Projectile velocity: This is a real world question.?

Question

I use 4 mortar like cannons to propel a projectile. Attached to the projectile is a net. The net is shot over birds to trap and relocate them. The motive force for the projectiles is compressed air at 120psi. The air is discharged into the mortar barrels simultaneously. I've been told that if I lengthen the barrel, I will be able to obtain greater projectile velocity. What are the parameters that would control the velocity? How can I calculate the optimal barrel length? I'm thinking with a short barrel, a lot of the compressed air escapes from the end of the barrel as the projectile leaves. Thus energy wasted. It seems like the optimal barrel length would be when the compressed air pressure has dropped to atmospheric pressure at the point at which the projectile exits the barrel. Assume a large tank feeds each mortar barrel and there is a negligible drop in pressure during the discharge. An electronically controlled orifice of diameter D opens for duration T.

Answer 1

Your instinct about a long barrel is correct but you probably do not want to expand all the way to atmospheric pressure. Begin by assuming you have a charge of air in your cylinder and you suddenly release the projectile. The energy available from the expanding air can be determined by assuming an adiabatic (quick enough for no heat transfer) expansion. As the gas expands it cools significantly so it does not follow Boyle's Law. Instead the pressure-volume relation is: P1/P2 = (V2/V1)^(1/k) where P1, V1 are the initial pressure and volume, P2, V2 are the final pressure and volume and k is the specific heats ratio (1.4 for air). Your cylinder has a cross-sectional area A and length A*L1 = V1, A*L2 = V2. By integrating AP dL over the length of the expansion. you get the total work (W) done by the gas on the projectile. This total work is converted to kinetic energy so that W = (m*v^2)/2 where m is the projectile mass (not weight) and v is the velocity.

If you do the calculations, you will find that a much shorter tube than the full expansion will give nearly full velocity. If you include the resistance (both frictional and air) of driving the projectile down the tube, the maximum velocity will require a shorter than full expansion tube.

All this assumes that you can get air into your cylinder fast enough. Unfortunately there is a real limit to that. It is called choked flow. You can estimate the rate at which air will come through the orifice by assuming a flow diameter of about 60% the orifice diameter and a compressed air pressure of 70% the initial pressure. Finally, the choked flow velocity is the speed of sound (around 1100 feet/second).

By integrating the energy relation above you can figure the velocity of the projectile at any time and by integrating that you can figure the time for the projectile to be at any position. If the time required to charge your cylinder is more than about 1/2 the time it takes the projectile to launch, you definitely need a larger orifice. In that case a longer tube won't really help. It is likely that you will find that your orifice is too small.

Sorry for the length and complexity of the answer but your problem is quite difficult.

Answer 2

In order to calculate your ideal barrel length, you need to know the initial volume of the chamber that you are pressurizing with your 120 psi. Then just use Boyle's gas law to calculate the volume of the gas when it has expanded to atmosphereic pressure, i.e. 14.7 psi (at sea level). However, this will not give maximum "kick" to your projectile. It will, however, give you the most energy efficient use of your air tank contents. If you want maximum "kick", then you should power your projectile at 120 psi through the whole length of your barrel, and your ideal barrel length is that length that matches the maximum capacity of your valve to supply 120psi to the projectile. That is, once the projectile is maximally accellerated to its maximum velocity with 120psi, any further travel in the barrel will have a braking effect, although you may still get some additional accelleration with lower psi's, using still more barrel length, I suppose. In that case, you have a multi-variable calculus question, not the least of which is the fact that the flow of a fluid through an orifice or barrel is proportional to the 4th power of the diameter. Good luck.

Answer 3

application of trigonometry value of Cable Oil Spill Pricing instantaneous provider figuring out Mountain Peaks and CBL test digital Transmission Jacob's field Sending photographs how are you able to construct or study vibration profile The Leaning Tower of Pisa sign Fades Compound activity Distorted Deployable area Reflector Antennas development a Bridge Depreciation of a sparkling automobile Thermal Fatigue

Answer 4

i had a 10 inch helicopter wheel pressurized at 127 psi explode. I m trying to figure out the speed of the rim when it exploded. The wheel assembly is a 2 piece rim that splits in half and is bolted together with an inner tube and tire mounted on it. It was laying on the ground when it exploded and one rim half hit the desk i was standing next to.