Paintball Spin Physics - Getting to the final Answer

[bjjb99]

Can we even measure the Magnus effect?

Woo hoo!

I found a webpage which describes the mathematical foundation for the Magnus effect. It is located at the following URL, and describes the effect for rotating cylinders of infinite length:

http://www.mathpages.com/home/kmath258/kmath258.htm

I think it could be applied to our paintball, at least as a first cut approximation. After staring blearily at the equations, we come up with

L = - (rho) * v0 * (gamma), where

rho is the density of the fluid,
v0 is the velocity of the fluid (relative to the object in question), and
gamma is something called the circulation, defined as the line integral of the flow velocity around a closed loop.

What gamma basically means for us is "take the surface speed of the object and multiply it by the object's circumference". Thus,

(gamma) = vc * 2 * (pi) * r, where

vc is the circumferential (surface) velocity of the object,
pi is 3.14159 or thereabouts, and
r is the object's radius.

Let's plug in some of the data derived from the test 101 picture.

rho = 1.293 kg/m^3 (reasonable value for the density of air)
v0 = 85.34 m/s (280 fps)
vc = 1.25 m/s (4.1 fps surface speed)
r = 0.0086 m (radius of a paintball 0.68 inches in diameter)

So from this we get

L = -1.293 * 85.34 * 1.25 * 2 * 3.14159 * 0.0086
L = -7.45 (units?)

I'm not sure what the units should be. Doing a bit of unit analysis on the equation for L, we have the following:

L-units = (kg/m^3) * (m/s) * (m/s) * (unitless) * (unitless) * (m)
L-units = kg/s^2 ???

That sure isn't a unit of force I'm familiar with. We're missing a distance unit in the numerator somewhere, and darn if I can find it. Any help, anyone?


I also have happened across the following webpage, which gives a different equation (of similar form) for the Magnus effect:

http://carini.physics.indiana.edu/E105/spinning-balls.html

Here they describe the effect as follows:

M = cM * (rho) * D^3 * f * v, where

cM is the Magnus force coefficient (1.23 works pretty well, according to the webpage),
rho is the density of the fluid,
D is the diameter of the object,
f is the object's rotational frequency (rotations per second), and
v is the velocity of the fluid (relative to the object).

If the Magnus force coefficient is unitless, then a unit analysis of this equation actually ends up with units of force coming out of it. Let's plug in some numbers derived from test 101:

cM = 1.23 (unitless?)
rho = 1.293 kg/m^3 (reasonable value for the density of air)
D = 0.0173 m (0.68 inch diameter paintball)
f = 23.1 rotations/s (15 degrees per strobe flash, one strobe flash every 1.8 milliseconds)
v = 85.34 m/s (280 fps)

M = 1.23 * 1.293 * 0.0173^3 * 23.1 * 85.34
M = 0.016 N

So for that amount of spin we end up with a Magnus effect force of 0.016 newtons. For a 3 gram paintball, this force results in an acceleration of 5.3 m/s^2, or right around 0.54 g's. Let's assume this equation has given us a correct answer, and see what the picture can tell us based on what we've calculated.

I am going to define the "first" strobe as the first image of the ball after it has exited the barrel, and incrementally name each successive ball image to the right of the first strobe (second, third, etc.).

An acceleration of 5.3 m/s should deflect the ball approximately 8.6 microns between the first and second strobes. This deflection is nearly two orders of magnitude smaller than the spatial sampling in the image (around 0.6 millimeters per pixel for the "bottom view" portion of test image 101). So even if the Magnus effect is at work, we simply can't see it from strobe to strobe. So let's look at the first and last strobes in the (strobes 1 and 5).

In this situation, the time interval is four times as large. Assuming the acceleration resulting from the Magnus effect is constant throughout the measured time, we should expect a deflection 16 times greater than that predicted between strobes 1 and 2, or around 140 microns (0.14 millimeters). This deflection is still smaller than the spatial sampling in the image.

If the ball is spinning at 15 degrees per strobe flash (and based on my other spin calculations and Tom's additional comments, I think we can safely assume the ball is not spinning at 195 or -165 degrees per strobe flash), and if the formula I used above is reasonable and accurate, then the high resolution pictures we have of the test are simply not sufficient to detect the resultant Magnus effect.

I looked at the "bottom view" portion of the test 101 picture to see if I could see any horizontal deviation in the ball's path, and I noticed something interesting... the laser aligned string is not straight. It curves slightly in the image. This leads me to believe we either have a camer/lens perspective effect going on here, or the string is vibrating during firing. The blast of air that escapes the barrel could be moving the string around.

I attempted to correct the slightly curved string by using Photoshop's transformation tools, but had little success. It seems that the transformation I'm looking for just isn't available in my version of Photoshop. Instead of measuring each ball's position from a single reference line, I generated local references corresponding to the string's location at each ball's position. I measured the following offsets:

Strobe 1: -4 pixels (-2.48 mm)
Strobe 2: -2 pixels (-1.24 mm)
Strobe 3: -2 pixels (-1.24 mm)
Strobe 4: -1 pixel (-0.62 mm)
Strobe 5: 0 pixels (0 mm)

These offsets are greater than the Magnus effect alone would suggest, unless the Magnus equation I used was incorrect. They may be the result of the escaping gas buffetting the ball around during the first few milliseconds of flight.

Well, that's about all I've got for now. Time to go do some work that actually fills up a paycheck.

BJJB

[Redkey]

Originally posted by flanders

as for airpoctes they allow a ball to not be so birrtal it pops in teh gun, while not makeing a shell even harder, if a bakl infact has no spin forward or back then the airpocet won't matter if it's facing backwards, or if it's roatating at a constant rate so tat it's never forward back up down etc then it will be ok do to compensation

As I struggle to read this and make sense of all your spelling errors / typos my only thoughts are that if you ever wish to be taken seriously you should read your post before submitting it.

Could you please explain how an airpocket in the ball will make the shell more brittle?

Originally posted by flanders

barrel do ahve something to do with accurac, not lengthj ( i dun know if theres a barrel to big or 2 small) but quality, if they are rifled to much and the ball has spin goes pop, if the barrel has burs pop, if the barrel is to big, bouncy bouncy pop bad accuracy, if the barrel aint supper clean pop, if the barrel has odd porting can cause poor release of air causing spin, to tight air can't get through in the right way or ball gets stuck or shell peels off

Here you are making some statements about barrels and accuracy. Were I to make claims like this I would also present some data to support my claims.

Originally posted by flanders

the ball can distort with high pressure bursts but it would have a reverse translation (as in all liquid filled objects) impact on oen side creats lump on other side this may or may not be a good thing (depending on spin) if spin occurs left or right ball witll be good havign a bullet effect, if ball spins up or down bad ball is lopided pops or screws it up more

An impact on one side of the ball will not cause a lump on the opposite side. The balls diameter will swell before a lump is created... unless of course there is a thin spot in the shell... it will be the weakest area and will deform first from the hydrostatic pressure.

If the spin occurs left or right the ball will hook left or right.

Originally posted by flanders

as for spin not hapening with liquid, if there was no air pocets then the ball would be hard like a solid object or atleast it doesn't impact or adjust every thign is filled, ball still spins, if there is an air pocket, and the liquid can still move then yes will cause lopsided pickle ball spin. but if the buble does not move it creats a weighted zone creating a similer odd spin, if spin occurs

huh?

Originally posted by flanders

General hypothesis

If spin lateral spin (left to right)occurs then one or many of the factros will effect accuracy

If spin longitudanal spin (up and down)occurs then one or many of the factros will effect accuracy

You could also say if the ball was blue then one or many of the factors will effect the accuracy.

Anyhow... I don't mean to be a jerk but, please review your posts before submitting them. Make sure they contain useful information that is similar to that being posted by the other people.

Thanks...

[AGD]

Pstan,

This is about getting the facts and involves more than just an open or closed bolt issue. In paintball this is as close as we get to publishing.

BJ,

Nice job, that's the kind of effort I was looking for. The result of your investigation points out that the magnus effect is SMALL. So if the expected deviation from the Magnus effect is 1% and in tracking the paintball we see a deviation of 10% then we can safely say that another force besides Magnus is acting on the ball. We don't have to actually see it to make sense of it.

Do not let the string fool you, it was streached tight between two posts and only looks curved because the mirror was not perfect.

Everyone concentrate on test number 114 because we have the additional data for the flight path on that one.

AGD

[Ostwar]

If Magnus force is dependant on spin, then what is involved to cause a ball to randomly move when little to no spin is applied. I take this from volleyball a sport in which if you serve the ball with a "flat" or minimized spin the ball will (for lack of a better word) "wiffle" in the air which will directly affect its trajectory. Is this a possibility in paintball?

Shaun

[bjjb99]

Originally posted by AGD

The result of your investigation points out that the magnus effect is SMALL.

I am withholding that conclusion until I recieve some validation of the equation I used to calculate the force resulting from the Magnus effect. It could well be that the equation I used applies well to things like baseballs and basketballs, but not necessarily to small, paintball sized spheres.

Originally posted by AGD

Do not let the string fool you, it was streached tight between two posts and only looks curved because the mirror was not perfect.

Ah, a slight sag in the mirror would definitely explain the string curvature I was seeing. Hadn't thought of that.

Originally posted by AGD

Everyone concentrate on test number 114 because we have the additional data for the flight path on that one.

I'll take a look at that one this evening and see what I can come up with.

While you're reading this, Tom, I've got a question I've been meaning to ask you. In the video tour of AGD's facility, you show off a large mirror you were grinding to make a large aperture telescope. Has the mirror been finished, and if so, what kind of figure does it have? I ask because if it still has a spherical figure it would be awesome to use it in some large scale Schlieren photography of the airflow behind the paintball as it exits the barrel. Even if it's got a parabolic figure it could still be used with a correction lens for such imaging.

BJJB

[Crimson_Turkey]

Sadly I cannot post the evidence, but the raw egg theory does not applie ot paintballs. Paintballs will spin while in flight regardless of the liquid fill. Once the shell is set in motion it will not stop spinning as it moves through the air. As I stood leaning out of my window with a camcorder i filmed and egg pushed off the 5th story of an apartment building. A slight spin was imparted upon the egg as it fell. Earlier I had drawn a red line around the egg and in slow motion I could clearly see the line rotate. I would post the video if I could but this camcorder will not let me.

Eggs spin in the air. I think this is due to the lack of friction on the egg. When you spin an egg on a table it is grinding againt the table, causing friction. In the air there is a much smaller amount of friction on the egg. In addition, I think that because the shell of a paintball accounts for more of the total mass and volume when compared to the fill than an eggs shell to it's "fill" the paintball would probably spin better.

[flanders]

california why?

*turns around with blunt object in hand*

[hitech]

Here is a site with formulas. It is about the physics of paintball and he explains his formulas. bjjb99, you could see if your magnus effect formulas match his theory. You will find that he claims that the magnus effect must be determined experimentally. He does give a "guess", I believe.

There is also an applet that attempts to predict the trajectory of a spinning paintball.

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

[bjjb99]

I've read significant portions of the site you mentioned before and have found it interesting if somewhat challenging to wrap one's mind around. I've computed the Reynolds number for a 0.68 inch diameter ball moving at 280 fps through air, and it comes out around 1.03x10^5. Judging from the graphs on the site you mentioned, this results in a positive lift coefficient under all conditions, instead of the reverse Magnus effect the site describes. It ends up following near to the curve fitted to the triangular shaped datapoints. Thus, I don't necessarily agree with the anti-Magnus conclusions the author describes.

Using test 101 data, the value for V/U used on that site would be (1.25/85.34), or 0.015. This puts our data point darn close to the left edge of the graph shown, and thus the lift (read "Magnus") coefficient is very very small to the point that it is difficult to even estimate it from the plot. I'd estimate the coefficient at around 0.02.

The site states that the Magnus effect force is characterized in a similar fashion to that of the drag force, and thus I used the drag equation to determine the Magnus force with a Magnus coefficient of 0.02. It works out to be around 0.04 newtons if I did my math right, which is about 2.5 times larger than the value I calculated using the equation on the carini.physics.indiana.edu site. Given the difficulty in estimating the Magnus coefficient from the plot, I think the result is close enough to say that either treatment is "good enough" for a first cut look at this phenomenon. I think the two methods agree with each other sufficiently to convince me that my original calculations are a reasonable approximation of the amount of displacement to be expected in test 101 (i.e. unmeasureable given the spatial sampling of the pictures taken during testing).

I am curious what this conclusion means in terms of the Flatline barrel system... I mean, I've seen floaters that just go and go and go coming out of that barrel, and I've seen horrendous curve balls when a Flatline gun is held sideways. I suppose the spin induced on Flatline-launched paintballs is much much greater than the mere 23 revs per second that test 101 exhibited, pushing the V/U point to the right and increasing the Magnus coefficient significantly.

BJJB

[Paladin]

Re: Paintball Spin Physics - Getting to the final Answer

Well, I've stared at the pictures until I'm cross-eyed and there seems to be very little that I can reach any value conclusions on that would fit into the ongoing discussion.
I cannot see anything here that addresses either, the issue of closed bolt versus open bolt or what effect internal ballistics has on the flight of the ball. However, I did do a bunch of shooting through powdered barrels as Tom suggested and arrived at the same conclusions that I reached through reading the scuff marks on paintballs shot through an un-powdered barrel. Results do seem to indicate that the ball does in fact distort or compress lineally from the forces of acceleration; causing it to tighten against the bore of the barrel for a period of time when launched.
My tests were done with a Blazer (closed bolt) operating with 400 to 450 psi input to the gun and firing Pro-ball paint at velocities of between 305 fps and 220 fps.
Only balls that demonstrated a consistent, loose fit in the barrel were used and each was blown through the unpowdered barrel with breath alone to relativly ensure consistent fit in the barrels before moving to higher pressures for launch.
In addition, each ball was chambered manually to ensure consistent positioning of the ball in the chamber prior to launch. Positioning of the ball was only made relative to the face of the bolt and did not address the position of the seem in relation to the axis of the bore.
Two barrels used: One with a straight bore of .690 and the other with an eliptically honed barrel, also with .690 base bore size but the center section of the barrel tapers out to .694 at 6" from the chamber and back down to .690 at 10" from the chamber. I did not have any Desenex brand powder on hand but Gold Bond, medicated powder seems close in consistency to Desenex.
The results: Almost every shot fired wiped the powder from the complete perimeter of the bore during the acceleration in the first part of the bore and then showed only a two-point track in the front half of the barrel. The length of time that the ball made full perimeter contact with the bore decreased as velocity was lowered. Also noted that the transition from full perimeter contact to a two-point track was more abrupt in the eliptically shaped barrel.
To further verify my results, the target was a bed sheet setup to catch the paint so I could read the balls as well as the barrel bore. Looking at the balls showed that the powder that was wiped from the bore was built up on the ball well forward of the center line of the ball with a wide "scuff" mark of imbeded powder. Thus indicating a significantly wide contact of the surface of the ball with the surface of the barrel bore.
Also, I did not see anything to indicate that any "spin" was happening inside the bore but I was not looking real close in that regard. My focus was on "data" that would indicate whether or not the ball would upset under acceleration. All indications to me are that the ball does in fact change its shape to a somewhat cylindrical form when pressure is applied and acceleration begins and the amount of distortion is relative to the velocity achieved. Your results may vary with different types of valving that might generate different rates of acceleration or different blast impact characteristics.

Now, to address some of the issues "on the table":

"Spin is the only major factor accounting for paintball inaccuracy. Promoted by Pbjosh"

In essence, a true statement IMHO. In this regard, I can only go by what I've seen which indicates to me that the less spin seen on a ball in flight, the more likely it is to go where it is intended. Less spin = tighter shot groups.

"Closed bolt operation has an effect on overall accuracy. Promoted by Glen Palmer." (two N's for this Glenn please

Actually, my contention is that closed bolt firing gives me the best opportunity to tune my gun (the whole gun) to maximize the effectiveness of the shot. Without appropriate setup and tuning, closed bolt firing is not likely to be any more effective than any other mode of operation.

"The paintball flight is subject to "knuckleball effect"."

It certainly is and I'd bet that we have all seen it at one time or another.

"Spin may or may not be possible because of the liquid in the paintball."

Spin is certainly possible but in relation to the effect on the flight of a paintball, is this discussion based on the lateral spin as would be imparted by rifling a barrel or the random spin generated by numerous other factors ??

"Barrels have something to do with accuracy."

This is one of the few points that I can see as being addressed in the "data" posted. The data in both pictures of "shot patterns" indicates that different barrels will achieve different shot groups. In both "shotpattern" jpgs, the Smart Parts barrel shows a tighter shot group than either, the Crown Point or Rail ? barrel. However, the tightest grouping seems to be shown in the lower left of the "shotpatterns2" jpg and I cannot make out what that barrel is.

"Seams have something to do with accuracy."

I believe that the seems themselves have less to do with overall accuracy than the size/condition and position of the seem on the ball which can and does effect the consistency of the flight path.

"Balls distort with the impact of the air blast."

A certain amount of distortion seems to be a fact. However, either as a result of impact of the air blast or the "G" forces of acceleration?

"Balls distort when leaving the barrel."

Lets hope not. Hopefully, the forces that cause distortion are relieved before the ball leaves the barrel. Although, the "smoke" tests seem to indicate a very interesting shape to the ball after it leaves the barrel.

The "smoke" shots also seem to show that there is not a collum of air being forced out ahead of the ball but that there is a small cushion of air around the ball. This brings up a question or three about the barrel and valving used for the smoke shots. Automag valving? Length of barrel? Venting in the barrel ?

The biggest problem that I run into with all of this is that I don't/can't use scientific calculations to prove out what I see and can measure. When you guys start spouting all sorts of scientific jargon and presenting formulas that often seem to me to be lacking in variables and such, you put the conversation well out of reach for me. I learned the old style math where 2+2=4 so I am relagated to believing what I see. When the things that I do can demonstrate consistent velocity readings and a tight shot group, I'm pretty well convinced that I'm doing something right. Then when something is changed and the results change too, it is quite easy to see whether or not the change was an improvement or not. Common sense and K.I.S.S. principle engineering has served me quite well for a long time. Unfortunately those things are just not accepted here.

Originally posted by AGD
Gentelmen,


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.

Ok lets have a pointed discussion on the subject. For those of you just reading this, this thread is a continuation of the "closed bolt" thread found here.

original thread

AGD

[bjjb99]

Speaking of the Flatline barrel...

Tom, do you know if anyone other than Tippmann has performed tests to measure the amount of spin imparted to a paintball fired from the Flatline barrel system? It would give us another set of datapoints to work with for a barrel that is supposed to put spin on the ball.

Got sidetracked last night and didn't get a chance to look at test 114. I'll see if I can work on it this evening instead.

BJJB

[hitech]

bjjb,
Thanks for doing the math. My college physics class was a LONG time ago, and I have never had any practical application for what I learned (I took the class for fun, I know, I'm strange). I can't even factor equations anymore! As the site I gave you stated, the Magnus effect must be determined experimentally. Maybe we will get enough data to determine what it is.

Based on bjjb calculations (I'm using his) we have the following answers (For test 101):

1. What is the ball's RPM? = 23
2. Is there only one spin axis or does it corkscrew on two spin axis? = One axis
3. Does the spin maintain, speed up or slow, down range? = Maintain*
4. What is difference in surface speed? = 8.2 fps

* = I do not have the equipment to measure the spin rate (I couldn't find anywhere that bjjb did) of the downrange paintballs. I also do not know what the difference is in spacing between the uprange and downrange strobes. Based on my observations, the downrange strobes are approx. twice the distance of the uprange strobes. Based on my observations the spin rate is the same downrange.

[bjjb99]

Originally posted by hitech

3. Does the spin maintain, speed up or slow, down range? = Maintain*

* = I do not have the equipment to measure the spin rate (I couldn't find anywhere that bjjb did) of the downrange paintballs. I also do not know what the difference is in spacing between the uprange and downrange strobes. Based on my observations, the downrange strobes are approx. twice the distance of the uprange strobes. Based on my observations the spin rate is the same downrange.

Exactly the problem I ran into...

The balls are chronoed at around 280 fps and travel around 6 inches between successive strobe flashes for the near-barrel case in test 101. This gave me a strobe rate of one flash every 1.8 milliseconds.

If we use the same strobe rate for the downrange image, we get a ball travel of around 10 inches in the same 1.8 milliseconds, for a ball velocity of 463 fps... which of course makes no sense... no ball is going to miraculously speed up to dangerous velocities during the downrange portion of its flight, no matter how many elves are behind it pushing with all their might. Thus, the strobe rate downrange must be different.

We don't know the ball velocity in the downrange images, as it is likely to have slowed down significantly from the 280 fps chronoed value. All we have is a distance of around 10 inches between strobes. I suppose one could estimate what the speed should be by using air resistance, but I think that's just adding more errors into the mix.

So I've basically ignored the downrange data until I can get a handle on how fast the ball is moving at that point, or else get a value for the strobe rate from someone. Without one of those two values I think wer're just shooting in the dark for the downrange data.

Tom, did the strobe unit have a readout for the strobe rate? I'm assuming it didn't since you didn't put those numbers up here for us to utilize. How did you go about figuring the downrange velocity or strobe rate back when the test was conducted?

BJJB

[AGD]

BJ,

Tippman as far as I know just did empirical testing and never measured anything.

The ball is moving slower down range, I would have to try and find the exact FPS. You can get close by shooting over a crono at 40 ft with a ball that leaves the barrel at 280.

Now that I think about it we most likely spaced the strobes wider apart so we could measure the spin in the same place.

Glenn (sorry about the n),

Intersting that you scraped off most of the powder half way down the barrel. Did you dry fire the excess powder out first? We have never seen that happen in our tests, I might have to repeat them. We have seen the ball on initial launch bang sideways into the bore but most of the time we just got two streaks.

Yes we are departing from the closed bolt issue temporarily. We are trying to come to terms with the influences on the ball so we can sort them out and rank them.

AGD

[ezrunner]

On Powder testing

What barrels are you guys ysing and what paint?

I would be interested to see these tests with a tight barrel
to paint match. Try turning the bead so that it is parallel to the
direction of the barrel, ie would leave 2 streaks down the
bore and find a match such that the entire ball was touching
as much as possible around the
circumfrence.

I get my best accuracy when shooting paint with this fit
characteristic. The consistency
is best I think with your fit
method, but mine takes you from
+/- 1/2 fps to +/- 3/4 fps in most of the better guns.

I will dig around and see if I have the equipment to duplicate
any of this testing, but we have a tourney this weekend.

You guys (Glenn and Tom) put a lot of thought and work into
this, thanks.

-rob from clemson