MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag. G. Leng, MDTS, NUS

Transcription

1 MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag

2 2.1. The design of supersonic airfoils For efficient lift generation at subsonic speeds, airfoils look like :

3 So why can t a similar airfoil work at transonic/supersonic speeds? subsonic region shock

4 A supersonic airfoil looks like this...

5 or like this...

6 2.2 The different types of drag 1. We can divide the flow field around a missile into 2 regions base fore body 2. Typically the fore body is the responsibility of the aerodynamist while the base comes under the propulsion engineer. Why?

7 3. There are three main contributions to the missile s drag Type Skin friction drag Cause Viscosity of air Pressure drag Shape of forebody Base drag Exhaust and wake

8 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

9 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 C Dfp / (Re l ) 1/6 for Re ~

10 Exercise : Derive an approximation for the skin friction drag coefficient of a missile of length l and diameter d ( = 2 r) C Df = F (1/2 V 2 ) ( r 2 ) = (1/2 V 2 ) (2 r l ) C Dfp (1/2 V 2 ) ( r 2 ) = 4 (l /d) C Dfp

11 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?

12 3. You can observe the high pressure at the missile s nose even when the missile flies at a small angle of attack

13 3. For lower speeds, pressure drag can still be more significant than skin friction drag. 4. Unless the object is streamlined

14 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.

15 2. Base drag can be reduced by tapering the tail (boat tailing). Looks like a good idea?

16 Boat tail missile exhaust Question : Is there a catch for missiles?

17 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

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

19 4. At supersonic speeds drag tends to level off

20 2.4 Drag reduction using sweepback 1. Critical aerodynamic surfaces are swept back to reduce this transonic drag rise

21 2. This works because... M n normal component... the wing sees a lower effective airspeed M n = M cos M velocity vector wing

22 Example : WWII German missiles V1 straight wings V2 swept back fins

23 An interesting example of the use of sweepback Me 262 first operational jet fighter What is the moral of the story?

24 Example : So what can you deduce from the sweep back angle? Maverick AGM = 80 o Bloodhound SAM = 26 o

25 = 26 o M n M

26 = 16 o

27 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?

28 A : slender body C : Equivalent body of revolution for wing-body B B : Wing-body combination with higher drag D : Pinched body A, i.e. lower drag c/o B

29 This concept was first applied to the F102 to achieve supersonic flight pinched waist But is it commonly used in missiles now?