Paintball Spin Physics - Getting to the final Answer

[bjjb99]

I hereby nominate Hitech for the "most diligent information gatherer of the year" award. How in the world did you find those two .pdf reports? I gave up a couple of weeks ago after no luck in finding anything concerning lateral forces on spheres. I am impressed!

Originally posted by hitech
It appears that the side drag coefficients for a sphere are only an order smaller magnitude than the "forward" drag coefficient. While I will have to determine what that really means, I believe THAT IS A HUGE FORCE. If that is true it is amazing that a paintball ever hit anywhere near where it is aimed.

Added on edit: If I am reading correctly the side coefficient is 0.1.

I would give the coefficient (Cs) an average value of around 0.06, judging from figure 1 in the file AIAA_Apr_2002.pdf.

To determine what this means, you need to plug that coefficient into a drag-like force equation; here ya go:

Fs = 0.5 * rho * V^2 * Cs * A, where

Fs is the side force experienced by the paintball,
rho is the density of the air (around 1.239 kg/m^3),
V is the velocity of the air relative to the paintball (around 85.3 m/s for a 280 fps shot),
Cs is the side force coefficient (around 0.06), and
A is the cross sectional area of the paintball (around 0.000234 m^2).

Plug in the numbers, stir gently, and you get a side force of around 0.063 newtons.

What does this mean? Well, let's see what we get for a lateral acceleration resulting from this side force. F = m * a is all we need. The mass of a paintball is around 0.003 kg.

a = F/m
a = 0.063 / 0.003 = 21.1 m/s^2

21 meters per second squared for a lateral acceleration... that's over 2 g's of sideways acceleration this thing is experiencing, and that's for only one shed vortex. There are a couple/few hundred shed vortices during the flight of a paintball. About the only thing that helps us get some level of accuracy out of a paintball is that those vortices seem to be shed in random orientations.

If I get a chance this weekend, I'll see what I can do about generating a random walk using this type of data. The walk will be a random direction walk using random step sizes. We can then plug the results of that walk into a motion model to see where the paintball should fall. Rinse/repeat several times and you end up with a distribution function describing where a paintball will likely strike relative to its aim point.

BJJB

[hitech]

Originally posted by bjjb99
I hereby nominate Hitech for the "most diligent information gatherer of the year" award. How in the world did you find those two .pdf reports?

Thanks. Actually, I'm just good at skimming. You are doing all the real work. Thanks, I really wanted to know the answer to how much lateral force there is. Thanks again.

BTW, has this changed your mind on paintball barrels?

[bjjb99]

It's been so long since the beginning of this thread (and the thread that spawned this one) that I don't remember what my original thoughts re. barrels actually were.

Something popped into my head while writing the above sentence...

We have determined that spin itself does not significantly affect the paintball's trajectory at the spin rates seen coming out of a normal barrel (i.e. not a barrel specifically designed to induce spin). We used something akin to Bernoulli's equations to determine the effects of spin on a paintball's trajectory. The calculated trajectory effects were significantly less than the deviations found in AGD's tests.

So a low spin rate Bernoulli-type differential airflow was not enough to screw up a paintball's flight. However, could that small amount of spin actually induce a preference in the way vortices are shed from the paintball? With no spin, vortex shedding is essentially random in orientation for spheres at these high Reynolds numbers; perhaps spin adds a bit of a bias in the vortex shedding orientation. We see that the vortices result in approximately 2 g's worth of acceleration each time one is shed, so a slight spin-induced preference in vortex orientation may cause a decrease in accuracy as compared to the no spin, pure random walk case.

Something to think about, I suppose...

BJJB

[AGD]

And here I thought this thread was dead! Hitech, man I have to hand it to you, you truely are the KING of internet searches! You should go out on the net and look for a pot of gold!

Its just incredible that we have some kind of number for the side force on the ball. This thread has gone so much farther than we took the research that I am incredibly impressed. Then again when we did the tests we didn't have the net

So if Bjj can come up with a random walk program we will actually have a mathematical formula that characterizes paintball accuracy! (and it doesn't include a barrel).

I posted this thread up on the main forum in hopes that the general paintball populace would read it. Again if I had any marketing sense I would have known that they really don't care. So it remains to the few to delve into the unknown in search of knowledge.........

AGD

[luke]

Again if I had any marketing sense I would have known that they really don't care.

[hitech]

Originally posted by luke
I don't think that's a fair statement. I think it's more that the technical jargon is TOO far over everyone's head. I am interested in the final answer though.

I think it is quite fair. The only "training" I have is a Junior College Physics class. Otherwise I write computer programs for a living.

In simple terms what makes paintballs so inaccurate is 2Gs worth of laterial (side) force from what is called vortex shedding. There isn't anything a barrel CAN do to affect it. The only difference a barrel can have is more consistant velocity. That makes a small difference. That's it.

[luke]

hitech, That's probably more physics than 95 percent of us on AO.

When I said "I don't think that's a fair statement" I was referring to Tom's statement "they really don't care." I was implying the debate was over most of our heads, not that we didn't care. In fact, most of us do care in the FINAL ANSWER , we just prefer it in laymen terms.

(look at the hits on the thread, to me that implies people are reading it)

[hitech]

I guess my reasoning for it being a fair statement is that almost every day some asks what barrel is better than another. Read the answers. Everyone thinks that paint to barrel match is king. Why? Does anyone know why? Some believe that it give better velocity consistancy. Anyone ever tested this? My simple observation is that it does NOT. Freaks and other barrel kits are very popular and very expensive. And yet NO ONE knows if they even work. I'll bet they don't make even 0.5% difference. My huge bore stock emag barrel often gives the EXACT same reading over the chrono for two shots. How much more consistant can you get?

BTW, I paid $25 shipped for it. Why, probably because it was ONLY a stock barrel.

Added: 3317 views. That is a lot. At least someone is reading this.

[[5x5]]

I just realized I posted a long discussion that tried to summarize some of the major views on this thread on the wrong forum. My discussion also considered an alternate mechanism for the 114 data.
The discussion is quite long, so I hate to repost it here. Please take a look at the last page of the Paintball Talk forum, Paintball Spin Physics thread. I would certainly like to hear this Group's views.

[AGD]

Luke,

Your right it probably was not fair. I just go for the summary when info in not in my hot list.

SO does everyone like Hitech's summary? 2g's lateral force randomly walking around the ball going down range?

AGD

[hitmanng]

Oh boy here I go.

Warning:
This is not strictly about the title of Spin physics since I think that has been solved,but it does relate to the original question of open and closed bolt and accuracy, and I think it is appropriate to discuss at this point.

Hi All,
I haven't talked about any of this since Deep blue was the fight club,we discussed reynolds factors and turbulence even back then.
I think there is a big part of the equation that is being missed. You have analysed until you are deep blue in the face what happens durring 99.5% of the paintball flight. That once you have a sphere traveling at 280fps, with the current wt of a paintball, you are going to have a certain level of randomness imparted by the turbulence behind the ball. I for one stand up and say bravo. You have explicitly defined something that we cannot change unless we play in a vaccum (deadly), or fundimentally change the paintball (not likely).
You have also effectively eliminated the need for people to worry about spin/rifleing unless the paintball gets heavier, changes shape, or we shoot it a lot faster.

I think Glenn's problem with all of this (not speaking for him of course), and mine, is that we are in an amazing way ignoring that first 12 inches of the balls travel. At this time we are not looking at the simple fluid dynamics of a ball. I am talking about what happens in the marker and in the barrel before it exits and the effect this has on the tragectory of the ball within the barrel and upon its immeadiate exit from the barrel.
This leads us away from much of Tom's data as he used the same gun and barrel for every shot and it was locked in a vise. This means he removed all of the parameters that we can effect and change to improve accuracy. All that was left was the randomness of air currents (Sorry Tom, not meaning to burst this scientific bubble, but I am the Slayer of scared cows, even yours).

So what matters the first 12 inches? Look at what we have.
1. We have a wall of force (air) accelerating the ball into the atmospheric air(no trailing currents there folks) and in some way disipating. Ok, that is why Tom created the Crown point barrel (he must have thought it mattered) and others created the ported barrel. If the barrel is ported and long enough the issues of the initial push may be eliminated (maybe longer barrels are more accurate).
2. We have the barrel. The ball is traveling through the barrel with forces places upon it. One is the force excellerating it, another is the force of the barrel pushing on a larger ball, or the force of the air passing the ball for a smaller ball.
3. We have a moving marker. I know you may think that doesn't matter but we know that a ball can ricochet around in the barrel from Tom's barrel tips and the talc test. The barel might not be perfectly straight or aligned or you may be moving it.
And doing the math:

The diameter of the paintball is 0.68 approx I am not sure of the bore of a 2 step barrel but let us assume 0.7. If the ball is going down the exact center (which I highly doubt considering manufacturing tolerences) that leaves 0.01 inch that the barrel would have to move. The ball is only in the barrel for about 0.006 seconds.
Thats 0.01 inch divided by 0.006 seconds = 1.66 inches per second. All it takes is moving your barrel 0.01 inches at a rate faster than 1.6in/sec. That is while shooting 6 bps of perfect balls out of a perfect barrel to have a hit. I think maybe it hits more than you think.

Extrapolated From: http://www.automags.org/ubb/Forum4/HTML/000019.html

So what who cares?.... Well you do. These are all elements you can change. They effect what direction the paintball is heading then it leaves the barrel.
So lets say our shot vector is one degree off straight when it leaves the barrel. At 5 feet it is 1 inch off mark, at 50 feet it is 10 inches off mark. Let us say our shot vector is at an angle of 0.5 degrees off center when it exits the barrel. That's 0.5 inch at 5 ft, and 5 inches at 50 ft, and 10 inches off mark at 100ft.

Maybe I am full of it maybe all paintballs leave all barrels and all guns at exactly the same angle. And maybe we always shoot with our gun in exactly the same position, and maybe we never move even 0.01 inch at a rate of 1.6in/sec while taking a shot.

I enjoyed the read on this post it was incredible. Keep up the good work. Now lets look at the other 0.5% of the game and maybe that will make all the difference.
Respectfully,
Your Friend
Hitmanng

[hitech]

Originally posted by AGD
Your right it probably was not fair.

I still think it was fair. Look at the results of this poll:

http://www.automags.org/forums/poll.php?s=&action=showresults&pollid=1143

[pbjosh]

Sorry for dropping out, but life an family have taken me out of this for a little bit. I want to drop a VERY quick couple of comments here-

I am completely in awe of the great numbers everybody has come up with, but I did want to reconnect with some thoughts I posted in the beginning.

There is a difference in accuracy, even on bench mounted guns, between different barrels, different markers, and different paint. If we are to acknoweldge the findings from PCRI for accuracy, we need to also acknowledge that all the guns shot different patterns, with some guns being more accurate than others. We have figured out what the ball does after is leaves the barrel, but we are still neglecting that there is something inherent in the action of a specific marker, even bench mounted, that leads to differences in accuracy. Even a clean to dirty barrel will affect the accuracy, and that IS NOT included in any of the numbers brought up yet.

The fore-ball air colume might be a culprit, but also I think we dismissed the balls rotation too quick. If I am allowed to reverse the Tippmann Flatline #'s (if they are correct) here is a quick thought.

10,000 rpm is 166 rotations per second, and at 280 fps, that is 14 ft traveled per second. 168 inches a second. Or about one revolution a inch. How does that affect the air column?

Can anybody figure out the sideload boundy affect knowing the amount the ball is held up and the amount the the ball is rotaing per second? I will clarify after some thought n my own.

Josh

[bjjb99]

Okay. I originally attempted to perform a full-blown simulation incorporating drag force to slow down the paintball, recalculation or the reynolds number at each time step, and a whole mess of other bells-n-whistles. It was a royal pain in the butt trying to keep track of all the variables, and generated results that just didn't make any sense. I had clearly made some errors in my coding somewhere along the way, and I just couldn't seem to track it down.

So, I decided to simplify things... a lot.

The parameters for the simulation are as follows:

1. The ball's axial velocity (U) is a constant 300 fps (91.44 m/s).
2. The Strouhal number (St) used was 0.2.
3. The paintball's diameter was 0.68 inches (0.017272 m).
4. The vortex shedding frequency (St * U / D) was approximately 1000 Hz.
5. The vortex shedding period was approximately 0.001 seconds.
6. The full distance travelled by the ball was 150 feet (45.72 m).
7. The time of flight from barrel exit to target was 0.5 seconds.
8. The number of vortices shed during flight was approximately 500.
9. The air density used was 1.239 kg/m^3.
10. The air viscosity used was 1.73x10^-5.
11. The Reynolds number used was approximately 113000.
12. The dimensionless lateral force coefficient was approximately 0.05.

This gives us a lateral force magnitude of approximately 0.06 Newtons, using the following formula:

f_lateral = (1/2) * air_density * velocity^2 * paintball_area * lateral_force_coefficient

13. The paintball's mass was 0.003 kilograms.
14. The lateral acceleration was approximately 20 m/sec^2.

The procedure:
Every time a vortex was shed (every 0.001 seconds according to items 3 and 4 above), a randomly oriented acceleration of 20 m/sec^2 was applied to the paintball. I interpolated between these acceleration "spikes" to generate a random-walk-like pattern.

I converted the acceleration random walk into a velocity walk, and then into a position walk.

I noted the endpoint of this position walk, and then repeated the whole process ten thousand times.


The results:
The following links point to plots of the results...cut-n-paste the URLs if necessary...

http://www.geocities.com/jeremiahswi...force_plot.gif <--Plot of forces on the ball as it flies downrange for a single simulation run. Divide these values by the paintball mass to get an acceleration plot.

http://www.geocities.com/jeremiahswi...ocity_plot.gif <--Plot of lateral ball velocity as it flies downrange for a single simulation run.

http://www.geocities.com/jeremiahswi...ition_plot.gif <--Plot of lateral ball position as it flies downrange for a single simulation run.

http://www.geocities.com/jeremiahswi...atter_plot.gif <--Scatter plot of the endpoint positions for 10000 simulation runs.

http://www.geocities.com/jeremiahswi..._histogram.gif <--Histogram of the final endpoint distances from the aim point, showing the distance of greates paintball concentration.

http://www.geocities.com/jeremiahswi...alk/index.html <--compilation of all 5 plots

Conclusion:

From the results of the simulation, I cannot conclude that a series of randomly oriented 2-G "kicks" is sufficient to knock the ball off course to the magnitude seen in AGD's tests. The greatest concentrations of simulated paintball strikes falls around 0.15 millimeters from the aim point... a distance much smaller than that observed in AGD's real data.

I suspect that there is still something else at work here, and I believe that it may lie in the possibility that a slight spin on a paintball would induce a preferential orientation for vortex shedding. This may cause the ball to be repeatedly "kicked" in the same direction and would thus end up with a greater deviation than a purely random "kick" orientation would generate. If the shot-to-shot orientation of slight paintball spin is not constant (and I suspect it's not), this greater deviation would be randomly oriented with respect to the aim point, as opposed to a simple off-center grouping.

It would be interesting to measure the spin orientation for many successive paintball shots to see if the orientation is reasonably constant or reasonably random. Tom, perhaps you could provide a bunch more test photos for measurement?

Why do I think we've just come full circle?

BJJB

{edited to add plot compilation link}

[hitech]

I originally attempted to perform a full-blown simulation incorporating drag force to slow down the paintball, recalculation or the reynolds number at each time step...

I hadn't thought of that before. However, I don't think you can get meaningful numbers without having the ball slow. Maybe not recalculate at every step, but at least use some predefined changes. Say five or ten different velocities at various points. I don't think we can use a simulation at only 300fps. The paintball has much more momentum at 300fps. Any idea how fast a paintball is traveling after 80 feet?

From the results of the simulation, I cannot conclude that a series of randomly oriented 2-G "kicks" is sufficient to knock the ball off course to the magnitude seen in AGD's tests. The greatest concentrations of simulated paintball strikes falls around 0.15 millimeters from the aim point... a distance much smaller than that observed in AGD's real data.

Am I missing something? As I read your plots and graphs I see more like 2 meters. What am I missing? Also, the problem is quite probably with using the numbers from only 300fps. The real world just isn't neat enough for that.