Paintball Spin Physics - Getting to the final Answer

[joeyjoe367]

Right, keeping velocities consisitant is the only thing that we paintballers can do in order to make our guns more accurate.

the graph that's on applet one shows where the ball would land, assuming that velocity is consistant, and that nothing else is effecting the ball's flight.

now having inconsisitant velocities is alltogether pointing the ball in a differant direction, wheter it be higher (higher velocity) or lower (lower velocities). It's like moving the graph itself around, and then re-drawing your random points.

[FooTemps]

My opinion is that the gun can't effect the paintball's accuracy besides consistency. Like joey said, the higher and lower velocities would move the target graph of the landing point. So that means it would take more steps or less steps in the random walk applet providing that it still gets pummeled by airflow at the same rate. That means the longer it flies the more chance of random movement and the shorter it flies the less chance of movement. The only problem with the shorter distance is... well... shorter distance.

[bjjb99]

Originally posted by 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.

I think you're missing the intent of my statement. It's not that the fill somehow changes the way the air travels around the ball, it's that a denser fill (and thus a heavier ball) is more resistant to the forces resulting from the way air travels around it. Since I don't know how much brand-to-brand (or batch-to-batch) variance there is in paintball fill density, I can't conclude that this is a signficant contributor to accuracy.

BJJB

[joeyjoe367]

Ah, I see. a denser fill/heavier ball would be less effected by the vortex shredding since it carries more momentum than a lighter ball.

I believe that there are regulations concerning the weight of a paintball. A heavier ball packs a bigger punch at 300 fps than a *EDIT*lighter*EDIT* ball, so safety concerns are there.

Unless you lower the speed at which you fire the ball. You might actually not lose any range since the heavier ball loses velocity slower than a lighter ball.

Hmm... How about a weighted 10 gram nylon ball? That could test our theory... I would be more than willing to bet that it would be more accurate.

[manike]

Last time I checked (years and years ago now...) paintballs averaged between 50 and 54 grains. I tend to use 52 grains as my average when doing calculations. They may weigh differently now?...

manike

[ES13Raven]

I think the average is about 3.2 grams.....

Some paintballs weigh A LOT less. RPS Lightning weighs 2.5 grams

Here are some weights I have found so far:

Inferno--3.27g
JT--3.19g
Flash--3.23g
Direct Hit--3.26g
PMI--3.21g
Marbalizer--3.25g
Lightning--2.56g (Now RPS Mercury)
Big Ball--3.18g
All Star--3.23g
All Star Yellow--3.14g
Evil Marbs--3.22g
Great American Premium--3.17g

[bjjb99]

Originally posted by 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

I could not get this one to work through the various firewalls and such... all I got was a page with some text on it but no java applet, so I wrote my own random walk using Matlab. It takes a series of one unit steps in random directions and computes the endpoint of the travel.

Originally posted by AGD
Here is another applet that records were each ball "hits" at the end of the walk. Every hit gets recorded as a red bar that builds vertically. The red bars are distributed to the left and right of center. This is only one dimensional but you should be able to get the idea. Hit start and let it run for a while.

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

You can't use this applet to describe the distribution of paintball hits. The behavior of a fixed stepsize position-based random walk in one dimension is not the same as a fixed stepsize position-based random walk with random direction in two dimensions. The "distance from center" distributions are nowhere near identical.

In the one dimensional case, the mean distance from center at the end of travel is equal to zero, and the standard deviation is equal to the square root of the number of steps taken. The distribution of distances from multiple trials fits a gaussian nicely.

In the two dimensional case things are quite different. Now the mean distance from center at the end of travel is equal to the square root of the number of steps taken. The standard deviation is darn near half the mean value. The distribution's shape is by no means gaussian anymore, and actually more resembles a Poisson distribution.

Additionally, a two dimensional position-based random walk is not identical to what's happening during a paintball's flight. At best it is a mapping of the ball's lateral velocity components during flight. This mapping must then be converted to the actual ball's position, which is a cumulative process.

After a bit of number crunching, it looks like the Poisson-like distribution is retained through the conversion of random walk based velocities into actual distances from the origin, but the magnitudes of the distances are much greater than for a plain positional random walk. Instead of the mean distance being around the square root of 250 (around 15.8 times the step size), the mean distance is now upwards of 1000 times the step size. In addition, the relationship between the mean distance and the number of steps taken now seems to be more quadratic in nature instead of the familiar "square root of number of steps taken".

So you're right in saying that a random series of "kicks" to the paintball during its flight will result in a randomization of the shot pattern. However the shot pattern you get from the effects of these "kicks" is not gaussian in nature, assuming the kicks are all of equal magnitude. Instead, it should be more Poisson-like than gaussian. This has the interesting effect of making the probability of hitting close to your intended point of aim very small, and giving the shot grouping a donut shape (if the Poisson distribution is sharp enough).

With respect to whether the "kicks" are randomly oriented, I still have reservations. I've yet to see a reference that explains why shed vortices would be periodic in time but random in orientation when they come off the back of the paintball. All I've seen so far is that at high Reynolds numbers the vortex shedding is periodic, and I still interpret that to mean "cyclic with respect to time and space".

BJJB

Incidentally, I created a short-lived Von Karman vortex street in my bathtub a couple of nights ago, using nothing more than my arm. Fascinating stuff...

[Paladin]

Hmmmmmm

Certainly, the pressure variables from a random shedding vortex is one element of the actual flight of a paintball but I think that to conclude that it is the only element involved in the size of the shot pattern on target, is really a stretch. If the hardware played no role in the event, it must then follow that any device or combination of hardware fired at the same velocities with the same batch of paint should show essentially identical shot groupings (in terms of the size of the shot group), but that is not the type of results that I've seen.
It seems to me that the calculations of the results of a single effect on a rigid sphere should not be held as the last word in predicting the flight path of a flexible and not so round projectile like a paintball. Since a paintball in flight can present both round and elliptical shapes to the airstream and at varying "angles of attack", it apears that the pressure variables in the vortex become much less random. The hardware can affect the status of the ball (relative to shape and rotation) when it enters the air stream; which in turn will influence the results or magnitude of other forces that act on the ball in flight.

[hitech]

Originally posted by bjjb99
I've yet to see a reference that explains why shed vortices would be periodic in time but random in orientation when they come off the back of the paintball. All I've seen so far is that at high Reynolds numbers the vortex shedding is periodic, and I still interpret that to mean "cyclic with respect to time and space".

I have been looking for the same evidence/explanation. However, it seems more likely that the shedding frequency is periodic and the orientation is random, at least random with respect to the previous vortex's orientation. After all, what would the orientation be? It seems that any slight difference in the air flow around the sphere would influence the shed orientation, especially with our not quite round spheres. It may not be truly random, but it doesn't seem that there is any way to predict it (the orientation).

I haven't played around with any of the applets, but I may. Or, I might write my own. The code for the walk is extremely simple, I just need to come up with a simple way to represent the results.

Man this is fun stuff. Now I know why I took physics in college just for fun.

[ben_JD]

I am not a Deep Blue member

If my posting this here is inappropriate, please erase.

My question may seem trite, but are the vortices shed by a paintball strong enough to influence a second paintball following along a similar path?

i.e. do vortices shed by prior paintballs further disrupt subsequent paintballs in a long string of shots (indepedent of the subsequent paintball's own vortex shedding issues)?

[bjjb99]

Re: I am not a Deep Blue member

Originally posted by ben_JD
If my posting this here is inappropriate, please erase.

My question may seem trite, but are the vortices shed by a paintball strong enough to influence a second paintball following along a similar path?

i.e. do vortices shed by prior paintballs further disrupt subsequent paintballs in a long string of shots (indepedent of the subsequent paintball's own vortex shedding issues)?

Good question. I do know that vortices can hang around for a surprisingly long time. And I do know that wing tip vortices from aircraft can disrupt the airflow over a subsequent aircraft's wing. So I suppose it is at least possible for a paintball's vortices to affect subsequent shots.

For now, however, I think I'm going to concern myself with how the vortices affect the paintball that's doing the shedding. Can anyone point me towards a reference describing the magnitude of momentum change imparted by a shed vortex? Preferably one with big writing and lots of pretty pictures...

BJJB

[bjjb99]

Originally posted by hitech


I have been looking for the same evidence/explanation. However, it seems more likely that the shedding frequency is periodic and the orientation is random, at least random with respect to the previous vortex's orientation. After all, what would the orientation be? It seems that any slight difference in the air flow around the sphere would influence the shed orientation, especially with our not quite round spheres. It may not be truly random, but it doesn't seem that there is any way to predict it (the orientation).

How about "two consecutive orientations are radially symmetric about the paintball's trajectory"? I'm not saying that we should be able to predict where the shedding occurs; rather, I'm suggesting that the shedding oscillates between a couple of distinct locations on the ball. Once the oscillation is started, it may well be tough to kick it out of such a back-and-forth mode... sort of a metastable oscillation state, if you will.

Originally posted by hitech


I haven't played around with any of the applets, but I may. Or, I might write my own. The code for the walk is extremely simple, I just need to come up with a simple way to represent the results.

What exactly are you trying to represent? A good scatter plot from multiple random walk trials is a decent way of showing where each path ends up. A histogram of "final distance from origin" data will show the distribution reasonably well. And of course there's the good old mean and standard deviation results to look at too.

Do you have access to Matlab? If so I've got random walk code already written, along with a transformation from acceleration/velocity to positional data. You can plot pretty much any variable against any other as long as the vectors/arrays are the same size.

Originally posted by hitech

Man this is fun stuff. Now I know why I took physics in college just for fun.

Heh. Guess I have fun for a living then.

BJJB

[Vegeta]

At 300 fps, firing 10 balls per second, the paintballs are going to be 30 feet apart in the air.

What we need to do is figure out if/how the vortices in the air will spinoff and possibly cause our next shot to vary off course. The thing is, at 10 balls per second at 300 fps, yes they may be 30 feet apart which seems like alot but they are travelling at that same speed so the balls will be 0.1 seconds behind each other. Will the air turbulence from the vortices shedding hang around for 0.1 seconds? because if so, that ball behind the first is going to come through that are where the first ball shed the vortice and hit that turbulence exactly 0.1 seconds later going 300fps, and possibly shedding vertices of it's own.

I might have to make some 3d animation of this process in real-time if i have a chance... that would really convince people.

[hitech]

BJJB,
Now I see what you are getting at. Yes, it would be nice to find something that states the vortices shed randomly. I could see them oscillating and the orientation spinning, possibly back and forth.

Not I do not have Matlab, I don't even know what it is. I was thinking of writing a simple VB program. Having the program walk is easy, showing it on the screen is what I have to figure out. Simply listing the ending point with direction and distance requires math formulas I don't know. I may have taken physics in college, but I've never used it since.

I'm sure it's not as much fun when it's work.

Here is a link on the force generated. Is it any good?

http://www.eas.asu.edu/~squires/sphere_summary.html

[bjjb99]

Hitech,
Matlab is a data processing and visualization programming language. It was designed to allow rapid scripting of processing algorithms. The scripts are processed interpretively instead of being compiled, like the old interpretive BASIC programs of yesteryear. Matlab operates on matrices very quickly, allowing the user to skip having to write a bunch of nested loops.

Distance from origin is simply the Pythagorean theorem:

distance_from_origin = sqrt(X_endpoint^2 + Y_endpoint^2)

Direction would be a trigonometric exercise if you want angles instead of a vector. I used a pre-canned function called atan2... it's a four-quadrant arctangent function, covering the full 360 degrees of a circle instead of just a portion of it.

The link you listed had a nice plot of force coefficient versus some formula that I couldn't identify. I think the greatest contribution I obtained from that link was a new suite of search terms to plug into search engines.

BJJB