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MDTS 5705 : Aerodynamics & Propulsion

Lecture 2 : Missile lift and drag

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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 regionshock

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A supersonic airfoil looks like this ...

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or like this ...

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2.2 The different types of drag

1. We can divide the flow field around a missile into 2 regions

fore body

base

2. Typically the fore body is the responsibility of the aerodynamist

while the base comes under the propulsion engineer. Why ?

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3. There are three main contributions to the missile’s drag

Type Cause

Skin friction drag Viscosity of air

Pressure drag Shape of forebody

Base drag Exhaust and wake

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2.2.1 Skin friction drag

The skin friction drag is the downstream resultant of all shear

(viscous) forces experience by the fore body

1. Shear forces are tangential to the missile’s surface

2. It is dependent on the amount of wetted area

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3. A quick estimate of the skin friction drag is to take the viscous

drag of a flat plate with the same surface area, length and

Reynolds number as the missile

Viscous drag

coefficient for a flat

plate

CDfp 0.043 / (Rel)1/6

for Re ~ 106 - 107

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CDf = F

(1/2 V2) ( r2)

= (1/2 V2 ) (2 r l ) CDfp

(1/2 V2) ( r2)

= 4 (l /d) CDfp

Exercise : Derive an approximation for the skin friction drag

coefficient of a missile of length l and diameter d ( = 2 r)

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2.2.2 Pressure drag

Pressure drag is the downstream resultant of all the pressure

forces on the forebody

1. Pressure forces acts normal to the missile surface

2. So which part of the forebody will contribute significantly to

pressure drag ?

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3. You can observe

the high pressure at

the missile’s nose

even when the

missile flies at a

small angle of attack

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3. For lower speeds,

pressure drag can still

be more significant than

skin friction drag.

4. Unless the object

is streamlined

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2.2.3 Base drag

Base drag is the drag resulting from the wake or “dead air”

region behind the missile.

1. Base drag is less of a problem during powered flight but

during free flight it can account for as much as 50% of total

drag.

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2. Base drag can be reduced by tapering the tail (boat tailing).

Looks like a good idea ?

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Boat tail missile exhaust

Question : Is there a catch for missiles ?

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2.3 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

2.4 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

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= 16o

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2.5 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