Paintball Spin Physics - Getting to the final Answer

[bjjb99]

While I agree that the paintball has more forward (read "along the flight path") momentum at 300 fps, its lateral momentum is very small. Given that the lateral forces are proportional to velocity squared, higher velocities will result in stronger sideways "kicks" to the paintball each time a vortex is shed.

Additionally, the 300 fps constant velocity results in a greater shedding frequency (though quite possibly an equal shedding spacing) than lesser velocities. So if you use a decelerating model, you end up with around the same number of vortes sheddings, each of which is smaller in magnitude than a shedding at 300 fps.

Then again, you have more time between sheddings, so those weaker "kicks" act over a longer period...

I think this could go either way, or could well end up coming out exactly equal in terms of paintball shot distribution. <--- and if that ain't a catch-all sentence, I don't know what is.

As for the 2 meters versus 0.2 millimeters... you're missing the units on the graphs. Matlab just loves to put powers of ten in the corners of plots. For example, the histogram has at the bottom right corner of the plot "x10^-4", meaning all the x-axis numbers should be divided by 10000. So you end up with 2/10000 meters, or 0.2 millimeters.

I plan to try to increase the complexity of the flight model to incorporate deceleration, but it truly was a nasty piece of code to work with during my first attempt. I'm thinking it may take a couple of weeks of off-and-on work to hammer the thing out properly. Working on my home computer leaves much to be desired, too... for some reason the software I'm using wants to poll all my hard drives each time I move between coding and execution windows... bizarre. Eventually I'll upgrade to something with a bit more sanity to it.

On a side note, I've also begun to take a look at what effects a slight bias of the shedding orientation would have on the paintball's flight characteristics by changing from a uniform orientation distribution to something more gaussian in nature. The effects can be quite profound (and sometimes bordering on the absurd) for certain gaussian standard deviation parameters. If a (relatively) slowly spinning paintball can induce such a shedding bias perpendicular to its axis of rotation, then this could well explain the deviations we're seeing.

Someday I'm gonna write all this up in a dissertation and get my Doctorate.

BJJB

[hitech]

Originally posted by bjjb99
Someday I'm gonna write all this up in a dissertation and get my Doctorate.

Actually, that is not all that farfetched. There appears to be very little information on the behavior of spheres. What you will have produced coupled with some of Tom's data would make a very interesting paper.

Just thinking about the forces for a minute. If the vortex shedding produces a 2G force in the exact same direction every time (possible if it is truly random) the paintball should be able to rise against gravity by the same amount it would otherwise fall with each vortex shed. Any idea how long of duration the force is present for? If it were applied for say 25% of the shedding frequency it would be able to rise 25% of the distance it would normally far if no forces other than gravity acted upon it. In general, that seems reasonable.

I would really like to see results with more complex calcs. I know, easy for me to say.

[Cristobal]

bjjb99: could you post, or otherwise make available the MATLAB code you used? I'd like to take a look at and try running it.

[bjjb99]

Originally posted by hitech

Any idea how long of duration the force is present for? If it were applied for say 25% of the shedding frequency it would be able to rise 25% of the distance it would normally far if no forces other than gravity acted upon it. In general, that seems reasonable.

What I did was the following:
Each time a vortex was scheduled to be shed (based on the velocity, diameter, and Strouhal number), I would randomly select an orientation for the vortex and used a fixed magnitude for the force exerted in the direction of that orientation. The magnitude was always equal to the lateral force for a paintball moving at 300 fps since we were doing a constant velocity simulation.

After I had a series of "kicks" at specific points in time, I could draw a smooth curve from "kick" to "kick" (spline interpolation) so that at any tick of my time clock (1/10000th of a second per tick) I could see what the forces were. I then applied those forces to the motion model to come up with an X-Y position plot as a function of time.

What this means is that the forces are continually shifting in magnitude and direction as we head from "kick" number N to "kick" number N+1. I believe this continuous method more reasonably describes reality than having a "kick" acting at full strength for some fraction of the shedding interval.

Originally posted by hitech

I would really like to see results with more complex calcs. I know, easy for me to say.

Yeah, easy for you to say.

I have been fiddling with the code here at home and I think I may have found an error. If I correct what I think is the error, I end up with a few orders of magnitude greater positional deviations... so no we're in the 0.1 meter range instead of the 0.0001 meter range. This more accurately represents what folks see in real life, but I do not yet know whether what I'm doing is both physically accurate and correct. :P

I have also been playing with a complete, from-scratch recoding of the deceleration model. I think I've actually written much cleaner code this time around, and it seems to also give results in the 0.1 meter range.

In neither case am I quite ready to conclude that my previous results are wrong and the new results I'm getting are correct... a bit more time will tell. After all, it takes on the order of 90 minutes for a single, 10000-shot test. I'd run fewer trials, but I want the statistical validity afforded me by such a large number of shots.

BJJB

[bjjb99]

Originally posted by Cristobal
bjjb99: could you post, or otherwise make available the MATLAB code you used? I'd like to take a look at and try running it.

Not a problem. Here's a hopefully functional link to the Matlab file. You'll have to remove the .txt extension so that Matlab will recognize the .m extension... Geocities didn't like my attempt to upload a .m file. If worse comes to worse, you could just copy/paste the text into Matlab, I suppose.

http://www.geocities.com/jeremiahswinson/random_walk/prandwalk3.m.txt

I just hope Geocities doens't screw up the formatting too badly.

BJJB

[bjjb99]

Well, I woke up this morning only to find yet more snow falling and traffic accidents everywhere. So I called in to work and told 'em that I'd be late if I was lucky or I'd not show at all, and then I proceeded to sit down and take a good look at the deceleration-based code that I posted last night. It looks physically reasonable to me, and the results look promising.

I've made a new set of plots and posted them on Geocities. Here's a link to all 5 of 'em.

http://www.geocities.com/jeremiahswinson/random_walk/index3.html

Note that now we're talking fractions of a meter instead of fractions of a millimeter. I think these results are probably pretty close to what one would expect. I get an average distance from the aim point of around 8.8 centimeters (about 3.5 inches) at 150 feet; standard deviation is around 4.6 centimeters. The average distance seems to be a bit on the low side, but I think that could be corrected by inducing a slight bias in the otherwise randomly oriented "kicks".

I really don't have much experience regarding shot groupings at this sort of range, so maybe a 7 inch grouping is reasonable after all... I know I'd love to shoot a 7 inch grouping at 150 feet, given my more likely 7 _meter_ shot grouping at that distance.

As for the first set of results with 0.1 millimeter deviations...
um... oops?

The deceleration code I posted yesterday also has a line near the beginning (commented out) which allows one to ignore the drag-induced deceleration and operate at a constant 300 fps. I've not run the trials for that scenario yet, but I'd imagine that the results will be comparable to the deceleration model now that all/most of the bugs are (hopefully) squashed.

BJJB

[pbjosh]

bjjb99

GREAT WORK!

And thank you. I was wondering though.......

If you could show a side ways flight path, maybe with a "shot from this high, went this far" type of programing. Just curious. Please realize I know very little about the programing capabilities on your end, and if you can't I won't protest.

Also you posted this a while back:

On a side note, I've also begun to take a look at what effects a slight bias of the shedding orientation would have on the paintball's flight characteristics by changing from a uniform orientation distribution to something more gaussian in nature. The effects can be quite profound (and sometimes bordering on the absurd) for certain gaussian standard deviation parameters. If a (relatively) slowly spinning paintball can induce such a shedding bias perpendicular to its axis of rotation, then this could well explain the deviations we're seeing.

Have you had any results? Or any even intuative thoughts from what you have seen.

And Back to the biginning again, we have checked the 'Ball in Flight' stuff, but started this whole issue on great ground with alot of questions to ask. Here is the beginning:

Gentelmen,

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.

What have we really answered in all of this? I must say the flight of a ball after it has left the barrel has been worked over grandly by some really great talent, but I still think we have missed something. Why?

Because not all guns shoot the same. Alot are close, but they all shoot different. To find what we were still searching for we need to explore more.

Josh

[AGD]

DO all guns shoot different? In what way?

AGD

[bjjb99]

Originally posted by pbjosh

If you could show a side ways flight path, maybe with a "shot from this high, went this far" type of programing. Just curious. Please realize I know very little about the programing capabilities on your end, and if you can't I won't protest.

I'll see what I can do about getting you a side view plot, though I am not certain that the code I wrote retained anything but the most recent time interval's position information in order to conserve memory. In other words, I think the data for position N+1 just overwrites the data for position N.

Originally posted by pbjosh

Also you posted this a while back:

{My text about vortex shedding bias snipped...}

Have you had any results? Or any even intuative thoughts from what you have seen.

Basically my conclusion was that I could, by introducing a specific amount of bias, cause a significant deviation of the paintball's flight path. For example, if I took the extreme case of forcing all vortices to be shed in the same direction, then you end up with roughly 2 G's of constant acceleration in a not-necessarily-downward direction and you have a paintball flying off into the wild blue yonder. By varying the azimuthal distribution of the shed vortices, I could essentially dial in any off-center bias I wanted to. I did not look into how the shape of the paintball impact distribution varied with vortex bias, as that would have taken far too long on my poor old home computer. Donations to bjjb's computer fund are not tax-deductible, in case anyone wants to send some dough.

BJJB

[LTLGRMLN]

Originally posted by AGD
Spin may or may not be possible because of the liquid in the paintball.

I think that if you find some possible way that you can put some sort of "seperator" in the middle of the paintball then the liquid might not spin. So what im saying is that you could make the paintball to where it has a seperator shaped like an x in the middle of the paintball, thus prohibiting the paintball from spinning. What the "x" would be doing would be sectioning the paintball into four different compartments, and since the liquid in the paintball was not spinning before, now the paint in the middle will spin with the ball.

What you also said before about paintballs distorting with an air blast also got me thinking. If the air blast "distorts" the paintball it seems as though the paintball would "seal" to the lining of the barrel, which would in turn kind of take away the imperfections in roundness of the paintball, but the more the paintball is like a perfect sphere, the less "effort" the paintball has to go through to destroy the imperfections.

[jtoothman25]

I'm a senior in Mechanical Engineering at OIT, and I've taken classes on fluid mechanics. The Reynolds number has nothing to do with a body moving through air, but it has to do with Air flowing through a body(pipe). The length dimension is the diameter of the pipe the air is flowing through. It doesnt make sense to why the other numbers in the equation have to do with air, and the measurement for diameter or the radius is for a paintball. This just doesnt compute. A reynolds number is there to find if air(fluid) is turbulent or laminar. If an Re(reynolds number) is found to be above 2000-3000, then its turbulent flow, and below that is to be laminar. The reason that a HUGE number was gotten was the fact that if a pipe had air going through it at 280 FPS, and the pipe was the diameter of a paintball, it would surely be turbulent flow.

PS: This discussion part is from a couple pages ago, but I needed to clarify this for this point was thought to be done.

[bjjb99]

Originally posted by jtoothman25
I'm a senior in Mechanical Engineering at OIT, and I've taken classes on fluid mechanics. The Reynolds number has nothing to do with a body moving through air, but it has to do with Air flowing through a body(pipe).

...which perfectly explains why Reynolds number has been used for years and years as a tool for examining the aerodynamic performance of airplane wings...

The Reynolds number is simply a dimensionless value used to represent the ratio of a flowing medium's inertial force and viscous force. Its application is not limited to fluid flow in pipes.

BJJB

[jtoothman25]

ok, i was wrong. I was looking at the wrong internet page, I didnt have my fluid book with me. Lesson learned "dont trust the internet" I just looked in my fluids book, and the equation it gives is 2xAirDensity x Diameter of sphere all divided by air viscosity. This is almost what was stated earlier, but instead of the radius used, its supposed to be the Diameter.
In my internet searches, i found a fun site for paintball.

http://home.attbi.com/~dyrgcmn/pball/pballCalc.html

It has more detail than i've seen on most sites, and its directly related to paintball.

[hitech]

Originally posted by jtoothman25
In my internet searches, i found a fun site for paintball.

http://home.attbi.com/~dyrgcmn/pball/pballCalc.html

It has more detail than i've seen on most sites, and its directly related to paintball.

Yes. The author has posted in this thread as [5x5].

[[5x5]]

originally posted by bjjb99

10. The air viscosity used was 1.73x10^-5.

bj would you please check your viscosity value. At 25 C and 760 mm I believe the viscosity is 0.000185 poises. I doubt that there would be much change in the value if the ambient conditions varied a bit from the stated T and pres. However, even if the viscosity is off by a factor of 10, it probably will not affect your calculations much. Although I don't understand Matlab code, if I make a guess as to what I see, the viscosity is only used to find the Reynolds number, which in turn is used in two arrays to interpolate the Strouhal number and the drag coefficients. Since the numbers don't change much in the region of interest, there probably will not be a big difference in the end result.