Posted: Wed Feb 02, 2011 4:06 pm
Using an apparatus like what is being described for measuring the energy of projectile impacts is not an intractable problem, assuming one has access to a pressure transducer capable of a usefully high sample rate.
How would it be done? Here's the approach I'd use:
1. do momentum calculation to find speed of piston+projectile immediately after impact.
2. Run time stepping program which holds piston acceleration (due to the pressure opposing its travel) constant for a short interval, updates volume remaining using distance traveled, then updates pressure using P*V<sup>γ</sup> = constant and repeats the process. Having it record the maximum pressure encountered during this process is a trivial matter.
With this setup, it's a matter of guessing a velocity interval and getting the program to run through it until it finds a close match to the pressure you measure. Even using very small timesteps and a high-overhead language like Python, this would spit out the correct velocity essentially instantly after the pressure was input.
The real trick would be finding out the correct piston mass, such that the travel was too fast for heat loss through the cylinder walls to be a problem, and too slow for a significant pressure gradient to build up due to shock effects in the gas.
Without a pressure transducer, the measurement could also be achieved by measuring the maximum displacement of the piston during its travel and doing an energy calculation - the kinetic energy carried by the piston+projectile is easily calculated when both masses and an input velocity are known, and the work required to cause a certain displacement is basic thermodynamics.
The second method is, of course, limited to the same piston velocity range as the first. The second method would likely be cheaper to build, but either one would probably end up being more expensive than a Chrony. Chronys have their limitations (EMP "blinds" them, not capable of measuring speeds over 2000 m/s ), but most people here don't build anything that runs into them. LockednLoaded certainly doesn't.
For weak shocks, which is presumably what we're causing here (I think it goes without saying that if the piston ends up going half the speed of sound in the gas, you're doing it wrong...), shocks propagate near the sound speed in the gas. In a 30cm cylinder, the gas at the end would "notice" the projectile impact about a millisecond after it occurred. As the SOS increases with the rising temperature, this delay decreases somewhat, but it's reasonable to say that there's about a millisecond delay in propagation of disturbances from the piston to where the gauge is located at the start of the impact, decreasing from there. Actually calculating the pressure difference between the two places at a given time is a bit more involved. It shouldn't be *too* bad as long as you're not dealing with strong shocks, but it's definitely something to consider. This device is possible, but it's LOADS more complicated than previous posts in this thread have implied. And calculating the lower speed bound, as regards the heat transfer problem? That one's even worse
How would it be done? Here's the approach I'd use:
1. do momentum calculation to find speed of piston+projectile immediately after impact.
2. Run time stepping program which holds piston acceleration (due to the pressure opposing its travel) constant for a short interval, updates volume remaining using distance traveled, then updates pressure using P*V<sup>γ</sup> = constant and repeats the process. Having it record the maximum pressure encountered during this process is a trivial matter.
With this setup, it's a matter of guessing a velocity interval and getting the program to run through it until it finds a close match to the pressure you measure. Even using very small timesteps and a high-overhead language like Python, this would spit out the correct velocity essentially instantly after the pressure was input.
The real trick would be finding out the correct piston mass, such that the travel was too fast for heat loss through the cylinder walls to be a problem, and too slow for a significant pressure gradient to build up due to shock effects in the gas.
Without a pressure transducer, the measurement could also be achieved by measuring the maximum displacement of the piston during its travel and doing an energy calculation - the kinetic energy carried by the piston+projectile is easily calculated when both masses and an input velocity are known, and the work required to cause a certain displacement is basic thermodynamics.
The second method is, of course, limited to the same piston velocity range as the first. The second method would likely be cheaper to build, but either one would probably end up being more expensive than a Chrony. Chronys have their limitations (EMP "blinds" them, not capable of measuring speeds over 2000 m/s ), but most people here don't build anything that runs into them. LockednLoaded certainly doesn't.
For weak shocks, which is presumably what we're causing here (I think it goes without saying that if the piston ends up going half the speed of sound in the gas, you're doing it wrong...), shocks propagate near the sound speed in the gas. In a 30cm cylinder, the gas at the end would "notice" the projectile impact about a millisecond after it occurred. As the SOS increases with the rising temperature, this delay decreases somewhat, but it's reasonable to say that there's about a millisecond delay in propagation of disturbances from the piston to where the gauge is located at the start of the impact, decreasing from there. Actually calculating the pressure difference between the two places at a given time is a bit more involved. It shouldn't be *too* bad as long as you're not dealing with strong shocks, but it's definitely something to consider. This device is possible, but it's LOADS more complicated than previous posts in this thread have implied. And calculating the lower speed bound, as regards the heat transfer problem? That one's even worse