G. Leng, MDTS, NUS

MDTS 5705 : Aerodynamics & PropulsionLecture 1 : Characteristics of high speed flight

G. Leng, MDTS, NUS

References

• Jack N. Nielsen, “Missile Aerodynamics”, AIAA Progress in Astronautics and Aeronautics, v104, 1986

• Michael J. Hemsch (ed), “Tactical Missile Aerodynamics : General Topics”, AIAA Progress in Astronautics and Aeronautics, v141, 1992

• Michael R. Mendenhall (ed), “Tactical Missile Aerodynamics : Predicition Methodology”, AIAA Progress in Astronautics and Aeronautics, v142, 1992

• Gordon E. Jensen, David W. Netzer, “Tactical Missile Propulsion”, AIAA Progress in Astronuatics and Aeronautics, v 170, 1996

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Training Programme

1. Characteristics of high speed flight

or understanding the flight environment

2. Missile lift and drag

or the aerodynamic forces on the missile

3. Missile propulsion for high speeds

or rockets, ramjets and scamjets

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Question : Is the Earth’s atmosphere uniform ?

0 km 20 km

Air pressure (N/m2) 101 325 6000

Air density (kg/m3) 1.225 0.1

Air temperature (oC ) 30 -60

Question :Any implications for missiles ?

1.1 The Earth’s Atmosphere

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1.2 Aerodynamic forces

Aerodynamic forces on a flight vehicle scale as :

Aerodynamic force V2

Air speed

Air density

Note the dependence on V2

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For missiles, there are two important aerodynamic forces

Axial force A = ½ V2 S CA

Normal force N = ½ V2 S CN

N

A

These forces are aligned with the missile body and not the velocity

V

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The symbols are :

S : reference area (m2) e.g. missile cross section area

CA : axial force coefficient (non dimensional)

CN : normal force coefficient (non dimensional)

½ V2 : dynamic pressure ( N/m2)

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L

D

V

Equivalently we can represent the aerodynamics forces as

lift and drag forces aligned with the velocity

Lift force L = ½ V2 S CL

Drag force D = ½ V2 S CD

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Example : Estimate CL for the AGM 65

Flight conditions

mass : 300 kg speed : 320 m/s

altitude : S.L diameter : 0.3048 m

For level flight,

CL =

=

=

S.L.

S =

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1.3 Aerodynamic flow parameters

Missile airspeeds can range from 100 – 103 m/s

Aerodynamic properties are determined by the Mach number M

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Question : Why does the speed of sound come in ?

1. Air is compressible.

2. A moving missile disturbs the surrounding air

3.These disturbances e.g. pressure variations, take a finite time

to propagate at the speed of sound through the surrounding air

4. The Mach number measures the importance of this

compressibility effect .

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1.3.1 Classification of flow regimes via Mach number

• M < 0.8 subsonic incompressible aerodynamics

• 0.8 < M < 1.2 transonic localized compressibility effects

• 1.2 < M < 5 supersonic compressible aerodynamics

• M > 5 hypersonic aerodynamic heating

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Example : Disturbance propagation M < 1

distrubance

missile

Consider the distances travelled by the disturbance and the missile in 1s

a

V0

What about the

disturbance created

mid way ?

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Example : Disturbance propagation M > 1

distrubance

missile

Consider the distances travelled by the disturbance and the missile in 1s

a

V0

sin = a/V

= 1/M

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So for M > 1, there is a discontinuity in the flow field “seen”

by the missile

Air properties like pressure, temperature and density changes

sharply across the discontinuity or shock

Schlieren photo of shock

waves

Question : Can you

estimate the Mach number ?

Light is refracted

differently because of

changes in air density

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The shape of the shock wave depends on the shape of the object

blunt nosed

object

detached

shock

Shocks created by high speed flight can be annoying ....

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1.3.2 Effects of a shock (sonic boom)

On the ground

On humans

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Condensation due to sudden changes in air temperature and pressure

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1.4 The placement of lift surfaces

Question : Can this missile fly at Mach 3 ?

= 25o

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The angle of the attached shock is related to the Mach number by :

sin = 1/M

At Mach 3, = sin-1 (1/3)

= 19.5o

= 19.5o

Is this a good design ? What is the max speed of this missile ?

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Now can you comment on the design of this configuration ?