Indigenous Super & hypersonic missiles in development

[JamD]

The geek in me is loving these. Could you please give me a 'teacher's explanation' of the simulation? I've been looking for books to help me get started on the flight dynamics of guided rockets/missiles, but i haven't found anything, courtesy of ITAR probably.

An overview of the governing equations used here would be most helpful.

I don't get to talk about these things much so always fun for me to geek out as well

I've assumed:
1. Spherical, nonrotating Earth
2. Newtonian central gravity ( F = GmM/r^2 acting towards center of spherical Earth)
3. Drag as q*S*Cd acting axially (no lift)
4. Cd computed using ballpark Beta values
5. Beta = Weight/(S*Cd)
6. Weight, S, guesstimated to compute beta, which gives you Cd.
7. Standard atmosphere used for density in q.
8. I am starting my simulation at burnout: where the rocket has reached it's maximum speed after burning all of its fuel. I'm assuming this is at 100km. This makes simulations much easier (constant mass).

Then using vector dynamics I derived EOMs in terms of altitude h and angular displacement theta. I am also computing speed V and flight-path angle gamma for analysis. Next, I simulated on MATLAB using ode45 with a termination condition when altitude reaches 10km. I also had the code spit out the data at h = 100 km.

If you are really interested I can do the derivation of the EOMs on latex and post it here. The stuff I've seen online is rather confusing.

Also, I'm attaching the code for you to mess around with and have fun


EDIT: The updated file includes a derivation of the EOMs. Enjoy!

 

[CombatSurgeon]

The geek in me is loving these. Could you please give me a 'teacher's explanation' of the simulation? I've been looking for books to help me get started on the flight dynamics of guided rockets/missiles, but i haven't found anything, courtesy of ITAR probably.

An overview of the governing equations used here would be most helpful.



To be fair, the Mach 6 figure in the above book is based on some obscure interview (You can check the references at the end of the book). It may be accurate to assume that the number is false.

The Scud can at best be classified as an early generation MRBM with a ballistic coefficient that gives it a terminal velocity similar to that calculated by @JamD for a Ghaznavi-like missile which can be also be classified as an early to mid gen BM.

The terminal velocity (in the most basic terms) depends on the weight of the missile (or atleast the part of it that is flying towards the target i.e. the re-entry vehicle). So, even if the RV re-enters the atmosphere at hypersonic speeds (>Mach 5), it will actually slow down post re-entry to attain the terminal velocity which would probably lie within the above mentioned range for the type of missile you mentioned.

Please try to be respectful when putting down someone's point instead of attacking them.

Well, well, Mr, thanks for giving me a lesson in respecting. But I fail to see where I disrespected anyone. As a matter of fact it was the other guy who was kinda mocking me. Read again his comments where he mentions Ghaznavi missile.
I see your esteemed poster has stuffed the thread with more gibberish in the name of science. For me it's simpler. I'm giving another reference, the writer being a professional air defense officer.
. For a Short-range Ballistic Missile (SRBM) or Tactical Ballistic Missile (TBM), typically weapons with ranges of around 300km, the missile will typically reach an altitude of 80-100km before reentry. Its velocity on return will hit around 1700 m/s (1.7 Km/s) and it will cover the distance of 300km in roughly five minutes. For a short-to-medium range missile that is launched at a target of, say, 650km away, the missile will reach an altitude of 130-150km before re-entry, travelling at a maximum speed of 2300 m/s to cover the distance in roughly seven minutes. For a Medium-range Ballistic Missile (MRBM) such as the Iranian Shehab-3, by reaching an altitude of 230-250km the missile can reach maximum speeds of 2650 m/s on its return to cover a distance of 1000km in roughly nine minutes. Controlling the range of flight of MRBMs can be achieved by cutting-off the missile engine at the velocity according to the program range or distance to be achieved.

http://www.inegma.com/Admin/Content/File-29122013111330.pdf

 

[S A L M A N.]

I don't get to talk about these things much so always fun for me to geek out as well

I've assumed:
1. Spherical, nonrotating Earth
2. Newtonian central gravity ( F = GmM/r^2 acting towards center of spherical Earth)
3. Drag as q*S*Cd acting axially (no lift)
4. Cd computed using ballpark Beta values
5. Beta = Weight/(S*Cd)
6. Weight, S, guesstimated to compute beta, which gives you Cd.
7. Standard atmosphere used for density in q.
8. I am starting my simulation at burnout: where the rocket has reached it's maximum speed after burning all of its fuel. I'm assuming this is at 100km. This makes simulations much easier (constant mass).

Then using vector dynamics I derived EOMs in terms of altitude h and angular displacement theta. I am also computing speed V and flight-path angle gamma for analysis. Next, I simulated on MATLAB using ode45 with a termination condition when altitude reaches 10km. I also had the code spit out the data at h = 100 km.

If you are really interested I can do the derivation of the EOMs on latex and post it here. The stuff I've seen online is rather confusing.

Also, I'm attaching the code for you to mess around with and have fun


EDIT: The updated file includes a derivation of the EOMs. Enjoy!

Wow wow wow.

I'm saving this answer, as a future reference.

Thank you very much for taking the time to geek out

The best approach to learn something new is to keep at it until it all clicks into place. Needless to say, you've given me something to spent dozens of hours on.

Thank you very much again.

Well, well, Mr, thanks for giving me a lesson in respecting. But I fail to see where I disrespected anyone. As a matter of fact it was the other guy who was kinda mocking me. Read again his comments where he mentions Ghaznavi missile.
I see your esteemed poster has stuffed the thread with more gibberish in the name of science. For me it's simpler. I'm giving another reference, the writer being a professional air defense officer.
. For a Short-range Ballistic Missile (SRBM) or Tactical Ballistic Missile (TBM), typically weapons with ranges of around 300km, the missile will typically reach an altitude of 80-100km before reentry. Its velocity on return will hit around 1700 m/s (1.7 Km/s) and it will cover the distance of 300km in roughly five minutes. For a short-to-medium range missile that is launched at a target of, say, 650km away, the missile will reach an altitude of 130-150km before re-entry, travelling at a maximum speed of 2300 m/s to cover the distance in roughly seven minutes. For a Medium-range Ballistic Missile (MRBM) such as the Iranian Shehab-3, by reaching an altitude of 230-250km the missile can reach maximum speeds of 2650 m/s on its return to cover a distance of 1000km in roughly nine minutes. Controlling the range of flight of MRBMs can be achieved by cutting-off the missile engine at the velocity according to the program range or distance to be achieved.

http://www.inegma.com/Admin/Content/File-29122013111330.pdf

I rest my case, having forgotten what we were arguing over in the first place.