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Unread postAuthor: DYI » 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 :roll: ), 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 :P
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Unread postAuthor: Lockednloaded » Thu Feb 03, 2011 3:02 pm

leave it to DYI to ruin everyone's hopes and dreams with real math and physics :lol:

I now understand that the transfer of energy is loads more complicated than I initially thought, but I don't need accuracy for this, because it'll be much more accurate than my current measure of speed which only has four readings: "that was weak", "Meh.", "that was pretty fast", and "SH*T"

I could never hope to make all the appropriate calculations to get my number zeroed into ±5fps, but i'd be totally happy with ±15fps with a cheap, homemade contraption
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Unread postAuthor: saefroch » Thu Feb 03, 2011 3:41 pm

Or you could just build a ballistics pendulum...
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Unread postAuthor: Lockednloaded » Thu Feb 03, 2011 3:47 pm

I've considered it, but even that begins to get too complicated
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Unread postAuthor: metalmeltr » Thu Feb 03, 2011 4:42 pm

Arent the calculationsthe only hard part? there may even be an online calculator for that, in fact i think i saw one once.

Edit
found one
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html
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Unread postAuthor: saefroch » Thu Feb 03, 2011 4:46 pm

Well on the other thread that LnL linked, the argument was that to achieve any meaningful accuracy with a ballistics pendulum you'd have to spend so much money you might as well buy a chrony.
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Unread postAuthor: DYI » Thu Feb 03, 2011 5:36 pm

leave it to DYI to ruin everyone's hopes and dreams with real math and physics


Thanks guys, I do my best.

If +/-15% is all you're looking for, use the second method in my last post (piston displacement measurement), take a wild guess at ~10m/s piston speed for effective operation, design and build from there and ignore any effects you don't want to calculate. :lol:

A ballistic pendulum would, however, be a better idea. I'd argue that a ballistic pendulum of better accuracy than LnL's current "measuring" system could be done for free by most people here. The only required parts are a wooden construction to hang the mass on, a scale to weigh the mass, a "striped board" type device, similar to what the Mythbusters are so fond of, and a camera (high framerate definitely not required). I built one with a soda can, fishing line, and some densely packed aluminum foil a few years ago for the ETG. Larda's is a good example of a larger, similarly improvised system.

Due to the mass of the strings/rope, and rotation of the pendulum (air resistance shouldn't be much of a problem at these low speeds) the free ballistic pendula can't approach Chrony accuracy, but for you +/-15% types that's no problem at all. The calculations are trivial when ignoring rotation and such, especially if you have a programmable calculator (or, you know, a computer...). The downside? Apart from the accuracy issue, they're not as forgiving of poor accuracy as a Chrony is, and take slightly longer to use due to the necessity of setting up a camera and the ruled board, then looking at the video afterward.

Certainly worth the effort, if you happen to have no remaining money, or just in case you start building 3000m/s launchers eventually. :roll:
Obviously, I need to add the requisite statement about how, for what they can do, Chronys are roughly free, and any remotely self-respecting spudder should have a pair and a spare, at the very least.
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Unread postAuthor: SpudBlaster15 » Thu Feb 03, 2011 7:57 pm

I'm in agreement with DYI here. A ballistic pendulum will typically have one of the highest accuracy to cost ratios among velocity measurement devices, provided they're constructed and set up with reasonably care.

If we're dealing with average spudgun velocities, my choice for a super inexpensive system would be an acoustic chronograph. You only need a laptop with Audacity (Who doesn't have one laying around the house these days?), a microphone, and a couple of evenly spaced sheets of paper to shoot through. Knowing the distance between the sheets, as well as the time between impacts, it's exceedingly simple to calculate the average velocity of the projectile during that time step. The reading will not be as close to the muzzle velocity as what a direct energy measurement would provide, but with an amateur budget and equipment, the experimental error will be significantly lower.
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Unread postAuthor: saefroch » Thu Feb 03, 2011 9:15 pm

Waveform I recorded a while back of a shot impacting a sheet of plywood. Can you show me where I'd say the projectile leaves the muzzle, and where it impacts the target?
Image
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Unread postAuthor: jackssmirkingrevenge » Fri Feb 04, 2011 2:27 am

Lockednloaded wrote:thats a good deal, but its nearly twice the price and lacks the DIY spirit. Its kind of like buying a QEV vs building your own piston valve


I think the DYI spirit made the point already, and I agree. A chrony is just another tool in my book, you wouldn't synthesise your own PVC and extrude the pipes, or mine the iron ore to make your own hacksaw blades, right?

A good basic chrony like the F1 is an inexpensive and accurate instrument which will help you gauge the power of your launchers to a very fine degree which is essential for serious development work.
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