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General Calculations?Im sure these are on this site somewhere, but i havent exactly found what im looking for. does anyone know some links or formulas off hand that could help be predict piston force as well as projectile velocity or acceleration? I know the basic physics calculations with velocity/accel/distance/force, but i dont know how air pressure fits into all that since its constant force, instead of impact.
Any help or redirection is appreciated
As for the projectile questions, this is handy:
http://www.thehallsinbfe.com/GGDT/ For predicting piston force, what's wrong with finding the area of the piston exposed to air pressure and using that to figure out the force applied to it (force = pressure x area)? I'm sure you could calculate acceleration and what not as well if required (acceleration = force/mass) it wont be exact but it would do. Perhaps I've misunderstood.
Pressure is force divided by area (In this case, cross sectional area), or P = F/A. Rearranging the equation and combining it with F = m*a, you get a = P*A/m for the acceleration of the projectile at constant pressure.
Unfortunately, this expression is not immediately useful for modelling launcher performance, as the pressure on the base of the projectile is not constant (Barring an exceptional case such as a tanker truck sized chamber connected to a pen tube barrel, where the pressure drop is negligible). The simplest way to work around this is to use average barrel pressure to find an average acceleration. In an adiabatic system, the final pressure of a decompressed gas is given by P<sub>final</sub> = P<sub>initial</sub>/(V<sub>final</sub>/V<sub>initial</sub>)<sup>1.4</sup>. From this, the pressure at the muzzle can be calculated, which allows an average value to be determined from the initial chamber pressure. This type of approach isn't very accurate, but it will get you in the ballpark. A much more accurate method is to use an iteration based model. For this, the calculations are performed in a series of time steps, where the projectile acceleration, displacement and change in velocity are computed for a fixed pressure over a very short time interval (0.1ms or so), then a new pressure is calculated based on the decompression of the gas over the displacement that occurred during the previous step, and the cycle is repeated until d<sub>total</sub> = l<sub>barrel</sub>. At the end of the cycle, the total velocity change is equal to the muzzle velocity of the projectile. The most effective approach (And the one used in GGDT) is to design a system of ordinary or partial differential equations to model the conditions inside the launcher, and solve the system using numerical methods. You probably won't be using this technique, as it requires a fairly significant background in CFD.
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Wow, thanks for the full explanation.
Also, very helpful calc MrCrowley So if i have a 2.6lb piston in a 4" chamber and 1.3" stroke at 1000psi, that would be: a = P*A/m, or 1000*12.56/2.6 = 4833 in/s^2 = 402ft/s^2 Then d=0.5at^2, or 1.3=0.5*402*t^2, so t=0.0804s Then Vf= a*t, so 32.33ft/s These last two might be unnecessary, but this is where i'm unclear. how is the impact force calculated? F=MA just gives me the initial force behind the piston, not the energy accumulated over its travel..
The final kinetic energy of the piston will be equal to the work performed on it, which if you're assuming constant pressure, is simply force multiplied by displacement.
E<sub>kinetic</sub> = F*d E<sub>kinetic</sub> = (1000PSI*((4")/2)<sup>2</sup>*pi)*((1.3")*(1ft/12")) E<sub>kinetic</sub> = 1361ftlbs Impact force is more difficult to calculate, as it depends upon how quickly the piston's momentum reaches zero after initial contact with the bumper/rear of the valve housing. Basically, the magnitude of the impact force is equal to the change in momentum divided by the time interval over which the change occurs, or F = (p<sub>final</sub>  p<sub>initial</sub>)/Δt. Determining the value of Δt from first principles is really not practical, so situations like this typically rely on empirical measurements.
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