34 replies to this topic

[Zero Talent]

Thanks for the clarification, bolt.

How would one account for the pressure drop in the barrel? I know with fluids it starts getting iffy when only initial and final volumes, initial pressure, and initial temperature is known, but are there any equations useful in figuring that out? I only have a crappy ideal gas law to work with in those situations, and I'm pretty sure PV =/= Energy (in SI units of Pa * m^3), so I'm hooped. Is final temperature a requirement in this kind of issue?

Any clarification will assist in my little project to properly calculate optimum barrel lengths.

[thiskid13]

boltsniper, if you could put that much effort into a post you have put in the effort to read all the posts. this has already been resolved, i left out the other projectiles that i shoot because i didn't think there would much difference between them and AA batteries. the other projectiles would have taken a little more explaining so i just said AA batteries. everyone has proved to me that there is a drastic difference between AA batteries and 0.4" lead balls, not as much in weight but in drag, which i didn't consider. I'll edit my original post so there is no more confusion.

[boltsniper]

Yeah I know. I just thought the whole thing was intriguing and I was really just curious as to what it would take to get a battery to 1000 fps. As I said it didn`t take that much effrot at all.

Zero, I`ll post agin later tonight on your question. I have to go to work right now/

Edited by boltsniper, 28 March 2004 - 12:28 PM.

[thiskid13]

ok, no problem then, i actually appreciate your work because i after finding out that my gun can't shoot batteries at that speed i wanted to know what it would take to do so.

[merlinski]

Area = (.5/2)^2*pi = 0.1963 in^2
Force on bullet = P*A = (125) * (0.1963) = 24.5 lbs
Acceleration of projectile = F/m = (24.5) / (0.00157) = 15605.1 ft/s^2
Muzzle Velocity = sqrt(2 * a * d) = sqrt(2 * (15605) * (10)) = 558.7 ft/s

Would I be correct in assuming that the unit of one slug is equivalent to one s^2/(ft*lb)?

[cxwq]

Boltsniper, thanks for the problem workup. Cool stuff.

The only place I would question it is your ~20% fudge factor for pressure drop due to expansion, pressure loss to poor seal, and friction. His tank/barrel volume ratio is only 2:1 and friction gets really nasty between objects that aren't made to work together when you travel at speeds like that.

Original poster, when I said ball valves are slow to open, I'm not talking about a difference you can hear or feel. I'm talking about milliseconds and I know for a fact that your ball valve is going to be limiting because you can't possibly have it fully open until after the projectile has started moving, maybe even after the projectile has left the barrel.

[boltsniper]

If you didn`t already pick up...a slug is the English unit for mass: 1 slug = 1 lb-sec^2/ft


Zero:

The optimum barrel length would be defined as the length for which the projectile is exposed to as much acceleration as possible. This would be the length at which the opposing forces (such as friction) are equal to the propelling forces. The propelling force is proportional to the pressure behind the projectile. AS the pressure drops so does the force. The ideal gas law will actually work decently well for calculating the pressure drop. The drop in pressure is inversly proportional to the change in volume. P_1*V_1 = P_2*V_2. Where point 2 is the end of the barrel and 1 is the chamber. Usually for most applications the volume of the tank (in an air gun) is suffucuently larger than the volume of the barrel. The drop in pressure as the bullet traverses the bore will be very small. With thiskid's barrel of 11 feet, drop in pressure due to expansion would likely be an issue, especially at a low pressure of 125 psi

Rather than trying to do this numerically I would go the experimental route. For a specific gun you know: barrel length, bore diameter, and chamber pressure (hopefully). You can find the no-loss muzzle velocity by performing the simple calculations I did an the above post. The value to know will be the force on the bullet. Then fire the rifle with the same settings and read the actual muzzle velocity with a chrono (this would be the part that might be difficult if you don`t happen to have a chronograph). The actual velocity will be lower. Backsolve the actual force on the bullet and you can then calculate a percent loss. The no-loss force minus the actual force would be the opposition force due friction and all other detrimental factors. This percent loss should be reasonably constant for all guns will the same barrel diameter and material and the same projectile.

So once you know the propulsion force and loss percentage you can find the barrel length where the propelling force is equal to the opposing forces. This will be the barrel that provides the projectile with the most acceleration possible. Anything longer will start decellerating the projectile. Mu guess is the optimum length is going to be longer than you would want to have. That is the way it is with firearms. Anyway that should give you a way of finding the optimum length. There are still some assumptions involved, but this should give a reasonably close value for the length.

CX: I wasn`t trying to give a 20% fudge. I was jsut ring to give a generous estimate. You are right though, the losses are probably greater than I had estimated. I actually didn`t catch the 2:1 ratio for the tank. That is low and the barrel is probably too long at 11'.

[thiskid13]

11 feet might be too long but with how i shoot high velocity shots, the barel could be 5 feet too long and affect the velocity very little. for starters, lead slides against brass very easily. the lead balls that i shoot are around 0.4" but it might be less, i've never measured. all i know is that they are fairly big in the barrel but if the were shot right at the very centre of the bore they wouldn't touch the sides. to shoot them i put a wadded up piece of ceran wrap or kleenex behind the lead ball in the barrel. when it's shot the sabot isn't connected to the lead ball in any way so when it begins to deccelerate the lead ball just keeps going with almost no friction on on it. thats why i use 10 foot barrels, so for shots where i use a sabot i get the most acceleration possible. also, i know with a ball valve the projectile gets going before the valve is entirely open but with a solenoid valve wouldn't the same thing happen. on a much smaller potato gun i had problems with the valve not opening fast enough because the barrel was 12". i'm guessing the projectile was out the barrel before the valve fully opened. where the brass tubing met the thread fitting on the inside of the barrel there was a lip. i would make an aluminum sabot that would catch this lip and take about 20 pounds of pressure to knock loose. that way when it was shot the pressure was at its highest and i guess the sudden dislodging helped with acceleration. with the 12" barrel i was able to shoot lead weights about 300 feet with about a 20* angle.
Gun Idea:
i bet i could make a mini gun like that, with about an 8" x 0.5"barrel and a tank that was about 8" x 1" (125psi). with the same sort of sabot method it would have decent range and power, and it would be very compact. i bet with the small volume of air a silencer would work well on it.

I have an even minier gun with a Co2 cartrige as a tank and a 10"x0.3" brass barrel. i called it 'the assassin' because if you're wearing a long sleeved shirt of any kind you can stick it up your sleeve with out it being seen. if you make a fist you can make it so the barrel comes up under your fore arm and just between two knuckles so that only the very tip of the barrel is showing. it shoots playdough balls about 100-150fps and because of the low volume of air it's extemely quiet. i took it to a school foot ball game with a hand pump that goes to 50psi. I shot about 20 people and no one ever found out it was me. my most prized shot was when i shot some people who were in the row infront of us as they were turned around talking to me and my friends. they couldn't figure out what the hell happened and we were laughing our asses off. it is basiacally invisible when its shot so even if it was loud at all no one would figure out where it came from. for the risk of getting caught, pumping it up is more risky than actually shooting because thats the only time it can be seen. i know i was sort of all over the place there but i just wanted to add some new ideas in this gun category.

Edited by thiskid13, 29 March 2004 - 04:19 PM.

[thiskid13]

i'm glad i have 1/2" copper tubing then