PaklovesTurkiye
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Hi dear @Genghis khan1
It isnt really that easy either.We are not talking about DIY rockets but advanced ICBMs that are design to fly more than 5500kms! Let me elaborate based on my own experience-
View attachment 309678
P.C- Missile guidance and control,George M sioris
Journey of any ICBM can be divided into three (in some literature two) stages-
(a)Powered flight
(b)Free fall
(c) Re-entry
Kindly note that both (b) and (c) are free falling.From a purely control engineering perspective,one would need to select optimum burnout point somewhere around 450-500kms altitude for a specific target. The steering of ICBM from launch point to burnout point is perhaps the most difficult and crucial phase of any ICBM as it has to encounter varying dynamic pressure.Now to understand the reason why is this phase most important,requires some decent amount of aerospace engineering.
View attachment 309681
Here is a simplified Free body diagram of a ICBM RV,I have resolved forces in perpendicular direction,hence in perpendicular direction
QSCl*cos(Theta-alpha)=W+QSCd*sin(theta-alpha)---------------------------(1)
Kindly note that I've not included thrust, but it'll appear on the LHS of (1).
where Q is the dynamic pressure,
S=surface area
Cl=coefficient of lift=which again can be approximated by Clalpha*alpha
Cd=coefficient of drag= which again can be approximated by Cd0+k*Cl^2
theta=attittude angle or pitch angle
alpha=AoA
gamma=flight path angle(between velocity vector and the local horizontal)---not shown in the pic
Eqn 1 must be balanced all the time,but the missile is constantly accelerated till the burnout point meaning an ever increasing velocity and hence a varying dynamic pressure Q. For (1) to hold and we wish to keep theta at a certain value(as will become apparent later in my explanation),we would have to have some control over alpha. And alpha can be controlled by elevator deflection or actuating the jet vanes(--like shaheen and other older missiles),or by deflecting the nozzle using a servo-mechanism(in agni-4 or agni-5).
Once it has reached the burnout point,the missile should have a requisite velocity and escape angle denoted by fi(subscript bo) in fig-1.These two parameters are determined by the type of elliptic trajectory we want- again depends on mission profile- whether we want a depressed trajectory or a normal min-energy trajectory.These two parameters are so important that a minor deficiency can lead to huge errors later during the re-entry. Kindly note that fi(bo) is closely related to theta above.
The trajectory after burnout point till re-entry is elliptical with centre of earth being at one of the foci,hence normal elliptical equations apply(considering a TWO-BODY PROBLEM!,for three-body problem involving the effect of other bodies,more robust numerical solutions are required).
With initial conditions fi(bo) and v(bo) we can solve the harmonic differential equation(again posing it as two-body problem) to yield the velocity with which it will splash again into atmosphere at the time of re-entry.I have done a simulation for shaheen missile here-->
https://defence.pk/threads/recent-i...-samar-mubarakmand.430471/page-6#post-8334986
Now the challenges for pakistan-
Here in this section of my post,i will briefly touch upon the engineering challenges being faced by pakistan and i am sure my friends @JamD and @The Deterrent would agree and perhaps shed some more light .
1)To cover a larger distance-downrange,missile must have a higher v(bo) and an optimal angle fi(bo) at burnout point.For a larger vi(bo) one would require a larger motor to accelerate the RV from 0(at the time of launching) to vi(bo) at burnout point. Now keeping aside the control challenges,pakistan would have to first fabricate such a big motor that will take a 1tonne payload from 0 to v(bo).This wont be too difficult to achieve(however i believe in tests and pakistan hasnt really shown such big solid rocket motor),However what is difficult to achieve is "weight reduction" by using composite motors and casing--- which is certainly off limits for pakistan at the moment. This in turns requires complex filament winding machines.The composite must be able to withstand the radial pressure exerted during the powered flight regime---unlike a liquid engine,in solid rocket,entire casing undergoes a radial pressure during itz operation.
2)Secondly pakistan would have to improve controls. They would have to let go external surfaces.Currently,pakistani missiles use external surfaces for stabilization and possibly jet vanes for control. This can be replaced by flex-nozzle with servo-mechanism,however it is much more complex arrangement and again none of the pakistani strategic missiles have been tested with this setup. Kindly note that external control surfaces increase drag!
Really awesome, man....
