Here you can see the missile and compare it with High Bore Of sight Missile like Aim9X which is meant to be more flexible and hence is capable of making and sustaining high G turns in low and high altitude.
Hi dear
@Tipu7
Let me write an explanation as to why WVR missiles like AIM9X have that specific aerodynamic profile vis-a-vis lets say a BVR AIM-120 or ASTRA. I will try my best to keep the mathematics at a bare minimum level.
First off,let us first understand what is angle of attack and proportional guidance scheme.
Picture Courtesy: Brian L Steven
As you can see the angle of attack is the angle subtended between the projection of velocity V=sqrt(v^2+u^2+w^2) on x-z plane and the zero lift line of the plane.This holds good for missiles as well.That is the reason why \alpha\=arctan(w/u)------------------from the figure above.
Now i will shed some light on the aerodynamic configuration of WVR and BVR.
First off,the control surface in a AIM9X is tail as opposed to the canard. AIM9L on the other hand has canard as the "control-surface". Now the basic flight dynamics would tell you that any surface mounted ahead of CG has a "de-stabilizing" affect on the longitudinal dynamics of the aerial vehicle.This is beautifully captured in the expression of-
Cm=Cm0+Cm(alpha)*alpha.
If one actually gets down to the dynamics one would find that Cmalpha (stability derivative) is a strong function of static margin,where static margin is defined as (Xcg-Xac)/c. For stability we would want Cmalpha to be negative,which would imply static margin to be negative as well.This in turn implies Xcg-Xac<0 or Xac>Xcg.That is the reason why canards have de-stabilizing effect on the stability of aerial vehicles.
Now bigger a canard,higher will be the destabilizing effect and hence a bigger tail would be required at the rear to stabilize the missile-which is precisely the case with AIM9L.
The primary advantage of canard control is better maneuverability at low angles of attack, but canards tend to become ineffective at high angles of attack because of flow separation that causes the surfaces to stall.
The WVR missiles currently in the arsenal of india are far more effective than those in PAF because of the following reason-
1)SPLIT CANARDS-
Split canard refers to the fact that the missile has two sets of canards in close proximity, usually one immediately behind the other. The first canard is fixed while the second set is movable.The advantage of this arrangement is that the first set of canards generates strong, energetic vortices that increase the speed of the airflow over the second set of canards making them more effective. In addition, the vortices delay flow separation and allow the canards to reach higher angles of attack before stalling. This high angle of attack performance gives the missile much greater maneuverability compared to a missile with single canard control. This is precisely the reason why russian AA-11 and python-4 are considered more deadly vis-a-vis AIM9 series.Python's aerodynamic performance is superior to even AA-11- especially itz capability to touch seemingly impossible AoA before stalling.
In the case of BVR though,the wings are static and are usually mounted aft of CG- this provides stability during flight.In the language of mathematics, stability means-
(a) Cmalpha<0
(b) Cnbeta>0
(c) Clbeta<0.
In AIM120,it is the tail that provides the control.
Now i will quickly touch upon the guidance scheme used by various BVR/WVR missiles and that is PROPORTIONAL GUIDANCE ALGORITHM.
Picture Courtesy:Advanced Control systems ferdinand
In this widely used algorithm,lateral acceleration of the missile is made dependent on the relative velocity of the missile and the rate of change of line of sight angle lambda(i so wish i had latex right now!).
ac=-k*v*lambda'
where v is nothing but the magnitude of the relative velocity between the missile and the target. The job of the integrated GNC loop in the missile is the keep this lambda constant.This will steer the missile on a "collision course" with the target. Guidance and Control(are two very distinct components of a missile) are usually integrated.Guidance system produces the error on which the "control" works.Guidance system comprises of your seeker and allied electronics at the front end of the missile.It not only measures the relative velocity of the missile but also the line of sight angle.The effectiveness of the BVR depends on a lot of parameters.Design of very accurate angle tracker is a challenge. Alongwith proportional guidance, OPTIMAL CONTROL is used to provide the optimal control input to the control surfaces(deflections) that will result in the collision with the target with least possible expenditure of energy.Here the fuel consumption becomes the cost function that needs to be minimized. A set of constraints are applied on the control surfaces and even on state variables.
optimal control strategies is part of my curriculum
