Cross Section Geometry

L / D Is Impacted by C D 0 , Body Fineness, and Lifting Body Cross Section Geometry

L / D,Lift / Drag

4

3

2

1

0 0 20 40 60 80 100

α, Angle of Attack, DegNote:• If α negative, L / D negative•d = 2 ( a b )1/2

•Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibil ity )

may limit missile aero configuration enhancements

L / D = CL / CD = ( CN cos α – CD0 sin α ) / ( CN sin α + CD0 cos α )For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

High drag, low fineness body ( a / b = 1, l / d = 10, CDO = 0.5 )Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 )High fineness, low drag ( a / b = 1, l / d = 20, CDO = 0.2 )

Lif ting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d =20, CDO = 0.2 )

φ2a

2bCN

Lifting Body Requires Flight at Low DynamicLifting Body Requires Flight at Low Dynamic



2/24/2008 ELF 36

Lifting Body Requires Flight at Low Dynamic

Pressure to Achieve High Aero Efficiency

Lifting Body Requires Flight at Low Dynamic

Pressure to Achieve High Aero Efficiency

0

1

2

3

4

100 1000 10000 100000

q, Dynamic Pressure, lb / ft2

E x a m

p l e L / D ,

L i f t / D r

a g

Circular Cross Section ( a / b = 1 ) Lif t ing Body ( a / b = 2 )

L / D = CL / CD = ( CN cos α – CDOsin α ) / ( CN sin α + CDO

cos α )⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

Note. Example figure based on following assumptions:Body l ift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2,l / d = 10, CD0

= 0.2

Example:

q = 500 psf •a / b = 1 ⇒ L / D = 2.40

•a / b = 2 ⇒ L / D = 3.37

q = 5,000 psf

•a / b = 1 ⇒ L / D = 0.91•a / b = 2 ⇒ L / D = 0.96

Trade-off of Low Observables and ( L / D )MaxTrade-off of Low Observables and ( L / D )Max



2/24/2008 ELF 37

6

5

4

3

Body Planform Area

( Body Volume )2/3

( L / D ) M a x ,

( L i f t / D r a g ) M

a x Lower

Radar Cross

Section

TailoredWeapons

ConventionalWeapons

( circular

cross section )

Trade off of Low Observables and ( L / D ) Max Versus Volumetric Efficiency

Trade off of Low Observables and ( L / D ) Max Versus Volumetric Efficiency

2 4 6 8 10

Advantages:• ( L / D )Max

• Low RCS

Advantages:• Payload• Launch PlatformIntegration

Circular Cross Section

C / and Static Margin Define StaticCm / and Static Margin Define Static



2/24/2008 ELF 38

Δ C m / Δ α and Static Margin Define Static

Stability

Δ C m / Δ α and Static Margin Define Static

Stability

Cm

Statically Stable: ΔCm / Δα < 0,with xac behind xcg

δ1 δ2

Cm

Statically Unstable: ΔCm / Δα > 0,with xac in front of xcg

δ1

δ2

Non-oscillatoryConvergent

OscillatoryConvergent

t

Non-oscillatoryDivergent

OscillatoryDivergent

t

α α

α

Note: Statically unstable missi le requires high bandwidth autopilot.

Autopi lot negative rate feedback provides stabili ty augmentat ion.

xCG

x AC

xCG

x AC

Body Aerodynamic Center Is a Function of Angle Body Aerodynamic Center Is a Function of Angle



2/24/2008 ELF 39

y y g

of Attack, Nose Fineness, and Body Length

y y g

of Attack, Nose Fineness, and Body Length

0

1

2

3

4

5

0 20 40 60 80 100

Angle of Attack, Deg

D i s t a n c e t o B o d y A e r o d y n a

m i c

C e n t e r / L e n g t h o f N o s e total length of body /

length of nose = 1

total length of body /length of nose = 2

total length of body /

length of nose = 5total length of body /length of nose = 10

( x AC )B / lN = 0.63 ( 1 - sin2 α ) + 0.5 ( lB / lN ) sin2 α

Note: Based on slender body theory ( Pitts , et al ) and cross flow theory ( Jorgensen ) references. No flare.

( x AC )B = Location of body aerodynamic center, lN = length of nose, α = angle of attack, lB = total length of body.

Example:

Rocket Baseline Body

lB / lN = 143.9 / 19.2 = 7.49

α = 13 deg

( x AC )B / lN = 0.81

19.2143.9

Fl I St ti St bilit



2/24/2008 ELF 40

Based on Slender Body Theory:

( CNα )F = 2 [( dF / d )2 – 1 ]

( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ] ( CNα

)B = 2 per rad

( xac )B = 0.63 lN

ΣM = 0 at Aerodynamic Center. For a Body-Flare:

( CNα )B {[ xCG – ( x AC )B ] / d } + ( CNα )F [ xCG – ( x AC )F ] / d = - [( CNα )B + ( CNα )F ][( x AC – xCG ) / d ]

Static Margin for a Body-Flare

( x AC – xCG ) / d = - {( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα

)F {[ xCG – ( x AC )F ] / d }} /[( CNα

)B + ( CNα)F ]

Flare Increases Static Stability Flare Increases Static Stability

+M

+α

x = 0 ( xac )B

( CNα)B ( CNα )F

lBlN

( xac )F

xF

9

xCG

d dF

x AC

CNα = ( CNα )B + ( CNα )F

Fl I St ti St bilit ( t )Fl I St ti St bilit ( t )



2/24/2008 ELF 41

Example of Static Margin for THAAD ( Statically Unstable Missile )

( CNα )F = 2 [( 18.7 / 14.6 )2 – 1 ] = 2 [(1.28)2 – 1 ] = 1.28 per rad

( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in

( xac )B = 0.63 ( 91.5 ) = 57.7 in

xCGLaunch = 146.9 in ( x AC – xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }}

/ [ 2 + 1.28 ] = - 0.41

Flare Increases Static Stability ( cont ) Flare Increases Static Stability ( cont )

9

( CNα)B

( xac )B = 57.7 91.5 146.9

14.6 18.7 in

( xac )F = 237.1230.9 242.9

( CNα )F

x AC = 140.9

CNα= ( CNα

)B + ( CNα )F

Tail Stabilizers Have Lower Drag While Flares Tail Stabilizers Have Lower Drag While Flares



2/24/2008 ELF 42

g

Have Lower Aero Heating and Stability Changes

g

Have Lower Aero Heating and Stability Changes

Type Stabilizer Drag Span Heating ΔCNα Tail ControlFlare ( e.g., THAAD )

Tails ( e.g., Standard Missile )

Note: Superior Good Average Poor –

– –

– –

Wi Si i T dWi Si i T d



2/24/2008 ELF 43

Wing Sizing Trades Wing Sizing Trades

Advantages of Small Wing / Strake / No Wing

• Range in high supersonic flight / high dynamic pressure

• Max angle of attack

• Launch platform compatibility

• Lower radar cross section

• Volume and weight for propellant / fuel

Advantages of Larger Wing

• Range in subsonic flight / low dynamic pressure• Lower guidance time constant*

• Normal acceleration*

• High altitude intercept*

• Less body bending aeroelasticity ( wing stiffens body )• Less seeker error due to dome error slope ( lower angle of attack )

• Less wipe velocity for warhead ( lower angle of attack )

• Lower gimbal requirement for seeker

*Based on assumption of aerodynamic control and angle of attack below wing stall

Most Supersonic Missiles AreWinglessMost Supersonic Missiles AreWingless



2/24/2008 ELF 44

Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two stage ) Gopher SA-13

Starburst Mistral Kegler AS-12 Archer AA-11

Gauntlet SA-15 Magic R550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Sidewinder AIM-9X

ASRAAM AIM-132 Grumble SA-10 / N-8 Patr io t MIM-104 Starstreak

Gladiator SA-12 PAC-3 Roland ( two stage ) Crotale

Hellf ire AGM-114 ATACM MGM-140 Standard Missi le 3 ( three stage ) THAAD

Most Supersonic Missiles Are Wingless Most Supersonic Missiles Are Wingless


Wings, Tails, and Canards with Large Area and Wings, Tails, and Canards with Large Area and



2/24/2008 ELF 45

at High Angle of Attack Have High Normal Force at High Angle of Attack Have High Normal Force

0

1

2

3

4

0 30 60 90

M < 1.35, based o n s lender wing theory + Newtonian impact theory

M = 2, based on linear wing theory + Newtonian impact theory

M = 5, based on linear wing theory + Newtonian impact theory

( C N ) W i n g

S R E F / S W ,

W i n g N o r m a l F o r c

e C o e f f i c i e n t

f o r R o c k e t B

a s e l i n e

α’ = αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg

⏐( CN )Surface ⏐ = [ 4⏐sin α’ cos α’⏐ / ( M2 – 1 )1/2 + 2 sin2α’ ] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )]2 }1/2

⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’ cos α’⏐ + 2 sin2α’ ] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )]2 }1/2

Note: Linear wing theory appl icable if M > { 1 + [ 8 / ( π A )] 2 }1/2, slender wing theory appl icable if M < { 1 + [ 8 / ( π A )]2 }1/2, A = Aspect Rat io < 3, SSurface = Surface Planform Area, SRef = Reference Area

Example for Rocket BaselineWing

AW = 2.82

SW = 2.55 ft2

SRef = 0.349 ft2

δ = 13 deg, α = 9 degM = 2

{ 1 +[ 8 / ( π A )]2 }1/2 = 1.35

Since M > 1.35, use linear wingtheory + Newtonian theory

α’ = αW

= α + δ = 22°( CN )Wing SRef / SW = 4 sin 22°cos 22° / ( 22 – 1 )1/2 + 2 sin2 22°= 1.083

( CN )Wing = 1.08 ( 2.55 ) / 0.349 =7.91

Aerodynamic Center of a Thin Surface ( e.g.,Aerodynamic Center of a Thin Surface ( e.g.,



2/24/2008 ELF 46

Wing, Tail, Canard ) Varies with Mach Number Wing, Tail, Canard ) Varies with Mach Number

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5

M, Mach Number

X A C / C M A C ,

S u r f a

c e N o n - d i m e n s i o n a l

A e r o d y n a

m i c C e n t e r

A = 1

A = 2 A = 3

Note: Based on linear wing theoryThin wing ⇒ M ( t / c ) << 1( x AC )Surface = Surface aerodynamic

center distance from leadingedge of ( c

MAC)SurfacecMAC = Mean aerodynamic chord

A = Aspect rat io = b2 / S

( x AC / cMAC )Surface = [ A ( M2 – 1 )1/2 – 0.67 ] / [ 2A ( M2 –1 )1/2 – 1 ], if M > ~ 2

( x AC / cMAC )Surface = 0.25, if M < ~ 0.7

Example: Rocket Baseline Wing

A = 2.82

cMAC = 13.3 in

( xMAC )Wing = 67.0 in

M = 2

( x AC / cMAC )Wing = 0.481

( x AC

)Wing

= 6.4 in from mac leadingedge = 73.4 in from nose tip

x AC

xMAC cMAC

Hinge Moment Increases with Dynamic Pressure Hinge Moment Increases with Dynamic Pressure



2/24/2008 ELF 47

and Effective Angle of Attack and Effective Angle of Attack

0

5000

10000

15000

20000

25000

30000

0 10 20 30

H M ,

E x a m p l e H i n g e M o

m e n t , i n - l b

q = 436 psf ( M = 0.8 ) q = 1242 psf ( M = 1.35 )

q = 2725 psf ( M = 2 ) q = 17031 psf ( M = 5 )

HM = NSurface ( x AC - xHL )Surface

α’ = αW = α + δ , Wing Effect ive Angle of Attack of Rocket Baseline, Deg

Note: Based on linear wingtheory, slender wing theory,and thin wing ( M ( t / c ) << 1 )

NSurface = Normal force on surface( two panels )

( x AC - xHL )W = distance fromsurface aerodynamic center tohinge line of surface

Example for Rocket BaselineWing Control

cmac = 13.3 in

xHL = 0.25 cmac

SRef = 0.349 ft2

SW = 2.55 ft2

δ = 13 deg, α = 9 degα’ = αW = α + δ = 22°

M = 2, h = 20k f t, q = 2725 psf

NW = [ CNW( SRef / SW )] qSW =

1.083 ( 2725 ) ( 2.55 ) = 7525 lb

x AC / cmac = 0.48

HM = 7525 ( 0.48 – 0.25 ) ( 13.3 )

= 23019 in – lb for two panels

NW

x H L

x A C

c m a c

Wings, Tails, and Canards Usually Have Greater Wings, Tails, and Canards Usually Have Greater



2/24/2008 ELF 48

Skin Friction Drag Than Shock Wave Drag Skin Friction Drag Than Shock Wave Drag

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50

M / ( q cmac ) = 0.00001 ft / lb M / ( q cmac ) = 0.0001 ft / lb

M / ( q cmac ) = 0.001 ft / lb M / ( q cmac ) = 0.01 ft / lb

( CD0 )Surface,Friction = nSurface { 0.0133 [ M / ( q cmac )]0.2 } ( 2 SSurface / SRef ), q in psf, cmac in ft( CDO

)Surface,Wave = nSurface ( 1.429 / MΛLE2 ){( 1.2 MΛLE

2 )3.5 [ 2.4 / ( 2.8 MΛLE2 – 0.4 )]2.5 – 1 } sin2 δLE cos ΛLE

tmac b / SRef , based on Newtonian impact theory( CDO

)Surface = ( CDO)Surface,Wave + ( CDO

)Surface,FrictionnSurfaces = number of surface planforms ( cruciform = 2 )

q = dynamic pressure in psf

cmac

= length of mean aero chord in ft

γ = Specif ic heat ratio = 1.4

MΛLE= M cos ΛLE = Mach number ⊥ leading edge

δLE = leading edge section total angle

ΛLE = leading edge sweep angle

tmac = max thickness of macb = span

Example for Rocket Baseline Wing:

nW = 2, M = 2, h = 20k ft ( q = 2,725 psf ), cmac = 1.108ft, SRef = 50.26 in2, SW = 367 in2, δLE = 10.01 deg, ΛLE =45 deg, t

mac

= 0.585 in, b = 32.2 in, MΛLE

= 1.41 ( M = 2 )

M / ( q cmac ) = 2 / [ 2725 ( 1.108 )] = 0.000662 ft / lb

n SSurface / SRef = 2 ( 367 ) / 50.26 = 14.60

( CDO)Wing,Friction = 0.090

( CD0)Wing,Wave = 0.024

( CDO )Wing = 0.024 + 0.090 = 0.11

E x a m p l e ( C D 0

) S u r f a c e , F r i c t i o n

n SSurface / SRef

Examples of Wing, Tail, and Canard Panel Examples of Wing, Tail, and Canard Panel



2/24/2008 ELF 49

Geometry Alternatives Geometry Alternatives

Parameter

Variation x AC

Bending Moment / Frict ion

Supersonic DragRCS

Span Constraint

Stability & Control

Aeroelastic Stab.

λ = Taper ratio = cT / cR

A = Aspect rat io = b2 / S = 2 b / [( 1 + λ ) cR ]yCP = Outboard center-of-pressure = ( b / 6 ) ( 1 + 2 λ ) / ( 1 + λ )

cMAC = Mean aerodynamic chord = ( 2 / 3 ) cR ( 1 + λ + λ2

) / ( 1 + λ )

Note: Superior Good Average Poor

Based on equal surface area and equal span.Surface area often has more impact than geometry.

–

–

–

–

–

–

Triangle

( Delta )

Aft Swept LE

Trapezoid

Double

Swept LEBow Tie Rectangle

–

–

Examples of Surface Arrangement and Examples of Surface Arrangement and



2/24/2008 ELF 50

Aerodynamic Control Alternatives Aerodynamic Control Alternatives

Two Panels( Mono-Wing )

Three( Tri-Tail )

Four ( Cruciform ) Six* Eight*

Folded Wraparound Extended Balanced ActuationControl

Flap Control

Interdigitated In-line

Note: More than four tails are usually free-to-roll pi tch / yaw stabilizers, for low induced roll.

Most Missiles Use Four Control Surfaces with Most Missiles Use Four Control Surfaces with

C bi d Pit h / Y / R ll C t l I t ti



2/24/2008 ELF 51

Control Integ Control Surfaces Example Control Effect Cost Packaging

Pitch / Yaw 2 Stinger FIM-92

Pitch / Roll 2 ALCM AGM-86

Pitch / Yaw / Roll 3 SRAM

Pitch / Yaw / Roll 4 Adder AA-12

Pitch + Yaw + Roll 5 Kitchen AS-4

Pitch / Yaw + Roll 6 Derby / R-Darter

Combined Pitch / Yaw / Roll Control Integration Combined Pitch / Yaw / Roll Control Integration


–

– –

–

–

–

–

There Are Many Flight Control Configuration There Are Many Flight Control Configuration

Alt ti



2/24/2008 ELF 52

Alternatives Alternatives

ControlControl Design Alternatives

Tail Cruciform ( 4 )Tri-tail ( 3 )Not Compressed

FoldedWraparoundSwitchblade

Canard AboveRolling Airframe ( 2 )

Wing Tail ( 3, 4, 6, 8 )Strake / Canard & TailIn Line with ControlsInterdigi tated with Controls

TVC or Reaction JetControl

Movable NozzleJet TabJet Vane

Axial PlateSecondary InjectionNormal Jet / JI

Spanwise Jet / JI

Fixed Surface Alternatives

WinglessWingStrake / Canard

In Line with ControlsInterdigi tated with ControlsNumber ( 2, 3, 4 )

Tail ( 3, 4, 6, 8 )Tail + WingIn Line with Controls

Interdigi tated with Controls

Tail ( 3, 4, 6, 8 )Tail + Canard / StrakeTail + Wing

Above

Tail Control Is Efficient at High Angle of AttackTail Control Is Efficient at High Angle of Attack



2/24/2008 ELF 53

Tail Control Is Efficient at High Angle of Attack Tail Control Is Efficient at High Angle of Attack

α

V∞

ΔCN

CN Trim

( assumed statically stable ) CN at δ = 0

CNCNegative δ

CNCat δ = 0

☺ Efficient Packaging

☺ Low Hinge Moment / Actuator Torque

☺ Low Induced Rolling Moment

☺ Efficient at High α

Decreased Lift at Low α if Statically Stable

c g

Tail Control Is More Effective Than Conventional

C d C t l t Hi h A l f Att k

Tail Control Is More Effective Than Conventional

C d C t l t Hi h A l f Att k



2/24/2008 ELF 54

Canard Control at High Angle of Attack Canard Control at High Angle of Attack

V∞

α

+ δ

• Assumed static stabili ty• Control surface local

angle of attack α’ = α + δ• Panel stalled at high α*

Conventional Canard Control

V∞

α

– δ

• Assumed static stabili ty• Control surface local

angle of attack α’ = α – δ• Panel not stalled at high α

Tail Control

α ~ Angle of Attack ( deg ) α ~ Angle of Attack ( deg )

C m

δ / ( C mδ )α

= 0 °

1.0

0

ConvenCanard

Control

Tail

Control☺

10 – 20° 20 – 30°

C lδ / ( C lδ )α = 0 ° 1.0

0

ConvenCanard

Control

Tail

Control☺

10 – 15° 15 – 30°

Ø = 0°

*Note: Additional forward fixed surfaces ( such as Python 4 ) in front of movable canards alleviate stallat high α. Free-to-rol l tails ( such as Python 4 ) alleviate induced roll from canard control at high α.

About 70%of Tail Control Missiles Also Have WingsAbout 70%of Tail Control Missiles Also Have Wings



2/24/2008 ELF 55

JASSM AGM-158 Maverick AGM-65 CALCM JSOW AGM-154

Tomahawk BGM-109 Taurus KEPD 350 Storm Shadow / Scalp Popeye AGM-142

Exocet MIM40 TOW2-BGM71D AMRAAM AIM-120 Sunburn SS-N-22

Standard RIM-66 / 67 RBS-70 / 90 Shipwreck SS-N-19 Super 530

Sea Dart ( two stage ) FSAS Aster R-37 ( AA-X-13 ) Mica

Adder AA-12 Rapier 2000 SD-10 / PL-12 Seawolf

About 70% of Tail Control Missiles Also Have Wings About 70% of Tail Control Missiles Also Have Wings


Tail Control Alternatives: Conventional Balanced

Actuation Fin Flap and Lattice Fin

Tail Control Alternatives: Conventional Balanced

Actuation Fin Flap and Lattice Fin



2/24/2008 ELF 56

Control Hinge

Type of Tail Control Effectiveness Drag Moment RCS

Balanced Actuation Fin ( Example: ASRAAM AIM-132 )

Flap ( Example: Hellfi re AGM-114 )

Lattice Fin ( Example: Adder AA-12 / R-77 )

Actuation Fin, Flap, and Lattice Fin Actuation Fin, Flap, and Lattice Fin

–

–


Lattice Fins Have Advantages for Low Subsonic

and High Supersonic Missiles

Lattice Fins Have Advantages for Low Subsonic

and High Supersonic Missiles



2/24/2008 ELF 57

and High Supersonic Missiles and High Supersonic Missiles

Advantages

High control effectiveness atlow subsonic and high

supersonic Mach number Low hinge moment

Short chord length

DisadvantagesHigh RCS ( cavities, normalleading edges )

High drag at transonic Mach

number ( choked flow )

Low Subsonic Transonic Low Supersonic High Supersonic

☺ ☺

Conventional Canard Control Is Efficient at Low

Angle of Attack But Stalls at High Alpha

Conventional Canard Control Is Efficient at Low

Angle of Attack But Stalls at High Alpha



2/24/2008 ELF 58

Angle of Attack But Stalls at High Alpha Angle of Attack But Stalls at High Alpha

α

V∞

δΔCN

CN Trim ( assumed statically stable )

CN at δ = 0C

N C

☺ Efficient Packaging

☺ Simplified

Manufacturing☺ Increased Lift at Low α

if Statically Stable

Stall at High α if Statically Stable

Induced Roll

Note: = CNC at δ = 0°

= CNC at δ = δ

*Note: Addit ional forward f ixed surface infront of movable canard alleviates stall athigh α. Free-to-roll tails alleviate inducedroll at high α. Dedicated rol l controlsurfaces avoid rol l control saturation andsimplify autopilot design.

c g

Canard Control Missiles Are Wingless and Most

Are Supersonic

Canard Control Missiles Are Wingless and Most

Are Supersonic



2/24/2008 ELF 59

Are Supersonic Are Supersonic


Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two-stage ) Gopher SA-13

Starburst Gauntlet SA-15 Mistral AIM-9L

Archer AA- 11 Magic R 550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Kegler AS-12

GBU-12 GBU-22 GBU-27 GBU-28

Missiles with Split Canards Have Enhanced

Maneuverability at High Angle of Attack

Missiles with Split Canards Have Enhanced

Maneuverability at High Angle of Attack



2/24/2008 ELF 60

Kegler AS-12 Archer AA-11 Aphid AA-8

Magic R 550 Python 4 U-Darter

Maneuverability at High Angle of Attack Maneuverability at High Angle of Attack

Note: Forward fixed surface reduces local angle-of-attack for movable canard, providing higher stall angle of attack. Forwardsurface also prov ides a fixed, symmetrical location for vortex shedding from the body.

Python 4 also has free-to-roll tails and separate roll control ailerons.

α’ ~ α α’ ~ δα

δΔCN

CN

C

Note: α’ = Local angle of attack

Wing Control Requires Less Body Rotation But

Has High Hinge Moment Induced Roll and Stall

Wing Control Requires Less Body Rotation But

Has High HingeMoment Induced Roll and Stall



2/24/2008 ELF 61

Has High Hinge Moment, Induced Roll and Stall Has High Hinge Moment, Induced Roll and Stall

δV

Δ CN ~ CN Trim

☺ Low Body α / Dome Error Slope

☺ Fast Response ( if skid-to-turn )

Poor Actuator Packaging

Large Hinge Moment

Larger Wing Size

Induced Roll

Wing Stall

( α small ) cg

Wing Control Missile Susceptible to High Vortex

Shedding

Wing Control Missile Susceptible to High Vortex

Shedding



2/24/2008 ELF 62

Shedding Shedding

Strong vortices from wing interact with tail

Source: Nielsen Engineering & Research ( NEAR ) web si te:

http://www.nearinc.com/near/project/MISDL.htm

Video of Vortices from DeltaWing at High Angle of Attack

Source: Universi ty of Notre Dame web site:http://www.nd.edu/~ame/facilities/SubsonicTunnels.html

Wing Control Missiles Are Old Technology Wing Control Missiles Are Old Technology



2/24/2008 ELF 63

Sparrow AIM-7: IOC 1956

Skyflash: IOC 1978

Alamo AA-10 / R-27: IOC 1980

HARM AGM-88: IOC 1983

Aspide: IOC 1986


TVC and Reaction Jet Flight Control TVC and Reaction Jet Flight Control



2/24/2008 ELF 64

Liquid Injection Hot Gas Injection

Axial Plate Jet Tab Movable Nozzle

± 7°± 12°

± 7°± 15° ± 20°

Note: Jet vanes provide roll cont rol and shareactuators with aero contro l, but have reduced ISP

Reaction JetM∞ Jet Flow

Jet Vane*

± 10°

Note:

•TVC and reaction jet flight control provide

high maneuverability at low dynamic pressure•TVC usually has lower time constant andmiss distance than aero control

•Reaction jets usually have lower timeconstant and miss distance than TVC

•Reaction jets can be either impulse jets or

controlled duration jets Jet inter. Thrust Jet interaction

Most Tactical Missiles with TVC or Reaction Jet

Control Also Use Aero Control

Most Tactical Missiles with TVC or Reaction Jet

Control Also Use Aero Control



2/24/2008 ELF 65

Jet Vane + Aero Control :

Mica Sea Sparrow RIM-7 AIM-9X

Sea Wolf GWS 26 IRIS-T A-Darter Javelin

Jet Tab + Aero Control : Archer AA-11

Reaction Jet + Aero Control:

PAC-3

Movable Nozzle + Aero Control + Reaction Jet:

SM-3 Standard Missile Aster FSAF 15

Movable Nozzle + Reaction Jet:

THAAD

Reaction Jet:

LOSAT

Control Also Use Aero Control Control Also Use Aero Control

Example Video of TVC ( FSAF-15 and Javelin )

Skid-to-Turn Is the Most Common Maneuver Law Skid-to-Turn Is the Most Common Maneuver Law



2/24/2008 ELF 66

Skid-To-Turn ( STT )• Advantage: Fast response• Features

– Does not require roll commands from autopilot – Works best for axisymmetric cruciform missiles

Bank-To-Turn ( BTT )

• Advantage: Provides higher maneuverabili ty for planar wing, noncircular / lifting bodies, and airbreathers

• Disadvantages – Time to rol l – Requires fast ro ll rate – May have higher dome error slope

• Features – Roll attitude commands from autopilot – Small sideslip

Rolling Air frame ( RA )• Advantage: Requires only two sets of gyros /

accelerometers / actuators ( packaging for small missile )

• Disadvantages for aero control – Reduced maneuverabili ty for aero cont rol – Requires high rate gyros / actuators – Requires precision geometry and thrust alignment

• Features – Bias roll rate and roll moment

– Can use impulse steering ( e.g., PAC-3, LOSAT ) – Compensates fo r thrust offset

Step 1: Roll Unt ilWing ⊥ LOS

Step 2: Maneuver @ RollRate = 0 and Wing ⊥ LOS

Bias Roll Rate ( e.g., 3 Hz )

Maneuver w / o Rol l Command

Target

Target

Target

L O S

Target

Maneuver with Bias RollMoment

L O S

L O S

L O S

STT

BTT ( withPlanar Wing )

RA

Asymmetric Inlets Require Bank-to-Turn Maneuvering

Asymmetric Inlets Require Bank-to-Turn Maneuvering



2/24/2008 ELF 67

Examples of Twin Inlet Missiles wi th Bank-to-Turn

Twin Side Inlets Ramjet: ASMP

Twin Cheek Inlets Ducted Rocket: HSAD

Twin Cheek Inlets Ducted Rocket: Meteor

Examples of Single Inlet Missiles with Bank-to-Turn

Chin Inlet Ramjet: ASALM

Bottom Inlet Turbojet: BGM-109 Tomahawk

Bottom Inlet Turbojet: Storm Shadow / Scalp

Top Inlet Turbofan: AGM-86 ALCM

gg

Note: Bank-to-turn maneuvering maintains low sideslip for better inlet efficiency.

X Roll Orientation Is Usually Better Than + Roll Orientation

X Roll Orientation Is Usually Better Than + Roll Orientation



2/24/2008 ELF 68

Yaw Right

Fin 1

Fin 3

Roll Right

+ Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base

X Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base

Roll Right

Note: + roll orientation usually has lower trim drag, less static stability and control effectiveness in pitch and yaw, andstatically unstable roll moment derivative ( Clφ > 0 ).X roll orientation has better launch platform compatibility , higher L / D, higher static stability and controleffectiveness in pitch and yaw, and statically stable roll moment derivative ( Clφ < 0 ).

4 1

3 2

Pitch Up Yaw Right

Pitch Up

Fin 2Fin 4 T r a i l i n g e d g e

d e f l e c t i o n

Trimmed Normal Force Is Defined at Zero

Pitching Moment

Trimmed Normal Force Is Defined at Zero

Pitching Moment



2/24/2008 ELF 69

gg

P i t c h i n g M o m e n t ,

C m

N o r m

a l F o r c e ,

C N

Angle of Attack ( Deg )

αTrim @ Cm = 0

δ = 0

δ = δ Trim for either statically stable tail

contro l or statically unstable canard control

δ = 0

δ = δ Max

δ = δ Trim for either statically unstable tailcontro l or statically stable canard control

Angle of At tack ( Deg )

Relaxed Static Margin Allows Higher Trim Angle

of Attack and Higher Normal Force

Relaxed Static Margin Allows Higher Trim Angle

of Attack and Higher Normal Force



2/24/2008 ELF 70

Note: Rocket BaselineXCG = 75.7 in.Mach 2

( α + δ )Max = 21.8 deg, ( CNTrim)Max

α / δ = 0.75, ( Static Margin = 0.88 Diam )

α / δ = 1.5, ( SM = 0.43 Diam )

α / δ = ∞, ( SM = 0 )

gg

( CN, Trim )max, MaxTrimmed NormalForce Coefficient of Rocket Baseline

0 4 8 12 16 20 24

16

12

8

4

0

( αTrim )max, Μax Trim Angle of Attack, deg

Tails Are Sized for Desired Static Margin Tails Are Sized for Desired Static Margin



2/24/2008 ELF 71

( CNα)B

( CNα )W

( CNα)T

( x AC )T

( x AC )B

( x AC )W

+M

+ α

x = 0

xCG

x = lB

x = lN

x AC

ΣM = 0 at aerodynamic center

( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα

)W {[ xCG – ( x AC )W ] / d } SW / SRef + ( CNα)T {[ xCG – ( x AC )T ] / d } ST / SRef

= - [( CNα)B + ( CNα

)W SW / SRef + ( CNα)T ST / SRef ] [( x AC – xCG ) / d ]

Static margin for a specified tail area is

( x AC – xCG ) / d = - {( CNα )B {[ xCG – ( x AC )B ] / d } + ( CNα )W {[ xCG – ( x AC )W ] / d } SW / SRef + ( CNα )T {[ x CG – ( x AC )T ] / d } ( ST / SRef )} /[(CNα)B + (CNα

)W SW / SRef + ( CNα)T ST / SRef ]

Required tail area for a specified static margin is

ST / SRef = ( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα

)W {[ xCG – ( x AC )W ] / d } ( SW / SRef ) + {[( CNα)B + ( CNα

)W SW / SRef ][( x AC – xCG ) / d ]}/ {( C

Nα)T

[( x AC

)T

– xCG

] / d - ( x AC

– xCG

) / d }

CNα

Larger Tail Area Is Required for Neutral Stability

at High Mach Number

Larger Tail Area Is Required for Neutral Stability

at High Mach Number



2/24/2008 ELF 72

0

1

2

3

0 1 2 3 4 5

M, Mach Number

( S T ) N e u t r a l / S R e f , N e

u t r a l S t a b i l i t y T a i l A r e a /

R e f e r e

n c e A r e a

(ST)Neutral / SRef = { (CNα)B [ xCG – (x AC)B ] / d + (CNα)W {[ xCG – (x AC)W ] / d } ( SW / SRef )} / {{[ (x AC)T – xCG ] / d } (CNα)T }

Assumptions fo r f igure:

•XCG ≈ l / 2, (X AC)B ≈ d, ( X AC )T ≈ l – d

•α < 6 deg, turbulent boundary layer

•(CN

α

)B

= 2 per rad

•(CNα)T = (CNα)W = 4 / [ M2 –1 ]1/2, if M> { 1 + [ 8 / ( π A )]2 }1/2

•(CNα)T = (CNα)W = π A / 2, if M < { 1 +[ 8 / ( π A )] 2 }1/2

Example Rocket Baseline:

l = 144 in, d = 8 in, SW = 2.55 ft2, SRef =0.349 ft2, AW = 2.82, (cMAC)W = 13.3 in,xMAC = 67.0 in from nose tip, burnout( xCG = 76.2 in from t ip ), Mmax = 3

(x AC)W = 0.49 ( 13.3 ) = 6.5 in fromleading edge of MAC

(x AC)W = 6.5 + 67.0 = 73.5 in f rom nose

{[ xCG – (x AC)W ] / l } ( SW / SRef ) = 0.14( forward wing )

(ST)Neutral / SRef = 1.69 provides neutralstability

(ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft2

{ [ x C G – ( x A C

) W ] / l }

( S W / S R e f ) =

0

{ [ x C G – ( x A C ) W

] / l } (

S W / S R e f

) = 0. 2 5

( f o r w a

r d w i n g )

{ [ x C G – ( x A C

) W ] / l } ( S

W / S R e f

) = - 0. 2 5

( a f t w

i n g )

Stability and Control Derivatives Conceptual Design Criteria

Stability and Control Derivatives Conceptual Design Criteria



2/24/2008 ELF 73

zy

xC

lδr Clδa

zy

xCnδa

Cnδr

zy

xC

lφ Clδa

z y

xCmα

Cmδ

z y

xClβ Clδa

| Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle )

| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α )

| Clβ / Clδa | < 0.3 ( Rol l Due to Sideslip ) | Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip )

zy

x

Cnδr

Cnβ

Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative.

Most of the Rocket Baseline Body Buildup Normal

Force Is Provided by the Wing

Most of the Rocket Baseline Body Buildup Normal

Force Is Provided by the Wing



2/24/2008 ELF 74

CN, Normal ForceCoefficient of

Rocket Baseline

15

10

5

0 0 5 10 15 20 25

α, Angle of Attack, Deg

Body + Wing + Tail

Body + Wing

Body

Note for figure: M = 2, δ = 0

( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail

Note: ( CD0)Total = ( CD0

)Wing-Body-Tail ≅ ( CD0)Body + ( CD0

)Wing + ( CD0)Tail

( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail

Summary of Aerodynamics Summary of Aerodynamics



2/24/2008 ELF 75

Conceptual Design Prediction Methods of Bodies and Surfaces Normal force coefficient

Drag coefficient

Aerodynamic center / pitching moment coefficient / hinge moment

Design Tradeoffs Diameter

Nose fineness

Boattail

Lifting body versus axisymmetric body

Wings versus no wings

Tails versus flares

Surface planform geometry

Flight control alternatives Maneuver alternatives

Roll orientation

Static margin / time to converge or diverge

Tail sizing

Summary of Aerodynamics ( cont ) Summary of Aerodynamics ( cont )



2/24/2008 ELF 76

Stability and Control Design Criteria Static stability

Control effectiveness

Cross coupling

Body Buildup

New Aerodynamics Technologies Faceted / window / multi-lens domes

Bank-to-turn maneuvering

Lifting body airframe Forward swept surfaces

Neutral static margin

Lattice fins

Split canard control Free-to-rol l tails


Classroom Exercise

Aerodynamics Problems Aerodynamics Problems



2/24/2008 ELF 77

1. Missile diameter tradeoffs include consideration of seeker range, warheadlethality, structural mode frequency, and d___.

2. Benefits of a high f ineness nose include lower supersonic drag and lower r____ c____ s______.

3. Three contributors to drag are base drag, wave drag, and s___ f_______drag.

4. To avoid flow separation, a boatail or flare angle should be less than __ deg.

5. A lifting body is most ef ficient at a d______ p_______ of about 700 psf.

6. At low angle of attack the aerodynamic center of the body is on the n___.

7. Subsonic missi les often have w____ for enhanced range.

8. The aerodynamic center of the wing is between 25% and 50% of the m___

a__________ c____.9. Hinge moment increases with the local flow angle due to control surface

deflection and the a____ o_ a_____.

10. Increasing the surface area increases the s___ f_______ d___.

Aerodynamics Problems ( cont ) Aerodynamics Problems ( cont )



2/24/2008 ELF 78

11. Leading edge sweep reduces drag and r____ c____ s______.

12. A missile with six control surfaces, four surfaces providing combined pitch /yaw control plus two surfaces providing roll control, has an advantage of good c______ e____________.

13. A missile with two control surfaces providing only combined pitch / yawcontrol has advantages of lower c____ and good p________.

14. A tail control missile has larger trim normal force if it is statically u_______.

15. Lattice fins have low h____ m_____.

16. Split canards allow higher maximum angle of attack and higher m______________.

17. Two types of unconventional control are thrust vector control and r_______ j__ control.

18. The most common type of TVC for tactical missiles is j__ v___ control.

19. Three maneuver laws are skid to turn, bank to turn, and r______ a_______.

20. Bank to turn maneuvering is usually required for missiles with a single wing

or with a_________ inlets.

Aerodynamics Problems ( cont ) Aerodynamics Problems ( cont )



2/24/2008 ELF 79

21. A missile is statically stable if the aero center is behind the c_____ o_g______.

22. Tail stabilizers have low drag while a f____ stabilizer has low aero heatingand a relatively small shift in static stability.

23. If the moments on the missile are zero the missile is in t___.

24. Total normal force on the missi le is approximately the sum of the normalforces on the surfaces ( e.g., wing, tail, canard ) plus normal force on theb___.

25. Increasing the tail area increases the s_____ m________.

Outline Outline



2/24/2008 ELF 80

Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design


Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design


Sizing Examples Development Process


References and Communication Appendices ( Homework Problems / Classroom Exercises,

Example of Request for Proposal, Nomenclature, Acronyms,








2/24/2008 ELF 81

Yes

Establish Baseline

Weight

Trajectory

MeetPerformance?


No

Yes


Al t Mission

Al t Baseline


Aerodynamics

Propulsion

High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption

High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption



2/24/2008 ELF 82

Scramjet: ISP typicallyconstrained by thermal choking

Turbojet: ISP typically constrained by turbine temperature limit

Ramjet: ISP typically constrained bycombustor insulation temperature limit

Solid Rocket: ISP typically constrainedby safety

4,000

3,000

2,000

1,000

0 I S P ,

S p e c i f i c I m p u l s e

, T h r u s t / ( F u e l o r P r o p e l l a n t

W e i g h

t F l o w R a t e ) , S

0 2 4 6 8 10 12

Mach Number

Ducted Rocket

Cruise Range Is Driven by L/D, sp , Velocity, and Propellant or Fuel Weight Fraction

Cruise Range Is Driven by L/D, sp , Velocity, and Propellant or Fuel Weight Fraction



2/24/2008 ELF 83

Typical Value for 2,000 lb Precision Strike Missi le

Note: Ramjet and Scramjet miss iles booster propellant for Mach 2.5 to 4 take-over speed not included in WP

for cru ise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages maybe required for rocket range greater than 200 nm.

R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation

Parameter

L / D, Lift / DragIsp, Specific Impulse

V AVG , Average Velocity

WP / WL, Cruise Propellant or

Fuel Weight / Launch WeightR, Cruise Range

103,000 s

1,000 ft / s

0.3

1,800 nm

51,300 s

3,500 ft / s

0.2

830 nm

31,000 s

6,000 ft / s

0.1

310 nm

5250 s

3,000 ft / s

0.4

250 nm

Solid RocketHydrocarbon FuelScramjet Missile

Liquid FuelRamjet Missile

Subsonic TurbojetMissile

Solid Rockets Have High Acceleration Capability Solid Rockets Have High Acceleration Capability



2/24/2008 ELF 84

1,000

100

10

1

0 1 2 3 4 5

RamjetTMax = (π / 4 ) d2 ρ0 V0

2 [( Ve / V0 ) -1 ]

Solid RocketT

Max= 2 P

c A

t= m

.V

e

M, Mach Number

( T / W ) M a x ,

( T h r u s t / W e i g h t ) M a x

Note:Pc = Chamber pressure, At = Nozzle throat area, m

.= Mass flow rate

d = Diameter, ρ0 = Free stream densi ty, V0 = Free stream velocity,V

e= Nozzle exit veloc ity ( Turbojet: V

e~ 2,000 ft / s, Ramjet: V

e~ 4,500 ft / s, Rocket: V

e~ 6,000 ft / s )

TurbojetTMax = (π / 4 ) d2 ρ0 V0

2 [( Ve / V0 ) -1 ]

Turbojet Nomenclature Turbojet Nomenclature



2/24/2008 ELF 85

0

Free Stream

1

Inlet Entrance

3

Compressor Exit

2

Compressor Entrance4

Turbine Entrance

Inlet Compressor Combustor Turbine Nozzle

5

Turbine Exit

High Temperature Compressors Are Required to

Achieve High Pressure Ratio at High Speed

High Temperature Compressors Are Required to

Achieve High Pressure Ratio at High Speed 2 ( γ - 1 ) / γ



2/24/2008 ELF 86

0

1000

2000

3000

0 1 2 3 4

M0, Free Stream Mach Number

T 3 ,

C o m p r e s

s o r E x i t T e m p e r a t u r e ,

p3 / p2 = 1

p3 / p2 = 2

p3 / p2 = 5

p3 / p2 = 10

T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M0 }( p3 / p2 ) 3 3

γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e-0.0007 T3

Note: Ideal in let; ideal compressor; low subsonic,isentropic flow

Example:M0 = 2, h = 60k ft ( T0 = 398 R )

p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36

T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat

ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure

T3

High Turbine Temperature Is Required for High

Speed Turbojet Missiles

High Turbine Temperature Is Required for High

Speed Turbojet Missiles

( / ) f /



2/24/2008 ELF 87

0

1000

2000

3000

4000

5000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

f / a, Fuel-to-Air Ratio

T 4 , T u r b o j e t

T u r b i n e T e m p e

r a t u r e ,

T3 = 500 R

T3 = 1000 R

T3 = 2000 R

T3 = 4000 R

T4 ≈ T3 + ( Hf / cp ) f / a, T in Rcp4

≈ 0.122 T40.109, cp in BTU / lb / R

Example:

M0 = 2, h = 60K ft ( T0 = 398 R ),p3 / p2 = 5 ⇒ T3 = 1118 R

RJ-5 fuel ( Hf = 14,525 BTU / lb ),cp = 0.302 BTU / lb / R , f / a =0.067 ( stochiometric ) ⇒ T4 =1118 + ( 14525 / 0.302 ) 0.067 =4,340 R

T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine,

Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio

T4

Turbine Material Temperature Limit Is a

Constraint for a High Speed Turbojet Missile

Turbine Material Temperature Limit Is a

Constraint for a High Speed Turbojet Missile

T t C t i d I f M hT bi M t i lM Sh t



2/24/2008 ELF 88

Slightly Constrained Turbojet

Moderately Constrained Turbojet

Moderately Constrained Turbojet

Highly Constrained Turbojet

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

Temperature Constrained

Turbines for Mach 4 Cruise

≈ 1,500 sCeramic Matrix Composites4,000R

≈ 2,000 sRhenium Alloys4,500R

≈ 2,500 sTungsten Alloys5,000R

≈ 1,200 sSingle Crystal Nickel Aluminides

≈ 3,500R

≈ 1,000 sTitanium Aluminides ( lighter weight than nickel super alloys )

≈ 3,000R

≈ 1,000 sNickel Super Alloys3,000R

ISP for Mach4 Cruise

Turbine MaterialMax ShortDuration Temp

Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraintscould consis t of a combination of:

• Constraint on compressor pressure ratio to limi t turb ine temperature

• Constraint on fuel-to-air ratio to limit turbine temperature

• Use of afterburner to limit turbine temperature

Turbin -Based Missiles Are Capable of Subsonic

to Supersonic Cruise

Turbin -Based Missiles Are Capable of Subsonic

to Supersonic Cruise

T b j t



2/24/2008 ELF 89

Turbojet

Turbo Ramjet

Air Turbo Rocket

Regulus II

Firebee II

SS-N-19 Shipwreck

SR-71

Compressor Pressure Ratio for Maximum Thrust

Turbojet Is Limited by Turbine Temperature

Compressor Pressure Ratio for Maximum Thrust

Turbojet Is Limited by Turbine Temperature

( p3 / p2 )@Tmax {( T4 / T0 )1/2

/ { 1 + [( 0 1 ) / 2 ] M02

}}γ4

/ ( γ4

- 1 )



2/24/2008 ELF 90

1

10

100

0 0.5 1 1.5 2 2.5 3 3.5 4

M0, Mach Number

( p 3 / p 2 ) @ T m a x

T4 = 2000 R T4 = 3000 R

T4 = 4000 R T4 = 5000 R

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974

( p3 / p2 )@Tmax ≈ {( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M0 }} 4 4

Assumptions: Ideal tu rbojet ( isentropic in let , compressor, turbine, nozzle; low subsonic and constant p ressurecombustion; exit pressure = free stream pressure )

Example:

M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R,γ4 = 1.31

( p3 / p2 )@Tmax = {{ ( 3000 / 390 )1/2 / { 1 + [ ( 1.4 -1 ) / 2 ] 2.02 }} 1.31/ ( 1.31 – 1 ) = 6.31

Note:

T0

= Free stream temperature

T4 = Turbine entrance temperature

γ = Specific heat ratio

Turbojet Thrust Is Limited by Turbine Maximum

Allowable Temperature

Turbojet Thrust Is Limited by Turbine Maximum

Allowable Temperature

TId lM / ( p0 A0 ) = ( 0 M0 / a0 ) ( T / m )Id lM Note:



2/24/2008 ELF 91

0

5

10

15

20

0 1 2 3 4

M0, Mach Number

T m a x / [ ( p 0 ) (

A 0 ) ] , N o n d i m e n s i o n a l M a x i m u m

T h r u s t

T4 = 2000 R T4 = 3000 R

T4 = 4000 R T4 = 5000 R

R

a m j e t ( p 3

/ p 2 = 1 )

Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0= 1.047 psi ), T4 = 3,000 R, γ4 = 1.31, ( p3 /

p2 )@Tmax = 6.31, p2 = 8.19 psi , p3 = 51.7 psi, A0 = 114 in2, T2 = 702 R, T3 = 1133 R, γ3 =1.36

T5t= 2569 R, γ5 = 1.32, p5t

= 23.0 psi , Ve =4524 ft / s, ( T / m

.)IdealMax = 2588 ft / s,

TIdealMax / p0 A0 = 7.49

TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb

TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m . )IdealMax

Assumption: Ideal turbojet

Note:

( T / m.)IdealMax = Ve – V0

Ve = { 2 cp T5t[ 1 – ( p0 / p5t

)( γ5 - 1 ) / γ5 ]}1/2

T5t≈ T4 – T3 + T2

T3

≈ T2

( p3

/ p2

)( γ3 - 1 ) / γ3

T2 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }

p5t≈ p4 ( T5 / T4 )γ4 / ( γ4 - 1 )

p4 = p3

p2 ≈ p0 { 1 + [( γ0 - 1 ) / 2 ] M02 }γ0 / ( γ0 - 1 )

p0 = Free stream static pressure

A0 = Free stream flow area into in let

T4 = Turbine entrance temperature

Turbojet Specific Impulse Decreases with

Supersonic Mach Number

Turbojet Specific Impulse Decreases with

Supersonic Mach Number

( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 0 M0 ) ( T4 T3 )]



2/24/2008 ELF 92

0

0.2

0.4

0.6

0.8

0 1 2 3 4M0, Mach Number

( I S P ) I d e a l ( g

c ) ( c p ) ( T 0 ) / [ ( a 0 )

( H f ) ] ,

N o n d i m e n s i o n a l I d e a l S p e c i f i c I m p

u l s e

T4 = 2000 R T4 = 3000 R

T4 = 4000 R T4 = 5000 R

( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 – T3 )] Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion;exit pressure = free stream pressure), max thrust

Example:

M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 =

3,000 R, cp = 0.293 BTU / lbm / R, γ0 = 1.4Calculate ( ISP )Ideal@Tmax

gc cp T0 / ( a0 Hf ) =0.559

( ISP )Ideal@Tmax = 0.559 ( 968 ) ( 14525 ) / [ 32.2( 0.293 ) ( 390 )] = 2136 s

Note:gc = Gravitational constant = 32.2

cp = Specific heat at constant pressure

T0 = Free stream temperature

a0 = Free stream speed of sound

Hf = Heating value of fuel

TIdealMax = Ideal maximum thrust


T4 = Combustor exit temperature

T3 = Compressor exit temperature

R a m j e t ( p 3 / p

2 = 1 )

Tactical Missile Ramjet Propulsion Alternatives Tactical Missile Ramjet Propulsion Alternatives

Liquid Fuel Ramjet



2/24/2008 ELF 93

Rocket Boost Inboard Profile

Ramjet Sustain Inboard Profi le

Liquid Fuel Ramjet

Solid Fuel Ramjet

Solid Ducted Rocket

Boost

Sustain

Boost

Sustain

Note:Booster PropellantFuel

High Specific Impulse for a Ramjet Occurs Using

High Heating Value Fuel at Mach 3 to 4

High Specific Impulse for a Ramjet Occurs Using

High Heating Value Fuel at Mach 3 to 4

( ISP

)Ideal

gc

cp

T0

/ ( a0

Hf

) = { M0

{{( T4

/ T0

) / { 1 + [( γ0

- 1 ) / 2 ] M0

2 }}1/2 - 1 } / {{ 1 + [( γ0

- 1 ) / 2 ] M0

2 } {( T4

/ T0

) / {1 + [( 0 - 1 ) / 2 ] M0

2 }} – 1 }



2/24/2008 ELF 94

0

0.2

0.4

0.6

0 1 2 3 4 5M0, Free Stream Mach Number

( I S P ) I d e a l ( g c

) ( c p ) ( T 0 ) / [ ( a 0 ) ( H f ) ] ,

N o n d i m e n s i o n a l I d e a l S p e c i f i c I m

p u l s e

T4 / T0 = 3 T4 / T0 = 5

T4 / T0 = 10 T4 / T0 = 15

p1 + [( γ0 1 ) / 2 ] M0 }} 1 }

Assumptions: Ideal ramjet , isentropic inlet and nozzle, low subsonic and constant pressure combustion, ex it pressure = freestream pressure, φ ≤ 1

Example for Ramjet Baseline:

M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ),RJ-5 fuel ( H

f

= 14,525 BTU / lbm ), T4

= 4,000 R,cp = 0.302 BTU / lbm / R, γ0 = 1.4

Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{(4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }} 1/2 - 1 } / {{1 + [( 1.4 - 1 ) / 2 ] 3.52 } { ( 4000 / 390 ) / { 1 + [(1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372

( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) (

390 ) = 1387 s

Note:

gc = Gravitational constant = 32.2

cp = Specific heat at constant pressure


a0 = Free stream speed of sound

Hf = Heating value of fuel


T4 = Combustor exit temperature


High Thrust for a Ramjet Occurs from Mach 3 to

5 with High Combustion Temperature

High Thrust for a Ramjet Occurs from Mach 3 to

5 with High Combustion Temperature

TIdeal / ( p0 A0 ) = 0 M0

2

{{[ T4 / T0 ] / { 1 + [( 0 - 1 ) / 2 ] M0

2

}}1/2

- 1 }



2/24/2008 ELF 95

0

5

10

15

20

25

0 1 2 3 4 5M0, Free Stream Mach Number

T / [ P H I ( p 0 )

( A 0 ) ] , N o n d i m i m e n s i o n a l

T h r u s t

T4 / T0 = 3 T4 / T0 = 5

T4 / T0 = 10 T4 / T0 = 15

T / ( φ p A ) γ M {{[ T / T ] / { 1 [( γ 1 ) / 2 ] M }} 1 } Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressurecombustion, exit pressure = free stream pressure, φ ≤ 1

Note: T4 and T0 in R Example for Ramjet Baseline:

M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 =

1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ =0.82, A0 = 114 in2, γ0 = 1.4

TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 )2 {{[ 4000 / 390 ] / { 1+ [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }} 1/2 – 1 } = 12.43

TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lb

Note:

( T )Ideal = Ideal thrus t

p0 = Free stream static pressure

A0 = Free stream flow area into inlet

γ0 = Free stream specific heat ratio

M0 = Free stream Mach number T4 = Combustor exit temperature


φ = Equivalence ratio = fuel-to-air ratio /stochiometric fuel-to-air ratio


Ramjet Combustor Temperature Increases with

Mach Number and Fuel Flow

Ramjet Combustor Temperature Increases with

Mach Number and Fuel Flow

T4 T0 { 1 + [( 0 - 1 ) / 2 ] M02

} + ( Hf / cp ) ( f / a )



2/24/2008 ELF 96

0

2000

4000

6000

0 1 2 3 4 5


T 4 , C o m b u s t o r E x

i t T e m p e r a t u r e f o r

R J - 5

F u e l , R a n k i n e

f / a = 0.01 f / a = 0.03 f / a = 0.05 f / a = 0.067

Example:

•M0 = 3.5

•h = 60k ft ( T0 = 390 R )

•RJ-5 fuel ( Hf = 14,525 BTU / lb / R )

•f / a = 0.055

•γ0 = 1.4

•cp = 0.122 T0.109 BTU / lbm / R.

Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R

•Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2

} +[( 14525 ) / ( 0.302 )] 0.055 = 3,991 R

Note: ( f / a )φ = 1

≈ 0.067 for stochiometric combustion of li quid hydrocarbon fuel, e.g., RJ-5.

T ≈ T { 1 [( γ 1 ) / 2 ] M } ( H / c ) ( f / a ) Assumptions: Low subsonic combust ion. No heat t ransfer through in let ( isentropicflow ). φ ≤ 1.

T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine,γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp =specific heat at constant pressure, f / a = fuel-to-air ratio.

Ramjet Combustor Entrance Mach Number

Should Be Low, to Avoid Thermal Choking

Ramjet Combustor Entrance Mach Number

Should Be Low, to Avoid Thermal Choking ( M

3

)TC

= {{ - b + [ b2 – 4 γ3

2 ]1/2 } / ( 2 γ3

2 )}1/2

b = 2 + ( T / T )( 1 + )2 / {( 1 + 0 2 M 2 )[ 1 + ( – 1 ) / 2 ]}



2/24/2008 ELF 97

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5


( M 3 ) T C ,

C o m

b u s t o r E n t r a n c e M

a c h

N u m b e r w i t h T h e r m a l C h o k i n

g

T4t / T0 = 3 T4t / T0 = 5

T4t / T0 = 10 T4t / T0 = 15

b = 2 γ3 + ( T4t/ T0 )( 1 + γ4 )2 / {( 1 + 0.2 M0

2 )[ 1 + ( γ4 – 1 ) / 2 ]}

Assumptions: Constant area combust ion, [( γ 3 – 1 ) / 2 ] M32 << 1, isentropic inlet

Example:

M0 = 2, h = 60k ft ( T0 = 390 R ), T4t= 4,000 R, γ0 = 1.4

γ4 = 1.29 + 0.16 e-0.0007 ( 4000 ) = 1.300

T0t= ( 1 + 0.2 M0

2 ) T0 = 702 R

γ 3 = 1.29 + 0.16 e-0.0007 ( 702 ) = 1.388

b = 2 ( 1.388 ) + ( 4000 / 390 )( 1 + 1.300 )2 / {( 1 + 0.2( 22 )[ 1 + ( 1.300 – 1 ) / 2 ]} = - 24.211

( M3 )TC = {{ 24.211 + [( -24.211 )2 – 4 ( 1.3882 )]1/2 } / [ 2 ( 1.3882 )]}1/2 = 0.204

Note:

( M3 )TC = Combustor entrance Mach number withthermal choking ( M4 = 1 )

γ3 = Specific heat ratio at combustor entranceM0 = Free stream Mach number

T4t= Combustor exit total temperature

T0 = Free stream static temperature

γ4 = Specific heat ratio in combust ion

A Ramjet Combustor with a Low Entrance Mach

Number Requires a Small Inlet Throat Area

A Ramjet Combustor with a Low Entrance Mach

Number Requires a Small Inlet Throat Area

AIT / A3 = [( + 1 ) / 2 ]( γ + 1 ) / [ 2 ( γ - 1 )] M3 {[ 1 + ( - 1 ) / 2 ] M32 }-( γ + 1 ) / [ 2 ( γ - 1 )] = ( 216 / 215 ) M3 ( 1 + M32 / 5 )-3



2/24/2008 ELF 98

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

( A )IT / A3, Inlet Throat Area to Combusto r Area Ratio

M 3 ,

C o m b u s t o r E n

t r a n c e M a c h N u m b e

r

[( γ ) ] {[ ( γ ) ] } ( ) ( ) Assumptions: Isentropic in let , MIT = 1, γ = 1.4

Note:

AIT = Inlet throat area

A3 = Combustor entrance areaM3 = Combustor entrance Mach number


Example:

Ramjet Baseline

AIT = 41.9 in2

A3 = 287 in2

AIT / A3 = 41.9 / 287 = 0.1459

Assume sonic flow ( M = 1 ) at AIT

M3 = 0.085M3 = 0.085 < ( M3 )TC = 0.204

Typical Ramjet Has Nearly Constant Pressure

Combustion

Typical Ramjet Has Nearly Constant Pressure

Combustion

Assume Rayleigh Flow, with Heat Addition at



2/24/2008 ELF 99

y g , Constant Area

Negligible Friction

Pressure Loss in Combustor is Given by p

4

/ p3

= ( 1 + γ3

M3

2 ) / ( 1 + γ4

M4

2 )

Mach Number Increase in Combustor Is Given by T4t

/ T0 = [( 1 + γ3 M32 ) / ( 1 + γ4 M4

2 )]2 ( M4 / M3 )2 { 1 + [( γ4 – 1 ) / 2 ] M42 } / { 1 + [( γ3 – 1 ) / 2 ] M3

2 }

From Prior Example

M0 = 2, h = 60k ft ( T0 = 390 R ), T4t= 4,000 R, γ0 = 1.4, γ4 = 1.300, and γ 3 = 1.388

Assume Ramjet Baseline with Sonic Inlet Throat

AIT / A3 = 41.9 / 287 = 0.1459 ⇒ M3 = 0.085

Solving Above Equations

M4

= 0.304

p4 / p3 = 0.902

Assumption of Nearly Constant Pressure Combustion Is Reasonably Accurate

10% error

Minimum Length for the Combustor Is a

Function of Combustion Velocity

Minimum Length for the Combustor Is a

Function of Combustion Velocity

( l ) = t V



2/24/2008 ELF 100

0.1

1

10

100 1000 10000

Vcomb, Combustion Velocity, ft / s

M i n i m u m C

o m b u s t o r L e n g

t h ,

f t

tcomb = 0.001 s

tcomb = 0.002 s

tcomb = 0.004 sExample for tcomb = 0.002 s and

Subsonic Combustion Ramjet:

•Vcomb = 200 ft / s

•( lcomb

)min

= 0.002 ( 200 ) = 0.4 ft

Example for tcomb = 0.002 s andScramjet:

•Vcomb = 3,000 ft / s

•( lcomb )min = 0.002 ( 3000 ) = 6.0 ft

( lcomb )min = tcomb Vcomb

Ramjet Engine / Booster Integration Options Ramjet Engine / Booster Integration Options

I t l R k t R j t ( IRR )

FuelBoost PropellantLow Cruise Drag ( Modern Ramjets )



2/24/2008 ELF 101

Integral-Rocket Ramjet ( IRR ) Af t Drop-of f Booster

Podded Drop-off Booster Forward Booster

Podded Ramjet

Podded Ramjet, Aft Drop-off Booster

Podded IRR

p

Source: Kinroth, G.D. and Anderson, W.R., “ RamjetDesign Handbook,” CPIA Pub. 319, June 1980

g ( j )

High Cruise Drag

Ramjet Engine / Booster Integration Trades Ramjet Engine / Booster Integration Trades

a g g l i t y

l i t ySelection Factors



2/24/2008 ELF 102

Superior Above Average Average Below average

L e n g t h

D i a m e t e r

W e i g h t

E j e c t a b l e s

C r u i s e D r a

C a r r y D r a g

C o s t

C y c l e

C o m p a t i b i

I n l e t

C o m p a t i b i

Source: Kinroth , G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319, June 1980

Integral Rocket – Ramjet ( IRR )

Af t Booster ( Drop-off )

Forward Booster

Podded Booster ( Drop-off )

Podded Ramjet

Podded IRR

Podded Ramjet Af t Booster ( Drop-off )

–

–

–

–

–

– –

–

– – – –

–

–

–

–

–

–

Ramjets with Internal Boosters and No Wings

Have Low Drag

Ramjets with Internal Boosters and No Wings

Have Low Drag

1 2



2/24/2008 ELF 103

1.2

0.8

0.4

0

2 3 4 5

M, Mach Number

CD0= DO / ( q SREF ), Zero-Lift Drag

Coefficient

Note:Nose Fineness Ratio ≥ 2.25Nose Bluntness Ratio ≤ 0.20

• IRR

• Af t Drop Off Booster

• Forward Booster

• Podded Drop Off Booster

With Wings

Without Wings• IRR

• Af t Drop-of f Booster

• Forward Booster

• Podded Drop-off Booster

• Podded Ramjet

• Podded IRR• Podded Ramjet, Aft Drop

Off Booster

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980

CD0

Sketch

Ramjet Inlet Options Ramjet Inlet Options

PlacementType Inlet



2/24/2008 ELF 104

Nose

Source: Kinroth, G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319, June 1980.

Nose-full axisymmetric

Af t-crucifo rm ( four ) two d imensional

Af t unders ide-belly mounted two dimensional

Af t unders ide-ful l ax isymmetri c

Af t-twin cheek-mounted two dimensional

Cruciform Two-dimensional

Underslung Two-dimensional

Underslung Axisymmetric

Twin Two-dimensional

Under Wing Axisymmetric

Af t Cruciform Axisymmetric

Forward Cruciform Axisymmetric

Chin

In planar wing compression field-twin axisymmetric

Af t-c ruci form ( four ) axisymmetric

Forward in nose compression field-cruciform ( four )axisymmetric

Forward underside in nose compression field-partial axisymmetric

Ramjet Inlet Concept Trades Ramjet Inlet Concept Trades

e t y n g

s t d d t y

Selection Factorse y



2/24/2008 ELF 105

Superior Above Average Average Below average

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980

–

C a r r i a g e

E n v e l o p e

A l p h a

C a p a b i l i t

W e i g h t

D r a g

W a r h e a d

S h r o u d i n

i n l e t C o s

P r e f e r r e d

S t e e r i n g

P r e f e r r e d

C o n t r o l

P r i m e

M i s s i o n

S u i t a b i l i t

Note:BTT = Bank to TurnSTT = Skid to TurnW = Wing C = CanardT = Tail

STT W, C ATS, STA

BTT T ATS, ATA, STA – – STT T ATS, ATA, STA

STT T ATS

BTT T ATS, ATA, STA –

BTT T ATS, ATA, STA

– BTT T ATS

– BTT T ATS, ATA, STA

STT T ATS

Type Inlet P r e s s u r e

R e c o v e r y

–

–

–

–

United Kingdom

Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets

Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets



2/24/2008 ELF 106

Sea Dart GWS-30

France

ASMP ANS

Russia

AS-17 / Kh-31 Kh-41 SS-N-22 / 3M80

SA-6 SS-N-19 SS-N-26

China

C-101 C-301

Taiwan

Hsiung Feng III

India

BrahMos

• Af t in lets have lower inlet volume and do not degrade lethali ty of fo rward located warhead.

• Nose Inlet may have higher f low capture, pressure recovery, smaller carriage envelope, and lower drag.

Shock on Inlet Cowl Lip Prevents Spillage Shock on Inlet Cowl Lip Prevents Spillage

Inlet w/o External CompressionInlet Swallows 100% of the Free



2/24/2008 ELF 107

Stream Flow

External Compression Required for Efficient Pressure Recovery if MachNumber > 2 and Inlet Start at LowSupersonic Mach number

External Compression Inlet ( wi thSpillage )

Shocks Converge Outside Inlet Lip( Results in Spillage Air )

External Compression Inlet ( w/o

Spillage )Inlet Swallows 100% of the FreeStream Flow

Shocks Converge at Inlet Lip ( InletCaptures Maximum Free Stream

Flow )

Shocks

Spillage

Shocks

Shock Wave Angle Increases with Deflection

Angle and Decreases with Mach Number

Shock Wave Angle Increases with Deflection

Angle and Decreases with Mach Number tan ( α + δ ) = 2 cot θ

2D

( M2 sin2 θ2D

– 1 ) / [ 2 + M2 ( γ + 1 – 2 sin2 θ2D

)] , for 2D flow, perfect gas

Note: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heatratio 0 81



2/24/2008 ELF 108

0

10

20

30

40

50

0 5 10 15 20

Alpha + Delta, Deflectio n Angle, Degrees

T h e t a , 2

D S h o c

k W a v e A n g l e @ G a m m a =

1 . 4 , D e g r e e s

Mach 2 ( Deltamax = 23 deg ) Mach 3 ( Deltamax = 34 deg )

Mach 5 ( Deltamax = 41 deg )

ratio, θconical ≈ 0.81 θ2D


δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4

⇒ θ2D = 32 deg

θconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg

δ

θ

α

Approximate est imate of θ:

θ2D ≈ μ + α + δ = sin-1

( 1 / M ) + α + δθconical ≈ 0.81 θ2D = 0.81 [ sin-1 ( 1 / M ) +α + δ ]

Capture Efficiency of an Inlet Increases with Mach

Number

Capture Efficiency of an Inlet Increases with Mach

Number ( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet

( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward in let



2/24/2008 ELF 109

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

M, Mach Numb er

A 0 / A c , B a s e l i n e R a m j e t I n l e t C a p t u r e

E f

f i c i e n c y

Alpha = 0 Deg Alpha = 10 Deg

Ac

A0 s tream l ine s t r e a m l i n e

oblique shock

h inlet

nose body

δ

s t r e a m l i n e s tream l ine

Note: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l =distance from nose tip to inlet

α

Example for baseline ramjet ( conicalnose )

h = 3 in

l = 23.5 in

h / l = 0.1277

AC

= 114 in2

δ = 17.7 deg ( 0.3089 rad )

M = 3.5, α = 0 deg

A0 / Ac = 0.81 ⇒ A0 = 92 in2

Spillage = Ac - A0 = 114 - 92 = 22 in2

Isentropic Compression Allows Inlet Start at

Lower Mach Number

Isentropic Compression Allows Inlet Start at

Lower Mach Number AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start

2 )-3, Assumptions: 2-D in let , Isentropic f low through in let ( n = ∞ ), γ = 1.4

AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start2 + 2 ] / [ 2.4 ( MIE )start

2 ]3.5 }{[2.8 ( MIE )start2 – 0.4 ] / 2.4 }2.5 {[ 1.2 / ( 1 + 0.2 (

MIE ) t t2 ]}3 Assumptions: 2-D inlet s ingle normal shock ( n = 1 ) = 1 4



2/24/2008 ELF 110

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

AIT / A0

( M ) I E , I n

l e t E n t r a n c e S t a r t M a c h

N

u m b e r

Inlet Start for Isentro pic Compression

Inlet Start for Single Normal Shock

MIE )start ]} , Assumptions: 2 D inlet, s ingle normal shock ( n = 1 ), γ = 1.4

Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heatratio, n = number of shocks

Example for ramjet baseline

AIT = 0.29 ft2

Ac = 114 in2 = 0.79 ft2 ⇒ AIT / Ac = 0.367

Process:

1. Assume ( MIE )start

2. Compute capture efficiency AIT / A0

3. Compute ( MIE )start and compare withassumed ( MIE )start

4. Iterate unti l convergence

Limit for isentropic compression

- From Prior Figure, A0 / Ac = 0.53- Compute AIT / A0 = ( A IT / Ac ) / ( A0 / Ac ) =

0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8

Ramjet baseline has mixed compressionwith n = 5. Actual inlet start Machnumber is ( MIE )start > 1.8

n = 1n = ∞

Forebody Shock Compression Reduces the Inlet

Entrance Mach Number

Forebody Shock Compression Reduces the Inlet

Entrance Mach Number ( MIE )2D = {{ 36 M0

4 sin2 θ2D - 5 [ M02 sin2 θ2D - 1 ][ 7 M0

2 sin2 θ2D + 5 ]} / {[ 7 M02 sin2 θ2D - 1 ] [ M0

2 sin2 θ2D + 5 ]}}1/2

tan ( α + δ ) = 2 cot θ2D ( M02 sin2 θ2D – 1 ) / [ 2 + M0

2 ( 2.4 – 2 sin2 θ2D )]



2/24/2008 ELF 111

0

1

2

3

4

0 10 20 30 40

Alpha + Delta, Local Angle of At tack at Inlet Entrance, Deg

( M ) I E ,

I n l e t E n t r a n c e M a c h N u m b e r

M0 = 2 M0 = 3 M0 = 5

Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4

Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = bodydeflection angle

Example for ramjet baseline

δ = 17.7 deg

( MIE )start = 1.8 ( from prior example )

Compute M0 = 2.55

Note: Ramjet baseline forebody isconical, not 2D

Optimum Forebody Deflection Angle(s) for Best

Pressure Recovery Increases with Mach Number

Optimum Forebody Deflection Angle(s) for Best

Pressure Recovery Increases with Mach Number

First External Shock

Second External Shock

Note: δTotal = Total deflection angle,δ1 = 1st deflection angle, δ2 = 2nd

deflection, δ3 = 3rd deflection.



2/24/2008 ELF 112

0

20

40

60

0 1 2 3 4


O p t i m u m T o t a l D e

f l e c t i o n A n g l e ,

D e g

n = 1 n = 2 n = 3 n = 4 Isentropic Compression

δ1

Second External Shock

δ2

3

Optimum deflection angle providesequal loss in total pressure acrosseach shock wave.

Optimum deflection angles arenearly equal for M > 4.

Reference: “ Technical Aerodynamics Manual,” North American Rockwell Corporation , DTIC AD 723823, June 1970.

Example: Optimum forebody deflection angles for double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2= 11.2 deg ⇒ δtotal = 10.4 + 11.2 = 21.6 deg

δTotal

10.4, 11.2

15.0, 18.816.1, 22.1

7.6, 8.2, 8.2

11.1, 13.0, 15.5

12.1, 15.2, 19.4

Oblique Shocks Prior to the Inlet Normal Shock

Are Required to Satisfy MIL-E-5008B

Oblique Shocks Prior to the Inlet Normal Shock

Are Required to Satisfy MIL-E-5008B

1

e ( l Sh k )

MIL-E-5008B Requirement: ptInlet / pt0 = 1 – 0.075 ( M – 1 )1.35



2/24/2008 ELF 113

0.01

0.1

0 1 2 3 4 5

M, Mach Number

P t I n l e t / p t 0 ,

I n l e t T o t a

l P r e s s u r e

R a t i o

n = 1 ( Normal Shock )

n = 2 ( 1 Optimum ObliqueShock + Normal Shock )

n = 3 ( 2 Opt ObliqueShocks + Normal Shock )

n = 4 ( 3 Opt ObliqueShocks + Normal Shock

Ideal Isentropic Inlet

MIL-E-5008B

Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at HighSupersonic Speeds”, NACA TM - 1140, 1947.

Example: MIL-E-5008B requirement for Mach 3.5 ( ptInlet/ p t0

= ηinlet = 0.74 ) can be satisf ied only if there are morethan three oblique shocks prior to inlet normal shock.

Note: 2D flow assumed

ptInlet= Inlet total pressure

pt0 = Free stream total pressure

High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables

High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables

Type FuelVolumetricPerformance,BTU / in3

LowObservables

Density,lb / in3



2/24/2008 ELF 114

Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 ) ~ 0.028 559

Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 ) ~ 0.040 581

HTPB ~ 0.034 606

Slurry ( 40% JP-10 / 60% carbon ) ~ 0.049 801

Solid Carbon ( graphite ) ~ 0.075 1132

Slurry ( 40% JP-10 / 60% aluminum ) ~ 0.072 866

Slurry ( 40% JP-10 / 60% boron carbide ) ~ 0.050 1191

Solid Mg ~ 0.068 1200

Solid Al ~ 0.101 1300

Solid Boron ~ 0.082 2040

–

yp BTU / in3

Superior Above average Average Below average

Observables

–

–

–

–

–

lb / in

–

Ducted Rocket Design Implications Ducted Rocket Design Implications

Excess Fuel from Gas Generator ~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn



2/24/2008 ELF 115

( g gtemperature, lower ISP )

~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower burn temperature )

Choice of Fuel Metal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher

observables

Carbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability,

lower ISP

Choice of Oxidizer AP ⇒ Higher burn rate, lower hazard, HCl contrail

Min Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value,lower burn rate, hazardous

Thrust Magnitude Control Approaches Pintle or valve in gas generator throat

Retractable wires in grain

High Propellant Fraction Increases Burnout Velocity

High Propellant Fraction Increases Burnout Velocity

5000

Assumption: T >> D, T >> W sin γ, γ = constΔV = -gc Isp ln (1 - Wp / Wi)



2/24/2008 ELF 116

0

4000

3000

2000

1000

0 0.1 0.2 0.3 0.4 0.5

Example: Rocket BaselineWi,boost = WL = 500 lb, Wp, boost = 84.8 lbISP, boost = 250 sWP, boost / Wi = 84.8 / 500 = 0.1696

ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s

ΔV, MissileIncremental

Burnout Velocity,

ft / s

WP / Wi, Propellant Weight / Initial Missi le Weight

Isp = 250 s

Isp = 200 s

High Specific Impulse Requires High Chamber

Pressure and Optimum Nozzle Expansion

High Specific Impulse Requires High Chamber

Pressure and Optimum Nozzle Expansion

ISP = cd {{[ 2 γ2 / ( γ - 1 )] [ 2 / ( γ + 1 )] ( γ + 1 ) / ( γ - 1 ) [ 1 – ( pe / pc ) ( γ - 1 ) / γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc

T = w.p ISP = ( gc / c* ) pc At ISP

= {[ 2 / ( + 1 )]1 / ( γ - 1 ) [( -1 ) / ( + 1 )]1/2 } / {( p / p )1 / γ [ 1 - ( p / p ) ( γ - 1 ) / γ ]1/2 }



2/24/2008 ELF 117

200

250

300

0 10 20 30Nozzle Expansion Ratio

I s p ,

S p e c i f i c I m p

u l s e o f R o c k e t B a s e l i n e , s

pc = 300 psi pc = 1000 psi

pc = 2000 psi pc = 3000 psi

Note:ε = nozzle expansion ratiope = exit pressure

pc = chamber pressurep0 = atmospheric pressurew.

P = propellant weight f low rate At = nozzle throat area ( minimum, sonic, choked )γ = specific heat ratio = 1.18 in figurecd = discharge coefficient = 0.96 in figure

c* = characterist ic veloc ity = 5,200 ft / s in f igureh = 20k ft, p0 = 6.75 psi in figure


ε = Ae / A t = 6.2 ⇒ pe / pc = 0.02488, A t = 1.81 in2

( pc )boost = 1769 psi, pe = 44 psi , ( ISP )boost = 257 s

( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb

( pc )sustain = 301 psi , pe = 7.49 psi , ( ISP )sustain = 239 s

( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20

( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb

ε {[ 2 / ( γ + 1 )] ( ) [( γ 1 ) / ( γ + 1 )] } / {( pe / pc ) [ 1 ( pe / pc ) ( ) ] }

High Propellant Weight Flow Rate Requires High

Chamber Pressure and Large Nozzle Throat

High Propellant Weight Flow Rate Requires High

Chamber Pressure and Large Nozzle Throat

100000

w.

p = gc pc At / c*



2/24/2008 ELF 118

100

1000

10000

100000

1 10 100

Propellant Weight Flow Rate, lb / s

( p c ) A t , C h a m

b e r P r e s s u r e x N o z z l e

T h

r o a t A r e a ,

l b

c* = 4800 ft / s

c* = 5200 ft / s

c* = 5600 ft / s

Rocket Baseline A t for Boost:

c* = 5200 ft / s

( pc )boost = 1,769 psi

w.

p = Wp / tb = 84.8 / 3.69 = 23.0 lb / s

pc At = c* w .p / gc = 5200 ( 23.0 ) / 32.2= 3,714 lb

At = 3714 / 1769 = 2.10 in2

Note: At = nozzle throat area, c* = characteristic velocity, w.

p = propellant weight flow rate, gc = gravitational constant,p

c

= chamber pressure

High Chamber Pressure Requires Large

Propellant Burn Area and Small Nozzle Throat

High Chamber Pressure Requires Large Propellant Burn Area and Small Nozzle Throat

600

a ,

i n 2

Ab

= gc

pc A

t/ ( ρc*r )

r = r pc=1000 psi ( pc / 1000 )n

Example Ab for Rocket

Baseline: At= 1.81 in2

= 0 065 lb / in3



2/24/2008 ELF 119

0

200

400

0 500 1000 1500 2000Pc, Rocket Baseline Motor Chamber Pressure, psi

A b ,

R o c k e t B a s e l i n e P r o p e l l a n t B u r n A r e a ρ = 0.065 lb / in3

n = 0.3

r pc = 1000 psi = 0.5 in / s

c* = 5,200 ft / s

Tatmosphere = 70 °F

For sustain ( pc = 301 psi ):

•r = 0.5 ( 301 / 1000 )0.3 = 0.35in / s

• Ab = 149 in2

For boost ( pc = 1,769 psi )

•r = 0.59 in / s

• Ab = 514 in2

Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area,ρ = density of propellant, c* = characteristic velocity,r = propellant burn rate, r pc=1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent

Conceptual Design Sizing Process for a Rocket

Motor

Conceptual Design Sizing Process for a Rocket

Motor 1. Define Altitude and Required Thrust-time

New Value ( s )

2. Assume Propellant ( Characterist ic Velocity, Nominal) C



2/24/2008 ELF 120

Yes

4. Compute Propellant Weight Flow Rate and Propellant Used

No

NoYes

5. Determine Diameter and Length to Satisfy wp and Ae

OK?

OK?

OK?

Yes

New Value ( s )

No

Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )

3. Compute ISP andThrust

Example Web Cross Section / Volumetric Loading

~ 82% ~95% ~90%

Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section

Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section

l b )

Constant

Example Mission•≈ Cruise

Thrust Profile



2/24/2008 ELF 121

82% 95% 90%

End Burner Radial Slotted Tube~ 79%

~ 87%

~ 85%

~ 85%

T h r u s t (

Burning Time ( s )

Thrust

RegressiveThrust

ProgressiveThrust

Boost-Sustain

Boost-Sustain-Boost

Burning Time ( s )

Burning Time ( s )

Burning Time ( s )

Burning Time ( s )

T h r u s t ( l b

)

T h r u s t ( l b )

T h r u s t ( l b )

T h r u s t ( l b )

Medium Burn Rate Propellant

High Burn Rate PropellantNote: High thrus t and chamber pressure require large surface burn area.

•Dive at ≈constantdynamicpressure

•Climb at ≈constant

dynamicpressure

•Fast launch –≈ cruise

•Fast launch –≈ cruise – highspeed terminal

Production of Star Web Propellant.Photo Courtesy of BAE

Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval

Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval

Conventional Fixed Burn Interval ( Boost )



2/24/2008 ELF 122

End Burning

Conventional Fixed Burn Interval ( Boost – Sustain )

Radial BoostEnd Burning Sustain

Simultaneous Burning

1st Pulse: Radial Boost2nd Pulse: End Burning Sustain

Separate Burning ( Pulsed Motor )

1st Pulse: Radial Boost2nd Pulse: Radial Sustain / Boost

Separate Burning ( Pulsed Motor )

Concentric Radial BurningHigh Burn Rate Boost

Low Burn Rate Sustain

Radial Burning

Boost Propellant

Sustain Propellant

Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )

Note: Each pulse increases motor cost approximately 40%.

Tactical Rocket Motor Thrust Magnitude Control

Alternatives

Tactical Rocket Motor Thrust Magnitude Control

Alternatives

Solid Pulse Motor

☺ High ISP



2/24/2008 ELF 123

SP

Limited Pulses

Solid Pintle Motor ☺ Continuously Select Up to

40:1 Variation in Thrust

☺ Reduce MEOP on Hot Day

Good ISP Only If Burn RateExponent n → 1

Bi-propellant Gel Motor

☺ High ISP

☺ Duty Cycle Thrust

☺ Insensitive Munition

Lower Max Thrust

Toxicity

Thermal or Mechanical Barriers

Pintle

Pressurization Gelled Oxidizer Gelled Fuel Combust ionChamber

Solid Rocket Propellant Alternatives Solid Rocket Propellant Alternatives

B



2/24/2008 ELF 124

250 - 260 0.062 0.1 - 1.5

Superior Above Average Average Below Average

• Min Smoke . No Al fuel or AP

oxidizer. Either Composite with

Nitramine Oxidizer ( CL-20, ADN,

HMX, RDX ) or Double Base. Very low

contrail (H2O).

• Reduced Smoke . No Al ( binder

fuel ). AP oxidizer. Low contrail ( HCl ).

• High Smoke . Al fuel. AP oxidizer.High smoke ( Al2O3).

–

ISP,Specific

Impulse, s

ρ,Density,lb / in3

BurnRate @

1,000 psi,in / s Safety Observables

– – –

–

Type

220 - 255 0.055 - 0.062 0.25 - 2.0

260 - 265 0.065 0.1 - 3.0

Steel is the Most Common Motor Case Material Steel is the Most Common Motor Case Material

VolumetricEffi i Weight

Airframe /Launcher

C tTypeTemper-

t IM



2/24/2008 ELF 125


Steel

Aluminum

Strip Steel /Epoxy Laminate

Composite

Titanium

–

Efficiency Weight Attachment Cost

–

Type

–

–

– –

– –

ature

–

IM

Heat Transfer Drives Rocket Nozzle Materials,

Weight, and Cost

Heat Transfer Drives Rocket Nozzle Materials,Weight, and Cost

HousingThroat

Exit Cone

Dome Closeout



2/24/2008 ELF 126

Throat

Rocket Nozzle Element High Heating ( High Chamber Pressure or Long Burn )⇒ High Cost / Heavy Nozzle

Low Heating ( Low Chamber Pressure or Short Burn ) ⇒ Low Cost / Light Weight Nozzle

♦ Housing Material Al ternat ives

♦ Steel ♦ Cellulose / Phenolic♦

Aluminum

♦ Throat Material Al ternatives

♦ Tungsten Insert♦ Rhenium Insert♦ Molybdenum Insert

♦ Cellulose / Phenolic Insert♦ Silica / Phenolic Insert♦ Graphite Insert♦ Carbon – Carbon Insert

♦ Exit Cone, Dome Closeout,and Blast Tube Material Al ternatives

♦ Silica / Phenol ic Insert♦ Graphite / Phenolic Insert♦ Silicone Elastomer Insert

♦ No Insert♦ Glass / Phenolic Insert

Summary of Propulsion Summary of Propulsion

Emphasis Turbojet propulsion

Ramjet propulsion



2/24/2008 ELF 127

Ramjet propulsion

Rocket propulsion

Conceptual Design Prediction Methods Thrust

Specific impulse

Design Trades

Turbojet turbine material, compressor ratio, and cycle Ramjet engine / booster / inlet integration

Ramjet fuel

Propellant burn area requirement

Nozzle throat area Nozzle expansion ratio

Rocket motor grain

Thrust magnitude control

Summary of Propulsion ( cont ) Summary of Propulsion ( cont )

Design Trades ( cont ) Solid propellant alternatives

Motor case material alternatives



2/24/2008 ELF 128

Nozzle materials

New Propulsion Technologies Hypersonic turbojet

Ramjet / ducted rocket

Scramjet

Combined cycle propulsion High temperature turbine materials

High temperature combustor

Oblique shock airframe compression

Mixed compression inlet Low drag inlet

High density fuel / propellant

Endothermic fuel

Summary of Propulsion ( cont ) Summary of Propulsion ( cont )

New Propulsion Technologies ( cont ) Solid rocket thrust magnitude control

High burn exponent propellant



2/24/2008 ELF 129

g p p p

Low observable fuel / propellant

Discussion / Questions? Classroom Exercise ( Appendix A )

Propulsion Problems Propulsion Problems

1. An advantage of turbojets compared to ramjets is s_____ thrust.2. The specific impulse of a turbojet is often limited by the maximum

allowable temperature of the t______.



2/24/2008 ELF 130

3. The specific impulse of a ramjet is often limited by the maximum allowable

temperature of the c________.4. Ducted rockets are based on a fuel-rich g__ g________.

5. A safety advantage of solid rocket propulsion over liquid propulsion is lesst_______.

6. A rocket boost to a take-over Mach number is required by ramjets ands________.

7. Parameters that enable the long range of subsonic cruise turbojet missilesare high lif t, low drag, available fuel volume, and high s_______ i______.

8. High thrust and high acceleration are achievable with s____ r_____propulsion.

9. In a turbojet the power to dr ive the compressor is provided by the t______.

Propulsion Problems ( cont ) Propulsion Problems ( cont )

10.The compressor exit temperature is a function of the flight Mach number and the compressor p_______ r____.

11. Compressor exit temperature, fuel heating value, and fuel-to-air ratio



2/24/2008 ELF 131

determine the turbojet t______ temperature.

12. Three types of turbine based propulsion are turbojet, turbo ramjet, and a__t____ r_____.

13. Mach number and fuel-to-air ratio determine the ramjet c________temperature.

14. An example of a ramjet with low drag and light weight is an i_______ r_____ramjet.

15. Russia, France, China, United Kingdom, Taiwan, and India are the onlycountries with currently operational r_____ missiles.

16. 100% inlet capture efficiency occurs when the forebody shock wavesintercept the i____ l__.

17. Excess air that does not flow into the inlet is called s_______ air.


18. Starting a ramjet inlet at lower supersonic Mach number requires a larger area of the inlet t_____.

19. Optimum pressure recovery across shock waves is achieved when the total



2/24/2008 ELF 132

pressure loss across each shock wave is e____.

20. The specific impulse and thrust of a ramjet are a function of the efficiencyof the combustor, nozzle, and i____.

21. High density fuels have high payoff for v_____ limited missiles.

22. The specific impulse of a ducted rocket with large excess fuel from the gas

generator can approach that of a r_____.23. High speed rockets require large p_________ weight.

24. At the throat, the flow area is minimum, sonic, and c_____ .

25. For an optimum nozzle expansion the nozzle exit pressure is equal to the

a__________ pressure.26. High thrust and chamber pressure are achievable through a large propellant

b___ area.


27. Three approaches to solid rocket thrust magnitude control are pulse motor,pintle motor, and g__ motor.

28. A high burn exponent propellant al lows a large change in thrust with only a



2/24/2008 ELF 133

small change in chamber p_______.

29. Three tradeoffs in selecting a sol id propellant are safety, observables, ands_______ i______.

30. A low cost motor case is usually based on steel or aluminum material whilea light weight motor case is usually based on c________ material.

31. Rockets with high chamber pressure or long burn time may require at_______ throat insert.

Outline Outline





2/24/2008 ELF 134

y g


Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design


Sizing Examples Development Process




Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration


Establish Baseline

Al t Mission

Alt Baseline




2/24/2008 ELF 135

Yes

Trajectory

MeetPerformance?


No

Yes


Al t Baseline

Aerodynamics

Propulsion

Weight

Designing Light Weight Missile Has High Payoff Designing Light Weight Missile Has High Payoff

Production cost



2/24/2008 ELF 136

Logistics cost

Size

Firepower

Observables

Mission flexibil ity

Expeditionary warfare

Flight Performance ( Range, Speed,Maneuverability ) Sensitive to Subsystem Weight

Flight Performance ( Range, Speed,Maneuverability ) Sensitive to Subsystem Weight

Dome - Seeker - Guidance and Propulsion Wings Stabilizers



2/24/2008 ELF 137

High Sensitivity Low Sensitivity - Minor Sensitivity

Control -

Warhead Insulation FlightControl

Power Supply

Structure DataLink -

Missile Range is a Function of Launch Weight,Propellant Weight, and Specific Impulse

Missile Range is a Function of Launch Weight,Propellant Weight, and Specific Impulse

1000

ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi )

R ≈ V2 sin ( 2θi ) / gc

Assumptions:

θI = Launch Incidence Angle = 45 deg for maxrange

Thrust Greater Than Drag and Weight



2/24/2008 ELF 138

10

100

100 1000 10000

Wi, Example Initial Launch Weight, lb

R m a

x , M a x i m u m R a n g e , n m

Sing le-Stag e Miss ile Two-Stag e Missile

Flat, Non-rotating Earth

For Two-Stage Missi le with ( Wi )Min : ΔV1 = ΔV2

Example: Two-Stage Missi le with Min imumWeight and Rmax = 200 nm = 1.216 x 106 ft

Assume ISP = 250 sec, WPayload = 500 lb, WInert =0.2 WPropellant

V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / sΔV1 = ΔV2 = V / 2 = 3125 ft / s

Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb

Wi, FirstStage = WInert + WPropellant = 85 + 427 = 512 lb

Wi = Wi,FirstStage + Wi,SecondStage = 1326 lbCompare: Single-Stage Missile, R = 200 nm

ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – WPropellant / (WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒Wi = 1420 lb

Missile Weight Is a Function of Diameter and Length

Missile Weight Is a Function of Diameter and Length

1000

10000

W e i g h t , l b

WL = 0.04 l d2

Units: WL( lb ), l ( in ), d ( in )



2/24/2008 ELF 139

10

100

1000

100 1000 10000 100000 1000000

ld2, Missile Length x Diameter2, in3

W L ,

M i s s i l e L a u

n c h W

FIM-92 SA-14 Javelin RBS-70 Starstreak Mistral HOT Trigat LR

LOCAAS AGM-114 Roland RIM-116 Crotale AIM-132 AIM-9M Magic 2Mica AA-11 Python 3 AIM-120C AA-12 Skyflash Aspide AIM-9P

Super 530F Super 530D AGM-65G PAC-3 AS-12 AGM-88 Penguin III AIM-54C

Arm at Sea Dart Sea Eagle Kormoran II AS34 AGM-84H MIM-23F ANS

MM40 AGM-142 AGM-86C SA-10 BGM-109C MGM-140 SSN-22 Kh-41

Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in 3

Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in 3

Guidance: Flight Control : Warhead: Propellant: Data Link:



2/24/2008 ELF 140

Guidance:0.04 lb / in3

Flight Control :0.04 lb / in3

Warhead:0.07 lb / in3

Propellant:0.06 lb / in3

Structure and Motor Case:0.10 ( Al ) to 0.27 ( steel ) lb / in3

Aero Surfaces:

0.05 ( bui lt-up Al ) to 0.27 ( solidsteel ) lb / in3

Data Link:0.04 lb / in3

Dome Material:0.1 lb / in3

Modeling Weight, Balance, and Moment-o -Inertia Is Based on a Build-up of Subsystems

Modeling Weight, Balance, and Moment-o -Inertia Is Based on a Build-up of Subsystems

Example Missile Configuration EngineInlet SectionWith Fuel

Wing SectionWith Fuel

FuelPl

Nose G&C Warhead



2/24/2008 ELF 141

Model

Structure and Subsystems Engine Structure and Subsystems

Warhead and Structure Fuel

Inlet Structure and Subsystems Aero Surfaces

Legend Assume Uniform Weight Distribut ion For a Given Segment

+x

Inlet

Plug

+z

Nose G&C Warhead

xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal

IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 - xCG )2 / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 - xCG )2 / gc + … ]

Moment-o -Inertia Is Higher for High Fineness Ratio Body

Moment-o -Inertia Is Higher for High Fineness Ratio Body

100

L o c a l M o m e n

C y l i n d e r

C o n e

( Iy,cylinder )local = [ W d2 / gc ] [ ( 1 / 16 ) + ( 1 / 12 ) ( l / d )2 ]

( Iy,cone )local = [ W d2 / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d )2 ]



2/24/2008 ELF 142

0.01

0.1

1

10

0 10 20 30

l / d, Length / Diameter

( I y , l o c a l ) g / ( W

d 2 )

, N o n d i m e n s i o n a l Y

a w

o f I n e r t i a

Example for Ramjet Baseline at Launch ( xcg = 8.04 ft )

Assume missi le can be approximated as a conical nose-cyl inder

For the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft

For the cyl inder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ft

Iy = ( Iy,cone )local + Wcone ( xcg,cone - xCG )2 / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder -xCG )2 / gc

( Iy,cone )local = [ 15.9 ( 1.25 )2 / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 )2 ] = 0.10 slug-ft2

( Iy,cylinder )local = [ 2214 ( 1.698 )2 / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 )2 ] = 872 slug-ft2

Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft2

Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions

Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions

3.0

Pressure Bott le ( 2.50 / 1.50 )Ground Handling Loads ( 1.50 / 1.15 )

Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 )



2/24/2008 ELF 143

2.0

1.0

0

FOS,Factor of Safety

( Ultimate / Yield )

Note:• MIL STDs include envi ronmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigid ity ( 8856 ), and captivecarr iage ( 8591 ).•The entire environment ( e.g., manufactur ing, transpor tation, storage, ground handling, captive carriage, launch separation,post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design.•FOS Δ for castings is expected to be reduced in future as casting technology matures.•Reduction in required factor of safety is expected as analysis accuracy improves wi ll result in reduced miss ile weight / cost.

Motor Case ( MEOP ) ( 1.50 / 1.10 )

Free Flight Loads ( 1.25 / 1.10 )

Δ Castings ( 1.25 / 1.25 )

Δ Fittings ( 1.15 / 1.15 )

Thermal Loads ( 1.00 / 1.00 )

Structure Concepts and Manufacturing Processes for Low Parts Count

Structure Concepts and Manufacturing Processes for Low Parts Count

Structure Manufacturing Process AlternativesComposites Metals

GeometryAl t t i

Vacuum Assist

VacuumBag /

HighSpeedCompression Filament Thermal

StructureConcept

Al t t iStrip



2/24/2008 ELF 144

Al ternat ivesRTM

g Autoclave

pMachine

pMold Wind Pultrusion Form FormingCast

MonocoqueIntegrally HoopStiffened

IntegrallyLongitudinalStiffened

Solid

Sandwich

Axisymmetr ic Ai rf rame

Surface

Lifting Body Ai rf rame

Al ternat ives

MonocoqueIntegrally HoopStiffened

IntegrallyLongitudinalStiffened

StripLaminate

Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cos t ( tooling ).

Note: Very Low Parts Count Low Parts Count Moderate Parts Count High Parts Count –

–

–

Low Parts Count Manufacturing Processes for Complex Airframes

Low Parts Count Manufacturing Processes for Complex Airframes

Vacuum Assisted RTM

Resin Pump



2/24/2008 ELF 145

Filament Wind

Pultrusion ………………………………….

Metal CastingMold Cavity

Riser

Pour Cup Vent

Parting Line

p3D Fiber Orientation

2D Fiber Orientation ( 0-±45-90 deg )Helical wind versusradial w ind

Tactical Missile Airframe Material Alternatives Tactical Missile Airframe Material Alternatives

Tension( σTU / ρ )

Aluminum 2219

MaterialTypeBucklingStability

( σBuckling / ρ )

MaxShort – Life

Temp

ThermalStress

Joining Cost Weight

MetallicIncreasing

– –



2/24/2008 ELF 146

Superior Above Average Average Below Average –Note:

Steel PH 15-7Mo

Titanium 6Al-4V

S994 Glass /Epoxy and S994Glass / Polyimide

Glass or Graphite ReinforceMolding

Graphite / Epoxyand Graphite

Polyimide

IncreasingCost

CompositeIncreasingCost

–

–

– –

–

–

Strength –Elasticity of Airframe Material Alternatives Strength –Elasticity of Airframe Material Alternatives

400

Glass Fiber w / o Matrix

Kevlar Fiber w / o Matrix

Graphite Fiber w / o Matrix

Note:• High strength fibers are:

– Very small d iameter – Unidirectional

Hi h d l f

σ

t = P / A = E ε



2/24/2008 ELF 147

Aluminum Al loy ( 2219-T81 )

300

200

100

0

σt, Tensile Stress,103 psi

0 1 2 3 4 5

ε, Strain, 10-2 in / in

Titanium Alloy ( Ti-6Al-4V )

Very High Strength Stainless Steel( PH 15-7 Mo, CH 900 )

( 400 – 800 Kpsi )

E, Young’s modulus of elasticity, psiP, Load, lbε, Strain, in / in A, Area, in2

Room temperature

– High modulus of elasticity

– Very elastic – No yield before failure – Non forgiving failure

• Metals: – Ductile,

– Yield before failure – Al low adjacent st ructure

to absorb load – Resist crack formation – Resist impact loads – More forgiving failure

High Strength Stainless Steel( PH 15-7 Mo, TH 1050 )

Structural Efficiency at High Temperature of Short Duration Airframe Material Alternatives Structural Efficiency at High Temperature of Short Duration Airframe Material Alternatives

10.0

12.0

g t h /

Graphite / Epoxy( ρ = 0.065 lb / in3 )0-±45-90 Laminate

Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate

Ti3 Al ( ρ = 0.15 lb / in3 )



2/24/2008 ELF 148

200 400 600 800 1,0000

Short Duration Temperature, ° F

8.0

6.0

4.0

2.0

0

σ T U /ρ ,

U l t i m

a t e T e n s i l e S t r e n g

D e

n s i t y ,

1 0 5 I n . Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in

3

)PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in3 ). Note:Thin wall steel susceptible to buckling.

Graphite

Glass

2219-T81 Aluminum

( ρ = 0.101 lb / in3 )

Chopped EpoxyComposites,Random Orientation( ρ = 0.094 lb / in3 )

3 ( )

Hypersonic Missiles without External Insulation Require High Temperature Structure

Hypersonic Missiles without External Insulation Require High Temperature Structure

F

2,000 r =

1

r =

0 . 8

r =

0 . 9

Tr = T0 ( 1 + 0.2 r M2 )

( Tmax )Nickel Alloys ( e.g., Inconel, Rene,Hastelloy, Haynes )

( Tmax )Titanium Aluminide ≈ 2,500 °F )

( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F( Tmax )Ceramic Matrix Composit e ≈ 3,500 °F



2/24/2008 ELF 149

M, Mach Number

T r ,

R e c o v e

r y T e m p e r a t u r e ,°

•••

•

•

•1,500

1,000

500

010 2 3 4 5 6

Note:

• γ = 1.4

• Tr = Recovery Temperature, R

• T0 = Free stream temperature, R

• Tmax = Max temperature capabili ty

• No external insulation assumed

• r is recovery factor • h = 40k f t ( TFree Stream = 390 R )• Stagnation r = 1

• Turbulent boundary layer r = 0.9• Laminar boundary layer r = 0.8• Short-duration flight ( less than

30 m ), but with thermal soak

( Tmax )Graphite Polyimide

( Tmax ) Al Al loy

( Tmax )Steel

( Tmax )Ti Alloy•

( Tmax )Graphite Epoxy

Structure / Insulation Trades for Short Duration Flight Structure / Insulation Trades for Short Duration Flight

Example Structure / Insulation Concepts Mach Tmax k c ρ α

Increasing

Hot Metal Structure ( e.g., Al ) withoutInsulation 600 0.027 0.22 0.101 0.000722



2/24/2008 ELF 150

Hot Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722

Cold Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722

Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

Note:• Tactical missiles use passive thermal protection ( no active cooling )• Small thickness allows more propellant / fuel for diameter const rained missi les ( e.g., VLS launcher )• Weight and cost are application specific• Tmax = max temp capability, ° F; k = thermal conduct ivi ty, BTU / s / ft2 / ° F / ft; c = specific heat or thermal

capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal dif fusivi ty = k / ( ρ c ), ft2 / s

Self-insulating Composite Structure( e.g., Graphite Polyimide ) 1100 0.000109 0.27 0.057 0.00000410

Ext Insulation ( e.g., Micro-Quartz Paint ) 1200 0.0000131 0.28 0.012 0.00000226

Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

External Insulation Has High Payoff for Short Duration Flight

External Insulation Has High Payoff for Short Duration Flight

1,000

900

800 F 4.0

Example Airf rame Temperature wi th No ExternalInsulator – Steel Airf rame Selected.



2/24/2008 ELF 151

800

700

600

500

400

300

200

1000

E x a m p l e T e m p e r a t u r e °

0 2 4 6 8 10 12 14

1.0

2.0

3.0

MachNumber

Time After Launch ~ s

Mach

Note: Short Range Air-to-Air MissileLaunch ~ 0.9 Mach at 10k ft Alt itude

Atmosphere ~ Hot Day ( 1% Risk ) Mi l-HDBK-310

Example Airf rame Temperature with 0.012 in Insulator – Aluminum Ai rf rame Acceptable for Short Duration.

Bulk Ceramics• Melt

Graphites• Burn• ρ ~ 0.08 lb / in3

• Carbon / Carbon

6,000

5,000

Medium Density PhenolicComposites

• Char • ρ ~ 0.06 lb / in3

• Nylon Phenolic, Silica

Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion



2/24/2008 ELF 152

Melt• ρ ~ 0.20 lb / in3

• Zirconium Ceramic,Hafnium Ceramic

Tmax, MaxTemperatureCapability,

R

4,000

3,000

2,000

00 1 2 3 4

Insulation Effic iency, Minutes To Reach 300° F at Back Wall

1,000

Note: Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2

Porous Ceramics• Melt• Resin Impregnated• ρ ~ 0.12 lb / in3

• Carbon-SiliconCarbide

y o e o c, S caPhenolic, Glass

Phenolic, CarbonPhenolic, GraphitePhenolic

Low DensityComposites

• Char

• ρ ~ 0.03 lb / in3

• Micro-QuartzPaint, Glass-Cork-Epoxy,Silicone Rubber

Plastics

• Sublime• Depolymerizing• ρ ~ 0.06 lb / in3

• Teflon

A “Thermally Thin” Surface ( e.g., Metal Airframe ) Has Uniform Internal Temperature A Thermally Thin Surface ( e.g., Metal

Airframe ) Has Uniform Internal Temperature

1000

r e R a t e f o r

/ s e c

( dT / dt )t = 0 = ( Tr - Tinitial ) h / ( c ρ z )

T = Tr – ( Tr – Tinitial ) e – h t / ( c ρ z )

h = k NNU / x

Thermally thin ⇒ h ( z / k )surface < 0.1

Example for Rocket Baseline Airf rame:

Aluminum skin w/o external insulationc = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / f t3,z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / f t2 / R / ft

Assume Mach 2 sustain f light, 20k f t al ti tude ( T0 =447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulentb d l 1 6 ft

x = 1.6 ft



2/24/2008 ELF 153

1

10

100

0 1 2 3 4 5 6

M, Mach Number

d T / d

t , I n i t i a l S k i n T e m p e r

a t u r

R o c k e t B a s e l i n e , D e g F /

h = sea level h = 20K ft h = 50K ft h = 80K ft

Note: No external insulation; thermally thin struc ture ( uniform internal temperature ); “ Perfect” insulation behind airframe; 1-Dheat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max )temperature, R; h = Convection heat transfer coeffic ient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Densi ty, lb / ft3; z =Thickness, ft; k = Conduct ivi ty, BTU / s / ft2 / R / ft; Re = Reynolds number; NNU = Nusselt number

boundary layer, x = 1.6 ft

Rex = ρ0 M a0 x / μ0 = 12.56 x 106

NNU = 0.0271 Re0.8 = 12947

h = k NNU / x = 0.0268 BTU / s / ft2 / R

Test: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thin

Calculate Tr

= T0

[ 1 + 0.2 r M2 ] = 447 [ 1 + 0.2 ( 0.9 )( 2 )2 ] = 769 R

At t = 0, Assume Tinitial = 460 R, or 0° F

( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 )(172.8 ) ( 0.01333 )] = 17°F / s

At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e –

0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )]

= 589 R, or 129° F

Reference: Jerger, J.J.,Systems Preliminary Design Principles of Guided Missile Design,D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960

A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient

A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient

1

[ T ( z, t ) - Tinitial ] / [ Tr – Tinitial ] = erfc { z / [ 2 ( α t )1/2 ] } – e( h z / k ) + h2 α t / k2erfc { z / [ 2 ( α t )1/2 ] + h ( α t )1/2 / k }

[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 - eh2

α t / k2

erfc [ h ( α t )1/2 / k ] Appl icable fo r thermal ly th ick sur face: z / [ 2 ( α t )1/2 ] > 1

Example: Rocket Baseline Radome

z = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R,

= 1 499 x 10-5 ft 2 / s1T ) i n i t i a l ] X = 1.6 ft

k= 0



2/24/2008 ELF 154

0

0.5

0.1 1 10 100

Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h =Heat transfer coeffic ient, BTU / ft2 / s / R; k = Thermal conduct ivity o f material, BTU / s / ft2 / R / ft ; α = Diffusivity o f material,ft 2 / s; zmax = Thickness of material, ft; erfc = Complementary error function

α = 1.499 x 10 5 ft 2 / s

Mach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer,x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R

⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t )1/2 = 0.491

Test: z / [ 2 ( α t )1/2 ] = 0.0208 / { 2 [ 1.499x10-5 ( 10 )]1/2 } =0.849 < 1 ⇒ not quite thermally thick

Inner wall ⇒ h z / k = 0.935[ T ( 0.0208, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.0608

T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial )

Surface ⇒ h z / k = 0

[ T ( 0, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.372

T ( 0, 10 ) = 575 R

Reference: Jerger, J.J.,Systems Preliminary Design Principles of Guided Missile Design,D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960

( h / k )( α t )1/2

h z

/ k

= 1

0 0

h z /

k 1

0

h z /

k = 1

h z / k =

0 . 1

[ T ( z , t

) - ( T ) i n i t i a l ] / [ ( T ) r – ( T

h z / k

Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction

Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction

1

[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e- z2 / ( 4 α t ) – ( π / α t )1 / 2 ( z / 2 ) erfc { z / [ 2 ( α t )1/2 ]}

Appl icable for thermally thick surface: z / [ 2 ( α t )1/2

] > 1 Example for Rocket Baseline Air frame Insulation:

0.10 in Min-K Internal Insulation behind 0.16 in aluminumSkin

X = 1.6 fti t i a

l ]

Aluminum

Min K

0.16 in

0 10 in



2/24/2008 ELF 155

0

0.5

0.1 1 10 100

Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulationat time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity o f insulation material,ft 2 / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function

Assume M = 2, 20k f t alt , x = 1.6 ft , Tinitial = 460 R, t = 10 s,zMin-K = 0.10 in = 0.00833 ft , αMin-K = 0.00000106 ft2 / s, k =5.96 x 10-4 BTU / s / f t, h = 0.0268 BTU / s / f t

Test: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} =1.279 > 1 ⇒ thermally thick

( α t )1/2 / z = [ 0.00000106 ( 10 ) ] 1/2 / 0.00833 = 0.3907

[ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359

Assume ( Tinner )aluminum = ( Touter )Min-K

From prior example, ( Tinner )aluminum = 569 R at = 10 s

Then, ( Touter )Min-K = 569 R at t = 10 s

Compute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4= 464 R

Reference: Carslaw, H. S. and Jaeger, J. C.,Conduction of Heat in Solids, Clarendon Press, 1989

( α t )1/2 / z

[ T ( z , t ) –

T i n i t i a l ] / [ T ( 0 ,

t ) –

T i n i Min-K 0.10 in

z

A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating

A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating

0.4

0.5

0.6

r a n s f e r C o e f f f o r

0 k f t , B T U / f t 2 / s / R

hr = NNUr kr / dNoseTip

NNUr = 1.321 RedNoseTip0.5 Pr 0.4

Example for Rocket Baseline Nose Tip:

Assume M = 2, 20k f t alt , stagnation ( Tr = 805R ) for a sharp nose tip ( e.g., 1% blunt )

dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8in ) = 0.08 in = 0.00557 ft

R V d / 3 39 104



2/24/2008 ELF 156

0

0.1

0.2

0.3

0 1 2 3 4 5 6

M, Mach Number

h r , S t a g n a t i o n H e a

t T

R o c k e t B a s e l i n e a t h = 2 0

1% Bluntness 2% Bluntness

5% Bluntness 10% Bluntness

Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convectionheat transfer coefficient fo r stagnation recovery, BTU / s / ft2 / R; NNUr

= Nusselt number for stagnation recovery; kr = Ai r thermal conductivi ty at s tagnat ion recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft;RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number

RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 104

NNUr = 223

hr = 0.1745 BTU / ft2 / s / R

Outer surface temperature after 10 s heatingin sustain flight ( M = const, Tr = const ):

[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 – eh2αt / k2

erfc { h ( α t )1/2 / k }

[ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 )2

( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845

T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R

Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of BallisticMissiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.

Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input

Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input

10

100QRad = 4.76 x 10

-13

ε T4

QRad in BTU / ft2 / s, T in R

Example: Ramjet Baseline

Assume:

•Titanium skin wi th emissivity =



2/24/2008 ELF 157

0.01

0.1

1

10

0 1 2 3 4 5 6

Cruise Mach Numb er

Radiation Heat

Flux at

Equilibrium

Temperature,

BTU / ft2 / s

Emissivity = 0.1 Emissivity = 1

•Titanium skin wi th emissivity ε =

0.3•Long duration ( equilib rium )heating at Mach 4

•h = 80k ft , T0 = 398 R

•Turbulent boundary layer ( r =0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M2 ) =

1513 R

Calculate:

QRad = 4.76 x 10-13 ( 0.3 ) ( 1513 )4

= 0.748 BTU / ft2 / s

Design Concerns for Localized Aerodynamic Heating and Thermal Stress

Design Concerns for Localized Aerodynamic Heating and Thermal Stress

Body JointsH t i il h ll

Flare / Wedge Corner FlowShock wave – boundary layer

interaction



2/24/2008 ELF 158

Hot missile shellCold frames or bulkheadsCauses premature buckling

IR Domes / RF RadomesLarge temp gradients due to low thermal conduct ionThermal st ress at attachmentLow tensile strengthDome fails in tension

Leading Edges

Hot stagnation temperature on leading edgeSmall radius prevents use of external insulationCold heat sink material as chord increases in thickness

leads to leading edge warpShock wave interaction with adjacent body structure

Separated FlowHigh heating at reattachment

Note: σTS

= Thermal stress from restraint in compression or tension = α E ΔT

α = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 – T1 = temperature difference.

Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psi

Assume M = 2, h = 20k f t alt , t = 10 s. Based on prior figure, ΔT = TOuterWall – TInnerWall = 102 R

Then σTS = 3 x 10-6 ( 13.3 x 106 ) ( 102 ) = 4,070 psi

Examples of Aerodynamic Hot Spots Examples of Aerodynamic Hot Spots

Nose Tip



2/24/2008 ELF 159

Leading Edge

Flare

Tactical Missile Body Structure Weight Is about 22% of the Launch Weight

Tactical Missile Body Structure Weight Is about 22% of the Launch Weight

1000

W e i g h t , l b

Hellf ire ( 0.22 )

Sidewinder ( 0.23 )

Sparrow ( 0 18 )

WBS

/ WL≈ 0.22



2/24/2008 ELF 160

10

100

100 1000 10000

WL, Launch Weight, lb

W B S , B

o d y S t r u c t u r e

W Sparrow ( 0.18 )

Phoenix ( 0.19 )

Harpoon ( 0.29 )

SM 2 ( 0.20 )

SRAM ( 0.21 )

ASALM ( 0.13 )

SETE ( 0.267 )

Tomahawk ( 0.24 )

TALOS ( 0.28 )

Example for 500 lb missile

WL = 500 lb

WBS = 0.22 ( 500 ) = 110 lb

Note: WBS includes all load carry ing body structure. If motor case, engine, or warhead case carry externalloads then they are included in WBS. WBS does not include tail, wing, or other surface weight.

Body Structure Thickness Is Based on Considering Many Design Conditions Body Structure Thickness Is Based on Considering Many Design Conditions

Structure Design Conditions That May Drive Air frame Thickness

Manufacturing

Transportation

Carriage

Launch



2/24/2008 ELF 161

Fly-out Maneuvering

Contributors to Required Thickness for Cylindrical Body Structure

Minimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ]0.4. t ≈ 0.06 in i f pext ≈ 10 psi

Localized Buck ling in Bending: t = 2.9 r σ / E

Localized Buckling in Ax ial Compression: t = 4.0 r σ / E

Thrust Force: t = T / ( 2 π σ r )

Bending Moment: t = M / ( π σ r 2 )

Internal Pressure: t = p r / σ

High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness1. t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , t AxialLoad , tBending , tInternalPressure )

2. t = FOS x ( t2MinGage + t2

Buckling,Bending + t2Buckling,AxialCompression + t2

Ax ialLoad + t2Bending + t2

InternalPressure )1/2

3. t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + t AxialLoad + tBending + tInternalPressure )

Localized Buckling May Be A Concern fo Thin Wall Structure

Localized Buckling May Be A Concern fo Thin Wall Structure

0.1

S t r e s s

Bending

Axial Compression

σBuckling,Bending

/ E ≈ 0.35 ( t / r )

σBuckling,AaxialCcompression / E ≈ 0.25 ( t / r )

Note: Thin wall cylinder with local buckling

σBuckling / E = Nondimensional buckling stress

Buckling stress in bending

r t



2/24/2008 ELF 162

0.0001

0.001

0.01

0.001 0.01 0.1

t / r, thickness / radius

N o n d i m e

n s i o n a l B u c k l i n g

σBucklingBending= Buckling stress in bending

σBucklingAxialCompression = Buckling st ress in axialcompression

E = Young’s modulus of elasticity

t = Air frame thickness

r = Air frame radiusMin thickness for fab and handling ≈ 0.06 in

Example for Rocket Baseline in Bending:

4130 steel motor case, E = 29.5 x 106 psi

σyield = 170,000 psi

t = 0.074 in, r = 4 in

t / r = 0.0185

σBuckling,Bending / E ≈ 0.35 ( 0.0185 ) = 0.006475σbuckling,Bending ≈ 191,000 psiσbuckling,Bending ~ σyield

Note: Actual buckling stress can vary +/- 50%, depending upon typicalimperfections in geometry and the loading.

Process for Captive and Free Flight Loads Calculation

Process for Captive and Free Flight Loads Calculation

Free Flight

Maneuver Per Design Requirements

Captive Flight

Max Aircraft Maneuver Per MIL-A-8591

Carriage Load



2/24/2008 ELF 163

Weight loadof bulkhead

section

Ai r LoadObtainedBy WindTunnel

Ai r Load

Weight loadof bulkhead

section

Ai r Load

Note: MIL-A-8591 Procedure A assumes max air loads combine with max g forces regardless of angle of attack.

Example of αmax Calculated by MIL-A-8591 UsingProcedure A fo r F-18 Aircraft Carriage:

αmax = 1.5 nz,max Wmax / ( CLα q SRef )aircraft

αmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] =12.5 deg

Maximum Bending Moment Depends Upon Load Distribution

Maximum Bending Moment Depends Upon Load Distribution


c = 4, ejection load

l = 144 in

⇒

N = 10,000 lb ( 20 g )

⇒ MB = 360,000 in-lb

Max Bending

MB = N l / c

C = 8 for uniform loading

C = 7.8 for linear loading

Total Coefficient C Length l

w = load per unit length

0 l = length



2/24/2008 ELF 164

Moment MB

C 7.8 for li near loading

C = 6 for linear loading to center

C = 4 for load at center ( e.g., ejection load )

6

440,00030,000

20,000

4 1 3

2 5

100

200

1,000,000

2,000,000

5,0004,0003,000

2,000

1,000

500

400300

200

100

500,000400,000300,000200,000

100,000

LoadN

g

8 7.8100,000

50,000

10,000

50,00040,00030,00020,000

10,000

5,0004,0003,0002,000

1,000

500400300200

100

w

0 l

w

0 l

l0

N = Normal Force

l / 2

10

C = 1 for load at end ( e.g., contro l force )

N = Normal Force

l0

l

1

Bending Moment May Drive Body Structure Weight

Bending Moment May Drive Body Structure Weight

A = 2 π r tIz = IY = π r 3 t

r

tt

MB



2/24/2008 ELF 165

Example for Rocket Baseline:• Body has circular cross section• 2219-T81 aluminum skin ( σult = 65,000 psi )• r = 4 in• Ejection load = 10,000 lb ( 20 g )• M

B= 360,000 in ⋅ lb

• FOS = 1.5• t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in

t = MB ( FOS ) / [ π r 2 σMax ] Note / Assumptions:

Thin cylinder

Circular cross section

Solid skin

Longitudinal strength

Axial load stress and thermalstress assumed small comparedto bending moment st ress

σ = MB r / IZ = MB r / (π r 3 t )

= MB / (π r 2 t )

Tactical Missile Propellant Weight Is about 72%of Rocket Motor Weight

Tactical Missile Propellant Weight Is about 72%of Rocket Motor Weight

10000

g h t , l Hellf ire ( 0.69 )

Sidewinder ( 0.61 )

WP / WM ≈ 0.72



2/24/2008 ELF 166

10

100

1000

10 100 1000 10000

WM, Total Motor Weight, lb

W P ,

P r o p e l l a n t W e i

Sparrow ( 0.64 )Phoenix ( 0.83 )

ASALM ( 0.86 )

SM-2 ( 0.76 )

SRAM ( 0.71 )TALOS ( 0.66 )

Example for Rocket BaselineWM = 209 lb

WP = 0.72 ( 209 ) = 150 lb

Note: WM includes propellant, motor case, nozzle, and insulation.

Increased propellant fraction if:

High volumetric loading

Composite case

Low chamber pressure

Low flight loads

Short burn time

Motor Case Weight Is Usually Driven By Stress from Internal Pressure

Motor Case Weight Is Usually Driven By Stress from Internal Pressure

Assume motor case is axisymmetric, wi th a front ellipsoid domeand an aft cylinder body

Motor CaseCylinder σt t = - 0∫

π/2p r sinθ dθ



2/24/2008 ELF 167

With metals – the material also reacts body bending

In composite motor designs, extra ( longitudinal ) fibers must usually beadded to accommodate body bending

HoopStress

Motor Dome

EllipsoidLongitudinalStress

p p

( σt )Longitudinal Stress

= [ 2 + ( a / b )

2

] p ( a b )

1/2

/ ( 6 t )

If a = b ( hemi dome of radius r ),then ( σt )Longitudinal Stress = p r / ( 2 t )

( σt )Hoop Stress = p r / t

Case Dome Nozzle

Case Cylinder

2 a

b

A Composite Motor Case Is Usually Lighter Weight

A Composite Motor Case Is Usually Lighter Weight

Calculate Maximum Effective Operating Pressure ( Burst Pressure )

pburst = pBoost, Room Temp x eπk Δ T x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty )

Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ell ipsoid dome a / b = 2, pBoost,RoomTemp =1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F

Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ



2/24/2008 ELF 168

Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 )3 = 2,582 psi

Assume Ultimate Factor of Safety FOS = 1.5

Rocket Baseline Steel Case ( σt )ult = 190,000 psi

tHoop

= ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 in

tDome = ( FOS ) x pburst x ( a b )1/2 x [ 2 + ( a / b )2 ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ]1/2 x [ 2 + ( 2 )2 ] / [ 6 x 190,000 ]= 0.058 in

Weight = WCylinder + WDome = ρ π d tHoop l + ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case

Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy Composite

tHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial f ibers for internal pressure load

tDome = 0.041 in, for internal pressure load

Weight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending f iber )

Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load

A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure

A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure

2

3

WSurface σmax1/2 / [ ρ S Nmax

1/2 ] = [ A ( 1 + 2 λ )]1/2

WSurface = ρ S tmac

troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,]1/2

Assumption: Uni form loading

Note:

Surface is 2 panels ( Cruci form wing has 4 panels )

WSurface = Surface weight sized by bending moment

ρ = Density

σmax = Maximum allowable ( ultimate ) stress

tmac = Thickness of mean aero chord cmac - d i m e n s i o n a l W e i g h t



2/24/2008 ELF 169

0

1

0 1 2 3

A, Aspect Ratio

Taper Ratio = 0 Taper ratio = 0.5 Taper Ratio = 1

troot = Thickness of root chord c root

Nmax = Maximum load

A = Aspect rat io

λ = Taper ratio

Example for Rocket Baseline Wing ( 2219-T81

Aluminum ): A = 2.82, λ = 0.175, cr = 19.4 in, σmax =σul t = 65k psi

Assume M = 2, h = 20k f t, α + δ = 22 deg

From prior example, Nmax = 7525 lb

Calculate troot = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) /65000 ]1/2 = 0.813 in

troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac

tmac = 0.0419 ( 13.3 ) = 0.557 in

Wwing σmax1/2 / [ ρ S Nmax

1/2 ] = [ A ( 1 + 2 λ )]1/2.= 1.95

Wwing = 20.6 lb for 1 wing ( 2 panels )

W S u r f a c eσ m a x

1 / 2

/ (ρ

S N m a x

1 / 2 ) , N o n

Seeker Dome

Material

Density( g / cm3 )

DielectricConstant

MWIR /LWIR

Bandpass

TransverseStrength( 103 psi )

ThermalExpansion( 10-6 / ο F )

Erosion,Knoop ( kg

/ mm2 )

Max Short -Duration

Temp ( ο F )

RF-IR Seeker

Zinc Sulfide( ZnS )

4.05 8.4 18 4 350 700

Zinc Selenide 5.16 9.0 8 4 150 600

Dome Material Is Driven by the Type of Seeker and Flight Environment

Dome Material Is Driven by the Type of Seeker and Flight Environment



2/24/2008 ELF 170

( ZnSe)Sapphire /Spinel

3.68 8.5 28 3 1650 1800

Quartz / FusedSilica ( SiO2)

2.20 3.7 8 0.3 600 2000

Silicon Nitride( Si3N4)

3.18 6.1 90 2 2200 2700

Diamond ( C ) 3.52 5.6 400 1 8800 3500RF Seeker

Pyroceram 2.55 5.8 25 3 700 2200Polyimide 1.54 3.2 17 40 70 400IR Seeker

Mag. Fluoride( MgF2)

3.18 5.5 7 6 420 1000

Alon( Al23O27N5)

3.67 9.3 44 3 1900 1800

Germanium( Ge )

5.33 16.2 15 4 780 200

Superior Above Average Average Below Average - Poor

-

--

- --

--



Missile Electrical Power Supply Alternatives Missile Electrical Power Supply Alternatives

Power SupplyMeasure of Merit

C t

Storage Life

Thermal BatteryLithium BatteryGenerator

W = WE E + WP P



2/24/2008 ELF 172

Voltage Stabil ity

0.31.51.4WP, Weight / Power ( kg / kW )

0.01250.00120.0007WE, Weight /Energy

( kg / kW-s )

Cost


Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kg

Note: Generator provides highest energy with l ight weight for long time of fl ight ( e.g., cruise missile ).

Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight.

Thermal battery provides highest power with light weight ( may be required for actuators ).

Electromechanical Actuators Are Light Weight and Reliable

Electromechanical Actuators Are Light Weight and Reliable

HydraulicCold Gas PneumaticEMMeasure of Merit

Up to 1000Up to 600Up to 800Rate ( deg / s )

0.00340.00500.0025WT, Weight / Stall Torque ( lb /in-lb )

W = WT TS



2/24/2008 ELF 173


Reliability

Cost

Up to 60Up to 20Up to 40Bandwidth ( Hz )

Note:

• Actuation system weight based on four actuators.

•Cold gas pneumatic actuation weight includes actuators, gas bot tle,valves, regulator, and supply lines.

•Hydraulic actuation weight includes actuators, gas generator or gasbottle, hydraulic reservoir, valves, and supply lines.

•Stall torque ≈ 1.5 maximum hinge moment of s ingle panel.

Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt , α = 9 deg, with max control deflection of wing ( δ= 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb

Schematic of Cold Gas Pneumatic Actuation

Examples of Electromechanical Actuator Packaging

Examples of Electromechanical Actuator Packaging

Canard ( Stinger ) ……………

Tail ( AMRAAM )



2/24/2008 ELF 174

Tail ( AMRAAM ) …………………………………………………………………

Jet Vane / Tail ( Javelin ) ……

Movable Nozzle ( THAAD ) ……………………………………………………………

Summary of Weight Summary of Weight

Conceptual Design Weight Prediction Methods and WeightConsiderations Missile system weight, cg, moment of inertia

Factors of safety

Aerodynamic heating

St t



2/24/2008 ELF 175

Structure

Dome

Propulsion

Insulation

Power supply

Actuator

Manufacturing Processes for Low Parts Count, Low Cost

Precision castings Vacuum assisted RTM

Pultrusion / Extrusion

Filament winding

Summary of Weight ( cont ) Summary of Weight ( cont )

Design Considerations

Airframe materials

Insulation materials

Seeker dome materials

Thermal stress

Aerodynamic heating



2/24/2008 ELF 176

Aerodynamic heating

Technologies

MEMS

Composites

Titanium alloys

High density insulation

High energy and power density power supply

High torque density actuators


Classroom Exercise ( Appendix A )

Weight Problems Weight Problems

1. Propulsion system and structure weight are driven by f_____ o_ s_____

requirements.

2. For a ballistic range greater than about 200 nautical miles, a t__ s____ missileis lighter weight.

3. Tactical missile weight is proportional to v_____.

4 Subsystem d for tactical missiles is about 0 05 lb / in3



2/24/2008 ELF 177

4. Subsystem d______ for tactical missiles is about 0.05 lb / in3

5. Modeling weight, balance, and moment-of-inertia is based on a build-up of s_________.

6. Missile structure factor of safety for free flight is usually about 1.25 for ultimate loads and about 1.10 for y____ loads.

7. Manufacturing processes that can allow low parts count include vacuumassisted resin transfer molding of composites and c______ of metals.

8.Low cost airframe materials are usually based on aluminum and steel whi lelight weight airframe materials are usually based c________ materials.

9. Graphite f iber has high strength and high m______ o_ e_________.

Weight Problems ( cont ) Weight Problems ( cont )

10. The recovery factors of stagnation, turbulent boundary layer, and laminar

boundary layer are 1.0, 0.9, and ___ respectively.

11. The most popular types of insulation for temperatures greater than 4,000 Rare charring insulators based on p_______ composites.

12. Tactical missiles experience transient heating, and with increasing time

the temperature approaches the r temperature



2/24/2008 ELF 178

the temperature approaches the r_______ temperature.

13. The inner wall temperature is nearly the same as the surface temperaturefor a t________ t___ structure.

14. A thermally thick surface is a good i________.

15. A low conductivity structure is susceptible to thermal s_____.

16. The minimum gauge thickness is often set by the m____________ process.

17. A very thin wall structure is susceptible to localized b_______.

18. Ejection loads and flight control loads often result in large b______moment.

19. An approach to increase the tactical missile propellant / motor weightfraction over the typical value of 72% would be c________ motor case.

Weight Problems ( cont ) Weight Problems ( cont )

20. The required rocket motor case thickness is often driven by thecombustion chamber p_______.

21. A low aspect ratio delta wing has reduced w_____.

22. For low speed missi les, a popular infrared dome material is z___ s______.

23. A thermal battery provides high p



2/24/2008 ELF 179

23. A thermal battery provides high p____.24. The most popular type of actuator for tactical missiles is an

e________________ actuator.

Outline Outline








2/24/2008 ELF 180



Sizing Examples

Development Process






Establish Baseline Al t Mission

Al t Baseline


Aerodynamics

Propulsion



2/24/2008 ELF 181

Yes

MeetPerformance?


No

Yes


opu s o

Weight

Trajectory

Flight Envelope Should Have Large Max Range,Small Min Range, and Large Off Boresight

Off Boresight Flyout Envelope / Range

•Max•Min



2/24/2008 ELF 182

•Min

Forward Flyout Envelope / Range•Max•Min

Examples of Max / Min Range Limitations:

Fire Control System Range and Off Boresight

Seeker Range, Gimbal Angle, and Tracking Rate

Maneuver CapabilityTime of Flight

Closing Velocity

Conceptual Design Modeling Versus Preliminary Design Modeling

Conceptual Design Modeling Versus Preliminary Design Modeling

Conceptual Design Modeling

1 DOF [ Axial force ( CDO), thrust, weight ]

2 DOF [ Normal force ( CN ), axial force, thrust, weight ]

3 DOF point mass [ 3 aero forces ( normal, axial, side ),

CDO

CN

CN

C A



2/24/2008 ELF 183

3 O po ass [ 3 ae o o ces ( o a , a a , s de ),thrust, weight ]

3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero

moment ( pitching ), thrust, weight ]4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments( pitching, roll ing ), thrust, weight ]

Preliminary Design Modeling

6 DOF [ 3 aero forces ( normal, axial, side ), 3 aeromoments ( pitching, rolling, yawing ), thrust, weight ]

CN Cm

C A

C A

C A

C A

Cl

ClCN Cm

CN Cm

CnCY

CY



-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing

-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing

+ Normal Force

α << 1 rad

γ+ MomentV

+ Thrust



2/24/2008 ELF 185

Configuration Sizing Implication

Ιy θ.. ≈ Ιy α.. ≈ q SRef d Cmα

α + q SRef d Cmδδ High Control Effectiveness ⇒ Cmδ

>Cmα

, Iy small ( W small ), q large

( W / gc ) V γ. ≈ q SRef CNαα + q SRef CNδ

δ - W cos γ Large / Fast Heading Change ⇒ CN

large, W small, q large

( W / gc ) V. ≈ T - C A SRef q - CNα α2 SRef q - W sin γ High Speed / Long Range ⇒ Total

Impulse large, C A small, q small

δW

+ Axial Force

Note: Based on aerodynamic cont rol

1.00E+07

1.00E+08

u i s e

R a n g e ,

f t

For Long Range Cruise, Maximize V sp , L / D,and Weight Fraction of Fuel / Propellant

For Long Range Cruise, Maximize V sp , L / D,and Weight Fraction of Fuel / Propellant

R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equation

l Rocketw i t h A x i

s y m m e t r i c A i r f r a m e

T y p i c a l R a m j e t w

i t h A x i s y m m e t r i c

A i r f r a m e

T y p i c a l S u b s o n i

c T u r b o j e t w i t h

W i n g



2/24/2008 ELF 186

1.00E+05

1.00E+06

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

WP / WBC, Propellant or Fuel Weigh t / Weigh t at Begin of Cruise

R ,

C r u

( V ISP )( L / D ) = 2,000,000 ft ( V ISP )( L / D ) = 10,000,000 ft

( V ISP )( L / D ) = 25,000,000 ft

Example: Ramjet Baseline at Mach 3 / 60k ft altR = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft= 500 nm

Note: R = cruise range, V = cruise veloci ty, ISP = specific impulse, L = lift, D = drag,WBC = weight at begin of cruise, WP = weight of propellant or fuel

T y p i c a l R o c k e t w

Efficient Steady Flight Is Enhanced by High L / D and Light Weight

Efficient Steady Flight Is Enhanced by High L / D and Light Weight

Steady Level Flight Steady Climb Steady Descent ( Glide )

T = DL = W

L

D T

W

γC

T – D

L

DT

W

V∞

γC VC

D – T

L

D

TW

γD

V



2/24/2008 ELF 187

SIN γD = ( D – T ) / W = VD / V∞

VD = ( D – T ) V∞/ WRD = Δh / tan γD = Δh ( L / D )

WγDVD

• Small Angle of At tack• Equilibrium Flight• VC = Velocity of Climb• VD = Velocity of Descent• γC = Flight Path Angle During Climb

• γD = Flight Path Angle During Descent• V∞ = Total Velocity• Δh = Incremental Altitude• RC = Horizontal Range in Steady Climb• RD = Horizontal Range in Steady Dive ( Glide )

Note:

Reference: Chin, S.S., “ Missile Configuration Design,”McGraw Hil l Book Company, New York, 1961

V∞T = W / ( L / D ) SIN γc = ( T – D ) / W = Vc / V∞

Vc = ( T – D ) V∞ / W

RC = Δh / tan γC = Δh ( L / D )

Flight Trajectory Lofting / Shaping Provides Extended Range

Flight Trajectory Lofting / Shaping Provides Extended Range

Altitude

Apogee or Cruise

Glide

Climb



2/24/2008 ELF 188

RangeRMAX

Rapid Pitch Up

Line-Of-Sight Trajectory

RMAX

Lofted Trajectory Design Guidelines for Horizontal Launch: – High thrust-to-weight ≈ 10 for safe separation – Rapid pi tch up minimizes time / propellant to reach efficient altitude – Climb at α ≈ 0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag /

propellant – Apogee at q ≈ 700 psf, fol lowed by either ( L / D )MAX cruise or ( L / D )MAX glide

Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight

Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight

100000

1000000

o u s T

u r n R a d i u s , f t

RT = V / γ. ≈ 2 W / ( gc CN SRef ρ )

Assumption: Hor izontal Turn

Note for Example Figure:W = Weight = 2,000 lba / b = 1 ( circu lar cross section ), No wingsCN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 αl / d = Length / Diameter = 10

SRef = 2 ft2

C = 0 2



2/24/2008 ELF 189

1000

10000

0 5 10 15 20

Delta Alph a, Deg

R T , E x a m p l e I n s t a n t a n e o

h = sea level h = 20k ft h = 40k ft

h = 60k ft h = 80k ft

CDO= 0.2

( L / D )Max = 2.5q( L / D )Max

≈ 700 psf α( L / D )Max

= 15 degT( L / D )Max

= 740 lb

Example:

Δ α = 10 deg

CN = 0.94

h = 40k ft ( ρ = 0.000585 slug / ft3 )

RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) (0.000585 )] = 112,000 ft

Note: Require ( RT )Missile ≤ ( RT )Target, for small miss distance

High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity

High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity

10

15

20

, T u r n R a t e , d e g / s

γ.= gc CN ρ V SRef / ( 2 W ), rad / s

Assumption: Hor izontal Turn

Example for Lif ting Body at Alti tude h = 20,000 ft: Assume:• W = Weight = 2,000 lb• a / b = 1 ( circu lar cross section )• No wings• Negligib le tail lift• Neutral static stabilityC = sin 2 cos ( / 2 ) + 2 ( l / d ) sin2

n = 1 0 0 g



2/24/2008 ELF 190

0

5

10

0 1000 2000 3000

Veloc ity, ft / s

E x a m p l e G a m m a D o t

Alpha = 15 deg Alpha = 30 deg

Alpha = 90 deg

CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α• SRef = 2 ft2

• l / d = Length / Diameter = 10• α = 15 deg• V = 2000 ft / s

Then:• N = Normal Force = CN q SRef

CN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin2 ( 15 ) =0.50 + 1.34 = 1.835

q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) (2000 )2 = 2534 psf

N = 1.835 ( 2534 ) ( 2 ) = 9,300 lbN / W = 9300 / 2000 = 4.65 gγ.

= 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )]= 0.0749 rad / s = 4.29 deg / s

For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient

For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient

0.6

0.8

1

V / Vi = { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }

{[ gc ρ AVG SRef ( CD0 ) AVG ] / ( 2 W )} R = ln { 1 – [ gc2ρ AVG SRef ( CD0 ) AVG / ( 2 W )] [ sin γ ] t

2

+ {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }

Note: Based on 1 DOF coast

dV / dt = - gc CD0SRef q / W – gc sin γ

Assumptions:

• γ = constant

V / Vi @ γ = 0 deg



2/24/2008 ELF 191

0

0.2

0.4

0 0.5 1 1.5 2


•W = WBO = 367 lb, SRef = 0.349 ft2, Vi = 2,151 ft / s , γ = 0 deg, ( CD0) AVG = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / f t3 ), t = 10 s

•[( gc ρ SRef ( CD0) AVG Vi ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376

•V / Vi = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, { [( gc ρ SRef ( CD 0) AVG )] / ( 2 W )} R = 0.319 ⇒ Rcoast = 18,300 ft or 3.0 nm

[( g c ρ SRef CD0Vi ) / ( 2W )] t , Non-dimensional Coast Time

• α ≈ 0 deg

• D > W sin γ

V = velocity during coast

Vi = initial velocity ( begin coast )

R = coast range

Vx = V cos γ, Vy = V sin γ

Rx = R cos γ, Ry = R sin γ

{[ g c ρ AVG SRef (CD0) AVG ] / ( 2 W )} R

@ γ = 0 deg

For Ballistic Range, Maximize Initial Velocity,Optimize Launch Angle, and Minimize Drag For Ballistic Range, Maximize Initial Velocity,Optimize Launch Angle, and Minimize Drag

0 4

0.6

0.8

1

1.2

Vx / Vi = cos γi / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }

( Vy + gc t ) / Vi = sin γi / { 1 + {[ gc ρ AVG SRef ( CD

0 ) AVG Vi ] / ( 2 W )} t }

{[ gc ρ AVG SRef (CD0) AVG ] / ( 2 W cos γi )} Rx

= ln { 1 + [ gc ( ρ ) AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }

{[ gc ρ AVG SRef (CD0) AVG ] / ( 2 W sin γi )} ( h – h i + gc t2 / 2 )

= ln { 1 + {[ gc ρ AVG SRef ( CD0 ) AVG Vi ] / ( 2 W ) t }



2/24/2008 ELF 192

0

0.2

0.4

0 0.5 1 1.5 2


•W = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 ft / s, γi = 0 deg, ( CD0) AVG = 0.9, h i = 20,000 ft, ρ AVG = 0.00182 slug / ft3, t = 35 s

•[ gc ρ SRef ( CD0) AVG Vi / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821

•Vx / Vi = 0.354 ⇒ Vx = 762 ft / s, ( Vy + 32.2 t ) / Vi = 0.354 ⇒ Vy = - 1127 ft / s, {[ gc ρ SRef ( CD 0)] / ( 2 W cos γi )} Rx = 1.037 ⇒

Rx = 42,900 ft o r 7.06 nm, {[ g c ρ AVG SRef ( CD 0) AVG ] / ( 2 W sin γi )} ( h – h i + 16.1 t2 ) = 1.037 ⇒ h = 0 ft

{[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t, Non-dimensional Time

Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth

Nomenclature: V= velocity dur ing ballistic f light, Vi = initialvelocity, Rx = horizontal range, h = altitude, hi = initial altitude,V

x

= horizontal velocity, Vy

= vertical velocity

High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity

High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity

0.3

0.4

0.5

0.6

0.7

S P ) ,

N o n d i m e n s i o n a l

m e n t a

l V e l o c i t y

ΔV / ( gc ISP ) = - [ 1 – ( D AVG / T ) – ( W AVG sin γ / T )] ln ( 1 - Wp / Wi )


Assume γ = 0 deg

Assume Mi = 0.8, h = 20k ft

Wi = WL = 500 lb

For boost, WP = 84.8 lb

WP / WL = 0.1696



2/24/2008 ELF 193

0

0.1

0.2

0 0.1 0.2 0.3 0.4 0.5

Wp / Wi, Propellant Fraction

D

e l t a V / ( g I

I n c r e m

DAVG / T = 0 DAVG / T = 0.5 DAVG / T = 1.0

ISP = 250 s

TB = 5750 lb

Assume D = D AVG = 635 lb

D AVG / T = 0.110ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 )ln ( 1 - 0.1696 ) = 0.1654

ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) =1331 ft / s

Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, Wi = initial weight, W AVG = average weight, WP =propellant weight, ISP = specific impulse, T = thrust, Mi = init ial Mach number, h = altitude, D AVG = average drag,ΔV = incremental veloc ity , gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γ

Note: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time

High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets

High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets

4

3 Note:Proportional Guidance

VM = Missi le Veloci tyVT = Target Veloci tyA = Target Aspect

VM VTL A

VM sin L = VT sin A, Proportional Guidance Trajectory



2/24/2008 ELF 194

VM / VT 2

00 10 20 30 40 50

L, Lead Angle, Deg

1

A = 90°

A = 45°

A Target AspectL = Missi le Lead Angle

≈Seeker Gimbal

Example:

L = 30 deg

A = 45 degVM / VT = sin ( 45° ) / sin ( 30° ) =

1.42




Al t Baseline


Aerodynamics

Propulsion



2/24/2008 ELF 195

Yes

MeetPerformance?


No

Yes

Resize / Alt Conf ig / Subsystems / TechWeight

Trajectory

Summary of Flight Performance Summary of Flight Performance

Flight Performance Activi ty in Missile Design

Compute range, velocity, time-to-target, off boresight Compare with requirements

Discussed in This Chapter

Equations of motion Flight performance drivers



2/24/2008 ELF 196

Propulsion alternatives range comparison

Steady level flight required thrust

Steady climb and steady dive range prediction Cruise prediction

Boost prediction

Coast prediction

Ballistic flight prediction

Turn radius and turn rate predict ion

Target lead for proport ional homing guidance

Summary of Flight Performance ( cont ) Summary of Flight Performance ( cont )

Flight Performance Strongly Impacted by Aerodynamics

Propulsion

Weight




2/24/2008 ELF 197


Flight Performance Problems Flight Performance Problems

1. Flight trajectory calculation requires input from aero, propulsion, and w_____.

2. Missi le flight envelope can be characterized by the maximum effective range,minimum effective range, and o__ b________.

3. Limitations to the missile effective range include the fire control system,seeker, time of flight, closing velocity, and m_______ capabili ty.

4. 1 DOF simulation requires modeling only the thrust, weight, and a____ f____.5 A 3 DOF simulation that models 3 aero forces is called p m simulation



2/24/2008 ELF 198

5. A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation.

6. A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation.

7. The pitch angular acceleration θ.. is approximately equal to the second timederivative of the a____ o_ a_____.

8. Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction.

9. If thrust is equal to drag and lift is equal to weight, the missi le is in s_____l____ flight .

10. Turn rate is a function of normal force, weight, and v_______.

Flight Performance Problems ( cont ) Flight Performance Problems ( cont )

11. Coast range is a function of initial velocity, weight, drag, and the t___ of flight.

12. Incremental velocity due to boost is a function of ISP, drag, and p_________weight fraction.

13. To intercept a high speed crossing target requires a high speed missile with ahigh g_____ angle seeker.

14. An analytical model of a rocket in co-altitude, non-maneuvering flight can bedeveloped by patching together the flight phases of boost and c



2/24/2008 ELF 199

developed by patching together the flight phases of boost and c____.

15. An analytical model of a rocket in a short range, off-boresight intercept can bedeveloped by patching the flight phases of boost and t___.

16. An analytical model of a guided bomb in non-maneuvering flight can bedeveloped from the flight phase of a steady d___.

17. An analytical model of an unguided weapon can be developed from theb________ flight phase.

18. An analytical model of a ramjet in co-altitude, non-maneuvering flight can bedeveloped by patching the flight phases of boost and c_____.

Outline Outline






M f M it d L h Pl tf I t ti



2/24/2008 ELF 200


Sizing Examples

Development Process







Al t Baseline


Aerodynamics

Propulsion



2/24/2008 ELF 201

Yes

MeetPerformance?

No

No

Yes

Resize / Alt Conf ig / Subsystems / TechWeight

Trajectory

Measures of Merit and Constraints

Measures of Merit and Launch Platform Integration Should Be Harmonized

Measures of Merit and Launch Platform Integration Should Be Harmonized

Robustness

LethalityCost

Launch Platform

Integration /

Firepower



2/24/2008 ELF 202

Miss Distance

Carriage and

LaunchObservables

Other

SurvivabilityConsiderations

Reliability

Balanced Design

Tactical Missiles Must Be Robust Tactical Missiles Must Be Robust

RobustnessTactical Missiles Must Have Robust Capability to

Handle Adverse Weather

Clutter

Local Climate

Robustness

Lethal i ty

Miss Distance

Carriage andLaunch

Observables

Other

Survivability

Cons iderati ons

Reliability

Cost

Launch P latform

Integrati on /Fi repower



2/24/2008 ELF 203

Flight Environment Variation

UncertaintyCountermeasures

EMI / EMP

This Section Provides Examples of Requirements for Robustness

Adverse Weather and Cloud Cover Are Pervasive Adverse Weather and Cloud Cover Are Pervasive

0.6

0.8

1.0

Cloud Cover Over Ocean

CloudCover

Annual Average

Fraction of Cloud Cover North Atlantic

Descending Ai r

Rising Ai r Rising Ai r

Descending

South Pole

Region

NOAA satelli te imageof earth cloud cover

North PoleRegion



2/24/2008 ELF 204

0.0

0.2

0.4

85°N 65°N 45°N 25°N 5°N 0° 5°S 25°S 45°S 65°S 85°S

Over Land

Note: Annual Average Cloud Cover Global Average = 61%Global Average Over Land = 52%Global Average Over Ocean = 65%

Latitude Zone

Deserts ( Sahara,Gobi, Mojave )

Argentina, Southern Af rica and Austral ia

Descending Ai r

Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather . Oxford University Press, 1996.

Radar Seekers Are Robust in Adverse Weather Radar Seekers Are Robust in Adverse Weather

Note:EO attenuation throughcloud at 0.1 g / m3 and 100m visibilityEO attenuation throughrain at 4 mm / hHumidi ty at 7.5 g / m3

Millimeter wave andmicrowave attenuationthrough cloud at 0.1gm / m3 or rain at 4 mm / h

1000

100

10

A T I O N ( d

B / k m )

H2O

O2, H2O

H2O

O2

O2

CO2

CO2

H2O, CO2

H2O



2/24/2008 ELF 205

3 cm 3 mm 0.3 mm 30 µm 3.0 µm

Increasing Wavelength

Increasing Frequency

Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997

0.3 µm

gm / m3 or rain at 4 mm / h1

0.1

0.01

A T T E N U A

100 1 THz 10 100 1000

INFRAREDSUBMILLIMETER

10 GHz

MILLIMETER VISIBLE

H2O

2

H2O20° C1 ATM

EO sensors are ineffectivethrough cloud cover

Radar sensors have good tosuperior performancethrough c loud cover and rain

RADAR

X Ku K Ka Q V W Very Long Long Mid Short

O3

Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover

40

30

h,Altitude

Cirrus ( 16 – 32k ft )

Cumulonimbus ( 2 – 36k ft )



2/24/2008 ELF 206

20

10

0

Altitude,103 ft

Note:•IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance•IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance.•mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength.

Fog

Altocumulus ( 9 – 19k ft )

Cumulus ( 2 – 9k ft )Stratus ( 1 – 7k ft )

Al tostratus ( 8 – 18k ft )

Sensor Adverse

Weather

Impact

ATR / ATA

in Clutter

Range Moving

Target

Volume

Search

Time

Hypersonic

Dome

Compat.

Diameter

Required

Weight and

Cost

Maturity

• SAR

• Acti veImagingmmW

• Passive

ImagingmmW• Acti ve

Imaging IR- -

-

-

-

Precision Strike Missile Target Sensors Are Complemented by GPS / INS / Data Link Sensors

-

-

- -



2/24/2008 ELF 207

Note: Superior Good Below Average Poor

(LADAR)• Active Non-

image IR(LADAR)

• Active Non-image mmW

• PassiveImaging IR

• Acoust ic

• GPS / INS /

Data Link

-

-

-

--

--

-

-

Imaging Sensors Enhance Target Acquisition / Discrimination

Imaging Sensors Enhance Target Acquisition / Discrimination

Imaging LADAR Imaging Infrared SAR



2/24/2008 ELF 208

Passive Imaging mmW Video of Imaging Infrared Video of SAR Physics



Example of Mid Wave –Long Wave IR Seeker Comparison ( cont )

Example of Mid Wave –Long Wave IR Seeker Comparison ( cont )

Next, Calculate LWIR Seeker Detection Range

RD = { ( IT )Δλ ηa Ao { D* / [( Δf p )1/2

( Ad )1/2

]} ( S / N )D-1

}1/2

, m ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr -1

Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }} , W cm -2 sr -2 μm-1

Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, then

Lλ = 0.00310 W cm-2 sr -2 μm-1, ( IT )Δλ = 26.7 W sr -1

Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 1010 cm1/2 Hz1/2 W-1

RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 1010 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 21,600 m

MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature



2/24/2008 ELF 210

MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature

0

5

10

15

0 500 1000 1500 2000

TT, Target Temperature, K

W a v e l e n g t h f o r M a x S p e c t r a l

R a d i a n c e ,

M i c r o n s

Subsonic Airframe

Mach 4 Air frame

Jet Engine

Rocket Plume

Flare

( λ )( Lλ )max= 2898 / TT, Wein’s Displacement Law, TT in K

M W I R

L W I R

Example: TT = 300 K

( λ )( Lλ )max= 2898 / TT

= 2898 / 300 = 10.0 μm

GPS / INS Provides Robust Seeker Lock-on in Adverse Weather and Clutter

GPS / INS Provides Robust Seeker Loc -on in Adverse Weather and Clutter •

4 8 0 P i x e l s

640 Pixels ( 300 m )

Target Image

175 m

Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m )

3 m GPS / INS error ⇒ nMreq= 0.15 g, σ < 0.1 m


3 m GPS / INS error ⇒ nMreq= 0.44 g, σ < 0.1 m



2/24/2008 ELF 211

44 m88 m

Note: = Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s.


3 m GPS / INS error ⇒ nMreq= 1.76 g, σ = 0.9 m


3 m GPS / INS error ⇒ nMreq= 7.04 g, σ = 2.2 m

Data Link Update at Seeker Lock-on Reduces Moving Target Error

Data Link Update at Seeker Lock-on Reduces Moving Target Error

100

1000

S e e k e r L

o c k - o n ,

VT = 1 m / s

VT = 10 m / s

VT 100 /

TESeekerLock-on

= [ TLE2 + ( VT

tLatency

)2 ]1/2



2/24/2008 ELF 212

10

0.1 1 10 100 1000

Target Latency at Seeker Lock-on, s

T a r g e t E

r r o r a t S VT = 100 m / s

VT = 1000 m / s

Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Veloci ty, TLE = Target LocationError at Update = 10 m

Example:TLE = 10 mtSeekerLock-on = 100 stUdate = 90 sVT = 10 m / stLatency = tSeeker - tUdate = 100 – 90 = 10 s

TESeekerLock-on = [ TLE2

+ ( VT tLatency )2

]1/2

= { 102 + [ 10 ( 10 )]2 ]1/2

= 100.5 m

Optimum Cruise Is a Function of Mach Number,Altitude, and Planform Geometry

Optimum Cruise Is a Function of Mach Number,Altitude, and Planform Geometry

40

60

80

100

120

h ,

A l t i t u d

e ,

k f t

q = 200 psf

q = 500 psf

q = 1,000 psf

q = 2,000 psf

q = 5,000 psf

Ramjet

Scramjet



2/24/2008 ELF 213

0

20

40

0 1 2 3 4 5 6 7

M, Mach number

hq = 10,000 psf

q = 20,000 psf

Note:• U.S. 1976 Standard Atmosphere• For Efficient Cruise, ( L / D )Max for Cruising L ift ing Body Typically Occurs for 500 < q < 1,000 psf • ( L / D )Max for Cruise Miss ile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf • q ≈ 200 psf lower limit for aero control

Note: q = 1 / 2 ( ρ V2 )Wingless Subsonic Turbojet

Subsonic Turbojet with Low Aspect Ratio Wing

Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment

Booster ShutdownTransient at High Mach

Engine Start Transient Pitch-Over atHigh Alpha

Example High Performance Missi le Has• Low-to-High Dynamic Pressure

• Negative-to-Posi tive Static Margin• Thrust / Weight / cg Transients• High Temperature• High Thermal Load• High Vibration• High Acoustics

Level Out

Cruise



2/24/2008 ELF 214

Engine Shutdown

Transient

Air Launch at LowMach ( high α ) /

DeployCompressedCarriage Surfaces

Booster Ignition

Pitch-Up at High Alpha

Climb Terminal at HighDynamic Pressure

Dive

Precision Impactat α ≈ 0 Deg

Vertical Launch in Cross Wind ( high α )/ Deploy Compressed Carriage Surfaces

Pitch-Over at High Alpha

Design Robustness Requires Consideration of Flight Altitude

Design Robustness Requires Consideration of Flight Altitude

1

0 20 40 60 80 100

A l t i t u d e /

S e a L e v e l

Temperature Ratio

Troposphere Stratosphere

Troposphere ( h < 36,089 ft )

T / TSL

= 1 – 6.875 x 10-6 h, h in ft

p / pSL = ( T / TSL )5.2561

ρ / ρSL = ( T / TSL )4.2561

Stratosphere ( h > 36089 ft )

T = constant = 390 R

p / pSL = 0.2234 e - ( h – 36089 ) / 20807

ρ / ρSL = 0.2971 e - ( h – 36089 ) / 20807



2/24/2008 ELF 215

0.01

0.1

h, Geometr ic Altitude, kf t

C h a r a c t e r

i s t i c a t

C h a r a c t e r i s t i c a t

p

Pressu re Ratio

Density Ratio

Speed o f Sound Ratio

Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speedof sound at sea level, h = altitude in ft .

U.S. Standard Atmosphere, 1976 – TSL = 519 R – pSL = 2116 lb / ft2

– ρSL

= 0.00238 slug / ft3

– cSL = 1116 ft / s

0.5

1

1.5

m S t a n d a r d A t m o s p h e r e Ratio: Cold-to-Standard

AtmosphereRatio: Hot-to-Standard Atmosphere

Ratio: Polar-to-Standard Atmosphere

Ratio: Tropic-to-Standard Atmosphere

( + 30 % )

( - 23% )

Design Robustness Requires Consideration of Cold and Hot Atmospheres

Design Robustness Requires Consideration of Cold and Hot Atmospheres



2/24/2008 ELF 216

0

0 5

Temp Density Speed of

Sound

V a r i a t i o n f r o

Note:

• Based on properties at sea level

•U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s

Design Robustness Is Required to Handle Uncertainty Design Robustness Is Required to Handle Uncertainty

0.5

1

N o r m a l i z e d P D F

Narrow Uncertainty ( e.g.,

SDD Flight Perfo rmance )

Broad Uncertain ty ( e.g.,Conceptual Design FlightPerformance )

Skewed Uncertainty ( e.g.,Cost, Weigh t, MissDistance )

Bimodal Uncertain ty ( e.g.,



2/24/2008 ELF 217

0

-20 -10 0 10 20

Typical % Error from Forecast Value

E x a m p l e Multi -mode Seeker Target

Location )

Uniform Bias Uncertainty( e.g., Seeker Aim PointBias )

Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ]2 / 2 }

Counter-Countermeasures by Missile Enhance Design Robustness Counter-Countermeasures by Missile Enhance Design Robustness

Examples of CM ( Threat )

EOCM directed laser

flare

smoke

RFCM active radar

jammer

Examples of CCM ( Missile )

Imaging Seeker Multi-spectral / Multi-

mode Seeker

Temporal Processing

Hardened GPS / INS standoff acquisition

Integrated GPS / INS



2/24/2008 ELF 218

chaff

Decoy

Low Observables

Speed

Altitude

Maneuverability

Lethal Defense

directional antenna

pseudolite / differential

GPS

ATR / ATA

Speed

Altitude

Maneuverability Low Observables

Saturation

IIR ( I2R AGM-130 ) ………………………………………………

Two Color IIR ( Python 5 )

Acoustic - IIR ( BAT ) …………………………………………..

Examples of Countermeasure-Resistant Seekers Examples of Countermeasure-Resistant Seekers



2/24/2008 ELF 219

IIR – LADAR ( LOCAAS ) ………………………………………

ARH – mmW ( AARGM )

ARH - IIR ( Armiger ) …………………………………………….

TBM / TELs

OilRefineries

Naval

Armor

Transportation ChokePoints ( Bridges,Railroad Yards, TruckParks )

Counter Air Aircraft

C3II

Artillery

Air Defense ( SAMs,

AAA )

A Target Set Varies in Size and Hardness

Lethality

Robustness

Lethal i ty

Miss Dis tance

Carriage and

LaunchObservables

Other

SurvivabilityCons iderati ons

Reliability

Cost

Launch P latform

Integrati on /

Fi repower

Example of Precision Strike Target Set



2/24/2008 ELF 220

Parks )

Examples of Targets where Size and Hardness Drive Warhead Design/ Technology

•Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE

Warhead

•Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead

•Large Size Target: Bui lding ⇒ Large Blast Frag WarheadVideo Example of Precis ion Str ike Targets

76% of Baghdad Targets Struck First Night of Desert Storm Were C 3 Time Critical Targets 76% of Baghdad Targets Struck First Night of Desert Storm Were C 3 Time Critical Targets Targets: 1. Directorate of Military Intelligence; 2, 5, 8,13, 34. Telephone switching stations; 3. Ministry of

Defense national computer complex; 4. Electrical transfer station; 6. Ministry of Defense headquarters; 7. Ashudad

highway bridge; 9. Railroad yard; 10. Muthenaairfield ( military

section ); 11. Air Force headquarters; 12. Iraqi Intelligence

Service; 14. Secret Police complex; 15. Army storage depot;

16. Republ ican Guard headquarters; 17. New presidentialpalace; 18. Electrical power station; 19. SRBM assembly

factory ( Scud ); 20. Baath Party headquarters; 21.Government conference center; 22 Ministry of Industry and

1

2

3

4

56

7

8

23

2425

2631

32



2/24/2008 ELF 221

Government conference center; 22. Ministry of Industry and

Military Production; 23. Ministry of Propaganda; 24. TV

transmitter; 25, 31. Communications relay stations; 26.Jumhuriya highway bridge; 27. Government Control Center

South; 28. Karadahighway bridge ( 14th July Bridge ); 29.

Presidential palace command center; 30. Presidential

palace command bunker; 32. Secret Police headquarters;

33. Iraqi Intelligence Service regional headquarters; 35.National Air Defense Operations Center; 36. Ad Dawrahoil

refinery; 37. Electrical power p lant

Source: AIR FORCE Magazine, 1 Apr il 1998

891011

12

13 1415 16

17

1819

20

2122

2426

27

28

2930

3233

3435

36

37

Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead )

AGM-154 Storm Shadow / Scalp KEPD-350 BGM-109 AGM-142

Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead )

AGM-88 AS-11 / Kh-58 ARMAT Armiger ALARM

Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude )

Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead

Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead



2/24/2008 ELF 222

MM40 AS-34 Kormoran AS-17 / Kh-31 BrahMos SS-N-22 / 3M80

Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead )

Hellfire LOCAAS MGM140 AGM-65 LOSAT

Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead )

CALCM GBU-28 GBU-31 Storm Shadow MGM-140Permission of Missile Index.

Examples of Light Weight Air Launched Multi- Purpose Precision Strike Weapons Examples of Light Weight Air Launched Multi- Purpose Precision Strike Weapons Weapon Fixed

SurfaceTargets(1)

Moving

Targets (2) Time

Critical

Targets (3)

Buried

Targets (4) Adverse

Weather (5) Firepower (6)

Example New Missile

AGM-65

Small Diameter Bomb

AGM-88

–

– –

– – –



2/24/2008 ELF 223

Hellfire / Brimstone /Longbow

LOCAAS –

–

Note:

Superior

Good

Average

Poor –

(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy.

(2) - Seeker or high bandwidth data link required for terminal homing.

(3) - High speed with duration required⇒ High payoff of high speed / loiter and powered submunition.

(4) - KE penetration warhead required⇒ High impact speed, low drag, high density, long length.

(5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff.

(6) - Light weight required. Light weight also provides low cost

Blast Is Effective at Small Miss Distance Blast Is Effective at Small Miss Distance

100

1000

e s s u r e R a t i o t o U n d i s t u r b e d P r e s s u r

Δ p / p0 = 37.95 / ( z p01/3 ) + 154.9 / ( z p0

1/3 )2 + 203.4 / ( z p01/3 )3 + 403.9 / ( z p0

1/3 )4

z = r / c1/3

Note:

Based on bare sphere of pentolite ( Ec1/2 = 8,500 ft / s )

Δp = overpressure at distance r from explosion

p0 = undisturbed atmospheric pressure, psi

z = scaling parameter = r / c1/3

r = distance from center of explosion, ft

c = explosive weight , lb



2/24/2008 ELF 224

1

10

0 2 4 6 8 10

z ( p0 )1/3

D e l t a p / p 0 , O

v e r p r e

Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980

Example for Rocket Baseline Warhead:

c = 38.8 lbh = 20k feet, p0 = 6.8 psi

r = 10 ft

z = 10 / ( 38.8 )1/3 = 2.95

z p01/3 = 5.58

Δp / p0 = 13.36

Δp = 90 psi

Guidance Accuracy Enhances Lethality Guidance Accuracy Enhances Lethality

Rocket Baseline Warhead Against Typical Aircraft TargetPK > 0.5 if σ < 5 ft ( Δ p > 330 psi,fragments impact energy > 130kft-lb / ft2 )

PK > 0.1 if σ < 25 ft ( Δp > 24 psi,

fragments impact energy > 5k ft-lb / ft2 )



2/24/2008 ELF 225

Note: Rocket Baseline 77.7 lb warheadC / M = 1, spherical blast, h = 20k f t.

Video of AIM-9X Flight Test Missile Impact on Target( No Warhead )

Warhead Blast and Fragments Are Effective at Small Miss Distance Warhead Blast and Fragments Are Effective at Small Miss Distance

Hellf ire 24 lb shaped charge warheadfragments are from natural fragmenting case

2.4 mwitness

plate

Roland 9 kg explosively formed warheadmulti -projectiles are from preformed case



2/24/2008 ELF 226

Video of Guided MLRS 180 lb b last f ragmentation warhead

Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio

0.2

0.3

0.4

o n - d i m e n s i o n

a l K i n e t i c E n e r g y

KE = ( 1 / 2 ) Mm Vf 2 = Ec Mc / ( 1 + 0.5 Mc / Mm )

Note:Based on Gurney EquationCylindr ical WarheadKE = Total Kinetic EnergyMm = Total Mass Metal FragmentsVf = Fragment Velocity

Ec = Energy Per Unit Mass ChargeMc = Mass of ChargeMwh = Mass of Warhead = Mm + Mc

L o w K E

H i g h K E

Example:



2/24/2008 ELF 227

0

0.1

0 0.5 1 1.5 2 2.5 3Mc / Mm, Charge-to-Metal Ratio

( K E / M w h ) / E c , N o

Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993.

Example:

Rocket Baseline Warhead

Mc = 1.207 slug

Mm = 1.207 slug

Mc / Mm = 1

Ec Mc = 52,300,000 ( 1.207 ) =63,100,000 ft -lb

KE = 63100000 / [1 + 0.5 ( 1 )]= 42,100,000 ft-lb

Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems

0.4

0.5

0.6

0.7

0.8

0.9

1

r o b a b i l i t y o f K i l

Av / Atp = 0.1

Av / Atp = 0.5

Av / Atp = 0.9

PK = 1 - ( 1 - Av / Atp)nhits

Note:• Av = Target vulnerable area• Atp

= Target presented area



2/24/2008 ELF 228

0

0.1

0.2

0.3

0 5 10 15 20 25 30

nhits, Number of Impacts on Target

P

k ,

P p

Example:If Av / Ap = 0.1, nhits = 22 gives PK = 0.9

If Av / Ap = 0.9, nhits = 1 gives PK = 0.9

Small Miss Distance Improves Number of Warhead Fragment Hits Small Miss Distance Improves Number of Warhead Fragment Hits

20

40

60

80

100

N u m b e r o f F

r a g m e n t H i t s Wwh = 5 lb

Wwh = 50 lb

Wwh = 500 lb


WWH = 77.7 lbMc / Mm = 1, Wm = 38.8 lb = 17,615 g

Average fragment weight = 3.2 g

nfragments = 17615 / 3.2 = 5505

nhits = nfragments [ AP / ( 4 π σ2 )]



2/24/2008 ELF 229

00 20 40 60 80 100

Sigma, Miss Distance, ft

N g

AP = Target presented area = 20 ft2

σ = Miss distance = 25 ft

nhits = 5505 { 20 / [( 4 π ) ( 25 )2 ]} = 14

Kinetic energy per square foot. = KE/ ( 4 π σ2 ) = 42100000 / [ 4 π ( 25 )2 ] =5,360 ft-lb / ft2

Note:• Spherical blast with uni formly distributed fragments• nhits = n fragments [ AP / ( 4 π σ2 )]• Warhead charge / metal weight = 1• Average fragment weight = 50 grains ( 3.2 g )• AP = Target presented area = 20 ft2

High Fragment Velocity Requires High Charge-to- Metal Ratio High Fragment Velocity Requires High Charge-to- Metal Ratio

4000

6000

8000

10000

m e n t V e l o c

i t y ,

f t / s

HMX Explosive

TNT Explosive

Note: Based on the Gurney equation for acylindrical warhead

HMX Explosive ( 2 EC )1/2 = 10,230 ft / s

TNT Explosive ( 2 EC )1/2 = 7,600 ft / sV = Fragment initial velocity ft / s

Vf = ( 2 Ec )1/2 [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )]1/2

Example:

Baseline Rocket Warhead

HMX E l i



2/24/2008 ELF 230

0

2000

0 1 2 3

Mc / Mm, Charge-to-Metal Ratio

V f , F r a g Vf = Fragment initial velocity , ft / s

Ec = Energy per uni t mass of charge, ft2

/ s2

Mc = Mass of chargeMm = Total mass of all metal fragmentsMwh = Mass of warhead = Mm + Mc

HMX Explosive

MC / Mm = 1Vf = 8,353 ft / s

P e r f o r a t i o n b y F r a g m e n t ( i n )

50 Grains( 3.2 g )

150 Grains ( 9.7 g )

.5

.375

.25

Small Miss Distance Improves Fragment Penetration Small Miss Distance Improves Fragment Penetration



2/24/2008 ELF 231

Note: Typical air-to-air missi le warhead

• Fragments init ial veloci ty 5,000 ft / s• Sea level• Average fragment weight 3.2 g• Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments• Small miss distance gives less reduction in f ragment velocity, enhancing penetration

2010 30 40 50 60 70 80 90 100 110 120

S t e e l P

.125

Miss Distance ( ft )

Hypersonic Hit-to-Kill Enhances Energy on Target for Missiles with Small Warheads

Hypersonic Hit-to-Kill Enhances Energy on Target

for Missiles with Small Warheads

3

4

5

6

7

8

9

a l E n e r g y o n

T a r g e t / W a r h e a d

C h a r g e E n e r g y

Weight o f missile /Weight o f charge = 20

Weight o f missile /Weight o f charge = 10

Weight o f

ET / EC = [( 1 / 2 ) ( WMissile / gc ) V2 + EC ( WC / gc )] / [ EC ( WC / gc )]


WMissile = 367 lb

WC = 38.8 lb

WMissile / WC = 9.46

V = 2,000 ft / s

( 1 / 2 ) ( WMissile / gc ) V2 = 22.8 x 106 ft-lb )

EC ( WC / gc ) = 63.1 x 106 ft-lb

E / E = 1 36



2/24/2008 ELF 232

0

1

2

0 1000 2000 3000 4000 5000 6000

Missi le Clos ing Veloc ity, ft / s

E T / E C ,

T o t Weight o f

missile /

Weight o f charge = 5

Weight o f missile /Weight o f

charge = 2

Note: Warhead explosive charge energy based on HMX, ( 2 EC )1/2 = 10,230 ft / s.

1 kg weight at Mach 3 clos ing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT.

ET / EC = 1.36

Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration

20

30

40

50

60

n e t r a t i o n / P e n e t r a t o r D i a m e t e r f o r

S t e e l o n C o n c r e t e

Note:V > 1,000 ft / s

l / d > 2Non-deforming ( high strength, sharp nose )

penetrator l = Penetrator lengthd = Penetrator diameter V = Impact velocity

ρP= Penetrator densityρT= Target densi tyσT= Target ultimate stress

Example for 250 lb Steel Penetrator l / d = 10

P / d = [( l / d ) – 1 ] ( ρP / ρT )1/2 + 3.67 ( ρP / ρT )2/3 [( ρT V2 ) / σT ]1/3



2/24/2008 ELF 233

0

10

20

0 1000 2000 3000 4000

V, Veloci ty, ft / s

P / d ,

T a r g e t P e n

l / d = 2 l / d = 5 l / d = 10

l / d = 10 l = 48 in ( 4 ft ) d = 4.8 in ( 0.4 ft ) Concrete target ρP = 0.283 lb / in3 ( 15.19 slug / f t3 ) ρT = 0.075 lb / in3 ( 4.02 slug / ft 3 ) V = 4,000 ft / s σT = 5,000 psi ( 720,000 psf )

P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19/ 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3

P = ( 57.3 ) ( 0.4 ) = 22.9 ft

Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966

Standard Missile 3 ( NTW ) PAC-3 THAAD

Examples of Kinetic-Kill Missiles Examples of Kinetic-Kill Missiles



2/24/2008 ELF 234

LOSAT LOSAT Video

CEP Approximately Equal to 1σ Miss Distance CEP Approximately Equal to 1σ Miss Distance

MedianTrajectory

Extreme MissileTrajectory

Missile Circu lar Error Probable ( 50%of shots within circle )

Missile 1σ Miss Distance ( 68%of shots within circle for anormal distribut ion of error )

Target

Presented Target Area

Miss DistanceRobustness

Lethality

Miss Distance

ObservablesSurvivability

Reliability

Cost

Launch Platform

Integration /Firepower



2/24/2008 ELF 235

Extreme MissileTrajectory

Hypothetical PlaneThrough Target

For a normal distribution of error:

Probability < 1σ miss distance = 0.68



Source: Heaston, R.J. and Smoots, C.W., “ Introduction to Precision Guided Munit ions,” GACIAC HB-83-01, May 1983.

A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target

Example of Miss

( Line-of-Sight Angle Diverging )( Line-of-Sight Angle Rate L

.≠ 0 )

Example of Collision Intercept

( Line-of-Sight Angle Constant )( Line-of-Sight Angle Rate L

.= 0 )

Overshoot Miss

( LO S ) 1 > ( LO S )

0 ( LOS )1 = ( LOS )0t

t1

t2

t

t1



2/24/2008 ELF 236

Missile Target

Seeker Line-of-Sight

Missile Target

t0 t0

Seeker Line-of-Sight

Note: L = Missile Lead A = Target Aspect

AL L

A

A Maneuvering Target and Initial Heading Error

Cause Miss

A Maneuvering Target and Initial Heading Error

Cause Miss Target

Missile

CollisionPoint

+ZγM0

L

Maneuvering : d2Z + dZ + N’ Z = – N’ cos A 1 aT t2

A



2/24/2008 ELF 237

Target: τ

dt2 dt to – t t

o – t cos L 2

aT t

Initial HeadingError

: τ d2Zdt2

+ dZdt

+ N’ Zto – t

= – VM γM0

Note: to - t = 0 at intercept, causing discontinuity in above equations.

N’ = Effective navigation ratio = N [ VM / ( VM - VT cos A )]N = Navigation ratio = ( dγ / dt ) / ( dL / dt )τ = Missile time constant, VM= Velocity of missile, γM0

= Initial fl ightpath angle error of missile, to = Total time of fl ight, aT = Accelerationof target, VT = Velocity of target

Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design , D. Van NostrandCompany, Inc., Princeton, New Jersey, 1960

Missile Time Constant Causes Miss Distance Missile Time Constant Causes Miss Distance

τ is a measure of missile ability to respond totarget condition changes

τ equals elapsed time from input of targetreturn unti l missile hascompleted 63% or ( 1 – e-1 ) of correctivemaneuver ( t = τ )

τ also called “ rise time”

Contributions to time constant τ Control effectiveness ( τδ )

Control dynamics ( e.g., actuator rate ) ( τ . )

Input

Output

t i

Time

Timet i

63%

τ



2/24/2008 ELF 238

y ( g ) ( δ )

Dome error slope ( τDome ) Guidance and control filters ( τFilter )

Other G&C dynamics ( gyro dynamics,accelerometer, processor latency, etc )

Seeker errors ( resolution, latency, blind range,tracking, noise, glint, amplitude )

Approach to estimate τ τ = τδ + τδ

. + τDome

Acceleration Achieved Acceleration Commanded

= 1 – e- t / τ


M = 2, h = 20k ft , coastτ = τδ + τδ

. + τDome

= 0.096 + 0.070 + 0.043 = 0.209 s

Time Constant τδ

for Control Effectiveness Is

Driven by Static Margin

Time Constant τδ

for Control Effectiveness Is

Driven by Static Margin

Assumptions for τδ Control surface deflection limited

Near neutral stability

Equation of motion is

α

..

= [ ρ V2

S d Cmδ / ( 2 Iy ) ] δMax

Integrate to solve for αMax

αMax= [ ρ V2 S d Cmδ/ ( 8 Iy ) ] δMax τδ

2

τδ is given by

αMax, δMax

– δMax

αMax

τδ / 2 τδ



2/24/2008 ELF 239

τδ = [ 8 Iy ( αMax / δMax ) / ( ρ V2

SRef d Cmδ )]1/2

Contributors to small τδ

Low fineness ( small Iy / ( SRef d ))

High dynamic pressure ( low altitude / highspeed )

Large Cmδ


W = 367 lb, d = 0.667 ft, SRef = 0.349 ft2, Iy = 94.0 slug-ft2,

M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ),

αMax= 9.4 deg, δMax

= 12.6 deg, Cmδ = 51.6 per rad,

τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 )2 ( 0.349 )( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s

Time Constant τδ

.

for Flight Control System Is Driven by Actuator Rate Dynamics Time Constant τ

δ

.

for Flight Control System Is Driven by Actuator Rate Dynamics

Assumptions for τδ.

Control surface rate limited ( δ.

= δ.

Max ) Near neutral stability

Equation of motion for δ.= +/- δ

.

Max

α...

= [ ρ V2 S d Cmδ / ( 2 Iy ) ] δ.

Max

Equation of motion for “ perfect” responseδ.= ∞, δ = δMax

α..

= [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax

τδ. is d ifference between actual response

to and “ perfect” ( ) response

α Max, δ Max α Max α Max

- δ Max

δ.

1

Example for Rocket Baseline.

τδ.τδ



2/24/2008 ELF 240

to αMax and perfect ( τδ ) response

Then

τδ. = 2 δMax / δ

.

Max

Note:Response for control rate limitResponse for no control rate limit

• δ.

Max= 360 deg / s, δ

Max= 12.6 deg

• τδ. = 2 ( 12.6 / 360 ) = 0. 070 s

| R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ )

τDome = N’ ( VC / VM ) | R | ( α / γ.

)

α / γ.= α ( W / gc ) VM / { q SRef [ CNα

+ CNδ/ ( α / δ )]}

Substituting gives τDome = N’ W VC | R | / { gc q SRef [ CNα+ CNδ

/ ( α / δ )]}

Time Constant τDome for Radome Is Driven by Dome Error Slope Time Constant

τDome for Radome Is Driven by Dome Error Slope

0.03

0.02 E r r o r S l o p e ,

g

TangentOgiveDomeΔ f / f = 0.05

f / f = 0 02

Example for Rocket Baseline at M = 2, h = 20k ft, q =2725 psf

Assume VT = 1,000 ft / s, giving VC = 3,074 ft / s

Assume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02



2/24/2008 ELF 241

0.01

0 | R |

@ d /λ

= 1

0 ,

R a d o m

e

D e g / D e g

0 1 2 3

lN / d, Nose Fineness

Faceted or WindowDome

Multi-lensDome

Δ f / f = 0.02

Δ f / f = 0Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349ft 2, W = 367 lb, CNα= 40 per rad, CNδ

= 15.5 per rad, α / δ= 0.75

Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 /1.18 ) = 0.0182 deg / deg

τDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 )

( 40 + 15.5 / 0.75 )] = 0.043 s

High Initial Acceleration Is Required to Eliminate a Heading Error High Initial Acceleration Is Required to Eliminate a Heading Error

aM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) N ’ – 2

aM t0 / ( VM γM ),Non-dimensional

Acceleration

6

4

2.5

3

4

6

Note: Proportional Guidanceτ = 0t0 = Total Time to CorrectHeading Error aM = Acceleration of MissileVM = Velocity of Missile

γM = Init ial Heading Error of MissileN’ = Effective Navigation Ratio

Example: Exoatmospheric Head-on Intercept, N’ = 4

Midcourse lateral error at t = 0 ( seeker lock-on ) =200 m, 1 σ

Rlock-on = 20000 m ⇒ γM = 200 / 20000 = 0.0100 rad

VM = 5000 m / s , VT = 5000 ⇒ t0 = Rlock-on / ( VM + VT ) =20000 / ( 5000 + 5000 ) = 2.00 s

aM t0 / ( VM γM ) = 4

aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s2

nM = 100 / 9.81 = 10.2 g



2/24/2008 ELF 242

2

00 0.2 0.4 0.6 0.8

t / t0, Non-dimensional Time1.0

N’ = 2

M g

Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error

0.1

0.3

0.2

N’ = 3

N’ = 4

N’ = 6

Note: Proportional Guidance

( σHE )Max shown in figure is the envelope of adjoint solution( σHE )Max = Max miss distance ( 1 σ ) from heading error, ft

VM = Velocity of missile, ft / sγM = Init ial heading error , radt0 = Total time to correct heading error, sτ = Missile time constant, sN’ = Effective navigation ratio

Example: Ground Target, N’ = 4, = 0.2, GPS /

| ( σHE )Max / ( VM γM to ) |

σHE = VM γM t0 e-( t0 / τ ) j = 1∑N ’ – 1 { ( N’ - 2 )! [ - ( t0 / τ )] j / [( j – 1 )! ( N’ – j – 1 )! j! ]}

If N’ = 3, σHE = VM γM t0 e-( t0 / τ ) [ ( t0 / τ ) - ( t0 / τ )2 / 2 ]If N’ = 4, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - ( t0 / τ )2 + ( t0 / τ )3 / 6 ]

If N’ = 5, σHE = VM γM t0 e-( t0/ τ ) [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ )2 + ( t0 / τ )3 / 2 – ( t0 / τ )4 / 24 ]If N’ = 6, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - 2 ( t0 / τ )2 + ( t0 / τ )3 - ( t0 / τ )4 / 6 + ( t0 / τ )5 / 120 ]



2/24/2008 ELF 243

0.1

0

0 2 4 6 8tO / τ 10References:

•Donatelli, G.A., et al, “ Methodology for Predict ing Miss Distance for Air Launched Missi les,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “ Analyt ical Determination of Miss Distances for Linear Homing Navigation ,” Hughes Memo 260, March 1952

Example: Ground Target, N 4, τ 0.2, GPS /

INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 =0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 s

t0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12

( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m

Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile

4

Assumptions:τ = 0

VM > VT

6

3

4

N’ = 2.5

N’ = 2 ∞↑

Wheret = Elapsed Timet0 = Time to TargetN’ = Effective Navigation Ratio

Missile-to-Target

nM

nT

,

nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 )N ’ – 2 ]

Example:

τ = 0, N’ = 3, t / t0 = 1

⇒ nM / nT = 3



2/24/2008 ELF 244

2

00 0.2 0.4 0.6 0.8 1.0

t / t0, Non-Dimensional Time

4

6

Missile to Target

AccelerationRatio

Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance

0 1

0.3

0.2

( σMAN )Max

gc nT τ2

N’ = 3

N’ = 4

Note: Proportional Guidance( σMAN )Max is the envelope of adjoint solu tion( σMAN )Max = Max miss ( 1 σ ) from target accel, ftnT = Target acceleration, ggc = Gravitation constant, 32.2τ = Missile time constant, s

σMAN = gc nT τ2 e-( t0 / τ ) j = 2∑N ’ – 1 { ( N’ - 3 )! [ - ( t0 / τ )] j / [( j – 2 )!

( N’ – j – 1 )! j! ]}If N’ = 3, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 ]If N’ = 4, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 6 ]If N’ = 5, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 3 + ( t0 /τ )4 / 24 ]If N’ = 6, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 2 + ( t0 /τ )4 / 8 - ( t0 / τ )5 / 120 ]



2/24/2008 ELF 245

0.1

00 2 4 6 8tO / τ 10

N’ = 6N’ = Effective navigation ratioτ0 = Time of flight, s

References:

•Donatelli, G.A., et al, “ Methodology for Predict ing Miss Distance for Air Launched Missi les,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “ Analyt ical Determination of Miss Distances for Linear Homing Navigation ,” Hughes Memo 260, March 1952

An Aero Control Missile Has Reduced Miss

Distance at Low Altitude / High Dynamic Pressure

An Aero Control Missile Has Reduced Miss

Distance at Low Altitude / High Dynamic Pressure

1

10

100

M a x i m u m M i s s D u e

t o M a n e u v e r i n g

T a r g e t , f t

h = SL

h = 20k f t

h = 40k f t

h = 60k f t

h = 80k f t

( σMan )Max = 0.13 gc nT τ2 @ N’ = 4, t0 / τ = 2Note: Proportional guidanceTarget maneuver init iated for max miss ( t0 / τ = 2 )

( σMan )Max in figure = Envelope of adjoint missdistanceτ = Missile time constant, sN’ = Effective navigation ratio = 4nT = Target acceleration, ggc = Gravitation constant = 32.2



2/24/2008 ELF 246

0.1

1

0 2 4 6 8 10

Target Maneuverability, g

R o c k e t B a s e l i n e

M

Example for Rocket Baseline at Mach 2, coasting

Assume:

• nT = 5g, VT = 1,000 ft / s, head-on intercept

•h = 20k ft ⇒ τ = 0.209 s

( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 )2 = 0.9 ft•h = 80k ft ⇒ τ = 1.17 s

( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 )2 = 28.7 ft

Glint Miss Distance Driven by Seeker Resolution,

Missile Time Constant, and Navigation Ratio

Glint Miss Distance Driven by Seeker Resolution,

Missile Time Constant, and Navigation Ratio

0.2

0.4

0.6

0.8

( b T ) R e s ,

N o n d i m e

n s i o n a l M i s s D i s t a n c

e

f r o m G l i n t @ 2 H z B a n d w i d t h

σGlint = KN’ ( W / τ )1/2

KN

’ = 0.5 ( 2 KN

’ = 4 )N’ / 4

KN’ = 4 = 1.206

W = ( bT )Res2 / ( 3 π2 B )

Note:Proportional guidance Adjo int miss distance

σGlint = Miss distance due to gl int noise, ftW = Glint no ise spectral density , ft2 / Hzτ = Missile time constant, sN’ = Effective navigation ratio( bT )Res = Target span resolut ion at seeker blind range, ftB = Noise bandwidth, Hz ( 1 < B < 5 Hz )

Example: Rocket Baseline at Mach 2, h= 20k ft altitude ⇒ τ = 0.209 s

Assume:

•N’ = 4

•B = 2 Hz



2/24/2008 ELF 247

0

0 0.2 0.4 0.6 0.8 1

Tau, Missi le Time Constant, s

S i g m a

/

N' = 3 N' = 4 N' = 6

•B = 2 Hz

•( bT )Res = b t = 40 ft ( radar seeker beamwidth resolution of target wing span )

Calculate:

W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / Hz

σGlint

/ ( bT

)Res

= KN

’ ( W / τ )1/2 / ( bt

)Res

= 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343

σGlint = 0.343 ( 40 ) = 13.7 ftReference:Bennett, R.R., et al, “Analyt ical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952



Missile Carriage RCS and Launch Plume Are

Considerations in Launch Platform Observables

Missile Carriage RCS and Launch Plume Are

Considerations in Launch Platform Observables

Missile Carriage Alternatives Internal Carriage: Lowest Carriage RCS

Conformal Carriage: Low Carriage RCS

Conventional External Pylon or External Rail Carriage: High Carriage RCS

Plume Alternatives Min Smoke: Lowest Launch Observables ( H2O Contrail )

Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from APOxidizer )

Carriage and

Launch Observables

Robustness

Lethality

Miss Distance


Reliability

Cost

Launch PlatformIntegration /Firepower



2/24/2008 ELF 249

High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )

Center Weapon Bay Best for Ejection Launchers

F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32 F-117 Bay Loadout: 1 GBU-27, 1 GBU-10 B-1 Bay Loadout: 8 AGM-69

Video Side Weapon Bay Best for Rail Launchers

Examples of Weapon Bay Internal Carriage and

Load-out

Examples of Weapon Bay Internal Carriage and

Load-out



2/24/2008 ELF 250

AMRAAM Loading in F-22 Bay F-22 Side Bay: 1 AIM-9 Each Side Bay RAH-66 Side Bay: 1 AGM-114, 2 FIM-92, 4 Hydra 70 Each Side Bay

Minimum Smoke Propellant Has Low Observables Minimum Smoke Propellant Has Low Observables

High Smoke Example: AIM-7

Particles ( e.g., metal fuel ) at allatmosphere temperature.

Reduced Smoke Example: AIM-120

Contrail ( HCl from AP oxidizer ) at T < -10° Fatmospheric temperature.

Minimum Smoke Example: Javelin

Contrail (H2O ) at T < -35º Fatmospheric temperature.



2/24/2008 ELF 251

High Smoke Motor

Reduced Smoke Motor

Minimum Smoke Motor

High Altitude Flight and Low RCS Enhance

Survivability

High Altitude Flight and Low RCS Enhance

Survivability

100

1000

10000

100000

1000000

10000000

P t , R a d a r T r a

n s m i t t e d P o w e

r

R e q u i r e d f o

r D e t e c t i o n , W

Example for Pt= 50,000 W:

Not detected if:

h > 25k ft for σ = 0.001 m2

h > 77k ft for σ = 0.1 m2

Pt = ( 4 π )3 Pr R4 / ( Gt Gr σ λ2 ) Other SurvivabilityConsiderations

Robustness

Lethality

Miss Distance


Reliability

Cost




2/24/2008 ELF 252

0 20 40 60 80 100

h, Geometric Alt itude, kft

RCS = 0.1 m2 RCS = 0.01 m2 RCS = 0.001 m2

Note: Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03

m, Pr = Receiver Sensitivity = 10-14 W, σ = radar cross section ( RCS ) Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight

Mission Planning and High Speed Enhance

Survivability

Mission Planning and High Speed Enhance

Survivability

0

1

2

x p ( V / R m a x ) , N o n - d i m e n s i o n a l T h r e a t

E x p o s u

r e T i m e

texp = 2 ( Rmax / V ) cos [ sin-1 ( yoffset / Rmax )] – treact

Example:

yoffset = 7 nm, Rmax = 10 nm = 60750 ft,y / R = 0.7, t = 15 s

R m a x treact V

texp V

Flyby

SAM

Siteyoffset



2/24/2008 ELF 253

0 0.2 0.4 0.6 0.8 1

yoffset / Rmax, Non-dimens ional Offset Distance from

Threat

t e

treac t ( V / Rmax ) = 0 treac t ( V / Rmax ) = 1.0

Note: Based on assumption of constant altitude, constant heading flyby of threat SAM site with an unobstructed line-of-sight. texp = exposure time toSAM threat, Rmax = max detection range by SAM threat, V = flyby veloci ty,yoffset = flyby offset, treact = SAM site reaction time from detection to launch

yoffset max react

If V = 1000 ft / s, t react ( V / Rmax ) = 0.247

•texp ( V / Rmax ) = 2 cos [ sin-1 ( 7 / 10 )] –15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181

•texp = 1.181 ( 60746 / 1000 ) = 71.7 s

If V = 4000 ft / s, t react ( V / Rmax ) = 0.988

•texp ( V / Rmax ) = 0.440

•texp = 0.440 ( 60746 / 4000 ) = 6.7 s

Low Altitude Flight and Terrain Obstacles

Provide Masking from Threat

Low Altitude Flight and Terrain Obstacles

Provide Masking from Threat

500

1000

1500

2000

h m a s k ,

A l t i t u d e t h a t

M a s k s L i n e - o f - S i g h t

E x p o s u r e t o S u

r f a c e T h r e a t , f t

hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 )2

hmask = alti tude that allows obstacle and earth

curvature to mask exposure to surface threat LOS, ft

hobstacle = height of obs tacle above terrain, ft

Rlos = line-of-sight range to surface threat, ft

Robstacle = range from surface threat to obstacle, ft

Height of low hill or tall tree ≈ 100 ft

Height of moderate hill ≈ 200 ft

Height of high hill ≈ 500 ft

Height of low mountain ≈ 1000 ft



2/24/2008 ELF 254

0

0 10 20 30 40

Rlos, Line-of-Sight Range to Surface Threat, nm

Rlos ( hobstacle / Robstacle ) = 100 ft

Rlos ( hobstacle / Robstacle ) = 200 ftRlos ( hobstacle / Robstacle ) = 500 ft

Rlos ( hobstacle / Robstacle ) = 1000 ft

Example:hobstacle = 200 ft

Robstaacle = 5.0 nm = 30395 ft

Rlos = 10.0 nm = 60790 ft

Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 /30395 ) = 400 ft

hmask = 200 ( 60790 / 30395 ) + ( 60790 /7113 )2 = 400 + 73 = 473 ft above terrain

Insensitive Munitions Improve Launch Platform

Survivability

Insensitive Munitions Improve Launch Platform

Survivability Critical Subsystems

Rocket motor or fuel tank

Warhead Severity Concerns Ranking of Power Output - Type

1. Detonation ( ~ 0.000002 s r ise time )

2. Partial detonation ( ~ 0.0001 s rise time )

3. Explosion ( ~ 0.001 s rise time )4. Deflagration or propulsion rise time ( ~ 0.1 s rise time )

5. Burning ( > 1 s )

Design and test considerations ( MIL STD 2105C )



2/24/2008 ELF 255

Fragment / bul let impact or blast Sympathetic detonation

Fast / slow cook-off fi re

Drop

Temperature Vibration

Carrier landing ( 18 ft / s sink rate )

Robustness

Lethality

Miss Distance


Reliability

Cost


High System Reliability Is Provided by High Subsystem Reliability and Low Parts Count High System Reliability Is Provided by High Subsystem Reliability and Low Parts Count

Typical Event /Subsystem

Rsystem ≈ 0.94 = R Arm X RLaunch X RStruct X R Auto XR Act X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H

Arm ( 0.995 – 0.999 )Launch ( 0.990 – 0.995 )

Structure ( 0.997 – 0.999 )

Autopi lot ( 0.993 – 0.995 )

Actuators ( 0.990 – 0.995 )

Seeker ( 0.985 – 0.990 )

Inertial Guidance ( 0.995 – 0.999 )

P S l ( 0 995 0 999 )

Reliability

Typical System Reliability



2/24/2008 ELF 256

Power Supply ( 0.995 – 0.999 )Propuls ion ( 0.995 – 0.999 )

Fuze ( 0.987 – 0.995 )

Warhead ( 0.995 – 0.999 )

0.90 0.92 0.94 0.96 0.98 1.00

Typical Reliability

Sensors, Electronics and Propulsion Drive

Missile Production Cost

Sensors, Electronics and Propulsion Drive

Missile Production Cost

Dome Seeker Guidance andControl

Propulsion•Rocket• Airbreather

Wings

Stabilizers

Warheadand Fuzing

AerothermalInsulation

FlightControl

Power Supply

Structure•Rocket• Airbreather

–

–

– – –

–

CostRobustness

Lethality

Miss Distance


Reliability

Cost


DataLink



2/24/2008 ELF 257

Very High( > 25% Production Cost )

–High( > 10% )

Moderate( > 5% )

Relatively Low( < 5% )

Note:System assembly and test ~ 10% production costPropulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets

Sensors and Electronics Occupy a Large Portion

of a High Performance / High Cost Missile.

Sensors and Electronics Occupy a Large Portion

of a High Performance / High Cost Missile.

Example: Derby / R-Darter Missile



2/24/2008 ELF 258

Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html

Cost Considerations Cost Considerations

Life Cycle

System Development and Demonstration ( SDD )

Production

Logistics

Culture / processes

Relative Emphasis of Cost, Performance, Reliabil ity, Organization Structure



2/24/2008 ELF 259

Relaxed Mil STDs

IPPD

Profit

Competition

SDD Cost Is Driven by Schedule Duration and

Risk

SDD Cost Is Driven by Schedule Duration and

Risk

10

100

1000

10000

0 2 4 6 8 10 12 14

C S D D ,

S D D

C o s t i n M i l l i o n s

CSDD = $20,000,000 tSDD1.90, ( tSDD in years )

Example:

5 year ( medium risk ) SDD program

CSDD = $20,000,000 tSDD1.90

= ( 20,000,000 ) ( 5 )1.90

= $426,000,000

Low

Risk

SDD

High

Risk

SDD

Moderate

Risk

SDD



2/24/2008 ELF 260

0 2 4 6 8 10 12 14

tSDD, SDD Schedule Duration in Years

AGM-142 TOW 2 SLAM-ER MLRS LB Hellfire J ASSM Hellfire II

SLAM J DAM AGM-130 Harpoon ATACMS Tomahawk ESSM

AIM-120A J SOW HARM J avelin BAT PAC-3 PatriotNote: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule.-- Source of data: Nicho las, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Assoc iates, 1999 – SDD cost based on 1999 US$

Light Weight Missiles Have Low Unit Production

Cost

Light Weight Missiles Have Low Unit Production

Cost

100000

1000000

10000000

Javelin

Longbow Hellfire

AMRAAMMLRS

HARM

JSOW

Tomahawk

C1000th ≈ $6,100 WL0.758, ( WL in lb )

C

o s t o f M i s s i l e N u

m b e r 1 0 0 0 ,

U . S . $



2/24/2008 ELF 261

10000

10 100 1000 10000

Example:

2,000 unit buy of 100 lb missile:

C1000th ≈ $6,100 WL0.758 = 6100 ( 100 )0.758 =

$200,000

Cost of 2,000 miss iles = 2000 ( $200000 ) =$400,000,000

Note:-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missi le Data Book, 1999,” Data Search Associates, 1999 – Unit product ion cost based on 1999 US$

C 1 0 0 0 t h , C

WL , Launch Weight, lb

Learning Curve and Large Production Reduce

Unit Production Cost

Learning Curve and Large Production Reduce

Unit Production Cost

0.1

1

/C 1 s t , C o s t o f U n i t x

/ C o s t o f F i r s t U n

i t

Javelin ( L = 0.764, C1st = $3.15M,Y1 = 1994 )

Long bow HF ( L = 0.761, C1st =$4.31M, Y1 = 1996 )

AMRAAM ( L = 0.738, C1st =$30.5M, Y1 = 1987 )

MLRS ( L = 0.811, C1st = $0.139M,Y1 = 1980 )

HARM ( L = 0.786, C1st = $9.73M,Y1 = 1981 )

JSOW ( L = 0.812, C1st = $2.98M,Y1 = 1997 )

Cx = C1st L log2x, C2x = L Cx , where C in U.S. 99$

Example:For a learningcurve coefficientof L = 80%, cost of uni t #1000 is 11%

the cost of the first

L = 1.0

L = 0.9

L = 0.8



2/24/2008 ELF 262

0.01

1 10 100 1000 10000 100000 1E+06

x, Number of Units Produced

C x / C Y1 1997 )

Tomahawk ( L = 0.817, C1st =$13.0M, Y1 = 1980 )

Source of data: Nicholas, T. and Rossi, R., “ U.S. Miss ile Data Book,1999,” Data Search Associates, 1999

Labor intensive learning curve: L < 0.8Machine intensive learning curve: L > 0.8 )

Contributors to the learning curve include:• More efficient labor • Reduced scrap• Improved processes

the cost of the firstunit L = 0.7

Low Parts Count Reduces Missile Unit

Production Cost

Low Parts Count Reduces Missile Unit

Production Cost

10

100

1000

10000

100000

1000000

P

a r t s C o u n t , H o u r s , o r C o s t ( U S

$ )



2/24/2008 ELF 263

0Parts Fasteners Circuit Cards Connectors Assembly /

Test Hours

Unit

Production

Cost ( US$ )

Current Tomahawk Tactical Tomahawk

Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA,modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include:casting , pultrusion / extrusion, centralized electronics, and COTS.

Copperhead Seeker and Electronics Production Patriot Control Section Production

Video of Hellfi re Seeker and Electronics Production

Tactical Missile Culture Is Driven by Rate

Production of Sensors and Electronics

Tactical Missile Culture Is Driven by Rate

Production of Sensors and Electronics



2/24/2008 ELF 264

Peacetime Logistics Activity

•Contractor Post-production Engineering•Training Manuals / Tech Data Package•Simulation and Software Maintenance•Configuration Management

•Engineering Support•System Analysis•Launch Platform Integration•Requirements Documents•Coordinate Suppliers

•Storage Alternatives

•Wooden Round ( Protected )O R d ( H idi t T C i Sh k )

Logistics Cost Considerations Logistics Cost Considerations

Wartime Logistics Activity

•Deployment Alternatives• Ai rli ft

•Sealift•Combat Logistics

•Launch Platform Integration•Mission Planning•Field Tests•Reliability Data

•Maintainability Data•Effectiveness Data



2/24/2008 ELF 265

( )•Open Round ( Humidi ty, Temp, Corrosion, Shock )

•Reliability Maintenance•Surveillance•Testing

•Maintenance Al ternatives

•First level ( depot )•Two level ( depot, field )

•Disposal

y•Effectiveness Data•Safety Data

Simple: St inger More Sophisticated: Hawk and SLAMRAAM Complex: PAC-3

Very Complex: THAAD Video of Logistics Alternatives

Logistics Cost Lower for Simple Missile Systems Logistics Cost Lower for Simple Missile Systems



2/24/2008 ELF 266

Logistics Is Simpler for Light Weight Missiles Logistics Is Simpler for Light Weight Missiles

0

2

4

6

10 100 1000 10000

Missile Weight, lb

S u p p o r t P e r s o n n e l r e q u i r e d

f o r I n

s t a l l a t i o n

Support personnel f or installation with 50 lb lif t limit per person

Support personnel for installation with 100 lb lif t limit per person

Machine lift f or installation

Video of Simple Logistics fo r aLight weight Missile



2/24/2008 ELF 267

Predator ( 21 lb ) Sidewinder ( 190 lb ) Sparrow ( 500 lb ) Laser Guided Bomb ( 2,500 lb )

Small MEMS Sensors Can Provide Health

Monitoring, Reducing Cost and Weight

Small MEMS Sensors Can Provide Health

Monitoring, Reducing Cost and Weight

Micro-machined Electro-Mechanical Systems ( MEMS )

Small size / low cost semiconductor manufacturing process2,000 to 5,000 sensors on a 5 in sil icon wafer

Wireless ( RF ) Data Collection and Health Monitor ing

Distributed Sensors Over Missi le

Stress / strain

Vibration

Acoustics

Temperature



2/24/2008 ELF 268

pPressure

Reduced Logist ics Cost and Improved Reliabili ty

Health monitor ing

Reduced Weight and Production Cost

More Efficient Design

Missile Carriage Size, Shape, and Weight Are

Driven by Launch Platform Compatibility

Missile Carriage Size, Shape, and Weight Are

Driven by Launch Platform Compatibility

Surface Ships

CLS

~24” x 24”

263”

263”

~168”

3400 lb

3400 lb

~500 lb to3000 lb

~ 2 2 ” ~ 2 2

”

Fighters /Bombers /UCAVs

Rail /Ejection

VLS

Submarines

Launch Platform Integration / Firepower

Robustness

Lethality

Miss Distance


Reliability

Cost


22”

US Launch Platform Launcher Carriage Span / Shape Length Weight



2/24/2008 ELF 269

Ground

Vehicles158” 3700 lb

Helos

LaunchPods

Rail ∼13” x 13” 70” 120 lb

~ 2 8 ” ~ 2 8

”

Light Weight Missiles Enhance Firepower Light Weight Missiles Enhance Firepower

E, carry 1

C, carry 3

C, carry 1

E, carry 2

C, carry 2E, carry 3

E, carry 1

C, carry 1

E, carry 2

C, carry 2

5,000 lb

4,000 lb

3,000 lb

2,000 lb

1,000 lb

M a x S t r i k e

W e a p o n

W e i g

h t

C l e

a n

C L T a

n k

d T a n

k s

2 A I M

- 9

A G M - 8 8

2 A I M

- 9

C l e

a n

C L T a

n k

T a n

k s

2 A I M

- 9

A G M - 8 8

2 A I M

- 9

F-18 C / E

Inboard Asymmetric

Bring-Back Load Limit

Outboard AsymmetricBring-Back Load Limit



2/24/2008 ELF 270

+ C

+ 2 I n b d

+ C L T k + 2

+ C L T k + 2 A

+ 2 I n b d T k + 2

Configuration for Day Operationwith Bring-Back Load

+ C

+ 2 I n b d

+ C L T k + 2

+ C L T k + 2 A

+ 2 I n b d T k + 2

Configuration for Night Operationwith Bring-Back Load

Launch Envelope Limitations in Missile / Launch

Platform Physical Integration

Launch Envelope Limitations in Missile / Launch

Platform Physical Integration

Off BoresightSeeker field of regard ⇒ potential obscur ing from launch platform

Minimum Range

Launcher rail clearance and aeroelasticity ⇒ miss at min range

Helo rotor downwash ⇒ miss at min range

Safety

Launcher retention ⇒ potential inadvertent release, potential hang-fire

Launch platform local flow field α, β ⇒ potential unsafe separationL h l tf i t ti l f ti



2/24/2008 ELF 271

Launch platform maneuvering ⇒ potential unsafe separation

Handling qualities with stores ⇒ potential unsafe handling qualities

Launch platform bay / canister acoustics ⇒ missi le factor of safety

Launch platform bay / canister vibration ⇒ missile factor of safety

Store Separation Wind Tunnel Tests Are

Required for Missile / Aircraft Compatibility

Store Separation Wind Tunnel Tests Are

Required for Missile / Aircraft Compatibility

F-18 Store Compatibi lity Test in AEDC 16T AV-8 Store Compatibil ity Test in AEDC 4T

Types of Wind Tunnel Testing for Store Compatibility

- Flow field mapping with probe



2/24/2008 ELF 272

pp g p

- Flow field mapping with store

- Captive trajectory simulation

- Drop testing

Example Stores with Flow Field Interaction: Kh-41 + AA-10

Examples of Rail Launched and Ejection

Launched Missiles

Examples of Rail Launched and Ejection

Launched Missiles

Example Rail Launcher: Hellf ire / Brimstone Example Ejection Launcher: AGM-86 ALCM



2/24/2008 ELF 273

Video of Hellf ire / Brimstone Carriage / Launch Video of AGM-86 Carriage / Launch

Examples of Safe Store Separation Examples of Safe Store Separation

Laser Guided Bombs Drop from F-117



2/24/2008 ELF 274

AMRAAM Rail Launch from F-16 Video of Rapid Drop ( 16 Bombs ) from B-2

Examples of Store Compatibility Problems Examples of Store Compatibility Problems

Unsafe Separation Hang-Fire Store Aeroelastic Instability



2/24/2008 ELF 275

MIL-STD-8591 Aircraft Store Suspension and

Ejection Launcher Requirements

MIL-STD-8591 Aircraft Store Suspension and

Ejection Launcher Requirements

Store Weight / Parameter 30 Inch Suspension 14 Inch Suspension

♦ Weight Up to 100 lb Not Appl icable Yes

• Lug height ( in ) 0.75

• Min ejector area ( in x in ) 4.0 x 26.0

♦ Weight 101 to 1,450 lb Yes Yes

• Lug height ( in ) 1.35 1.00• Min lug well ( in ) 0.515 0.515

• Min ejector area ( in x in ) 4. 0 x 36.0 4.0 x 26.0

♦ Weight Over 1,451 lb Yes Not Appl icable

• Lug height ( in ) 1.35

• Min lug well ( in ) 1.080• Min ejector area ( in x in ) 4.0 x 36.0



2/24/2008 ELF 276

Ejection Stroke

Rail Launcher Forward Hanger Aft Hanger

LAU-7 Sidewinder Launcher 2.260 2.260

LAU 117 Maverick Launcher 1.14 7.23

MIL-STD-8591 Aircraft Store Rail Launcher

Examples

MIL-STD-8591 Aircraft Store Rail Launcher

Examples



2/24/2008 ELF 277

Note: Dimensions in inches.

• LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in

•LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in

Baseline AIM-120B AMRAAM

Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )

Compressed Carriage Missiles Provide Higher

Firepower

Compressed Carriage Missiles Provide Higher

Firepower

17 5 in 17 5 in

Baseline AMRAAM: Loadout

of 2 AMRAAM per F-22 Semi-Bay



2/24/2008 ELF 278

17.5 in 17.5 in

12.5 in 12.5 in 12.5 in

Compressed Carriage AMRAAM: Loadout of 3 AMRAAM per F-22 Semi-Bay

Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wraparound surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ).

Video of Longshot Kit on CBU-97

Example of Aircraft Carriage and Fire Control

Interfaces

Example of Aircraft Carriage and Fire Control

Interfaces

WingWing Deploy

Safety Pin

Folding

Suspension

Lug

Fire Control /

Avionics

UmbilicalConnector

Flight Control

Access Cover Electrical

Safety Pin

Folding

SuspensionLug



2/24/2008 ELF 279

Example: ADM-141 TALD ( Tactical Air-Launched Decoy )Carriage and Fire Control Interfaces

Example of Ship Weapon Carriage and Launcher,

Mk41 VLS

Example of Ship Weapon Carriage and Launcher,

Mk41 VLS

8 Modules / Magazine Module Gas Management

Canister Cell Hatch

Cell

Before

Firing

Cell

After

Firing

Ship DeckExhaust Hatch

Missile Cover

Plenum



2/24/2008 ELF 280

Tomahawk Launch 8 Canister Cells / Module Standard Missi le Launch

Robustness Is Required for Carriage, Shipping,

and Storage Environment

Robustness Is Required for Carriage, Shipping,

and Storage Environment Environmental Parameter Typical Requirement Video: Ground / Sea Environment

Surface Temperature -60° F* to 160° F

Surface Humidity 5% to 100%

Rain Rate 120 mm / h**

Surface Wind 100 km / h steady***

150 km / h gusts****Salt fog 3 g / mm2 deposited per year

Vibration 10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A

Shock Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670A

Acoustic 160 dB



2/24/2008 ELF 281

Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement.

* Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location.

** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location.*** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of wors t location.

**** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location.

Summary of Measures of Merit and Launch

Platform Integration

Summary of Measures of Merit and Launch

Platform Integration Measures of Merit

Robustness

Warhead lethali ty Miss distance

Carriage and launch observables

Other survivability considerations

Reliability

Cost

Launch Platform Integration Firepower, weight, fitment

Store separation

Launch platform handling qualities, aeroelasticity Hang-fire



2/24/2008 ELF 282

g

Vibration

Standard launchers

Carriage and storage environment Discussion / Questions?


Measures of Merit and Launch Platform

Integration Problems


Integration Problems 1. IR signal attenuation is greater than 100 dB per km through a c____.

2. GPS / INS enhances seeker lock-on in adverse weather and ground c______.

3. A data link can enhance missile seeker lock-on against a m_____ target.

4. An example of a missile counter-counter measure to flares is an i______i_____ seeker.

5. Compared to a mid-wave IR seeker, a long wave IR seeker receives moreenergy from a c___ target.

6. High f ineness kinetic energy penetrators are required to defeat b_____targets.

7. For the same lethality with a blast fragmentation warhead, a small decrease inmiss distance allows a large decrease in the required weight of the w______.

F bl t / f h d h t t l ti f b t i i d t



2/24/2008 ELF 283

8. For a blast / frag warhead, a charge-to-metal ratio of about one is required toachieve a high total fragment k______ e_____.

9. A blast fragmentation warhead tradeoff is the number of fragments versus theindividual fragment w_____.


Integration Problems ( cont )


Integration Problems ( cont ) 10. Kinetic energy penetration is a function of the penetrator diameter, length,

density, and v_______.

11. In proport ional homing guidance, the objective is to make the line-of-sightangle rate equal to z___.

12. Aeromechanics contributors to missile time constant are flight controleffectiveness, flight control system dynamics, and dome e____ s____.

13. Miss distance due to heading error is a function of missile navigation ratio,velocity, time to correct the heading error, and the missile t___ c_______.

14. A missile must have about t_____ times the maneuverability of the target.

15. Minimizing the miss distance due to radar glint requires a high resolution

seeker, an optimum missile time constant and an optimum n_________ r____.

16 Weapons on low observable launch platforms use i carriage



2/24/2008 ELF 284

16. Weapons on low observable launch platforms use i_______ carriage.

17. Weapons on low observable launch platforms use m______ smoke propellant.

18. For an insensit ive munition, burning is preferable to detonation because itreleases less p____.





19. Missile system reliability is enhanced by subsystem reliability and low p____count.

20. High cost subsystems of missiles are sensors, electronics, and p_________.

21. Missile SDD cost is driven by the program duration and r___.

22. Missile unit production cost is driven by the number of units produced,learning curve, and w_____.

23. First level maintenance is conducted at a d____.

24. A standard launch system for U.S. Navy ships is the V_______ L_____ S_____.

25. Most light weight missiles use rail launchers while most heavy weight missiles

use e_______ launchers.26. Higher firepower is provided by c_________ carriage.



2/24/2008 ELF 285

27. The typical environmental requirement from MIL-HDBK-310 is the _% world-wide climatic extreme.

Outline Outline Introduction / Key Drivers in the Design Process






Sizing Examples

Development Process




2/24/2008 ELF 286


Appendices ( Homework Problems / Classroom Exercises,

Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )

Sizing Examples Sizing Examples Rocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control



2/24/2008 ELF 287

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

Ai -to-Air Engagement Analysis Process and

Assumptions

Ai -to-Air Engagement Analysis Process and

Assumptions

F-pole range provides kil l of head-on threat outside of

threat weapon launch range Aircraft contrast for typical engagement

C = 0.18

Typical visual detection range by target ( Required F-polerange ) RD = 3.3 nm

Typical alti tude and speed of launch aircraft, target aircraft,

and missile h = 20k ft altitude



2/24/2008 ELF 288

VL = Mach 0.8 = 820 ft / s

VT = Mach 0.8 = 820 ft / s

VM = 2 VT = 1,640 ft / s

Assumed Ai -to-Air Engagement Scenario for

Head-on Intercept

Assumed Ai -to-Air Engagement Scenario for

Head-on Intercept

t = 0 s (Launch Missi le)

RL= Launch Range = 10.0 nm

Red Aircraft

( 820 ft / s )

Blue Aircraft

t = tf = 24.4 s ( Missile Impacts Target )

Red Aircraft

Blue Aircraft( 820 ft / s )

Blue Missile( 1640 ft / s )

RL= VM t f + VT tf

RF-Pole = VM t f - VL tf

RF = Missile Flight Range = 6.7 nm



2/24/2008 ELF 289

( 820 ft / s )

R F-pole = 3.3 nm

Destroyed

0

2

4

6

8

R , V i s i b l e R a n g e f o r

5 0 f t 2 T a r g e t ,

n

Visual Detection Range,nm

Visual RecognitionRange, nm

Target Contrast and Size Drive Visual Detection

and Recognition Range

Target Contrast and Size Drive Visual Detection

and Recognition Range

Note:

RD

= Visual detection range for probability of detection PD = 0.5

C = Contrast

CT = Visual threshold contrast = 0.02

Atp= Target presented area = 50 ft2

RR = Visual recognition range

θF = Pilot v isual fovial angle = 0.8 deg

Clear weather

Pilot search glimpse time = 1 / 3 s

Example:

If C = 0.18

RD = 3.3 nm

RR = 1.0 nm

RD = 1.15 [ A tp( C – CT )]1/2, RD in nm, A tp

in ft2

RR = 0.29 RD



2/24/2008 ELF 290

0

0.01 0.1 1C, Contrast

Pilot search g limpse time = 1 / 3 s

C = 0.01 C = 0.02 C = 0.05 C = 0.1 C = 0.2 C = 0.5 C = 1.0

High Missile Velocity Improves Standoff Range High Missile Velocity Improves Standoff Range

0.2

0.4

0.6

0.8

1

F - P o l e R a n g e / L a u n c h R a n g

VL / VM = 0VL / VM = 0.2

VL / VM = 0.5

VL / VM = 1.0

Example:• VL = VT

• VM = 2 VT

RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT ) Note: Head-on intercept

RF-Pole = Standoff range at intercept

RL= Launch rangeVM = Missi le average velocity

VT = Target velocity

VL = Launch velocity



2/24/2008 ELF 291

0

0 0.2 0.4 0.6 0.8 1

Target Velocity / Missile Velocity

VM 2 VT

• Then VT / VM = VL / VM = 0.5• RF-Pole / RL = 0.33

• RF-Pole = RD = 3.3 nm• RL = 3.3 / 0.33 = 10.0 nm

Missile Flight Range Requirement Is Greatest for

a Tail Chase Intercept

Missile Flight Range Requirement Is Greatest for

a Tail Chase Intercept

0

0.5

1

1.5

2

2.5

3

R F / R L ,

M i s s i l e F l i g h t R a

n g e / L a u n c h R a

n g e

( RF / RL ) Head-on( RF / RL ) Tail Chase

Examples:

•Head-on Intercept

• VM = 1,640 ft / s, VT = 820 ft / s• VM / VT = 1640 / 820 = 2• RF / RL = 2 / ( 2 + 1 ) = 0.667• R = 10 0 nm

( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]

( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]



2/24/2008 ELF 292

0

0 1 2 3 4 5

VM / VT, Missi le Veloc ity / Target Veloc ity

• RL = 10.0 nm• RF = 0.667 ( 10.0 ) = 6.67 nm

•Tail Intercept at same condi tions• R

F/ R

L= 2 / ( 2 – 1 ) = 2.0

• RF = 2.0 ( 10.0 ) = 20.0 nm

Drawing of Rocket Baseline Missile Configuration Drawing of Rocket Baseline Missile Configuration

STA 60.8

19.4

3.418.5

STA 125.4

LEmac at STA 67.0BL 10.2

Λ = 45°

40.2STA 0 19.2 46.1 62.6 84.5 138.6

Nose Forebody PayloadBay

Midbody Aftbody Tailcone

Rocket Motor

Λ = 57°

12.0

LEmac atSTA 131.6

BL 8.0

16.18.0 d

cgBO cgLaunch

143.9



2/24/2008 ELF 293

Note: Dimensions in inches

Source: Bithell, R.A. and Stoner, R.C., “ Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis

Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.

Mass Properties of Rocket Baseline Missile Mass Properties of Rocket Baseline Missile

1 Nose ( Radome ) 4.1 12.0

3 Forebody structure 12.4 30.5Guidance 46.6 32.62 Payload Bay Structure 7.6 54.3

Warhead 77.7 54.34 Midbody Structure 10.2 73.5

Control Actuation System 61.0 75.55 Aftbody Structure 0.0 –

Rocket Motor Case 47.3 107.5Insulation ( EDPM – Silica ) 23.0 117.2

6 Tailcone Structure 6.5 141.2

Nozzle 5.8 141.2Fixed Surfaces 26.2 137.8Movable Surfaces 38.6 75.5

Component Weight, lb. C.G. STA, in.



2/24/2008 ELF 294

Burnout Total 367.0 76.2Propellant 133.0 107.8

Launch Total 500.0 84.6

Rocket Baseline Missile Definition Rocket Baseline Missile Definition Body

Dome Material Pyroceram Airf rame Material Aluminum 2219-T81

Length, in 143.9Diameter, in 8.0

Airf rame thickness, in 0.16Fineness ratio 17.99Volume, ft3 3.82Wetted area, ft2 24.06

Nozzle exit area, ft2 0.078Boattail fineness ratio 0.38Nose fineness ratio 2.40Nose bluntness 0.0Boattail angle, deg 7.5

Movable surfaces ( forward )

Material Aluminum 2219-T81Planform area, ft2 ( 2 panels exposed ) 2.55Wetted area, ft2 ( 4 panels ) 10.20Aspect ratio ( 2 panels exposed ) 2 82



2/24/2008 ELF 295

Aspect ratio ( 2 panels exposed ) 2.82Taper ratio 0.175Root chord, in 19.4

Tip chord, in 3.4Span, in ( 2 panels exposed ) 32.2Leading edge sweep, deg 45.0

Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont )

Movable surfaces ( continued )Mean aerodynamic chord, in 13.3Thickness ratio 0.044Section type Modified double wedgeSection leading edge total angle, deg 10.01xmac, in 67.0ymac, in ( from root chord ) 6.2

Actuator rate l imit, deg / s 360.0Fixed surfaces ( aft )

Material Aluminum 2219-T81Modulus of elastici ty, 106 psi 10.5Planform area, ft2 ( 2 panels exposed ) 1.54Wetted area, ft2 ( 4 panels ) 6.17

Aspect ratio ( 2 panels exposed ) 2.59Taper ratio 0.0

Root chord, in 18.5Tip chord, in 0.0Span, in ( 2 panels exposed ) 24.0Leading edge sweep, deg 57.0



2/24/2008 ELF 296

g g p, gMean aerodynamic chord, in 12.3Thickness ratio 0.027

Section type Modified double wedgeSection leading edge total angle, deg 6.17xmac, in 131.6ymac, in ( from root chord ) 4.0

Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont ) References values

Reference area, ft2 0.349Reference length, ft 0.667

Pitch / Yaw Moment of inertia at launch, slug-ft2 117.0Pitch / Yaw Moment of inert ia at burnout, slug-ft2 94.0

Rocket Motor Performance ( altitude = 20k ft, temp = 70° F )

Burning time, sec ( boost / sustain ) 3.69 / 10.86

Maximum pressure, psi 2042

Average pressure, psi ( boost / sustain ) 1769 / 301

Average thrust, lbf ( boost / sustain ) 5750 / 1018

Total impulse, lbf-s ( boost / sustain ) 21217 / 11055

Specific impulse, lbf-s / lbm ( boost / sustain ) 250 / 230.4

PropellantWeight, lbm ( boost / sustain ) 84.8 / 48.2

Flame temperature @ 1 000 psi F 5282 / 5228



2/24/2008 ELF 297

Flame temperature @ 1,000 psi, °F 5282 / 5228

Propellant density, lbm / in3 0.065

Characteristic velocity, ft / s 5200

Burn rate @ 1000 psi, in / s 0.5

Burn rate pressure exponent 0.3

Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont ) Propellant ( continued )

Burn rate sensitivity with temperature, % / °F 0.10

Pressure sensitivity with temperature, % / °F 0.14Rocket Motor Case

Yield / ultimate strength, psi 170,000 / 190,000Material 4130 Steel

Modulus of elasticity, psi 29.5 x 106 psiLength, in 59.4Outside diameter, in 8.00Thickness, in (minimum) 0.074Burst pressure, psi 3140Volumetric efficiency 0.76

Grain configuration Three slots + web

Dome ellipse ratio 2.0Nozzle

Housing material 4130 Steel

Exit geometry Contoured ( equiv 15° )



2/24/2008 ELF 298

Exit geometry Contoured ( equiv. 15 )Throat area, in2 1.81Expansion ratio 6.2Length, in 4.9Exit diameter, in 3.78

Rocket Baseline Missile Has Boost-Sustain

Thrust - Time History

Rocket Baseline Missile Has Boost-Sustain

Thrust - Time History

2

4

6

8

Thrust – 1,000 lb

Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s

Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s



2/24/2008 ELF 299

Time – seconds0 4 8 12 16

0

Note: Alti tude = 20k ft, Temperature = 70° FTotal impu lse drives velocity change

Rocket Baseline Missile Aerodynamic

Characteristics


Characteristics

12

8m

a l F o r c e

~ C N

P i t c h i n g M o m e n t – C m

20

16

-16.0

-8.0

-12.0

0

-4.0

1.2

0.6

M

1.5

2.02.352.873.954.60

2.352.0

M = 1.2 and 1.5

4.600.6

3.95

SRef = 0.349 ft2, lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg



2/24/2008 ELF 300

4

00 4 8 12 16

α, Angle of Attack – Deg20

N o r m

24


Characteristics ( cont )


Characteristics ( cont )

0.4

1.2

0.8

C A a tα = 0 d e g

0.1

0

Power Off

Power On

0.2

0.3

C

Nδ a

tα

= 0 d e g

, P e r D e g

0.4

1.2

0.8

.002

0

.004

.006

K2

K1

C A = C Aα = 0 + K1 δ2 + K2 α δ

a tα

= 0

d e g ,

P e r D e g

K 1 ,

K 2 ~ P e r

D e g 2



2/24/2008 ELF 301

00 1 2 3 4

M, Mach Number 5

0 C mδ

0 1 2 3 4M, Mach Number

5

High Altitude Launch Enhances Rocket Baseline

Range

High Altitude Launch Enhances Rocket Baseline

Range

10

20

30

40

A l t i t u d e ~ 1 0 3 f t

Burnout

Boost /

Sustain

TerminationMach = 1.5

Coast

Vmax = 2147 ft / s

V = 1916 ft / s

Vmax = 2524 ft / s

ML = 0.7

CD AVG= 0.65

Constant Altitude Flight



2/24/2008 ELF 302

Range ~ nm0 5 10 15 20

025

Vmax 1916 ft / s

Low Altitude Launch and High Alpha Maneuvers

Enhance Rocket Baseline Turn Performance

Low Altitude Launch and High Alpha Maneuvers

Enhance Rocket Baseline Turn Performance

C r o s s R a n g e

1 , 0

0 0 f t .

25

20

15

10

5Termination at M = 1.0

Marks at 2 s intervals

Alt.

10k f t

10k f t

40k f t

40k ft

α

15°

10°

15°

10°

1

2

3

4

1

2

3

4



2/24/2008 ELF 303

0-10 -5 0 5 10

Down Range 1,000 ft.

40k f t 10°4

Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ).

Paredo Shows Range of Rocket Baseline Driven

by I SP , Propellant Weight, Drag, and Static Margin

Paredo Shows Range of Rocket Baseline Driven

by I SP , Propellant Weight, Drag, and Static Margin

-0.5

0

0.5

1

1.5

Isp Prop.

Weight

CD0 Drag-

Due-to-Lift

Static

Margin

Thrust Inert

Weight

Nondimensional

Range

Sensitivity to

Parameter

Note: Rocket baseline:

hL = 20k ft, ML = 0.7, MEC = 1.5

R@ ML = 0.7, hL = 20k ft = 9.5 nm

Example: 10% increase in propellantweight ⇒ 8.8% increase in f light range



2/24/2008 ELF 304

-1

Parameter

Boost - Sustain Trajectory Assumptions Boost - Sustain Trajectory Assumptions

Assumptions

1 degree of freedom Constant altitude

Simplif ied equation for axial acceleration based on thrust,drag, and weight nX = ( T – D ) / W

Missile weight varies with burn rate and time W = WL – WP t / tB

Drag is approximated by D = CDO

q S



2/24/2008 ELF 305

0

5

10

15

0 5 10 15 20 25

n x ,

A x i a l A c c e l e r a t i o n ,

Example of Rocket Baseline Axial Acceleration Example of Rocket Baseline Axial Acceleration

Note:

tf = 24.4 sML = 0.8hL = 20,000 ftTB = 5750 lbtB = 3.69 sTS = 1018 lb

tS = 10.86 sD = 99 lb at Mach 0.8D = 1020 lb at Mach 2.1WL = 500 lbWP = 133 lb

nX = ( T - D ) / W

Boost

Sustain

Coast



2/24/2008 ELF 306

-5

t, Time, s

0

1000

2000

3000

V ,

V e l o c i t y

, f t / s

Example of Rocket Baseline Missile Velocity vs

Time

Example of Rocket Baseline Missile Velocity vs

Time

Boost

Sustain

Coast

ΔV / ( gc ISP ) = - ( 1 - D AVG / T ) ln ( 1 - Wp / Wi ), During Boost-Sustain

V / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρ AVG SRef ( CD0) AVG VBO ]}}, During Coast

Note:

ML = 0.8hL = 20k feet



2/24/2008 ELF 307

0 5 10 15 20 25

t, Time, s

Range and Time-to-Target of Rocket Baseline

Missile Meet Requirements

Range and Time-to-Target of Rocket Baseline

Missile Meet Requirements

0

2

4

6

8

10

R ,

F l i g h t R a n

g e , n m

Boost

Sustain

Coast

(RF)Req = 6.7 nm @ t =24.4 s

R = Δ Rboost

+ Δ Rsustain

+ Δ Rcoast

Note:ML = 0.8

hL = 20k ft



2/24/2008 ELF 308

0 5 10 15 20 25

t, Time, s







Range robustness


Velocity control



2/24/2008 ELF 309



Example of Wing Sizing to Satisfy Required

Maneuver Acceleration

Example of Wing Sizing to Satisfy Required

Maneuver Acceleration Size Wing for the Assumptions

( nZ )Required = 30 g to counter 9 g maneuvering target )( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail

Rocket Baseline @Mach 220,000 ft altitude367 lb weight ( burnout )

From Prior Example, ComputeαWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline

α = 0.75δ, αBody = αTail = 9.4 deg

Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( f rom body )

Δ ( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail )

Video of Intercept of Maneuvering Target



2/24/2008 ELF 310

Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g

( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef / SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft2

Note: ( SW )RocketBaseline = 2.55 ft2

Wing Sizing to Satisfy Required Turn Rate Wing Sizing to Satisfy Required Turn Rate Assume

( γ.)Required > 18 deg / s to counter 18 deg / s maneuvering aircraft

Rocket Baseline @

Mach 2

20,000 ft altitude

367 lb weight ( burnout )

γi = 0 deg

Compute

γ.= gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ]

α / δ = 0.75

α’ = α + δ = 22 deg ⇒ δ = 12.6 deg, α = 9.4 deg

γ.= [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31

rad / s or 18 deg / s

Note: ( S ) 18 deg / s Turn Rate



2/24/2008 ELF 311

Note: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate

Wing Sizing to Satisfy Required Turn Radius Wing Sizing to Satisfy Required Turn Radius Assume Maneuvering Aircraft Target with

γ.= 18 deg / s = 0.314 rad / s

V = 1000 ft / s

( RT )Target = V / γ.= 1000 / 0.314 = 3183 ft

Assume Rocket Baseline @

Mach 2

20,000 ft altitude 367 lb weight ( burnout )

Compute γ.

= 18 deg / s ( prior f igure )

( RT )RocketBaselinet = V / γ.= 2074 / 0.314 = 6602 ft

Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Counter-measured by Target in a Tight Turn

Counter-Countermeasure Alternatives Larger Wing



2/24/2008 ELF 312

g g

Higher Angle of Attack

Longer Burn Motor with TVC







Range robustness


Velocity control



2/24/2008 ELF 313



Combined Weight / Miss Distance Drivers: Nozzle

Expansion and Motor Volumetric Efficiency

Combined Weight / Miss Distance Drivers: Nozzle

Expansion and Motor Volumetric Efficiency

Fixed surface number of panels 4 3 +0.054 +0.100Movable surface number of panels 4 2 +0.071 +0.106Design static margin at launch 0.40 0.30 +0.095 +0.167Wing movable surface sweep ( deg ) 45.0 49.5 -0.205 +0.015Tail fixed surface sweep ( deg ) 57.0 60.0 +0.027 +0.039Wing movable surface thickness ratio 0.044 0.034 +0.041 +0.005

Nose fineness ratio 2.4 2.6 -0.016 -0.745Rocket chamber sustain pressure ( psi ) 301 330 -0.076 -0.045Boattail fineness ratio ( length / diameter ) 0.38 0.342 +0.096 +0.140Nozzle expansion ratio 6.2 6.82 -0.114 -0.181Motor volumetric efficiency 0.76 0.84 -0.136 -0.453Propellant density ( lb / in3 ) 0.065 0.084 -0.062 +0.012

Boost thrust ( lb ) 5,750 6,325 +0.014 -0.018Sustain thrust ( lb ) 1,018 1,119 +0.088 +0.246Characteristic velocity ( ft / s ) 5,200 5,720 -0.063 -0.077Wing location ( percent total length ) 47.5 42.75 +0.181 -0.036

Parameter Baseline W* σ*SensitivityVariation

Note: Strong impact with synergyB li W i ht 500 lb Mi di t 62 3 ft



2/24/2008 ELF 314

Note: Strong impact with synergy

Strong impact

Moderate impact with synergy

Moderate impact

Baseline: Weight = 500 lb, Miss distance = 62.3 ft

W* = weight sensitivity for parameter variation = ΔW / Wσ* = miss distance sensitiv ity for parameter variation = Δ σ / σ

A Harmonized Missile Can Have Smaller Miss

Distance and Lighter Weight

A Harmonized Missile Can Have Smaller Miss

Distance and Lighter Weight

Judicious changes

Boost thrust ( lb ) 5,750 3,382 3,382 3,382Wing location ( percent missile length to 1/4 mac ) 47.5 47 44 46Wing taper ratio 0.18 0.2 0.2 0.2Nose fineness ratio 2.4 3.2 2.55 2.6Nose blunting ratio 0.0 0.05 0.05 0.05Nozzle expansion ratio 6.2 15 15 15Sustain chamber pressure ( psi ) 301 1,000 1,000 1,000Boattail fineness ratio 0.38 0.21 0.21 0.21

Tail leading edge sweep ( deg ) 57 50 50 50Technology limited changes

No. wing panels 4 2 2 2No. tail panels 4 3 3 3Wing thickness ratio 0.044 0.030 0.030 0.030Wing leading edge sweep ( deg ) 45 55 55 55Static margin at launch ( diam ) 0.4 0.0 0.0 0.0

Propellant density ( lb / in3

) 0.065 0.084 0.084 0.084Motor volumetric efficiency 0.76 0.84 0.84 0.84

Measures of MeritTotal weight ( lb ) 500 385.9 395.0 390.1Miss distance ( ft ) 62.3 63.1 16.2 16.6Time to target ( s ) 21.6 23.8 23.6 23.8

Parameter Baseline Value Weight Miss Distance Harmonized

Missile Configured for Minimum:



2/24/2008 ELF 315

g ( )Length ( in ) 144 112.7 114.7 114.9Mach No. at burnout 2.20 2.08 2.09 2.07Weight of propellant ( lb ) 133 78.3 85.4 85.9Wing area ( in2 ) 368.6 175.5 150.7 173.8Tail area ( in2 ) 221.8 109.1 134.5 112.0

*Note: Value of driving parameter

Baseline Missile vs Harmonized Missile Baseline Missile vs Harmonized Missile

144”

57°45°

Propellant Density( lb / in3 );

0.0650.084

50°55°

NoseFineness;

2.42.6

Surfaces; {4 wings / 4 tails

2 wings / 3 tailsWeight ( lb ); 500

390



2/24/2008 ELF 316

50°55°

115”







Range robustness


Velocity control




2/24/2008 ELF 317



Lofted Glide Trajectory Provides Extended Range Lofted Glide Trajectory Provides Extended Range

Using Rocket Baseline, Compare

Lofted Launch-Coast-Glide Trajectory

Lofted Launch-Ballis tic Trajectory Constant Altitude Trajectory

Assume for Lofted Launch-Coast-Glide Trajectory:

γi = 45 deg

γ = 45 deg dur ing boost and sustain

γ = 45 deg coast

Switch to ( L / D )max glide at optimum altitude

( L / D )maxg glide trajectory after apogee

hi = hf = 0 ft

Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 degΔV = - gc ISP [ 1 – ( D AVG / T ) - ( W AVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 /

5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / s

ΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ft



2/24/2008 ELF 318

ΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ft

ΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 ft

h = h i + ΔRy = 0 + 1700 = 1,700 ft

Lofted Glide Trajectory Provides Extended

Range ( cont )


Range ( cont ) Velocity, Horizontal Range, and Alti tude During Sustain @ γ = 45 deg

ΔV = - gc ISP [ 1 – ( D AVG / T ) – ( W AVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 /1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / sec

VBO = 1303 + 81 = 1,384 ft / s

ΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ft

ΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ft

ΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 ft

h = h i + ΔRy = 1700 + 10315 = 12,015 ft Velocity, Horizontal Range, and Alti tude During Coast @ γ = 45 deg to h@( L / D )max

Vcoast = Vi { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t } = 1384 { 1 –

[( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))}21 } = 674 ft / s

Rcoast = { 2 W / [ gc ρ AVG SRef ( CD0) AVG )]} ln { 1 – [ gc

2 ρ AVG SRef ( CD0) AVG / ( 2 W )] [ s in γ ] t2 +

{[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln

{ 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 )( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft



2/24/2008 ELF 319

( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft

Lofted Glide Trajectory Provides Extended Range

( cont )

Lofted Glide Trajectory Provides Extended Range

( cont )

Flight Conditions At End-of-Coast Are:

t = 35 s

V = 674 ft / s

h = 24,189 ft

q = 251 psf

M = 0.66

( L / D )max = 5.22 α( L / D )max

= 5.5 deg

Initiate α = α( L / D )max= 5.5 deg at h = 24,189 ft

Incremental Horizontal Range During ( L / D )max Glide Is

ΔRx

= ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ft

Total Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is

Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 =150406 ft = 24.8 nm



2/24/2008 ELF 320


Range ( cont )


Range ( cont )

0

10

20

30

0 10 20 30

R Range nm

h ,

A l t i t u d e ,

k f t

S u s t a i n

B a l l i s

t i c

®z

²

B a l l i s

t i c

G l i d e @ ( L / D ) m a x

z ÄCo-altitude

Note: Rocket Baseline

z End of boost

End of sustain

ÈLof ted ball istic apogee, t = 35 s, V = 667 ft / s, h = 21,590 ft

ÊLof ted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft

®Lofted ballistic impact, t = 68 s, γ = - 71 deg, V = 1368 ft / s

²Lofted glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s

Ä Co-alti tude fl ight impact, t = 115 s, V = 500 ft / s

ÈØ

C o a s t @

γ =

4 5

d e g



2/24/2008 ELF 321

R, Range, nm







Range robustness


Velocity control




2/24/2008 ELF 322

p p g g


Ramjet Baseline Is a Chin Inlet Integral Rocket

Ramjet ( IRR )

Ramjet Baseline Is a Chin Inlet Integral Rocket

Ramjet ( IRR )

Sta 0.

Guidance WarheadRamjet Fuel Boost Propellant

Booster, andRamjet Engine

Boost Nozzle

Tail Cone Af t-bodyMid-bodyPayload BayForebody

23.5 43.5 76.5 126.0

159.0 171.0

Sta 150.311.6

11.5

16.5

37°

Note: Dimensions are in inches

ChinInlet Transport A ir Duct

20.375 dia

Nose



2/24/2008 ELF 323

Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis” , Vol. II, Air -breathingSynthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.

Component Weight, lb CG Sta, in

Nose 15.9 15.7

Forebody Structure 42.4 33.5Guidance 129.0 33.5

Payload Bay Structure 64.5 60.0Warhead 510.0 60.0

Midbody Structure 95.2 101.2Inlet 103.0 80.0Electrical 30.0 112.0Hydraulic System for Control Actuation 20.0 121.0

Fuel Distribution 5.0 121.0 Af tbody Structure 44.5 142.5

Engine 33.5 142.5

Tailcone Structure 31.6 165.0Ramjet Nozzle 31.0 165.0Flight Control Actuators 37.0 164.0

Fins ( 4 ) 70.0 157.2End of Cruise 1,262.6 81.8

Ramjet Fuel ( 11900 in3 ) 476.0 87.0

Start of Cruise 1,738.6 83.2Boost Nozzle ( Ejected ) 31.0 164.0

Mass Properties of Ramjet Baseline Missile Mass Properties of Ramjet Baseline Missile



2/24/2008 ELF 324

Frangible Port 11.5 126.0

End of Boost 1,781.1 84.9

Boost Propellant 449.0 142.5

Booster Ignition 2,230.1 96.5

Ramjet Baseline Missile Definition Ramjet Baseline Missile Definition

InletType Mixed compression

Material TitaniumConical forebody half angle, deg 17.7Ramp wedge angle, deg 8.36Cowl angle, deg 8.24Internal contraction ratio 12.2 PercentCapture area, ft2 0.79

Throat area, ft

2

0.29BodyDome Material Silicon nitride

Airframe Material TitaniumCombustor Material Insulated InconelLength, in 171.0

Diameter, in 20.375Fineness ratio 8.39Volume, ft3 28.33Wetted area, ft2 68.81Base area, ft2 ( cruise ) 0.58Boattail fineness ratio N/A



2/24/2008 ELF 325

Nose half angle, deg 17.7Nose length, in 23.5

Ramjet Baseline Missile Definition ( cont ) Ramjet Baseline Missile Definition ( cont )

Tail ( Exposed )Material Titanium

Planform area ( 2 panels ), ft2

2.24Wetted area ( 4 panels ), ft2 8.96

Aspect ratio ( 2 panels exposed ) 1.64

Taper ratio 0.70

Root chord, in 16.5

Span, in. ( 2 panels exposed ) 23.0Leading edge sweep, deg 37.0

Mean aerodynamic chord, in 14.2

Thickness ratio 0.04

Section type Modified double wedge

Section leading edge total angle, deg 9.1xmac, in 150.3

ymac, in ( from root chord ) 5.4

Reference valuesReference area ft2 2 264



2/24/2008 ELF 326

Reference area, ft2 2.264

Reference length, ft 1.698

0 1 2 3 4 5 6Subscripts0 Free stream f low into inlet ( Example, Ramjet Basel ine at Mach 4, α = 0 deg ⇒ A0 = 104 in2. Note: AC = 114 in2 )1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )4 Combustor exit ( Ramjet Baseline A = 287 1 in2 )

Ac = Inlet capture area

SRef = Reference area

Engine Nomenclature and Flowpath Geometry for

Ramjet Baseline

Engine Nomenclature and Flowpath Geometry for

Ramjet Baseline

Ramjet Engine Station Identification

( CD0)Nose Corrected = ( CD0

)Nose Uncorrected x ( 1 - Ac / SREF )

120°

Ac = 114 in2

20.375 in

SRef



2/24/2008 ELF 327

4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )

5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )6 Nozzle exit ( Ramjet Baseline A6 = 233.6 in2 )Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )

N o r m

a l F o r c e C o e f f i c

i e n t , C N

α, Angle of Attack ~ deg

0 4 8 12 16

Mach1.21.52.0

3.04.0

.40

.30

.20

.10

0

A x i a l F o r c e C o e f f i c i e n t , C A

0 4 8 12 16

Mach1.2

1.5

2.0

3.0

4.0

SRef = 2.264 ft2

lRef = dRef = 1.698 ftXcg @ Sta 82.5 in

δ = 0 deg

4.0

3.0

2.0

1.0

0

α, Angle of Attack ~ deg

Aerodynamic Characteristics of Ramjet Baseline Aerodynamic Characteristics of Ramjet Baseline



2/24/2008 ELF 328

Source: Reference 27, based on year 1974 computer program from Reference 32.

+ .4

0

-.4

-.8

-1.2

-1.6

Aerodynamic Characteristics of Ramjet Baseline

( cont )


( cont )

P i t c h i n g M o m e n t C o e f f i c i e n t , C m

α, Angle of Attack ~ deg0 4 8 12 16

Mach4.0

3.0

2.0

1.5

1.2

SRef = 2.264 ft2

lRef

= dRef

= 1.698 ftXcg @ Sta 82.5 inδ = 0 deg



2/24/2008 ELF 329

, g g

Source: Reference 27, based on year 1974 computer program from Reference 32.


( cont )


( cont )

.4

.3

.2

.1

0

C D 0

M, Mach Number

0 1 2 3 4

C N

δ ~ p e r d

e g

C m

δ ~ p e r d e g

.10

.05

SRef = 2.264 ft2

lRef = dRef = 1.698 ftXcg @ Sta 82.5 inδ= 0 deg

α = 0 deg.-.4

0

-.2

Source: Reference 27 based on year 1974 computer program from



2/24/2008 ELF 330

0 1 2 3 40M, Mach Number

Source: Reference 27, based on year 1974 computer program from

Reference 32.

100

1000

10000

100000

0 1 2 3 4

T m a x ,

M a x

T h r u s t , l b

h = Sea Level

h = 20k ft

h = 40k fth = 60k ft

h = 80k ft

Thrust Modeling of Ramjet Baseline Thrust Modeling of Ramjet Baseline

Note:

Standard atmosphere

T = Tmax ϕ

φ = 1 if stochiometric ( f / a = 0.0667 )

α = 0 deg

Example: M = 3.5, h = 60k ft, ϕ= 1 ⇒ Max Thrust = 1,750 lb



2/24/2008 ELF 331

M, Mach Number

Figure based on Reference 27 predict ion

Specific Impulse Modeling of Ramjet Baseline Specific Impulse Modeling of Ramjet Baseline

•

•

•

•

•

•

•

••

•

I S P ,

S p e c i f i c I m

p u l s e , s

1,500

1,000

500

00 1 2 3 4

Note:

Standard atmosphere

ϕ ≤ 1

ISP based on Reference 27 computer prediction.

Example: M = 3.5 ⇒ ISP = 1,120 s



2/24/2008 ELF 332

M, Mach Number

Rocket Booster Acceleration / Performance of

Ramjet Baseline

Rocket Booster Acceleration / Performance of

Ramjet Baseline 30

20

10

0

0 1.0 2.0 3.0 4.0

B o o s t T h r u s t ~ 1 0 0 0 l b

Time ~ s5.0 6.0

( ISP )Booster = 250 s

3.0

2.5

2 0B u r n o u t M a c h N u m b e r

2.0

1.0

0

Standard atmosphere

ML = 0.80Constant altitude flyout

B o o s t R a n g e

~ n m

0 20 40 60



2/24/2008 ELF 333

2.0 B

h, Altitude 1,000 ft

0 20 40 600 20 40 60 80h, Altitude 1,000 ft

Ramjet Baseline Has Best Performance at High

Altitude

Ramjet Baseline Has Best Performance at High

Altitude

500

400

300

200

100

00 1 2 3 4

R a n g e ~

n m

M, Mach Number

h = SL

20,000 ft

40,000 ft

60,000 ft

Note: ML = 0.8, Constant Al titude Fly-out



2/24/2008 ELF 334

,

Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Predict ion is R = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )] = 2901 ( 1040 )( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missi le data.

L , y

From Paredo Sensitivity, Ramjet Baseline Range

Driven by I SP , Fuel Weight, Thrust, and C D 0

From Paredo Sensitivity, Ramjet Baseline Range

Driven by I SP , Fuel Weight, Thrust, and C D 0

-1

-0.5

0

0.5

1

1.5

ISP Fuel

Weight

Thrust CD0, Zero-

Lift Drag

Coefficient

CLA, Lift-

Curve-

Slope

Coefficient

Inert

Weight

Parameter

N o

n d i m e n s i o n a l R

a n g e S e n s i t i v i t y

t o P a r

a m e t e r

Sea Level Flyout at Mach 2.3 20k ft Flyout at Mach 2.5

Example: At Mach 3.0 / 60k f t alti tude

cruise, 10% increase in fuel weight⇒ 9.6% increase in fl ight range



2/24/2008 ELF 335

40k ft Flyout at Mach 2.8 60k ft Flyout at Mach 3.0

Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σRamjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σ

Parameter Baseline Value at Mach 3.0 / 60k ft Uncertainty in Parameter ΔR / R from Uncertain ty

1. Specific Impulse 1040 s +/- 5%, 1σ +/- 5%, 1σ

2. Ramjet Fuel Weight 476 lb +/- 1%, 1σ +/- 0.9%, 1σ

3. Cruise Thrust ( φ = 0.39 ) 458 lb +/- 5%, 1σ +/- 2%, 1σ

4. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1σ +/- 4%, 1σ

5. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1σ +/- 1%, 1σ

6. inert Weight 1205 lb +/- 2%, 1σ +/- 0.8%, 1σ

Level of Maturi ty Based on Flight Demo of Prototype, Subsystem Tests, and Integration

Wind tunnel tests

Direct connect, freejet, and booster firing propulsion tests

Structure test

Mock-up

Hardware-in-loop simulation

Flight Test

Total Flight Range Uncertainty at Mach 3.0 / 60k ft Flyout



2/24/2008 ELF 336

g g y y

ΔR / R = [ (ΔR / R )12 + (ΔR / R )2

2 + (ΔR / R )32 + (ΔR / R )4

2 + (ΔR / R )52 + (ΔR / R )6

2 ]1/2 = +/- 6.9%, 1σ

R = 445 nm +/- 31 nm, 1σ

Sizing Examples Sizing Examples

Rocket Baseline Missile






Range robustness


Velocity control




2/24/2008 ELF 337


Slurry Fuel and Efficient Packaging Provide

Extended Range Ramjet

Slurry Fuel and Efficient Packaging Provide

Extended Range Ramjet Propuls ion / Configuration Fuel Type / Volumetric

Performance (BTU / in3) /Density (lb / in3)

Fuel Volume (in3) /Fuel Weight (lb)

ISP (s) / CruiseRange at Mach 3.5,60k ft (nm)

Liquid Fuel Ramjet RJ-5 / 581 / 0.040 11900 / 476 1120 / 390

Ducted Rocket ( Low Smoke ) Solid Hydrocarbon / 1132 /0.075

7922 / 594 677 / 294

Ducted Rocket ( HighPerformance )

Boron / 2040 / 0.082 7922 / 649 769 / 366

Solid Fuel Ramjet Boron / 2040 / 0.082 7056 / 579 1170 / 496

Slurry Fuel Ramjet 40% JP-10, 60% boroncarbide / 1191 / 0.050

11900 / 595 1835 / 770



2/24/2008 ELF 338

Note: Flow Path Available Fuel Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]








Range robustness


Velocity control




2/24/2008 ELF 339

Soda Straw Rocket, Design, Build, and Fly

Example of Ramjet Velocity Control Through Fuel

Control

Example of Ramjet Velocity Control Through Fuel

Control

0.1

1

10

0 1 2 3 4

Mi, Impact Mach Number at Sea Level

Ramjet BaselineEquivalence Ratio

Ramjet Baseline Fuel

Flow Rate, lb / s

T

W

D

N t R j t b li ti l i t t l l t d t t l i t t i t T th t W i ht D d


Mi = 4, h = sea level, T0 = 519R

T + W - D = 0

W = WBO = 1263 lb

D = CD0q SRef = 3353 CD0

MI2 = 3353 ( 0.14 )

( 4 )2 = 7511 lb

Trequired = D - W = 7511 - 1263 = 6248 lb

wf

.= T / ISP = 6248 / 1000 = 6.25 lb / s

φ = Trequired / Tφ = 1 = 6248 / 25000 = 0.25

Note: Excess air provides cooling of combustor



2/24/2008 ELF 340

Note: Ramjet baseline, vertical impact at sea level, steady state veloci ty at impact, T = thrust, W = weight, D = drag,WBO = burnout weight, CD0

= zero-lift drag coefficient, Mi= impact Mach number, Trequired = required thrust for steadystate flight, w f

.= fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric )







Ramjet Baseline Missi le

Range robustness


Surface impact velocity


S d St R k t D i B ild d Fl



2/24/2008 ELF 341


Computer Sizing Code Should Have Fast

Turnaround and Be Easy to Use

Computer Sizing Code Should Have Fast

Turnaround and Be Easy to Use Objective of Conceptual Design

Search Broad Solution Space

Iterate to Design Convergence

Characteristics of Good Conceptual Design Sizing Code Fast Turnaround Time

Easy to Use Directly Connect Predictions of Aeromechanics and Physical

Parameters to Trajectory Code

Simple, Physics Based Methods

Includes Most Important, Driving Parameters Provides Insight into Relationships of Design Parameters

Stable Computation

Imbedded Baseline Missile Data



2/24/2008 ELF 342

Human Designer Makes the Creative Decisions

Example of DO -Based Conceptual Sizing

Computer Code –ADAM

Example of DO -Based Conceptual Sizing

Computer Code –ADAM Conceptual Sizing Computer Program

Advanced Design of Aerodynamic Missiles ( ADAM )

PC compatible Written in DOS

Aerodynamic Module Based on NACA 1307 Calculates Static and dynamic stability derivatives

Control effectiveness and trim conditions 3, 4, 5, and 6-DOF Simulation Modules

Proportional guidance

Input provided automatically by aerodynamic module

Configurations Benchmarked with Wind Tunnel Data Greater than 50 Input Parameters Available

Defaults to benchmark configuration ( s )



2/24/2008 ELF 343

Example of Spreadsheet Based Conceptual

Sizing Computer Code - TMD Spreadsheet


Sizing Computer Code - TMD Spreadsheet

Conceptual Sizing Computer Code Tactical Missile Design ( TMD ) Spreadsheet

PC compatible

Windows Excel spreadsheet

Based on Tactical Missile Design Short Course and Textbook Aerodynamics

Propulsion

Weight

Flight trajectory Measures of merit



2/24/2008 ELF 344


Sizing Computer Code, TMD Spreadsheet


Sizing Computer Code, TMD Spreadsheet Define Mission Requirements [ Flight Performance ( RMax, RMin, V AVG ) , MOM, Const raints ]

Establish Baseline ( Rocket , Ramjet )

Aerodynamics Input ( d, l, lN, A, c, t, xcg ) Aerodynamics Output [ CD0

, CN, xac, Cmδ, L / D, ST ]

Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf , ϕ, T4, Inlet Type )Propulsion Output [ Isp, Tcruise, p t2

/ p t0, w

., Tboost, Tsustain, ΔV

Boost]

Weight Input ( WL, WP, ρ, σmax )Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ]

Trajectory Input ( h i, Vi, Type ( cruise, boost , coast, ballistic, turn, glide )

Trajectory Output ( R, h, V, and γ versus time )

MeetPerformance?


No [ pBlast, PK, nHit,

Vfragments PKEKE

No [ RMax, RMin, V AVG ]

Yes

Al t Mission

Al t Baseline

Resize / Alt Config /Subsystems / Tech



2/24/2008 ELF 345

Measures of Merit and Constraints V g , P ,KEWarhead, τTotal,σHE, σMAN, Rdetect,

CSDD, C1000th, Cunit x ]Yes

Example of TMD Spreadsheet Sizing Code

Verification: Air-to-Air Range Requirement

Example of TMD Spreadsheet Sizing Code

Verification: Air-to-Air Range Requirement Example Launch Conditions

hL = 20k f t

ML = 0.8 Example Requirement

RF = 6.7 nm with tf < 24.4 s

Solutions for Rocket Baseline

ADAM: RF = 6.7 nm at t f = 18 s TMD Spreadsheet: RF = 6.7 nm at t f = 19 s

3 DOF using wind tunnel aero data: RF = 6.7 nm at t f = 21 s

Differences in Flight Time to 6.7 nm Most ly Due to Zero-Lift Drag Coefficient.For Example: ADAM prediction at Mach 2.0: ( CD0

)coast = 0.53

TMD Spreadsheet prediction at Mach 2.0: ( CD0)coast = 0.57

Wind tunnel aero data at Mach 2.0: ( CD0)coast = 1.05

Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce

Uncertainty in CD0



2/24/2008 ELF 346

Uncertainty in CD0







Ramjet Baseline Missi le

Range robustness


Surface impact velocity


Soda Straw Rocket Design Build and Fly



2/24/2008 ELF 347


Example of Design, Build, and Fly Customer

Requirements


Requirements Objective – Design, Build, and Fly Soda Straw Rocket with:

Flight Range Greater Than 90 ft

Weight Less Than 2 g

Furnished Property

Launch System

Distance Measuring Wheel

Weight Scale Micrometer Scale

Engineer’s Scale

Scissors

Furnished Material 1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g

1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g

1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g

1 “Super Jumbo” Soda Straw: 0 25 in Diameter by 7 75 in Length



2/24/2008 ELF 348

1 Super Jumbo Soda Straw: 0.25 in Diameter by 7.75 in Length


Requirements ( cont )


Requirements ( cont )

Furnished Property Launch System with Specified Launch Conditions

Launch Tube Diameter: 0.25 in

Launch Tube Length ( e.g., 6 in )

Launch Pressure ( e.g., 30 psi )

Launch Elevation Angle ( e.g., 40 deg )

Predict Flight Trajectory Range and Compare with Test



2/24/2008 ELF 349

Soda Straw Rocket Launcher and Targeting Soda Straw Rocket Launcher and Targeting

9. Rocket on Launcher

8. Launch Tube

7. Incl inometer

6b. Manual ValveLauncher ( 0.1 saverage response )

6a. Solenoid ValveLauncher ( 0.025 saverage response )

5. Launch Switch

4. Pressure Gauge

3. Air Hose

2. Pressure Tank

1. Pump

11. Rockets wi th Various Length, Tail Geometry, Nose Geometry, and Other Surfaces



2/24/2008 ELF 350

g , y, y,

10. Laser Pointer Targeting Device

It Is Easy to Make a Soda Straw Rocket It Is Easy to Make a Soda Straw Rocket

1. Cut Large Diameter “ Giant” Soda Straw to DesiredLength

3. Slide Ear Plug Inside Soda Straw

5. Apply Adhesive Tabs to Soda Straw

4. Cut Adhesive Tabs to Desired Height and Width of Surfaces

7. Slide Giant Soda Straw Rocket Over Smaller

Diameter “Super Jumbo” Soda Straw Launch Tube

2. Twist and Squeeze Ear Plug to Fit Inside SodaStraw

6. Wrap Front of Ear Plug and Straw with Tape



2/24/2008 ELF 351

Soda Straw Rocket Baseline Configuration Soda Straw Rocket Baseline Configuration

llcc = 6.0 in= 6.0 in

l = 7.0 inl = 7.0 in

Ear Plug Soda Straw Strip Tabbing

0.28 in0.25 in

0.5 in



2/24/2008 ELF 352

Soda Straw Rocket Baseline Weight and Balance Soda Straw Rocket Baseline Weight and Balance

Component Weight, g cg Station, inNose ( Plug ) 0.6 0.5

Body ( Soda Straw ) 0.5 3.5

Fins ( Four ) 0.5 6.75

Total 1.6 3.39



2/24/2008 ELF 353

Soda Straw Rocket Baseline Definition Soda Straw Rocket Baseline Definition

Body

Material Type HDPE Plastic

Material density, lb / in3 0.043

Material strength, psi 4,600Thickness, in 0.004

Length, in 7.0

Diameter, in 0.28

Fineness ratio 25.0

Nose fineness ratio 0.5Fins

Material Plastic

Planform area, in2 ( 2 panels exposed ) 0.25

Wetted area, in2 ( 4 panels ) 1.00

Aspect ratio ( 2 panels exposed ) 1.00Taper ratio 1.0

Chord, in 0.5

Span ( exposed ), in 0.5

Span ( total including body ), in 0.78

Leading edge sweep, deg 0

xmac, in 6.625



2/24/2008 ELF 354

Soda Straw Rocket Baseline Definition ( cont ) Soda Straw Rocket Baseline Definition ( cont )

Nose

Material Type Foam

Material densi ty, lb / in3 0.012 Average diameter 0.39 in

Length 0.90 in

Reference Values

Reference area, in2 0.0616

Reference length, in 0.28

Thrust Performance

Inside cavity length, in 6.0

Typical Pressure, psi 30

Maximum thrust @ 30 psi pressure, lb 1.47

Time constant, s ( standard temperature ) 0.025



2/24/2008 ELF 355

For body-tail geometry, static margin given by

( x AC – xCG ) / d = - {( CN α )B {[ xCG – ( x AC )B ] / d } + ( CNα )T {[ xCG – ( x AC )T ] / d }( ST /SRef )} / [( CNα )B + ( CNα )T ST / SRef ]

For baseline soda straw configurationxCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in2, SRef = 0.0616 in2

( x AC )B = [( x AC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in

( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57( x AC )T = 6.5 + 0.25 ( cmac )T = 6.63

Substituting( x AC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [ ( 0.25 ) /

0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable )

x AC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose

Soda Straw Rocket Baseline Static Margin Soda Straw Rocket Baseline Static Margin

(( xx AC )Tl

( x AC ) B

x x AC AC

x x CG CG

d



2/24/2008 ELF 356

Soda Straw Rocket Has High Acceleration Boost

Performance

Soda Straw Rocket Has High Acceleration Boost

Performance

0

20

40

60

80

100

0 2 4 6 8 10

s, Distance Traveled During Launch, Inches

V ,

V e l o

c i t y ,

f p s

pgauge = 15 psi pgauge = 30 psi

pgauge = 60 psi

T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A

a ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dtThrust ( T ) from Pressur ized Tube of Area A

T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A

A = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time

Example: Assume pgauge = 30 psi , lt = 6 in, τ = 0.025 s ( Averagefor Solenoid Valve ), s = lc = 6 in

Thrust Equation Is:

T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t )

Note: Ac tual Boost Thrust Lower ( Pressure Loss,

Boundary Layer, Launch Tube Leakage, LaunchTube Friction )

Equations for Acceleration ( a ), Velocity ( V ), andDistance ( s ) During Boost Are:

a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352= 13471.1 ( 1 - e – 40.00 t )

V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78

s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t +8.419

End of Boost Conditions Are:

s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 s

a = 7123 ft / s2 = 221 g

V = 75.2 ft / sq = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psf

Note: Time TicsEvery 0.01 s



2/24/2008 ELF 357

M = V / c = 75.2 / 1116 = 0.0674

Most of the Soda Straw Rocket Drag Coefficient

Is from Body Skin Friction

Most of the Soda Straw Rocket Drag Coefficient

Is from Body Skin Friction

0

0.5

1

1.5

0 2 4 6 8 10

ST / SRef, Tail Planform Area / Reference Area

C D 0 ,

Z e r o - L i f t D r

a g C o e f f i c i e n t

V = 40 fps V = 80 fps

Example: V = 75.2 fps, ST = 0.00174 ft2, SRef =0.000428 ft2 ⇒ ST / SRef = 4.07

Compute:CD0

= 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 +0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]} 0.2 }[ 2

( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86Note:• Above Drag Coefficient Not Exact• Based on Assumption of Turbulent Boundary

Layer • Soda Straw Rocket Small Size and Low Velocity ⇒

Laminar Boundary Layer ⇒ Large Boundary Layer Thickness on Aft Body at Tails

Compute Drag Force:Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) =

0.00247 lbCompare Drag Force to Weight:Dmax / W = 0.00247 / 0.00352 = 0.70

Note: Drag Force Smaller Than Weight

CD0= ( CD0

)Body,Friction + ( CD0)Base,Coast + ( CD0

)Tail,Friction

= 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )



2/24/2008 ELF 358

0

10

20

30

40

0 20 40 60 80 100

Rx, Horizontal Range, ft

h - h i , H e i g h t a b o v e I n i

t i a l L a u n c h

H e i g h t , f t

Gamma = 10 Deg Gamma = 30 Deg Gamma = 50 Deg

Soda Straw Rocket Baseline Has a Ballistic Flight

Range Greater Than 90 Feet

Soda Straw Rocket Baseline Has a Ballistic Flight

Range Greater Than 90 Feet Rx = { 2 W cos γi / [ gc ρ SRef CD0

]} ln { 1 + t / { 2W / [ gc ρ SRef CD0

Vi ]}}

h = { 2 W sin γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2

W / [ gc ρ SRef CD0 Vi ]}} + h i - gc t2

/ 2

Note: Time Ticsevery 0.5 s

Example, Assume l t = 6 in, pgauge = 30 psi , γi= 30 deg, τ = 0.025 sec, Soda StrawBaseline, t = t impact = 1.8 s

Horizontal Range At Impact = Rx = { 2 (0.00352 ) cos γi / [ 32.2 ( 0.002378 ) (0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 (0.00352 ) / [ 32.2 ( 0.002378 ) (0.000428 ) ( 0.86 ) ( 75.2 )]}}

= 249.8 cos γi ln ( 1 + 0.301 t )

= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] =93.7 ft

Height At Impact = h = { 2 ( 0.00352 )sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) (0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2)]}} + h i – 32.2 t2 / 2

= 249.8 sin γi ln ( 1 + 0.301 t ) + hi –32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 (

1.8 )] + h i – 32.2 ( 1.2 )2

/ 2= h + 1 9 ft



2/24/2008 ELF 359

= h i + 1.9 ft

Soda Straw Rocket Range Driven by Inside

Chamber Length and Launch Angle

Soda Straw Rocket Range Driven by Inside

Chamber Length and Launch Angle

-0.2

0

0.2

0.4

0.6

0.8

lc Gamma pgauge W tau CD0

NondimensionalRange

Sensitivity to

Parameter

Note: Decreased chamber length ⇒shorter duration thrust ( decreasedtotal impulse ) ⇒ decreased end-of-boost velocity

Soda Straw Rocket Baseline:

W = Weight = 0.00423 lb

lc = inside chamber length = 6 in

τ = Time constant to open solenoidvalve = 0.025 s

pgauge = gauge pressure = 30 psi

γi = Initial / launch angle angle = 30 deg

l t = 7 inV = Launch veloci ty = 75.2 fps

CD0= Zero-lift drag coefficient = 0.86

t impact = Time from launch to impact =1.8 s

Rx = Horizontal range = 94 ft

Example: 10% decrease in

inside chamber length ⇒7.7% decrease in range at t =1.8 s. Note: Result isnonlinear because insidechamber length = launcher length. Increase in lc alsoleads to decrease in range.



2/24/2008 ELF 360

Soda Straw Rocket Baseline Flight Range

Uncertainty Is +/- 2.4%, 1 σ

Soda Straw Rocket Baseline Flight Range

Uncertainty Is +/- 2.4%, 1 σ

Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based on

Wind tunnel test

Thrust static test

Weight measurement

Prediction methods

Total Flight Range Uncertainty for 30 psi launch at 30 deg

ΔR / R = [ (ΔR / R )1

2 + (ΔR / R )2

2 + (ΔR / R )3

2 + (ΔR / R )4

2 + (ΔR / R )5

2 + (ΔR / R )6

2 ]1/2 = +/- 2.4%, 1σ

R = 94 ft +/- 2.3 ft, 1σ

+/- 0.2%, 1σ+/- 20%, 1σ0.866. Zero-Lift Drag Coefficient

+/- 0.2%, 1σ+/- 20%, 1σ0.025 s5. Solenoid Time Constant

+/- 0.4%, 1σ+/- 6%, 1σ1.6 g4. Weight

+/- 0.5%, 1σ+/- 3%, 1σ30 psi3. Gauge Pressure

+/- 1.7%, 1σ+/- 3%, 1σ30 deg2. Launch Angle

+/- 1.5%, 1σ+/- 2%, 1 σ6 in1. Inside Chamber Length

ΔR / R Due toUncertainty

Uncertainty inParameter

Baseline ValueParameter



2/24/2008 ELF 361

1 - Customer Requirements2 – Customer Importance Rating ( Total = 10 )

3 – Design Characteristics

4 – Design Characterist ics Impor tance Rating ( Total = 10 )

5 – Design Characteristics Sensitivity Matrix

6 – Design Characteristics Weighted Importance7 – Design Characteristics Relative Importance

House of Quality Translates Customer

Requirements into Engineering Emphasis

House of Quality Translates Customer

Requirements into Engineering Emphasis

Weight

Flight Range

3

7

Tail Planform AreaChamber Length

46

28

26 = ( 7x2 + 3x4 )74 = ( 7x8 + 3x6 )

21

0

Note on Design Characteristics SensitivityMatrix: ( Room 5 ):

++ Strong Synergy

+ Synergy

0 Near Neutral Synergy

- Anti-Synergy- - Strong Anti-Synergy

Note: Based on House of Quality, ins ide chamber length most important design parameter.



2/24/2008 ELF 362

DOE Explores the Broad Possible Design Space

with a Reasonably Small Set of Alternatives

DOE Explores the Broad Possible Design Space

with a Reasonably Small Set of Alternatives

0.1254Lower Value

0.256Upper Value

ST, Tail Planform Area,

in2

lc, Inside Chamber

Length, in

Engineering

Characteristics Range

“Petite”

“Stiletto”

“Shorty”“ Big Kahuna”

Concept Sketch

0.1254

0.1256

0.2540.256

ST, Tail Planform Area,in2

lc, Inside Chamber Length, in

Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters:Number of Combinations = 2k = 22 = 4

Design Space for Design of Experiments ( DOE )

Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics.



2/24/2008 ELF 363

Engineering Experience Should Guide the DOE

Set of Alternatives and the Preferred Design


Set of Alternatives and the Preferred Design As an Example, for the Soda Straw Rocket, from

Experience We Know That

Soda Straw Rocket Must Fit on Launcher Maximum Boost Veloci ty Occurs When Chamber Length = Launch

Tube Length

Three or Four Tails Best for Stability

Tails That Are Too Small May Result in an Unstable Flight

Tails That Are Too Large Add Weight and Cause TrajectoryDispersal

Canards Require Larger Tails for Stabil ity, Add Weight, and CauseTrajectory Dispersal

Wings Add Weight, Add Drag, and Cause Trajectory Dispersal



2/24/2008 ELF 364


Set of Alternatives and Preferred Design ( cont )


Set of Alternatives and Preferred Design ( cont )

As an Example, Soda Straw Rocket Geometry Should Be Comparable to an OperationalRocket with Near-Neutral Static Stabil ity ( e.g., Hydra70 )

2.66

1.89

1.89

2.79

2.79

b / d,

Total Tail Span /Diameter

217.9“Petite”

Hydra 70

“Stiletto”

“Shorty”

“ Big Kahuna”

Concept Sketch

115.1

225

217.9

225

c / d,

Tail Chord /Diameter

l / d,

Total Length /Diameter

Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender

surface theory give total tail span and chord for neutral stability of b NeutralStability ≈ 2 d and cNeutralStability > ≈ drespectively.



2/24/2008 ELF 365

Optimum Design Should Have Balanced

Engineering Characteristics

Optimum Design Should Have Balanced

Engineering Characteristics

As an Example, for the Soda Straw Rocket Design We

Should Reflect Customer Emphasis of Requirements for

Range

Weight

Provide Balanced Emphasis of Most Important EngineeringCharacteristics

Chamber Length

Tail Size / Span



2/24/2008 ELF 366

Summary of Sizing Examples Summary of Sizing Examples

Rocket Powered Missile ( Sparrow Derived Baseline ) Standoff range requirement

Wing area sizing requirements for maneuverability, turn rate, andturn radius


Ballistic versus lofted glide flight range

Ramjet Powered Missile ( ASALM Derived Baseline ) Robustness in range uncertainty


Surface target impact velocity Computer Aided Sizing Tools for Conceptual Design

ADAM

Analytical prediction of aerodynamics

Numerical solution of equations of motion



2/24/2008 ELF 367

Summary of Sizing Examples ( cont ) Summary of Sizing Examples ( cont )

Computer Aided Sizing Tools for Conceptual Design ( cont ) TMD analytical sizing spreadsheet ( based on this text )

Analytical prediction of aero, propulsion, and weight

Closed form analytical solution of s implif ied equations of motion


Static margin Drag

Performance

Sensitivity study

House of Quality Design of Experiment ( DOE )





2/24/2008 ELF 368

2/24/2008

Sizing Examples Problems Sizing Examples Problems

1. Required flight range is shorter for a head-on intercept and it is longer for a t___ c____ intercept.

2. The rocket baseline center-of-gravity moves f______ with motor burn.

3. The rocket baseline is an a_______ airf rame.4. The rocket baseline thrust profi le is b____ s______.

5. The rocket baseline motor case and nozzle are made of s____.

6. The rocket baseline flight range is driven by ISP, propellant weightfraction, drag, and s_____ m_____.

7. Contributors to the maneuverabili ty of the rocket baseline are its body,tail , and w___.

8. Although the rocket baseline has sufficient g’s and turn rate tointercept a maneuvering aircraft, it needs a smaller turn r_____.

9. Compared to a co-altitude trajectory, the rocket baseline has extendedrange with a l_____ glide trajectory.

10. The ramjet baseline has a c___ inlet.

11. The Mach 4 ramjet baseline has a t_______ airframe.



2/24/2008 ELF 369

2/24/2008 ELF 370

Sizing Examples Problems ( cont ) Sizing Examples Problems ( cont )

12. Although the ramjet baseline combustor is a nickel-based super alloy, itrequires insulation, due high temperature. The super alloy is i______.

13. The flight range of the ramjet baseline is dr iven by ISP, weight, thrust,

zero-lift coefficient, and the weight fraction of f___.14. Extended range for the ramjet baseline would be provided by more

efficient packaging of subsystems and the use of s_____ fuels.

15. A conceptual design sizing code should be based on the simplicity,

speed, and robustness of p______ based methods.16. The House of Quality room for design characteristics weighted

importance indicates which engineering design characteristics are mostimportant in meeting the c_______ r___________.

17. Paredo sensitivity identifies the design parameters that are mosti________.

18. DOE concepts should emphasize the customer driving requirements andthe dr iving e__________ characteristics

19. If the total tail span ( including body diameter ) is twice the bodydiameter, the missile is approximately n________ s_____.



2/24/2008 ELF 370

2/24/2008 ELF 371

Outline Outline






Development Process





2/24/2008 ELF 371

2/24/2008 ELF 372

Relationship of Technology Assessment /

Roadmap to the Development Process

Relationship of Technology Assessment /

Roadmap to the Development Process Technology Roadmap Establishes Time-phased

Interrelationships for Technology development and validation tasks

Technology options

Technology goals

Technology transition ( ATD, ACTD, DemVal, PDRR, SDD )

Technology Roadmap Identifies Key, enabling, high payoff technologies

Technology drivers

Key decision points Critical paths

Facili ty requirements

Resource needs



2/24/2008 ELF 372

2/24/2008 ELF 373

Research Technology Acquisition

Relationship of Design Maturity to the US

Research, Technology, and Acquisition Process

Relationship of Design Maturity to the US

Research, Technology, and Acquisition Process

BasicResearch

ExploratoryDevelopment

AdvancedDevelopment

Demonstration& Validation

SystemDevelopment

andDemonstration

Production

~ $0.1B ~ $0.9B~ $0.3B ~ $0.5B ~ $1.0B ~ $6.1B ~ $1.2B

6.1 6.2 6.3 6.4 6.5

SystemUpgrades

Technology

Development~ 10 Years

Technology

Demonstration~ 8 Years

Prototype

Demonstration~ 4 Years

Full Scale

Development~ 5 Years

Limited~ 2 Years

1-3 Block

Upgrades~ 5-15 Years

First

Block~ 5Years

ProductionNote:Total US DoD Research and Technology for Tactical Missi les ≈ $1.8 Billi on per year

Total US DoD Acquisi tion ( SDD + Production + Upgrades ) for Tactical Miss iles ≈ $8.3 Billi on per year Tactical Missiles ≈ 11% of U.S. DoD RT&A budgetUS Indust ry IR&D typically s imi lar to US DoD 6.2 and 6.3A

Matur ity Level Conceptual Design Prel iminary Design Detai l Design Production Design

Drawings ( type ) < 10 ( subsystems ) < 100 ( components ) > 100 ( parts ) > 1000 ( parts )



2/24/2008 ELF 373

2/24/2008 ELF 374

Technology Readiness Level ( TRL ) Indicates

the Maturity of Technology

Technology Readiness Level ( TRL ) Indicates

the Maturity of Technology TRL 1- 3

Category 6.1

Basicresearch

TRL 4

Category 6.2A

Exploratorydevelopmentof acomponent,conceptualdesignstudies, andpredictionmethods

TRL 5

Category 6.2B

Exploratorydevelopmentof asubsystem

TRL 6

Category 6.3

Advanced techdemo of asubsystem

TRL 7

Category 6.4

Prototypedemonstration

Initial assessment ⇒ component test ⇒ subsystem test ⇒ integrated subsystems ⇒ integrated missile



2/24/2008 ELF 374

2/24/2008 ELF 375

Conceptual Design Has Broad Alternatives

While Detail Design Has High Definition

Conceptual Design Has Broad Alternatives

While Detail Design Has High Definition

1

10

100

1000

0 5 10 15

Time ( Years )

T y p i c a l N u m b e r

o f A l t e r n a t i v e C o

n c e p t s

o r N u m b e r o f D e s i g n D r a w i n

g s

Number of Concepts

Number of Drawings

Conceptual Prelim. Detail Product ionDesign Design Design Design



3 5

2/24/2008 ELF 376

US Tactical Missile Follow-On Programs Occur

about Every 24 Years

US Tactical Missile Follow-On Programs Occur

about Every 24 Years

Year Entering SDD

AIM-9X ( maneuverabili ty ), 1996 - Hughes

AIM-120 ( autonomous, speed,

range, weight ), 1981 - Hughes

Long Range ATS, AGM-86, 1973 - Boeing AGM-129 ( RCS ), 1983 - General Dynamics

PAC-3 (accuracy), 1992 - Lockheed MartinLong Range STA, MIM-104, 1966 - Raytheon

1950 1965 1970 1975 1980 1985 1990 1995 > 2000

AGM-88 ( speed, range ), 1983 - TI

Man-portable STS, M-47, 1970 - McDonnell Douglas

Anti -radar ATS, AGM-45, 1961 - TI

Short Range ATA, AIM-9, 1949 - Raytheon

Javelin ( gunner survivability,lethality , weight ), 1989 - TI

Medium Range ATA, AIM-7,1951 - Raytheon

Medium Range ATS, AGM-130, 1983 - Rockwell JASSM ( cost, range,observables ), 1999 - LM

Hypersonic Missile, > 2007

Hypersonic Missile > 2007

Long Range STS, BGM-109, 1972 - General Dynamics Hypersonic Missile > 2007



2/24/2008 ELF 377

Missile Design Validation / Technology

Development Is an Integrated Process

Missile Design Validation / Technology

Development Is an Integrated Process •Rocket Static•Turbojet Static•Ramjet Tests-Direct Connect-Freejet

StructureTest

HardwareIn-Loop

Simulation

Ballistic Tests

Lab Tests

Seeker

Ac tuators / Init iators

Sensors

Propulsion Model

Aero Model

Model Digital Simulation

Wind TunnelTests

Propulsion

Ai rf rame

Guidanceand Control

Power Supply

Warhead

EnvironmentTests•Vibration•Temperature

Sled Tests

IM Tests

IM Tests

Flight Test Progression( Captive Carry,Jettison,Separation, Unpowered

Guided Flights, PoweredGuided Flights, LiveWarhead Flights )Lab Tests

Tower Tests

Autopi lo t / Electronics

Witness / Arena Tests



2/24/2008 ELF 378

Airframe Wind Tunnel Test ………………………………………………………

Propulsion Static Firing with TVC ……..

Propulsion Direct Connect Test …………………………………….

Propulsion Freejet Test …………

Examples of Missile Development Tests and

Facilities


Facilities



2/24/2008 ELF 379


Facilities ( cont )


Facilities ( cont ) Warhead Arena Test ……………………………………………………….

Warhead Sled Test ………………………

Insensitive Munition Test ……………………………………………..

Structure Test …………………………………………..



2/24/2008 ELF 380


Facilities ( cont )


Facilities ( cont ) Seeker Test ……………………………………………………….

Hardware-In-Loop ………

Environmental Test ……………………………………………..

Submunition Dispenser Sled Test ……………………



2/24/2008 ELF 381

RCS Test ……………………………………………………………….

Store / Avionics Test

Flight Test ……………………………………………………………………….

Video of Facil ities and Tests


Facilities ( cont )


Facilities ( cont )



2/24/2008 ELF 382

Missile Flight Test Should Cover Extremes of

Flight Envelope

Missile Flight Test Should Cover Extremes of

Flight Envelope

Flight 7

Flight 7

Flight 3

Flight 7

Flight 1

Flight 3

F l ig h t 7

Flight 3

Flight 7

H i g h D

y n a m

i c P r

e s s u

r e

High Aero Heating

High L / D Cruise

L o w D y

n a m i

c P r e s

s u r e

B o o s t e r

T r a n s i t i o n :

T h r u s t - D r a g

Note: Seven Flights from Oct 1979 to May 1980.Flight 1 failure of fuel control. As a result of the high thrust , the flight Mach number exceeded the design Mach number.

Example: Ramjet Baseline Propuls ion Test Validation ( PTV )



2/24/2008 ELF 383

Example of Aero Technology Development Example of Aero Technology Development

Conceptual Design ( 5 to 50 input parameters ) Prediction

Preliminary Design ( 50 to 200 input parameters ) Prediction

Missile DATCOM. Contact: AFRL. Attr ibutes include: Low cost MISL3. Contact: NEAR. Attr ibutes include: Modeling vortex shedding

SUPL. Contact: NEAR. Attr ibutes include: Paneling complex geometry

AP02. Contact: NSWC. Attributes include: Periodic updates

CFD. Contact: Georgia Tech. Attributes include: Model runs on ParallelProcessing PCs

Preliminary Design Optimization

Response Surface Model: Contact: Georgia Tech. Attributes include10x more rapid computation

Probabilistic Analysis: Contact: Georgia Tech. Attr ibutes include anevaluation of design robustness



2/24/2008 ELF 385

Example of Missile Technology State-o -the-Art

Advancement: Air-to-Air Missile Maneuverability


Advancement: Air-to-Air Missile Maneuverability

0

10

20

30

40

50

60

1950 1960 1970 1980 1990 2000 2010

Year IOC

O p e r a t i o n a l A

n g l e o f A t t a c k ,

D e

AIM-7A

AM-9B

R530

AA-8 AIM-54

R550

Skyflash

Python 3

AA-10 Aspide

Super 530D

AA-11

AIM-120

Python 4

AA-12

MICA

AIM-132

AIM-9X

Controls Augmentedwith PropulsionDevices ( TVC,Reaction Jet )



2/24/2008 ELF 386


Advancement: Ramjet Propulsion


Advancement: Ramjet Propulsion

0

1

2

3

45

6

7

1950 1960 1970 1980 1990 2000 2010

Year Flight Demonstration

M c r u i s e ,

C r u i s e M a c h

N u m b e r

Cobra X-7 Vandal/Talos St-450 SE 4400RARE Bloodhound BOMARC Typhon STATEXD-21 CROW SA-6 Sea Dart LASRM ALVRJ 3M80 ASAL M AS-17 / Kh-31 ASMP

ANS Kh-41 SLAT BrahMos Meteor HyFly SED

Scramjet

Ramjet



2/24/2008 ELF 387

Enabling Technologies for Tactical Missiles Enabling Technologies for Tactical Missiles DomeFaceted / WindowMulti-modeMulti-spectralMulti-lens

Seeker

Multi-modeMulti-spectralSARStrapdownUncooled ImagingHigh Gimbal

G & CGPS / INSIn-flight Optimizeα, β Feedback ATR

Propulsion

Hypersonic Turbine-BasedLiqu id / Solid Fuel RamjetVariable Flow Ducted RocketScramjetCombined Cycle PropulsionHigh Temperature Turbine

High Temperature Combustor High Density Fuel / PropellantHigh Throttle Fuel ControlEndothermic FuelComposite CasePintle / Pulsed / Gel Motor High Burn Rate Exponent PropellantLow Observable

WarheadHigh Energy DensityMulti-modeHigh Density Penetrator Boosted Penetrator Smart Dispenser

Powered Submunition

InsulationHypersonicHigh Density

Flight ControlEM andPiezoelectricTVC / Reaction JetDedicated RollPower

MEMS

AirframeLifting BodyNeutral Static MarginLattice FinsSplit CanardLow Δx AC Wing / Low Hinge Moment ControlFree-to-Roll TailsCompressed Carriage

Low Drag InletMixed Compression InletSingle Cast StructureVARTM, Pultrusion, Extrusion , Filament WindHigh Temperature Compos itesTitanium Alloy

MEMS Data CollectionLow Observable Shaping and Materials

Electronics

COTS

Central

Data LinkBDI / BDAIn-flight RetargetMoving TargetPhased Array



2/24/2008 ELF 388

Summary of Development Process Summary of Development Process

Development Process

Technology roadmap

Development activities

Time frame

Level of Design Maturi ty Related to Stage of Development

Missile Follow-on Programs

Subsystems Development Activi ties

Subsystems Integration and Missile System Development

Flight Test Activi ties

Missi le Development Tests and Facil ities

State-of-the-Art Advancement in Tactical Missiles New Technologies for Tactical Missiles





2/24/2008 ELF 389

Development Process Problems Development Process Problems

1. A technology roadmap establishes the high payoff technologies g____.

2. The levels of design maturity from the most mature to least mature areproduction, detail, preliminary, and c_________ design.

3. Technology transitions occur from basic research to exploratorydevelopment, to advanced development, to d____________ and v_________.

4. Approximately 11% of the U.S. RT&A budget is allocated to t_______m_______.

5. In the U.S., a tactical missile has a follow-on program about every __ years.

6. Compared to the AIM-9L, the AIM-9X has enhanced m______________.

7. Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter weight, higher speed, and longer r____.

8. Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy.

9. Guidance & control is verified in the h_______ in l___ simulation.

10. Airbreathing propulsion ground tests include direct connect tests and

f______ tests.11. Aerodynamic force and moment data are acquired in w___ t_____ tests.



2/24/2008 ELF 390

Outline Outline






Development Process





2/24/2008 ELF 391

Evaluate Alternatives and Iterate the System-o -

Systems Design

Evaluate Alternatives and Iterate the System-o -

Systems Design • Mission / Scenario

Definition

• WeaponRequirements,Trade Studiesand Sensitivity

Analysis

• Launch PlatformIntegration

• Weapon ConceptDesign Synthesis

• Technology Assessment andDev Roadmap

InitialTech

InitialReqs

BaselineSelected

Al tConcepts

Initial Carriage /Launch

Iteration

RefineWeapons

Req

Initial Revised

Trades / Eval Effectiveness / Eval

TechTrades

InitialRoadmap

RevisedRoadmap

Update

Note: Typical design cycle for conceptual design is usually 3 to 9 months

Al ternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine



2/24/2008 ELF 392

Exploit Diverse Skills for a Balanced Design Exploit Diverse Skills for a Balanced Design

Customer ( requirements pull )

⇒ mission / MIR weight ing

Operations analysts⇒ system-of-systems analysis

System integration engineers⇒ launch platform integration

Missile design engineers⇒ missile concept synthesis

Technical specialists ( technology push )⇒ technology assessment / roadmap



2/24/2008 ELF 393

Utilize Creative Skills Utilize Creative Skills

Use Creative Skil ls to Consider Broad Range of Alternatives

Ask Why? of Requirements / Constraints

Project into Future ( e.g., 5 – 15 years )

State-of-the-art ( SOTA )

Threat

Scenario / Tactics / Doctrine

Concepts

Technology Impact Forecast Recognize and Disti ll the Most Important, Key Drivers

Develop Missile Concept that is Synergistic within aSystem-of-Systems

Develop Synergistic / Balanced Combination of HighLeverage Subsystems / Technologies



2/24/2008 ELF 394

Identify and Quantify the High Payoff Measures of Merit

Identify and Quantify the High Payoff Measures of Merit

Max / MinRange

Time toTarget

Robustness

WeightSurvivability

Lethality Miss Distance

Observables

Reliability



2/24/2008 ELF 395

Start with a Good Baseline Start with a Good Baseline

I would haveused the wheelas a baseline.



2/24/2008 ELF 396

Conduct Balanced, Unbiased Tradeoffs Conduct Balanced, Unbiased Tradeoffs

Aerodynamics

Propulsion

Structures

Seeker

Guidance andControl

Warhead – Fuze

Production



2/24/2008 ELF 397

AA- 8 / R-60 Python 4 Magic 550 U-Darter

Python 5 Derby / R-Darter AIM-9L Aspide

AA-10 / R-27 Skyflash AIM-7 R-37

AA-12 / R-77 AIM-9x Super 530D AIM-132

AA-11 / R-73 AIM-54 AIM-120 Mica

IRIS-T Meteor A-Darter Taildog

Evaluate Many Alternatives Evaluate Many Alternatives

Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry



2/24/2008 ELF 398

Search a Broad Design Solution Space ( Global

Optimization vs Local Optimization )

Search a Broad Design Solution Space ( Global

Optimization vs Local Optimization )

Local Optimum ( e.g., Lowest Cost

Only in Local Solut ion Space )

Local Optimum ( e.g., Lowest CostOnly in Local Solut ion Space )

Global Optimum ( e.g., Lowest Cost inGlobal Solution Space ) within Constraints



2/24/2008 ELF 399

Evaluate and Refine as Often as Possible Evaluate and Refine as Often as Possible



2/24/2008 ELF 400

Provide Balanced Emphasis of Analytical vs

Experimental

Provide Balanced Emphasis of Analytical vs

Experimental

Thomas Edison: " Genius is 1%

inspiration and 99% perspiration."

Albert Einstein: " The only real

valuable thing is in tuition."



2/24/2008 ELF 401

Use Design, Build, and Fly Process, for

Feedback That Leads to Broader Knowledge

Use Design, Build, and Fly Process, for

Feedback That Leads to Broader Knowledge

Design

Build

Fly ( Test )

Prediction SatisfiesCustomer

Requirements?

Test Results SatisfyCustomer Requirements

and Consistent withPrediction?

Is it Producible?

No

Yes

C l i m

b L

a d d

e r o

f K

n o w

l e d g e

Data

Failure /

Success

Information

Understanding

Wisdom

No

No

Where is the wisdom we have lost inknowledge? Where is the knowledgewe have lost in information?--T. S.

Eliot ( The Rock ) Knowledge comes by taking thingsapart: analysis. But wisdom comes byputting things together.--John A.Morrison

We are drowning in information but

starved for knowledge.--John Naisbitt( Megatrends: Ten New Directions Transforming Our Lives )

We learn wisdom from failure muchmore than from success. We oftendiscover what will do, by finding outwhat will no t do; and probably he who

never made a mistake never made adiscovery.--Samuel Smiles ( Self Help )

Knowledge



2/24/2008 ELF 402

Evaluate Technology Risk Evaluate Technology Risk



2/24/2008 ELF 403

Keep Track of Assumptions and Develop Real-

Time Documentation

Keep Track of Assumptions and Develop Real-

Time Documentation

It’s finallyfinished ! . . .



2/24/2008 ELF 405

Utilize Group Skills Utilize Group Skills

Source: Nicolai, L.M., “ Designing a Better Engineer,” AIAA Aerospace America, April 1992

Detail /ProductionDesign –

30%

Other ThanDesign –

60%

Preliminary Design – 8%Conceptual Design – 2%

(Test, Analysis,Configuration

Management, Software,Program Management,

Integration,Requirements,

etc.)



2/24/2008 ELF 406

Balance the Tradeoff of Importance vs Priority Balance the Tradeoff of Importance vs Priority

Advanced Programs /

Conceptual Design

SDD Programs /

Preliminary Design

Production Programs /

Detail Design



2/24/2008 ELF 407

Evaluate Alternatives and Iterate the

Configuration Design

Evaluate Alternatives and Iterate the

Configuration Design

Yes

Establish Baseline

Meet

Performance?

No

No

Yes


Al t Mission

Al t Baseline


Aerodynamics

Propulsion

Weight

Trajectory




2/24/2008 ELF 408

Configuration Sizing Conceptual Design

Guidelines: Aeromechanics


Guidelines: Aeromechanics

Configuration Sizing Parameter Aeromechanics Design Guideline Body fineness ratio 5 < l / d < 25

Nose fineness ratio lN / d ≈ 2 if M > 1 Boattail or flare angle < 10 deg

Efficient cruise dynamic pressure q < 1,000 psf

Missile homing velocity VM / VT > 1.5

Ramjet combustion temperature > 4,000° F Oblique shocks prior to inlet normal > 2 obl ique shocks / compressions i f M >

shock to satisfy MIL-E-5008B 3.0, > 3 shocks / compressions if M > 3.5

Inlet flow capture Shock on cowl lip at Mmax cruise

Ramjet Minimum cruise Mach number M > 1.2 x MInletStart , M > 1.2 MMaxThrust = Drag

Subsystems packaging Maximize available volume for fuel /propellant



2/24/2008 ELF 409


Guidelines: Guidance & Control


Guidelines: Guidance & Control

Configuration Sizing Parameter G&C Design Guideline Body bending frequency ωBB > 2 ω ACT

Trim control power α / δ > 1 Neutral stability tail-body If low aspect ratio, b / d ≈ 2, c / d > ≈ 1

Stability & control cross coupling < 30%

Airframe time constant τ < 0.2 s

Missile maneuverability nM / nT > 3

Proportional guidance ratio 3 < N’ < 5

Target span resolution by seeker < btarget

Missile heading rate γ.

M> γ.

T Missile turn radius RTM

< RTT



2/24/2008 ELF 410

Wrap Up ( Part 1 of 2 ) Wrap Up ( Part 1 of 2 )

Missile design is a creative and i terative process that includes System considerations

Missile concepts and sizing Flight trajectory evaluation

Cost / performance drivers may be “ locked in” duringconceptual design

Missile design is an opportunity for a diverse group to worktogether for a better product Military customer ⇒ mission / scenario definition

Operations analysts ⇒ system-of-systems modeling System integration engineers ⇒ launch platform integration

Missi le design engineers ⇒ missile concept synthesis

Technical specialists ⇒ technology assessment / technology roadmap



2/24/2008 ELF 411

Wrap Up ( Part 2 ) Wrap Up ( Part 2 )

The missile conceptual design philosophy requires Iteration, iteration, iteration

Evaluation of a broad range of alternatives Traceable flow-down allocation of requirements

Starting with a good baseline

Paredo sensitivity analysis to determine the most important, driving

parameters Synergistic compromise / balanced subsystems and technologies

that are high leverage

Awareness of technology SOTA / technology assessment

Technology impact forecast

Robust design

Creative design decisions made by the designer ( not the computer )

Fast, simple, robust, physics-based prediction methods



2/24/2008 ELF 412

Outline Outline







Sizing Examples

Development Process



Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,




2/24/2008 ELF 413

References References

1. “Missile.index,” http://missile.index.ne.jp/en/

2. AIAA Aerospace Design Engineers Guide, American Institu te of Aeronautics and Astronautics , 1993

3. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice , “ Principles of Guided Missile Design” ,D. Van Nostrand Company, Inc., 1956

4. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design , “ Principles of Guided Missile Design” , D.Van Nostrand Company, Inc., 1960

5. Chin, S.S., Missile Configuration Design , McGraw-Hill Book Company, 1961

6. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981

7. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lif t and Center of Pressure of Wing-Body-Tail Combinations at Subsonic,Transonic, and Supersonic Speeds,” NACA Report 1307, 1957

8. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shutt le-Like, and Other Bodies at Anglesof Attack From 0° to 180°,” NASA TND 6996, January 1973

9. Hoak, D.E., et al., “ USAF Stabil ity and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 1978

10. “ Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm

11. Ash ley, H., Engineering Analysis of Flight Vehicles,Dover Publications, Inc., 1974

12. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill , 1990

13. Kinro th, G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 1980

14. “Technical Aerodynamics Manual,” North American Rockwell Corporation , DTIC AD 723823, June 1970

15. Oswatitsch, K.L., “Pressure Recovery for Missi les with Reaction Propuls ion at High Supersonic Speeds” , NACA TM -1140, 1947

16. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988



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References ( cont ) References ( cont )

17. Allen, J. and Eggers, A.J., “ A Study of the Motion and Aerodynamic Heating of Balli stic Missiles Entering the Earth ’s Atmosphere at High Supersonic Speeds” , NACA Report 1381, Apri l 1953.

18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996

19. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997

20. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980

21. Carleone, J. (Editor), Tactical Missile Warheads, “ AIAA Vol . 155 Progress in Astronautics and Aeronaut ics,” AmericanInstitute of Aeronautics and Astronautics, 1993

22. Christman, D.R. and Gehring, J.W., “ Analysis of High-Veloci ty Projecti le Penetration Mechanics,” Journal of AppliedPhysics, Vol. 37, 1966

23. Heaston, R.J. and Smoots, C.W., “Precision Guided Munit ions,” GACIAC Report HB-83-01, May 1983

24. Donatelli, G.A. and Fleeman, E.L., “ Methodology for Predict ing Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982

25. Bennett, R.R. and Mathews, W.E., “ Analyt ical Determination of Miss Distances for L inear Homing NavigationSystems,” Hughes Tech Memo 260, 31 March 1952

26. Nicholas, T. and Rossi, R., “US Missi le Data Book, 1996,” Data Search Associates, 1996

27. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 1982

28. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 81-1688, August 1981

29. Hindes, J.W., “ Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993

30. Frits, A.P., et al, “ A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missi le Sciences Conference, November 2002

31. Bruns, K.D., Moore, M.E., Stoy , S.L., Vukelich, S.R., and Blake, W.B., “ Missile DATCOM,” AFWAL-TR-91-3039, Apr il

1991



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References ( cont ) References ( cont )

32. Moore, F.G., et al, “ The 2002 Version of the Aeroprediction Code” , Naval Surface Warfare Warfare Center, March 2002

33. Nicolai, L.M., “Design ing a Better Engineer,” AIAA Aerospace America, April 1992



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Bibliography of Other Reports and Web Sites Bibliography of Other Reports and Web Sites

System Design

Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006

“ DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html

“Periscope,” http://www.periscope1.com/

Defense Technical Information Center, http://www.dtic.mil/ NATO Research & Technology Organisation, http://www.rta.nato.int/

“ Missile System Flight Mechanics,” AGARD CP270, May 1979

Hogan, J.C., et al., “ Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980

Rapp, G.H., “Performance Improvements With Sidewinder Missi le Airf rame,” AIAA Paper 79-0091, January 1979

Nicolai, L.M., Fundamentals of Aircraft Design , METS, Inc., 1984

Lindsey, G.H. and Redman, D.R., “ Tactical Missile Design,” Naval Postgraduate School, 1986

Lee, R.G., et al, Guided Weapons, Third Edition , Brassey’s, 1998

Giragosian, P.A., “ Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Appl ied Aerodynamics Conference, June 1992

Fleeman, E.L. “ Aeromechanics Technologies for Tactical and Strategic Guided Missi les,” AGARD Paper

presented at FMP Meeting in London, England, May 1979 Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronaut ics and Ast ronautics, 1989

Ball , R.E., The Fundamentals of Aircraft Combat Survivabili ty Analysis and Design, American Institute of Aeronautics and Astronaut ics, 1985

“ National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia



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Bibliography of Other Reports and Web Sites ( cont ) Bibliography of Other Reports and Web Sites ( cont )

System Design ( continued ) Eichblatt , E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronaut ics and Astronautics,

1989 “ Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp “ Advanced Sidewinder Missi le AIM-9X Cost Analysis Requirements Description (CARD),”

http://deskbook.dau.mil/jsp/default.jsp Wertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic

Publishers, 1999

“ Directory of U.S. Military Rockets and Missiles” , http://www.designation-systems.net/

Fleeman, E.L., et al, “ Technologies for Future Precision Strike Miss ile Systems,” NATO RTO EN-018, July 2001

“ The Ordnance Shop” , http://www.ordnance.org/portal/

“ Conversion Factors by Sandelius Instruments” , http://www.sandelius.com/reference/conversions.htm “Defense Acquisition Guidebook”, http://akss.dau.mil/dag/

Aerodynamics “ A Digital Library for NACA,” http://naca.larc.nasa.gov/ Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics , “AIAA Vol.

141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992 Briggs, M.M., et al., “ Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977 “ Missile Aerodynamics,” NATO AGARD LS-98, February 1979 “ Missile Aerodynamics,” NATO AGARD CP-336, February 1983 “ Missile Aerodynamics,” NATO AGARD CP-493, April 1990 “ Missile Aerodynamics,” NATO RTO-MP-5, November 1998

Nielsen, J.N., Missile Aerodynamics , McGraw-Hill Book Company, 1960



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Aerodynamics ( cont inued ) Mendenhall, M.R. et al, “ Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989 Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979 Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Predict ion Methods and

Appl ications,” Journal of Spacecraft and Rockets, Vo l. 36, No. 5, September-October, 1999

Nielsen, J.N., and Pitts, W.C., “ Wing-Body Interference at Supersonic Speeds wi th an Application toCombinations with Rectangular Wings,” NACA Tech. Note 2677, 1952

Spreiter, J.R., “ The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations” , NACAReport 962, 1950

Simon, J.M., et al, “ Missile DATCOM: High Angle of Attack Capabili ties, AIAA-99-4258 Burns, K.A., et al, “ Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995

Lesieutre, D., et al, “ Recent Appl ications and Improvements to the Engineering-Level Aerodynamic Predict ionSoftware MISL3,’’ AIAA-2002-0274 Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronaut ics and

Astronaut ics, 2000 “1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/ “ Compressible Aerodynamics Calculator” , http://www.aoe.vt.edu/~devenpor/aoe3114/calc.html Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies , Dover Publications, 1965 John, James E.A., Gas Dynamics , Second Edition, Prentice Hall, 1984 Zucker, Robert D., Fundamentals of Gas Dynamics , Matrix Publ ishers, 1977

Propulsion Chemical Information Propulsion Agency, http://www.cpia.jhu.edu/

St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of Excellence, ASME International Gas Turbine Inst itute, 1999



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Propulsion ( continued ) Mahoney, J.J., Inlets for Supersonic Missiles, American Ins ti tu te of Aeronaut ics and Ast ronautics, 1990 Sutton, G.P., Rocket Propulsion Elements , John Wiley & Sons, 1986 “ Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980

Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill , 1995 Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institu te of Aeronaut ics and Astronautics,

1996

Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961

Bathie, W.W., Fundamentals of Gas Turbines , John Wiley and Sons, 1996

Hill , P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion , Addison-Weshley Publishing

Company, 1970 Mattingly, J.D., et al, Aircraft Engine Design , American Institute of Aeronautics and Astronautics, 1987

Materials and Heat Transfer

Budinski , K.G. and Budinski , M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999 “ Matweb’s Material Properties Index Page,” http://www.matweb.com

“ NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database” ,http://tpsx.arc.nasa.gov/tpsxhome.shtml

Harris , D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999 Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997 MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures” , Jan 2003 “ Metallic Material Properties Development and Standardization ( MMPDS )” , http://www.mmpds.org



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Materials and Heat Transfer ( continued ) Malli ck, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design , Second Edition, Maecel

Dekker, 1993 Chapman, A.J., Heat Transfer , Third Edition, Macmil lan Publishing Company, 1974 Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer , Fourth Edition, John Wiley and

Sons, 1996

Guidance, Navigation, Control, and Sensors Zarchan, P., Tactical and Strategic Missile Guidance , “ AIAA Vol. 124 Progress in Ast ronautics and

Aeronautics,” American Insti tu te of Aeronautics and Astronaut ics, 1990 “ Proceedings of AGARD G&C Conference on Guidance & Contro l of Tactical Miss iles,” AGARD LS-52, May 1972

Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980 Locke, A. S., Guidance , “ Principles of Guided Missile Design” , D. Van Nostrand, 1955 Blakelock, J. H.,Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965 Lawrence, A.L., Modern Inertial Technology , Springer, 1998 Siouris, G.M., Aerospace Avionics Systems , Academic Press, 1993 Stimson, G.W., Introduction to Airborne Radar, SciTech Publish ing, 1998

Lecomme, P., Hardange, J.P., Marchais , J.C., and Normant, E.,Air and Spaceborne Radar Systems, SciTechPublishing and William Andrew Publishing, 2001 Wehner, D.R., High-Resolution Radar, Ar tech House, Norwood, MA, 1995 Donati, S., Photodetectors, Prentice-Hall , 2000 Jha, A.R., Infrared Technology , John Wiley and Sons, 2000 Schlessinger, M., Infrared Technology Fundamentals , Marcel Decker, 1995



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Follow-up Communication Follow-up Communication

I would appreciate receiving your comments and

corrections on this text, as well as any data,

examples, or references that you may offer.

Thank you,Gene FleemanTactical Missile Design

E-mail: [email protected] Site: http://genefleeman.home.mindspring.com