MDTS 5734 : Aerodynamics & Propulsion Lecture 1 : Characteristics of high speed flight
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
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
1.1 The Earth s Atmosphere Question : Is the Earth s atmosphere uniform? 0 km 20 km Air pressure (N/m 2 ) 101 325 6000 Air density (kg/m 3 ) 1.225 0.1 Air temperature ( o C ) 30-60 Question :Any implications for missiles?
1.2 Aerodynamic forces Aerodynamic forces on a flight vehicle scale as : Aerodynamic force V 2 Air speed Note the dependence on V 2 Air density
For missiles, there are two important aerodynamic forces Axial force A = ½ V 2 S C A Normal force N = ½ V 2 S C N V N A These forces are aligned with the missile body and not the velocity
The symbols are : S : reference area (m 2 ) e.g. missile cross section area C A : axial force coefficient (non dimensional) C N : normal force coefficient (non dimensional) ½ V 2 : dynamic pressure ( N/m 2 )
Equivalently we can represent the aerodynamics forces as lift and drag forces aligned with the velocity Lift force L = ½ V 2 S C L Drag force D = ½ V 2 S C D V L D
Example : Estimate C L for the AGM 65 Flight conditions mass : 300 kg speed : 320 m/s altitude : S.L diameter : 0.3048 m S.L. S = For level flight, C L = = =
1.3 Aerodynamic flow parameters Missile airspeeds can range from 10 0 10 3 m/s Aerodynamic properties are determined by the Mach number M
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.
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
Example : Disturbance propagation M < 1 Consider the distances travelled by the disturbance and the missile in 1s distrubance a missile 0 V What about the disturbance created mid way?
Example : Disturbance propagation M > 1 Consider the distances travelled by the disturbance and the missile in 1s distrubance a missile 0 V sin = a/v = 1/M
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 Light is refracted differently because of changes in air density Question : Can you estimate the Mach number?
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...
1.3.2 Effects of a shock (sonic boom) On the ground On humans
Condensation due to sudden changes in air temperature and pressure
1.4 The placement of lift surfaces Question : Can this missile fly at Mach 3? = 25 o
The angle of the attached shock is related to the Mach number by : sin = 1/M At Mach 3, = sin -1 (1/3) = 19.5 o = 19.5 o Is this a good design? What is the max speed of this missile?
Now can you comment on the design of this configuration?
2.1. The design of supersonic airfoils For efficient lift generation at subsonic speeds, airfoils look like :
So why can t a similar airfoil work at transonic/supersonic speeds? subsonic region shock
A supersonic airfoil looks like this...
or like this...
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
3. Missiles have to pass through this transonic drag rise to get to supersonic speeds
4. At supersonic speeds drag tends to level off
2.3 Drag reduction using sweepback 1. Critical aerodynamic surfaces are swept back to reduce this transonic drag rise
2. This works because... M n normal component... the wing sees a lower effective airspeed M velocity vector M n = M cos wing
Example : WWII German missiles V1 straight wings V2 swept back fins
An interesting example of the use of sweepback Me 262 first operational jet fighter What is the moral of the story?
Example : So what can you deduce from the sweep back angle? Maverick AGM = 80 o Bloodhound SAM = 26 o
It would seem that the sweep angle doesn t provide much info... = 26 o M n M
= 16 o
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?
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
This concept was first applied to the F102 to achieve supersonic flight pinched waist But is it commonly used in missiles now?