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Old 07-17-2017, 06:38 PM   #31 (permalink)
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I did a final project that involves these calculations, and a machine shop. It was fun. I'll see if I can post some good numbers and derivations this week... Pm me if I forget! I do fluids and mechanics all day now, so it's gotten pretty straightforward.

thanks. that would be awesome
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Old 07-17-2017, 08:08 PM   #32 (permalink)
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ok, just thought of this. the force 124lbs i calculated, is that the force the paintball HAS at that distance or the force that accelerated it???
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Old 07-17-2017, 08:16 PM   #33 (permalink)
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Ok, so basic parameters:
I'd start with a paintball mass of 3.0g, as that's about average. I'd use a chamber pressure of 60psig, and a chamber volume of 1.5 cubic inches. Those are relatively average, but should be altered as needed. Then, you have diameter, which gives area (and remember, force = Pressure x Area, in the plane of action, so it's just acting on the circular cross section, so .688" diameter), and you have the oft-forgotten barrel length.

I'd set up a Riemann sum for simplicity, with a timestep of 5 milliseconds. Take your initial chamber pressure to get your initial force, to give an initial acceleration, given an initial velocity and position of 0. From here, you can derive the velocity at the next timestep (5ms), and then your position can be simply approximated as change in time (5ms) x average velocity (average of your velocity at 5ms, and velocity at 0ms).

Here's where the rubber meets the road- as your position changes, your chamber volume now includes all the space in the barrel behind the paintball. Your pressure remains constant throughout that volume, but if your volume doubles, your pressure is now half. Thus, your force decreases as the paintball moves down the barrel.

Keep stepping through, until you get to a position that's equal to your barrel length (assume an unported barrel that perfectly matches, to start). Your velocity should be around 280ft/sec, or 85m/s, at this point if you have your chamber pressure and volume set up correctly, and the equations are checking out. Once the paintball leaves the barrel, obviously pressure is now 0, thus force is now 0.

It's basically a force, integrated over time. Calc 1/ Physics 1 stuff, but challenging to set up correctly.


Downrange:

It's a lot easier. Calculate energy and momentum based on mass and velocity (muzzle velocity is 280 ft/sec, mass is 0.3g) and that's a pretty straightforward calculation. Then your impulse is derived from energy and contact time. Wikipedia and Engineer's Edge are both great resources to help remember the equations precisely; I use both monthly. https://en.wikipedia.org/wiki/Impulse_(physics)
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Last edited by flyweightnate; 07-17-2017 at 08:21 PM.
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Old 07-17-2017, 08:52 PM   #34 (permalink)
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i can do all thos calculations. i will start asap. i do have one side question... 60PSI is so small, how does it make the paintball shoot out at 300fps?? or is the 60PSI used to just power the mechanical hammer that creates more pressure in the powertube to launch the ball??

this feels like a partial pressure situation.. p1/v1=p2/v2 type of thing. I know if you take a small pressure then cram it into a small volume, you can create more pressure

i know this is a complecated question and i thank all of you. im doing this because my physics has been untouched for 3 years haha. funny thing is, never needed physics in diff eq, calc 3 or linear algebra.... oh and i guess i didnt need spelling either haha

EDIT

yeah i calculated the momentum to show a point to someone but then i started thinking.. again and now look wheres im at haha

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Old 07-17-2017, 10:21 PM   #35 (permalink)
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Originally Posted by LT72884 View Post
i can do all thos calculations. i will start asap. i do have one side question... 60PSI is so small, how does it make the paintball shoot out at 300fps?? or is the 60PSI used to just power the mechanical hammer that creates more pressure in the powertube to launch the ball??

this feels like a partial pressure situation.. p1/v1=p2/v2 type of thing. I know if you take a small pressure then cram it into a small volume, you can create more pressure

i know this is a complecated question and i thank all of you. im doing this because my physics has been untouched for 3 years haha. funny thing is, never needed physics in diff eq, calc 3 or linear algebra.... oh and i guess i didnt need spelling either haha

EDIT

yeah i calculated the momentum to show a point to someone but then i started thinking.. again and now look wheres im at haha
60 psi is a tremendous amount of pressure considering the small area it has to work in and the lightweight projectile it needs to move... and that number, IIRC, is specific to Automags... I believe the article also mentions the old shoebox Shockers as having an actual breech pressure of roughly 100psi.

Back in the day, Tom Kaye spent a lot of time measuring stuff.

Spend some time on ZDSPB.com and check out the marker animation section.
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Old 07-18-2017, 10:25 AM   #36 (permalink)
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60 psi is a tremendous amount of pressure considering the small area it has to work in and the lightweight projectile it needs to move... and that number, IIRC, is specific to Automags... I believe the article also mentions the old shoebox Shockers as having an actual breech pressure of roughly 100psi.

Back in the day, Tom Kaye spent a lot of time measuring stuff.

Spend some time on ZDSPB.com and check out the marker animation section.

Dude! Bunny on AO has fixed many of the links in the old data thread! Apparently, the impulse also had 60 psi also (from the comments). I had seen all of those pics, once upon a time.

Official Data Thread

Over the years, that thread has suffered multiple "photobucket episodes" where links were lost.

On the second page, after the peanut gallery kicks-in, is another link by bjjb99 to some more missing photos in earlier AGD posts;

Historic Paintball Data Photo Gallery by Paul at pbase.com

Tiff 303 shows a paintball knuckle-balling through strobes, which has been my contention about rifled barrels; a screw-ball tends to return to center, whereas a knuckle-ball can continue off course.

Has anyone seen those videos of the shots in the clear barrel lately?

[it was a glass barrel, re: manike here, http://www.automags.org/forums/showt...s+barrel+video ; LT, some good ball-in-barrel info in there as well] still not found

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Last edited by Spider!; 07-18-2017 at 11:34 AM.
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Old 07-18-2017, 02:33 PM   #37 (permalink)
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see thats what is odd. when i use 60psi, the fps comes out to be 135, however, thats in the first 2 inches. If i calculate for a longer distance:

time = sqrt((.0032)(0.1016meters)/(99newtons))

time = 0.001812 seconds to travel 4 inches

now if i solve for velocity i get:

v=56.07mps or 168fps

now if i calculate the entire length of different sized barrels, i get a whole slew of different fps's. the longer the barrel, the larger the fps is which we know is not true haha.

Here is what i found to be the issue with just calculating the way i have been above. If you think of a draw string on a bow, and the length you pull it back, lets say 18 inches or 0.475meters, then if you let it go, the string is pushing that arrow with a given force for that distance of 0.475m. If you attach a fish scale to the string, you can get the force and solve for time and fps just fine. BUT for a paintball gun, we do not have a draw string that accelerates the ball for a length of distance.

HOWEVER, reading back on some of the first threads, i noticed one about volume. The volume is like the drawstring of the bow. So now if i figure out which law and equation to use, i can figure the correct force based on volume that actually propells the ball and then we will be in business.

Then after that i can figure out velocities at differnt distances and then the amount of energy or force the paintball hits a object.

For now. using p=(mass)(velocity) gives me enough info to make some choices haha.

Thanks for all the help. Once i figured out the drawstring thing, i realized i was missing something that someone had said earlier. thanks
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Old 07-18-2017, 02:33 PM   #38 (permalink)
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see thats what is odd. when i use 60psi, the fps comes out to be 135, however, thats in the first 2 inches. If i calculate for a longer distance:

time = sqrt((.0032)(0.1016meters)/(99newtons))

time = 0.001812 seconds to travel 4 inches

now if i solve for velocity i get:

v=56.07mps or 168fps

now if i calculate the entire length of different sized barrels, i get a whole slew of different fps's. the longer the barrel, the larger the fps is which we know is not true haha.

Here is what i found to be the issue with just calculating the way i have been above. If you think of a draw string on a bow, and the length you pull it back, lets say 18 inches or 0.475meters, then if you let it go, the string is pushing that arrow with a given force for that distance of 0.475m. If you attach a fish scale to the string, you can get the force and solve for time and fps just fine. BUT for a paintball gun, we do not have a draw string that accelerates the ball for a length of distance.

HOWEVER, reading back on some of the first threads, i noticed one about volume. The volume is like the drawstring of the bow. So now if i figure out which law and equation to use, i can figure the correct force based on volume that actually propells the ball and then we will be in business.

Then after that i can figure out velocities at differnt distances and then the amount of energy or force the paintball hits a object.

For now. using p=(mass)(velocity) gives me enough info to make some choices haha.

Thanks for all the help. Once i figured out the drawstring thing, i realized i was missing something that someone had said earlier. thanks
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Old 07-18-2017, 02:47 PM   #39 (permalink)
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p1/v1=p2/v2
Use this in a spreadsheet (poor man's finite elements), adjust pressure at every step.
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Old 07-18-2017, 04:09 PM   #40 (permalink)
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In my spreadsheet, I picked 60psig, but only 1 cubic inch. By 14", I think, the barrel pressure was within a few PSI of ambient.

There's also friction, which is close to linear to velocity for dry friction from paintball to barrel.

With a large enough chamber volume, velocity is strongly linked to barrel length. If your chamber volume is small enough, you can actually create a vacuum behind the paintball as it continues forward. But, again, this is neglecting friction, or the air escaping around the paintball.
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