Paintball Spin Physics - Getting to the final Answer

[s.centralpirate]

The fact that the ball changes direction in mid flight indicates that something, "X", is affecting the ball in flight.

Well, i usally don't tend to get involved in these types of discussions, but since this thread was mentioned on another forum and i am sitting here w/ nothing to do but read today i though i would flex my brain on this topic.

COULD force "X" be caused by a shift in the center of gravity within the paintball itself? since paintballs are liquid filled and the contents prone to separation / settlment over a undetermined period of time.

SINCE every other varible seems to have been accounted for. Inconstencies of the PBs in question i.e. seams, dimples,ectera. ball spin, atmospheric conditions, air sources co2 or hpa, barrel movement, and so on.....

It would be reasonable to assume after elimating all of these EXTERNAL forces that what else would be left to be accounted for....the internal forces of the fill being " stirred" while in flight due to ball spin. Since each ball being fired have its own unique properties( size, weight, shape,fill constency, and "x-factor")....

Anyway thats my best guess

[ph0b]

Originally posted by s.centralpirate
... COULD force "X" be caused by a shift in the center of gravity within the paintball itself? since paintballs are liquid filled and the contents prone to separation / settlment over a undetermined period of time. ...

No, because:

Originally posted by AGD
... In fact the shot group for nylon balls is hard to differentiate from regular paint. ...

[hitech]

The mysterious "X" force appears to be the von Karman Vortex Street phenomenon. This phenomenon causes an oscillating turbulent wake behind a cylinder (or sphere). An oscillating wake would most certainly cause a knuckle ball effect. I have not been able to find a good explanation of why this occurs, but it appears to be a well-known phenomenon, at least among fluid dynamics guys. Here are a couple of links that demonstrate this phenomenon:

http://www.csa.ru/~ignatiev/examples_2d_1.html

http://kuwahara.isas.ac.jp/KARMAN/KR1.HTM

Added: Another example of this phenomenon is the vibration of a taut wire as air flows past it. If/when the oscillation frequency of the wake matches the resonant frequency of the wire (the frequency the wire vibrates at) the wire vibrates. We have all seen (heard) this before.

Okay, it appears that I can't find an explanation of why this occurs because no one is sure. Here are some theories:

http://www.pcnet.com/~jdutka/thesis/thesis1.html

[Paladin]

Originally posted by Paladin
There is nothing at all mysterious about the forces that act on a paintball in flight. (even though I don't know how to explain it in scientific terms)
--------------------------------------------------------------------------------
OK, now HiTech has labeled it for us but I tend to think of it as an effect rather than a "force". The actual force involed is air pressure and the way it varies around the projectile as the current flow behind the ball "oscilates".

Originally posted by AGD


Glen,

The discussion so far has lead to the knowledge that spin does not correlate to where the ball hits down range.

Well, you have not yet convince me of that. So far, all that I have seen in that regard is an agreement that a high speed spin (like what is generated by the Flatline barrel) will overcome or diminish the effect of "X". There is a large gap between the high speed rotation and no rotation at all that seems to have been overlooked; or in this case, "discounted". I'm quite convinced that the rate of rotation that the ball has when it leaves the barrel does in fact have an effect on the ball in flight but I can only argue my personal observations. In short, the less rotation, the tighter the shot group.

Originally posted by AGD


The fact that the ball changes direction in mid flight indicates that something, "X", is affecting the ball in flight. If you want to say that the barrel is causing this you have to make a reasonable argument on what it is. We all know the barrel can induce spin but this has been discounted in this case study.

I've not said that I think the barrel causes "X"; just that "X" is not the only factor involved in the flight of the ball.
Certainly "X" affects a ball in flight but the properties of the ball and its movement after the gun is done with it have an influence on the magnitude of the force created by "X". That is what I was eluding to when I mentioned having followed various objects in freefall and had the opportunity to witness first hand and close up, the variable effects of air flow over an object.

Originally posted by AGD
Your claim of seam problems is discounted because shooting round nylon balls of the same weight shows no improvement in accuracy.

The seam itself is far less of an influence than the not -round shape that influences the shape and frequency of the wake behind the ball. Pressure builds and falls in varying degrees relative to the shape of the object and the speed of its rotation. In freefall, "X" apears to have more influence on the line of flight of a true sphere than on something like a paintball and rigid objects are affected differently than flexible ones are.

Originally posted by AGD

We were proceeding down a path that was getting somewhere but we seemed to have stalled as we got closer to the truth.

AGD

Actually, I'm still not sure just where it is we are going with this.
What is it that the truth is going to conclude ?

[hitech]

Glenn,
are you aware of the phenomenon know as vortex shedding or the von Karman Vortex Street? I believe this is the major problem with paintball accuracy. It causes an oscillating wake behind a cylinder (or sphere). Here is an example of that wake:

[ES13Raven]

That definitely looks like it would cause the ball to "S" curve....

[Paladin]

Originally posted by hitech
Glenn,
are you aware of the phenomenon know as vortex shedding or the von Karman Vortex Street? I believe this is the major problem with paintball accuracy. It causes an oscillating wake behind a cylinder (or sphere). Here is an example of that wake:

Yes, in fact I am aware of and somewhat familiar with the phenomenon. I just didn't know the name for it or even how to describe what I do know about it. I learned much about objects in flight about 30 years ago, while trying to follow or catch things in freefall at velocities very similar to firing paintballs. Alas, I have only emperical obsevations to work with.

[Paladin]

Originally posted by hitech
Glenn,
are you aware of the phenomenon know as vortex shedding or the von Karman Vortex Street? I believe this is the major problem with paintball accuracy. It causes an oscillating wake behind a cylinder (or sphere). Here is an example of that wake:

Yes, in fact I am aware of and somewhat familiar with the phenomenon. I just didn't know the name for it or even how to describe what I do know about it. I learned much about objects in flight about 30 years ago, while trying to follow or catch things in freefall at velocities very similar to firing paintballs. Alas, I have only emperical obsevations to work with but I believe that the more stable the object is when flight begins, the less drastic the results of the oscillating wake/vortex.

[Paladin]

Originally posted by hitech
Glenn,
are you aware of the phenomenon know as vortex shedding or the von Karman Vortex Street? I believe this is the major problem with paintball accuracy. It causes an oscillating wake behind a cylinder (or sphere). Here is an example of that wake:

In the attached images, what does the "R=xx" reference indicate ??

[hitech]

Originally posted by Paladin
Yes, in fact I am aware of and somewhat familiar with the phenomenon...Alas, I have only empirical observations to work with but I believe that the more stable the object is when flight begins, the less drastic the results of the oscillating wake/vortex.

From what I have been able to read it has to do with the reynolds number (in our case, the fps). I even found an equation that predicted the effect. All the testing I have found was for stable objects. There are even pictures of the effect occurring in the wind wake of an island. Based on all the flow patterns I have looked at (the internet is great for find this kind of thing, search for "Karman Vortex") it would appear that this phenomenon whould have a large effect on a paintballs trajectory.

Just for fun, here is a picture of the vortex shedding around an island (the bottom is a 3d view, use a red lens over your left eye).

[ezrunner]

question

does the positioning and posible
movement of the seam of the ball
affect these patterns of airflow?

In hull designs (boats) there is
much attention paid to these small
details, are we seeing the same
thing?

i.e., if the ball is in flight
and turbulence is being induced
as air flows over the seam, and
that turbulence changes as the
ball is rotated in response to
the turbulence.


-rob

[hitech]

Originally posted by Paladin
In the attached images, what does the "R=xx" reference indicate ??

That is the reynolds number. I don't know how to calculate it. However someone here said at 280 fps it is ~ 10^5. It is a function of speed, so as the paintball slowed the number would decrease. I think the effect would be more apparent "down range" as the paintball slowed.

[AGD]

Hitech....those pictures (falling to knees).....ARE BEAUTIFULL!.....(tears come to eyes)..we have arrived at the altar...

AGD

[manike]

How's about an animation of this effect



Apparently...

This animation shows the shedding vortical structures at Re = 300 computed using Jeong and Hussain's lambda-2 method. Along with the hairpin vortices revealed by the numerical streaklines, oppositely-oriented induced hairpins can be observed shedding from the sphere.

You can imagine how the effect of this would cause the ball to follow that 's' shaped path.

manike

[bjjb99]

I've been reading up a bit about how the Reynolds number is calculated, and I figured I'd toss in a basic formula [ref. 1]:

Re = r * d * v / u, where

r is the radius of the sphere in question (could be diameter... there's some dispute over this)
d is the density of air
v is the velocity of the sphere relative to the air, and
u is the viscosity of air

For our paintball case,

r = 0.34 inches = 8.64x10-3 meters
v = 280 fps = 85.3 m/s
d = 1.229 kg/m^3 (air density at sea level, according to a NASA website [ref. 2])
u = 1.73x10-5 N-s/m^2 (air viscosity at sea level, from same NASA site as air density value)

Plugging in our paintball-related values gives us a Reynolds number of right around 52000 (or twice that if the paintball's diameter is supposed to be used instead of its radius). The highest Reynolds number in the photograph presented was Re = 161, and the animated model presented used a Reynolds number of Re = 300.

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.

If we can get our hands on some Re = 25000 or higher pictures, I'd be more inclined to believe that Karman vortices were a major contributor to the paintball's behavior in flight. As it stands now, I remain at least somewhat skeptical.

BJJB

References:
[1] - http://www.aero.ufl.edu/~uhk/STOKES2.pdf
[2] - http://www.grc.nasa.gov/WWW/K-12/airplane/airprop.html