Paintball Spin Physics - Getting to the final Answer
I have posted a framework of info in the data thread. This is from an extensive study we did in the early 90's. The data is representative of our findings.
Currently on the table:
Spin is the only major factor accounting for paintball inaccuracy. Promoted by Pbjosh
Closed bolt operation has an effect on overall accuracy. Promoted by Glen Palmer.
The paintball flight is subject to "knuckleball effect".
Spin may or may not be possible because of the liquid in the paintball.
Barrels have something to do with accuracy.
Seams have something to do with accuracy.
Balls distort with the impact of the air blast.
Balls distort when leaving the barrel.
Ok lets have a pointed discussion on the subject. For those of you just reading this, this thread is a continuation of the "closed bolt" thread found here.
Re: Paintball Spin Physics - Getting to the final Answer
i think that this would be better phraised as the firing system has an impact on the overall accuracy of a paintball. because the same firing system in open or closed bolt configurations will have the same accuracy.
Originally posted by AGD
Closed bolt operation has an effect on overall accuracy. Promoted by Glen Palmer.AGD
Pics are in the Official Data Thread
Don't feel lost in your search for the pictures Tom is referring to; they're in Deep Blue's Official Data Thread. It took me a while to find them. Now I feel kinda silly because I didn't go to the Official Data Thread right away, especially since I now see that Tom mentioned that the data was located there in his original post to this thread. I guess I just missed that sentence the first time through.
Yep, I'm awake... honest... really, I zzzzzzzzz. ;)
Some noodlings before I get home. :)
Why would we need a high speed camera? A good 35mm camera with a bulb setting, a dark environment, and an accurately timed high speed strobe light should be more than sufficient. The faster the strobe, the more data we have to play with, of course. I think we can safely discount any more than a 180 degree rotation per strobe flash in the AGD tests; see below for details.
Assuming the measurements in test 101 are accurate, the ball travels approximately 6 inches between successive stobe flashes as it leaves the marker at approximately 280 fps. This means the stobe flashes are about 1.8 milliseconds apart. I don't know if it's possible to determine what the "further down range" strobe rate is since we don't know the ball's velocity at that point, so I'm going to look only at the near-barrel portion of the test.
Eyeballing the images (I'm not at home right now and thus lack access to proper image processing software), I'd say the ball in test 101 spins around 15 degrees +/- N*180 degrees per strobe flash, where N is an integer. This accounts for the discrete nature of the strobe and the fact that the ball could additionally make one or more complete 180 degree spins and we might not notice it. The spin axis in test 101 appears to be nearly vertical, judging from the underside view portion of the image. There may be a slight precession of the spin axis, but I cannot identify this well from the posted images; I might do better once I get home.
Let's assume the ball spins 15 degrees per strobe flash to start with. This means that the surface velocity of the ball is around 0.089 inches per strobe flash, or 4.1 feet per second; this yields a differential surface speed of 8.2 fps for opposite sides of the ball. The "against the wind" side of the ball sees a 284.1 fps headwind, while the "with the wind" side of the ball sees a 275.9 fps headwind. I'm not all that familiar with the Magnus effect, so I'll leave it to others to utilize this data (if it's is can be used at all) in determining the lateral forces induced as a result of spin.
Now, let's assume the ball spins 195 degrees per strobe flash (15 + a 180 degree rotation that we cannot discern due to the discrete nature of the strobe). Then we end up with a surface velocity of around 53.5 fps, and a differential velocity of twice that. The "against the wind" side of the ball sees 333.5 fps and the "with the wind" side sees 226.5 fps.
Suppose the ball spins -165 degrees per strobe flash (15 - a 180 degree rotation that we cannot discern). Then we end up with a surface velocity of around 45.1 fps and (again) a differential surface speed of twice that. The "against the wind" and "with the wind" sides of the ball have swapped locations, since the spin vector is pointing in the opposite direction this time.
Personally, I don't think the ball spins more than 195 degrees between strobe flashes... 195 degrees per 1.8 milliseconds is already 301 revolutions per second, or around 18000 rpm. Centripetal acceleration is given by V^2/r, if I remember correctly. The surface velocity at 195 degrees per strobe flash is 53.5 fps (16.3 m/s) and the radius is 8.6 mm... this yields a centripetal acceleration of 31000 m/s^2, or around 3150 g's.
In contrast, during firing the paintball experiences a minimum linear acceleration of around 12000 m/s^2 (1220 g's) to go from rest to 280 fps in a 12 inch barrel. A linear acceleration of 31000 m/s^2 yields an exit velocity of around 450 fps. I have no idea whether paintballs can survive being fired at such velocities, but I suspect they don't more often than do. This leads me to believe that centripetal forces resulting from 18000 rpm spin would result in paintball self-disassembly upon exiting the barrel.
I think we can safely limit ourselves to the +/- 180 degree spin regime, and may well be able to ignore the +/- 180 degree portion altogether. This leaves us with at most three scenarios to plug into the Magnus effect for each spin measurement performed.
Happy Magnus-ing! ;)