Supersonic aerodynamic drag in a barrel - Help! 2

[em85]

Does anyone know if there is a relatively simple way of calculating an approximation to the amount of drag acting on a projectile in a gun barrel travelling supersonically?

 

[rb1957]

I'm willing to bet the answer is "no".

if i had to determine it, i'd start with the energy of combustion of the explosive, and the muzzle velocity (which would give me the useful kinetic energy)

 

[MikeHalloran]

Some of the drag has to come from cold working of the projectile by any rifling in the barrel. A simple geometric calculation may be inaccurate, because the barrel expands from the (high) pressure of the gun gas.

I was going to write that a projectile has to rub the bore of a smoothbore gun, but on reflection I don't think that's necessarily true, depending on the nature of the flow around the projectile.

I suspect that the dynamics and drag are different for two possible cases:

1. A projectile inserted by unspecified means at supersonic velocity into a barrel filled with initially motionless air. This appears to be what you are trying to model, but I'm not sure that it's physically realizable, or of any practical consequence.

2. A projectile being accelerated within a barrel by means of high pressure gas acting on its projected area, and influenced by gas flowing past it through any available or induced (expansion by pressure) clearance. You might find clues in the literature on hydrostatic and gas bearings.



Mike Halloran
Pembroke Pines, FL, USA

 

[IRstuff]

The drag is quite high in some rounds. The obdurating ring in high performance rounds are plastically deformed to provide the gas tight seal.

TTFN

 

[GregLocock]

The aerodynamic drag of projectiles, as a function of speed, is well known. However, that is not much help in the barrel.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[magicme]

by "drag" do you literaly mean (1) the force of drag as a function of distance down the barrel?
or do you need to know (2) how much total energy was lost due to all the drag effects on the projectile while in the barrel (aerodynamic + mechanical)?

i wouldn't have a clue about calculating item (1).... i think you need velocity measurements inside the barrel as well as pressure measurements versus time.

but i think that rb1957 has the answer to item (2) .... if you could estimate the total propellant energy and the kinetic energy of the exiting bullet and some guess as to the exit energy of the expelled gas, the difference is the work due to all drag effects in the barrel. the average drag force would then be work / barrel length.

now you're going to ask me exactly how to get those numbers, and i am going to say "beats the heck out of me".

regards

magicme

------------------------------------
"not all that glitters is gold"

 

[IRstuff]

There's a really nice program called Prodas, which is used for this type of analysis. Unfortunately, it runs $6K for the basic package.

As an example, the 30mm PG-14 API round has an obdurating band that's 31.2mm in diameter, while its boattail is only 30mm in diameter.

The interior ballistics module of Prodas predicted maximum resistance pressure of 36 MPa, with initial resistance pressure of 17MPa and final of 4MPa

TTFN

 

[rb1957]

i guess IR's post says it all about this site ...
someone somewhere can answer any question !

 

[IRstuff]

Prodas is pretty cool. I built a model of 60 mm mortar shell from various descriptions and got pretty close to the max range from various tables.

If anyone is seriously interested:

http://www.prodas.com/

They do offer a 30-day trial.

TTFN

 

[em85]

Thank you.

So basically the answer is no, unless I want to spend more money than the total budget allows. I thought it might be.
I might try out the free trial of Prodas though.
It is just the total energy lost that I was hoping to calculate.
This is for a gas gun firing FSPs (fragment simulating projectiles) in a sabot. Sorry, I might have had more useful answers if I had clarified that at the start. This is my first posting.
I have already calculated the kinetic energy and theoretical muzzle velocity, however, all the equations I can find use several assumptions (including no friction or air resistance), and I was hoping to be able to calculate to a greater accuracy.

Regards,
Emilia

 

[IRstuff]

The biggest drag component should be the band that seals the round to the barrel, if there is one.

If you have existing hardware that you can test, the thing to try would be a measurement of the force required to pull hte sabot through the barrel, which would allow you to swag the KE loss.

TTFN

 

[btrueblood]

em85,

There's more than one way to skin a cat - or to "roll your own" solution technique.

You got a big hint with IRstuff's post. If you have access to a local library, go search using the term "interior ballistics". This is a branch of mechanical engineering that has been studied for more than 500 years, and some stunningly precise approximations have probably been developed for the problem you described. Most of that work was accomplished without (gasp!) a PC, or even (horror!) an electronic calculator.

I recall at least one good textbook from my Aero 401 course, title I belive was "Gas Dynamics", by Liepmann and Roshko, which had a solution for the pressure wave created by step-function motion of a piston in a semi-infinite tube. I think the pub. date was ca. 1960. I'd give you the page numbers, but the book is in a box at home. Also look up papers regarding shock tube dynamics. You should, using such resources, be able to at least put a bounding limit on the energy expended in expelling the air in the barrel ahead of the projectile. Good luck.

 

[AminG]

Hello,

Please do a search on the term "Ballistics Equation", there are some more links and information on this topic. It may help you.

Good luck

 

[mighoser]

em85,

Try Textbook of "Ballistics and Gunnery" Vol. 1, A/C 71336.

Internal ballistics is concerned with the burning of propellant, and the motion of a projectile within the gun barrel. To answer your question, if the rotating band seals perfectly with the rifling then there won't be any aerodynamic drag. The only affect that air will have is the energy required to move it out of the way. You can calc. the mass of the air and the time between projectile inital motion and projectile exit. The major force being overcome is friction between the rotating band and rifling.

These force is comprised of three forces(the rest can usually be assumed negl.)which act over different lengths of the barrel: the extrusion force Fex, the incision force Finc, and the fifling resistance foce Fr. The book has the formulas for these and you can determine projectile motion using them. Hope this helps.