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How to calculate the velocity of a bullet fired by a rifle? 
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#1
Jun2511, 04:26 AM

P: 4

Hi everybody,
I'm trying to calculate the spontaneous energy of a projectile fired by a rifle, handgun, or a canon. The amount of the powder in the cartridge is known and with a reasonable assumption of the following we can calculate the initial pressure produced in the chamber as the rifle fired: "For every 10g of powder, there will be 3.2 litters of gas produced in the chamber" The next step is to find the Force acting behind the bullet with known caliber. Next, we can calculate the initial acceleration using F=m*a. So, now that we have the acceleration, how do we calculate the velocity of the bullet right at the start of firing. I have forgotten the formula. Could somebody please answer this question. I'm grateful if you would be kind enough to write the formula. Thanks. P.S. All dimensions are known: Calibre, mass of bullet, length of the barrel, etc. 


#2
Jun2511, 11:24 AM

P: 351

You need more information on the total free volume of the chamber behind the projectile, but even with that there is no simple solution. Assuming instantaneous combustion and production of your 3.2 liters, and that the powder has no volume, you will think how many times that volume right behind the bullet in the shell casing will go into 3.2 liters, and you can multiply that result by atmospheric pressure/square measure and calculate the force using the back end area of the projectile. But THEN it gets messy, as the pressure will half with each doubling of the volume as it goes down the barrel, even discounting that the heat/pressure relationship may not be linear. 


#3
Jun2511, 01:00 PM

P: 1

You could use v^2=2*a*s
where s is length of barrel But if you calculate acceleration just from initial force on bullet and exclude air friction you'll probably get some silly speed. I would try this F_{Pr}F_{Fr}=m*a and then a= F_{Pr}F_{Fr}/m F_{Pr} is force caused by pressure of expanding gas F_{Fr} is friction(air friction and friction of barrel surface) Or you could try to calculate speed from potential energy of powder that's transferred to kinetic energy, but here you also have loses because some of that energy is transferred into heat. 


#4
Jun2511, 01:32 PM

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How to calculate the velocity of a bullet fired by a rifle?
AM 


#5
Jun2511, 02:33 PM

P: 318

Namaste.
first of all using gas laws find the pressure of the gas inside tube. now we know from the definition of pressure that it is equal to force*area so from here you got net force on the bullet(we can assume pressure as constant). now it depends on the length of pistol,rifle that how long this force exerted on bullet. since barrel may not too long so we can consider pressure constant. now you have acceleration distance so using v^{2}=2as find final velocity. here friction are not considered. so you are done. 


#6
Jun2511, 02:58 PM

P: 351

My answer to the start of firing, of course, would be 0. So maybe that's not what was meant. Perhaps it was acceleration at start. 


#7
Jun2511, 04:33 PM

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[tex]PV^\gamma = K = \text{Constant} = P_0V_0^\gamma[/tex] So if you know the initial pressure and volume: [tex]Work = \int_{V_0}^V PdV = \int_{V_0}^V \frac{P_0V_0^\gamma}{V^\gamma}dV[/tex] That will give you the bullet energy at the muzzle. [Addendum: That integral will give you the work done by the expanding gases. This work is done on the bullet and on the atmosphere, so you will have to subtract the latter: [itex]P_{atm}\Delta V[/itex] to get the work done on the bullet. There are losses due to friction and rifling (which adds rotational kinetic energy to the bullet) which would have to be estimated in order to determine the muzzle energy of the bullet.] AM 


#8
Jun2611, 04:26 AM

P: 4

my question is you have initial acceleration and the mass of the bullet. there is no distance or time involved yet. we have only the initial acceleration and the mass. since there is acceleration, then, there should be a Velocity. How do we calculate this very first velocity? The way I tried before, was that I calculate the velocity at the time the bullet left the muzzle then, using excel program, calculated the velocity and increasing acceleration (decreasing acc. forward) for every mm that the bullet is distant from the MUZZLE. THANK YOU ALL FOR YOUR RECOMMENDATIONS BUT FOR THE TIME BEING WE IGNORE EVERY DETAIL ABOUT FRICTION, HEAT, DELTA VS AND DELTA Ps. I just would like to know is there a formula that one can calculate the speed of a bullet just at the START OF FIRING. say 1mm from the chamber. 


#9
Jun2611, 09:40 AM

P: 351

f=ma a=f/m 


#10
Jun2611, 10:37 AM

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What you really need to know is the initial volume and number of moles of the gas immediately after firing. Addendum: The physics of firing a bullet is similar to the physics of an internal combustion engine. Expanding gas does work on a piston sending it down a cylinder. (This transmits energy to the wheels so the piston speed does not increase like a bullet's speed). The compression ratio is key to determining the work done by the down stroke: that is V_{f}/V_{0}. In the case of the rifle, V_{0} is the initial volume of the combustion chamber (this would be the volume of the casing behind the bullet, assuming complete combustion) . V_{f} is the volume of the entire gun barrel. [itex]V_f = V_0 + L\pi d^2/4[/itex] where L is the barrel length and d is the bore diameter. AM 


#11
Jun2611, 02:51 PM

P: 351

That would give us the immediate pressure, from which we can derive the force f on the back area of the projectile. a=f/m. He only needs the mass of the slug. I would ask why this particular question. Just curiosity. 


#12
Jun2611, 03:57 PM

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AM 


#13
Jun2611, 05:16 PM

P: 351




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