G. Leng, MDTS, NUS

MDTS 5734 : Aerodynamics & Propulsion Lecture 1 : Characteristics of high speed flight

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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 supersonic flight

or the aerodynamic forces on the missile

2. 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

V 0

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

V 0

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 ?

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2.1. The design of supersonic airfoils

For efficient lift generation at subsonic speeds, airfoils look like :

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So why can’t a similar airfoil work at transonic/supersonic speeds ?

subsonic region shock

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A supersonic airfoil looks like this ...

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or like this ...

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2.2 Drag variation with speed

1. As a missile approaches M = 1, drag increases significantly

2. This is known as the transonic drag rise

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3. Missiles have to pass through this transonic drag rise to get

to supersonic speeds

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4. At supersonic speeds drag tends to level off

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1. Critical aerodynamic surfaces are swept back to reduce this

transonic drag rise

2.3 Drag reduction using sweepback

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2. This works because ...

wing

M

velocity vector

Mn

normal component

... the wing “sees” a

lower effective airspeed

Mn = M cos

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Example : WWII German missiles

V1 – straight wings V2 – swept back fins

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An “interesting” example of the use of sweepback

Me 262 – first operational jet fighter

What is the moral of the story ?

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Example : So what can you deduce from the

sweep back angle ?

Maverick AGM = 80 o

Bloodhound SAM = 26 o

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= 26o

M

Mn

It would seem that the sweep angle doesn’t provide much info ...

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= 16o

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2.4 Drag reduction using the Area-Rule

Near Mach 1,

the drag of a slender wing-body combination

is equal to

that of a body of revolution having the same

cross-sectional area distribution

What does this mean ?

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A : slender body

B : Wing-body combination

with higher drag

C : Equivalent body of

revolution for wing-body B

D : “Pinched” body

A, i.e. lower drag c/o B

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This concept was first applied to the F102 to achieve supersonic flight

But is it commonly used in missiles now ?

“pinched” waist