Paintball Spin Physics - Getting to the final Answer

[s.centralpirate]

Well... I'm no scientist, but i would have to agree with bjjb99 to some extent about the Reynolds number in relation to the aerodyamics of the PB in question.

It was my impression that the discussion was relating to the Paintball that, out of a series of shots would, for no explainable reason change directions in mid flight. Now I ask is did this same change of direction occur with the nylon balls as well as the paintballs in the test firing?
If so then the answer would point towards a issue of aerodynamics to a sphere in flight. If that were so I would rest my case.

It is only my obervations on the paintball field that lead me to this conclusion. that all paintballs are not created equal, no ball is without its own characteristics as I said earlier...To what final conclusion this thread takes toward the determation of "x" a person must discount all other factors...THEN account for the varible characterists of each ball fired.

But then thats what we call science...

Play on....

[ezrunner]

hmm

any reynolds affect would be more pronounced on a paintball
than say a black powder ball. This is because of the surface
area/weight ratio, or desity.

That makes things interesting, I know that for distance shooting
we load boat tail bullets which have the back edge of the bullet
tapered to decrease turbulence behind the projectile.

.............
well, I thought I would have free time this week, guess not.

-rob

[hitech]

Originally posted by bjjb99
I am leery about extrapolating behavior seen at these Reynolds number values up into the regime occupied by a paintball moving at 280 fps. If my constants and Reynolds number forumla are reasonably accurate, then an Re = 300 paintball would be moving at around 1.6 fps. That's two full orders of magnitude we're extrapolating over here, and it makes me nervous.

I read that the effect continued well past those numbers. I think it's just easier to photograph at the slower speeds. I'll try to find the information and post it (with links).

Okay, I found it. Everything I have posted has been about flows past a cylinder. Here is what they say about spheres. It appears that the cross over point from minor to major influence is at approximately the reynolds numbers paintballs fly at.

Flow Past a Sphere

Wakes behind spheres are observed to be steady for Reynolds numbers below 300-400. Above this limit (which also depends on the surface finish) vortices break off and are periodically released to form vortex loops that are connected like in a chain.

At Re above 6000 the vortex shedding is very periodic, with Strouhal number ranging from 0.125 to 0.20, the largest figure being a limit at high Reynolds numbers (Achenbach, 1974). Similar wakes can be observed behind particles falling in water. Effects of the surface geometry have been studied for the evaluation of the aerodynamic performances of sports balls (Metha, 1985)

Here is the link that includes the above text:

http://www.aerodyn.org/Unsteady/unsteady.html

[bjjb99]

*chuckle* In the time between my reading your initial statement about finding and posting the link and your actually posting the link, I happened across the very same link!

I'll agree that the Karman vortex effect does occur at high Reynolds numbers. As part of the link I found while you were posting it, they mention something called the Strouhal number. I dug into this a bit, and it seems that the vortex shedding frequency can be determined from this number, the object's diameter, and the object's velocity. Here's only one of several links I found. This one in particular has Strouhal numbers in the Re ~ 10^5 range, so it worked out nicely with our paintball studies.

http://www.enseeiht.fr/hmf/travaux/CD0102/travaux/optmfn/gpfmho/01-02/grp6/pages/strouhal.htm

For a 68 caliber paintball moving at 280 fps, I get a vortex shedding frequency of about 940 hertz. I don't know if that means one vortex every 1/940th of a second, or one vortex pair per 1/940th of a second. This would mean that we have a vortex (or vortex pair) every 4 inches or so as the ball heads downrange. Given that the vortex shedding is "very periodic" at high Reynolds numbers, wouldn't this result in a purely oscillatory motion instead of what Tom is seeing, namely a strong divergence in one direction near the end of a ball's travel? Even near the end of its flight, a paintball that has enough energy to break on a target still has a pretty darn high Reynolds number.

On another note

Since vortex shedding alters the pressure distribution of the air surrounding it, do you think this shedding would be audible? Do you think that might be the characteristic "whoosh" sound you hear when a paintball flys past your head? On a lark, I played a 940 hertz pure tone using Mathematica, and it sounds fairly similar to the fundamental tone you hear when a paintball goes by... something to think about, I suppose.

BJJB

[hitech]

Originally posted by bjjb99
Given that the vortex shedding is "very periodic" at high Reynolds numbers, wouldn't this result in a purely oscillatory motion instead of what Tom is seeing, namely a strong divergence in one direction near the end of a ball's travel? Even near the end of its flight, a paintball that has enough energy to break on a target still has a pretty darn high Reynolds number.

I'm thinking that very periodic could easily mean significantly more vortices are shed from one area of the sphere that the other. It would follow that the sphere would then change course. This would alter the angle of attack and maybe that could further alter things. As you have probably guessed, I don't know. However, it sure seems feasible to me.

Originally posted by bjjb99
For a 68 caliber paintball moving at 280 fps, I get a vortex shedding frequency of about 940 hertz...This would mean that we have a vortex (or vortex pair) every 4 inches or so as the ball heads downrange. Since vortex shedding alters the pressure distribution of the air surrounding it, do you think this shedding would be audible?...On a lark, I played a 940 hertz pure tone using Mathematica, and it sounds fairly similar to the fundamental tone you hear when a paintball goes by your head...

Very interesting. Something has to be causing the vibrations that cause that noise.

[AGD]

YES!!!!! YESSSS!!!! I LOVE YOU GUYS!!!!

We have arrived!! I didn't think it would ever happen that players would take the time to investigate the science behind paintball flight to its logical conclusion but the magic of AO comes through.

YES vortex shedding happens in the R numbers we are talking about.

YES we can verify this because paintballs make a buzzing sound when they go by.

YES this happens with perfectly round nylon balls too.

Now for the last step. BJ mentioned that well maybe its just oscillating so it really doesnt have an effect on accuracy. Here is the last thing to look up. Its called "The drunken mans walk". Its a statistical model that fits what we are talking about here to a tee. Go get it!!

A very excited,

AGD

[joeyjoe367]

Wow, I just read this thread, from page 3 (yeah, I skimmed a bit) and this is just incredible. Only on AO could you see this kind of thing. Absolutly amazing.

It's awesome that we've found out (apparantly TK's always known) about this "reynolds number" but more importantly (to me anyway ) how do we combat this? or Can we?

Is the future of paintball going to see differantly shaped paintballs?

[bjjb99]

Originally posted by AGD
YES!!!!! YESSSS!!!! I LOVE YOU GUYS!!!!

Awwww... shucks.

Originally posted by AGD


YES vortex shedding happens in the R numbers we are talking about.

YES we can verify this because paintballs make a buzzing sound when they go by.

YES this happens with perfectly round nylon balls too.

Now for the last step. BJ mentioned that well maybe its just oscillating so it really doesnt have an effect on accuracy. Here is the last thing to look up. Its called "The drunken mans walk". Its a statistical model that fits what we are talking about here to a tee. Go get it!!

I'm already familiar with random walks of many sorts, and I would agree that a series of random "kicks" perpendicular to the ball's trajectory would result in a random walk sort of behavior.

In a normal random walk, if the steps are of uniform length but each in a random direction, then the average distance between the start and end location is directly related to the square root of the number of steps taken. I cannot remember off the top of my head what happens if the steps are of both a random length and a random direction... gonna have to think on that one a bit.

For a paintball, the steps change the ball's velocity perpendicular to its trajectory... more along the lines of a random walk with random stepsize and direction.

However, to conclude that vortex shedding and a random walk are reasonable culprits for the observed inaccuracies of paintballs, we need to establish two things first:

1. The vortex shedding must be random in nature. The references I've seen so far seem to indicate that the shedding is periodic (i.e. repetitive and thus nonrandom, at least the way I interpret the term "periodic") at high Reynolds numbers.

2. The shed vortices must impart enough momentum to the ball in a direction perpendicular to the ball's trajectory to affect its flight by the amount observed at the end of the ball's travel.

Once we establish these two and can do a bit of modeling, I think we might have a nearly complete explanation of what's happening with respect to paintball accuracy.

Incidentally, if vortex shedding is the cause, then the shed vortices can only impart so much momentum to the ball during its flight. If the paintball is more massive (thicker/denser fills, anyone?), then that momentum would not change the ball's lateral velocity as much. Similarly, heavier balls are less sensitive air resistance and would tend to travel farther (I think... it's early and I'm operating on about 8 hours sleep for two days).

Tom, have you witnessed lighter balls having a statistically larger shot grouping than heavier balls fired at the same initial velocity?

BJJB

[confedman75]

whats the hypothesis, and conclusion? I am realy not in the mood to read 7 pages of posts.

[hitech]

Here is the definition of a random walk (I'm assuming that the "Drunken Man's Walk" is a random walk):

A random process consisting of a sequence of discrete steps of fixed length. The random thermal perturbations in a liquid are responsible for a random walk phenomenon known as Brownian motion, and the collisions of molecules in a gas are a random walk responsible for diffusion. Random walks have interesting mathematical properties that vary greatly depending on the dimension in which the walk occurs and whether it is confined to a lattice.

Here is a link that elaborates on this more:

http://mathworld.wolfram.com/RandomWalk2-Dimensional.html

It seems like a very simple concept to me. Each vortex shed would "pull" the paintball in the opposite direction that it was shed in. If they shed in random directions then the paintballs flight should follow a random walk. Tom, you never managed to photograph evidence of the vortices shedding from the paintballs, did you?

[Vegeta]

Confedman-

what this means is.. we have been looking for what this "X" force is that is making hte balls go all walkabout on us.

We find that when the Reynolds number in in this certain range or higher, vortexes are shed off of parts of the ball in that neat little chain loop fashion seen in the pics. Each one of these sheddings would pull the ball in on the opposite side. The sheddings pullign the ball here and there make for that nice unpredictable movement we all see.

Now we just must define it better.

Unfortunately I don't see any real world fix for this. It is a natural occouring thing.

I think I got all that right. That was sorta a recap for me.

[confedman75]

hmm does the walk about worst or better with thicker fill?(im guessing better). we should try like a powder ball, but not too fine since some people would have a horrible time breathing if they got hit in the mouth(throught the mask). how about a fill thats like a damp flour? muddy but not dusty.

[joeyjoe367]

I don't think it has anything to do with the fill of the paintball. It's simply a naturally occuring phenomenon that happens when you've got a non-spinning object that's traveling though the air at high speeds/reynolds numbers.

[AGD]

Ok look at these applets. They demonstrate where the ball will end up (usually off center) at the end of the random walk.

http://math.furman.edu/~dcs/java/rw.html

http://stp.clarku.edu/simulations/one-dimensional-walk.html

[ES13Raven]

The barrel can make your shot more accurate by keeping the velocity more consistant with the proper paint/barrel match.....