![[5x5]](data:image/svg+xml;base64,CgkJCTxzdmcgeG1sbnM9J2h0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnJyB2aWV3Qm94PScwIDAgNTAgNTAnPgoJCQkJPHJlY3Qgd2lkdGg9JzEwMCUnIGhlaWdodD0nMTAwJScgZmlsbD0nI2FhNGNjZScgLz4KCQkJCTx0ZXh0IHg9JzUwJScgeT0nNTAlJyBmaWxsPSd3aGl0ZScgZm9udC13ZWlnaHQ9J2JvbGQnIGZvbnQtZmFtaWx5PSdBcmlhbCcgZm9udC1zaXplPSczMDAlJyBkb21pbmFudC1iYXNlbGluZT0nY2VudHJhbCcgdGV4dC1hbmNob3I9J21pZGRsZSc+WzwvdGV4dD4KCQkJPC9zdmc+CgkJ "[5x5]")
I want to amplify on the discussion that there must be another force "x" that is operating in addition to the Magnus effect.
First let me try and summarize and verify facts and strong beliefs by at least the majority on this thread to this point:
*Paintballs do spin. Most paintballs will have a spin. This applies even to nylon balls that do not have any seams or protuberances (I hope paint marks on the balls in the pictures do not qualify them as rough nylon surfaces.)
*The spin rate is moderate, and probably under 5K for a barrel in good condition and with a good barrel/ball fit.
[quotes]
[5x5] Did all shots show the balls spinning or were there a large fraction that did not spin at all?
[from hitech]
AGD: most were under 5k and a small percentage had no spin
*The paintballs do not seem to drop their spin rate much throughout the trajectory. This comes from the analysis of the pictures. (However, that the spin rate does not decrease dramatically for baseballs is also known, )
*Shot patterns are even random for nylon balls where no seam is found. [obvious from the photos]
One of the questions asked is whether the Magnus effect explain the issue. Well, the conclusion that has been reached is yes and no.
bjjb
Based on tests 101 and 114, I think that the Magnus effect is not what causes the shot-to-shot inconsistency seen in modern markers; the spin resulting from a barrel not specifically designed to induce spin (i.e. Flatline, etc.) is not sufficient to deflect the ball from its normal course. The inconsistency may be the result of nonuniform release of air behind the ball as it exits the barrel. In normal gameplay, pockets of air turbulence may be a factor.
AGD:
----------------------------------------------------------
The next claim is that maybe the ball is kicked sideways right out of the barrel. If this were true you would expect to see it deviate in one direction and that direction would be significantly increased in the second camera trap. If you look at the picture called "3D interpretation" you will see the balls position plotted as relative movement from one pic to another. If you look at the first position in the second trap (flash #6) you will see that the ball trended LEFT from the #5 flash postion but it hits WAY RIGHT at the final target backdrop.
So if we interpret the data correctly the ball "S" curved in flight. This is not consistent with a ball knocked off course at launch.
--------------------------------------------------------
More AGD:
Importantly we see it overcoming the slower spin WHILE THE BALL IS IN FLIGHT. This is the next point of debate so I will start. If the X force happened in the barrel or say a foot from it, then the spin no matter how small should affect the flight path in a direction consistent with the axis of rotation as it flies down range. To state it another way, if the ball in flight was not being affected by X then spin should be the major factor causing deviation. From another point of view, the force X has to be happening while the ball is in flight because in 114 it pushes the ball in two different directions while its going down range. So in order to argue against this you have to explain how something in the gun or barrel can affect the ball down range as we see in 114. The one thing the barrel can do is impart spin to the ball and that affects it down range but since we have that under control you have to come up with something else. Fire away.
Paladin
---------------------------------------
Since the ball seems to have a rotation to the right, it makes sense that it would have "S" curved in flight even if it had gotten a little "kick" to the left as it exited the barrel. Based on the orientation of the seem of the ball to the line of flight, as seen in test #1:01 any muzzle blast could easily move it to the left a bit and then allow the rotation to move it back to the right
-------------------------------------
AGD rebuttal to Paladin:
You have to explain the muzzle blast effect in context of the smoke pictures. It is not apparent to me that there is a pressure jet exiting the barrel right when the ball leaves
AEGIS
One thing that I have yet to see in ANY discussion on any forum is reference to the crown of the barrel. I shoot for accuracy with anything from a .17 hornet to a 6BR and I can state without a doubt that the condition of my barrel crown is vital to accuracy, due to the effect that the expanding gases can have on the departing bullet. If that is true for a bullet leaving the muzzle at >4000FPS, I would think that a paintball at <300 FPS would be affected greatly
So we have two schools of thought: One promoted by the AGD Group is that there is another force in addition to the Magnus effect that must be causing the behavior in a case like 114. How else can we explain the strange "S" shaped trajectory curve!
On the other hand, we have the Paladin Group which believe that something, possibly a asymmetric blast of gas from the barrel kicks the ball first to the left, and then the Magnus spin aerodynamics mechanism kicks in.
First, I, like Glenn Palmer, aka Paladin, am not convinced that we have to invoke another mysterious force to explain the random shot pattern in well formed rigid spheres. After thinking about this for the last week or so off and on I have decided I am more confused then ever, and will transfer my confusion to the group. Maybe you all can help me out.
I am of aware of an entire bunch of forces that are often considered small, that must come into play such as the coriolis effect and the gyroscopic effect between the gravity and the spinning ball. In addition, maybe part of the problem is definitional as well. Once you start looking at these forces beyond drag and gravity, you find that with one exception, spin is related to all the other effects. The one exception has been identified so far is the Von Karman street for non spinning balls, but more on that later.
As background I urge you to take a look at this thesis I just located while thinking about all this stuff again. The thesis has to do primarily with prediction of baseball trajectories, but there is a lot a stuff mentioned that is pertinent to quite a few of the discussions and questions that have come up in this thread - http://www.geocities.com/baseballdocs/ Even better, because it is a thesis, it tends to discuss issues in a more easily understandable and detailed form than found in published aerodynamics papers - Including detailed derivation of the trajectory differential equations.
As we have seen, the single argument that would seem to counter the idea of spin alone being the cause of the deviation is the 114 image and data where we see a nylon ball do two curious, counter-intuitive moves. The ball rises in flight throughout the entire region from muzzle to final target. Second, the ball veers left of the barrel axis starting nearly right out of the muzzle and continues going left some 40 ft down range. However, at the final point, which I believe is 60 ft down range, the ball hits the target to the right of the barrel axis. Keep both of these conditions in mind, they are critical.
Whatever is causing the trajectory change in114, it produces a force higher than the force due to gravity, otherwise the ball would certainly not climb through the entire 60 ft range.
Can the Magnus effect help us explain any of this? At first I thought it could. As I hope I can bring out here, what it ends up showing is that things are indeed more complicated, but it is possible we do not need to invoke any other forces.
What I want to determine first is whether a relatively modest spin can account for the shot patterns we observe. This partly goes to AGD's comments about the magnitude of the effect being out of whack. I am going to concentrate on 10027 shot patterns data. As far as I am concerned, the nylon ball data is critical for getting to the bottom of this type of discussion. From measuring the actual center points of the circles, the mean of the cluster is 0.12" to the right of the center and 3.4" down. However, a drop of only 3.4" at the stated velocity and suspected target distance of 60 ft is hard to reconcile. Even completely neglecting drag, the drop in a vacuum would be 8.4" at 60 ft. (You only need your good old high school physics to show this. How far will a released ball drop in 60/286.9 = 0.21 sec?) What am I missing here? If the target center was coincident with the barrel axis, then there is a consistent factor that is causing all the balls to rise. Or the target distance was about 30 ft away.
Well lets stay with the 60 ft and hope that the targets were off-axis. What about the dispersion of the shots? The only way I have to look at this in detail is with my trajectory calculator. By no means am I willing to make it the final authority, but it least gives us something to start with, and can give at least a feeling of whether an idea is on the right track or not. Now the first thing to keep in mind is that my calculator will only provide a value for the maximum deviation from a "normal" trajectory when a ball spins. This is because the calculator only considers the spin axis to be able to rotate in a plane perpendicular to the ball velocity.
First, some data to crunch. Based on the fact that the circles in 100027.tif represent ball diameters, I was able to get a good idea of the scatter. Each target tic mark appears to represent two inches. What we see is that ~90 % of the shots are within four inches of the center of the cluster.
Now for the calculation: Ball speed was 286.9 ft/s. The ball diameter used was 0.679 and the ball density (mass) was assumed to be similar to a regular paintball, which is 1.18 g/cc. (I did find a density for one type of nylon at 1.1 g/cc.) I assumed a gun angle of 0 degrees (horizontal) and used a spin of 3000 rpm. This is a relatively low spin and is not at all out of keeping with the speeds seen in the photos. The spin angle axis was set at 90 degrees which means side spin only. Air temperature was set at 25 C. At 60 ft the ball dropped 11.9" and had a side deflection of 2.95" from the straight line trajectory. This amount of side deflection is just about the right amount to allow spin to explain away all the deflection we see in the figure. So the Magnus effect can at least explain the data. The random pattern produced does not bother me. All that is needed to create a scatter pattern (ignoring linear velocity variations) is to change the spin axis and the spin rate
As I already stated, the bad news is the actual balls where not dropping anywhere near the expected amount due to gravity and drag. (This assumes the target center was indeed co-linear with the laser and the laser was exactly co-linear with the gun barrel. This difference is particularly disturbing since the air temperature was lower than I used for the calculation which would have increased the drag even more. This could mean that the drag coefficients I used are too high. If this were true this would reduce the spin deflection I calculate a bit because it is related to the ball's linear velocity. About all that can be said at this point is that even with the discrepancies the data is in the right range for being the dominant effect.
Next problem, the 114 data:
As I indicated above there are two elements to consider in the 114 data. The ball does not drop, and the "S" curve. Is it possible to predict a trajectory that changes from a negative to positive deviation from the barrel axis? The answer is - yes. A specific example of exactly this happening can be seen on my website here: http://home.attbi.com/~dyrgcmn/pball....html#sidespin
This occurs because of the shape of the lift coefficient for smooth spheres: From my website: http://home.attbi.com/~dyrgcmn/pball/pballphys1.html or in case the graph does not show up - http://home.attbi.com/~dyrgcmn/pball/pballCalc.html
CdCl.gif
It shows the drag coefficient and the Magnus lift coefficient used in the trajectory calculator. These values are a combination of data that was found in the literature for smooth spheres. For a paintball, the values above 0.4 are most important. Such values will result in lift. There are two ways to get into > 0.4 region. The initial paintball spin can be very high at the muzzle throwing the V/U into the positive CL region at time zero. For moderate or low spins, as drag decreases the paintballs velocity the V/U value will slowly increase. The value of CL will first be negative and then go positive. This is one reason why balls can S curve. Finally, at very low spins only a negative value will be observed. Now people don't really like the idea of a negative lift coefficient, but there at least two studies on smooth spheres which both observe the effect in the same Reynolds number region of paintballs which is indeed about 10^5. (The value varies depending on air density and air viscosity so temperature, pressure, and humidity are important.) Balls with rough surfaces do not show this negative behavior.
So we can get an "S" shaped curve, but there are problems compared to the numbers relative to the 114 data. Such effects only become pronounced at high spin velocities of 25K or higher. There already has been a good discussion with respect to the images and their faithfulness in showing the spin rate. I believe the data and the observed rates are much lower than 25K. So even though an "S" shaped trajectory is possible the spin rates seem quite low.
How about the second problem of the trajectory rising continually over the 60 ft range?. Again, it is easy to produce a trajectory even at distances close to the muzzle that can fairly well match the "gravity defying" vertical increase in distance we see along the 114axis.tif data. But again the problem is that very high spin rates on the order of 40-50K rpm are necessary to have this occur as early in the trajectory.
If hard pressed one could say that maybe the CL data for smooth paintballs is not the same as for much larger smooth spheres even though the Re is the same. Certainly, if the CL values were much higher and/or the curve shifted to the left this would fix the high spin rate problem relative to the 114 data. However, there is another bigger problem. As mightily as I try there is no way for any CL curves of the form shown in the diagram to predict both an S curve in the horizontal plane (lateral, yaw or side motion) and a rising ball in the vertical plane AT THE SAME TIME. This is an indication that indeed some other degree-of-freedom is missing from the calculation. I guess the mysterious force "X" is the nomenclature used here.
So what is going on? I think the AGD Group would say that there is another force, probably related to spin and vortices down range. The Paladin Group would say that the problem occurs because of an initial asymmetry in the pressure field near the muzzle. I have what I believe is a third possibility. One problem is that we may have trapped ourselves into thinking two dimensionally about the Magnus force. (I am definitely in this group.) All the calculations on ball trajectories that I remember having seen and every example of the Magnus effect for balls assumes that the ball spin axis is restricted to a plane perpendicular to the balls motion (including my own calculator). Basically, there is no consideration of a spin axis that points to the front or back of the ball. There are several reasons for this limit. One is that it simplifies the math. Second, think about how most sports balls like a golf ball are sent into a spin. The axis would most likely lie very close to the perpendicular plane to the forward motion. So it makes some sense to allow this assumption. The question is whether the same is true for paintballs. I suspect that there may be somewhat more variation than for other sportballs. And we do know the spin axis for the114 and 101 data is indeed not perpendicular to the down range axis. Why may this be important to consider this? Because I believe once the axis is no longer restricted to a single plane, we find ourselves with a new spin aerodynamic effect to worry about. To be quite honest, I don't know if this is the answer. At first I thought that maybe the only thing that would happen is that the amount of off axis ball deflection would be attenuated. Now I am not so sure. The reason is that the air flow now interacts with the spinning boundary layer at an angle and the layer does not see the air "head on" and flow completely with or against it. So now what happens to the region where the boundary layer separates from the ball and forms the wake or vortex region? The separation line or point will no longer be in the line of the ball motion since the boundary layer will now see different asymmetric air pressures on all sides. Could the ball corkscrew because of this? I hope some of you can help shed light on this possibility. I have this nagging suspicion the effect may also fall in the category with gyroscopic action. In this case, the spin axis could precess like a gyroscope does against the earth gravity field. Except in this case instead of the force of gravity, we have the force of the ball moving through the air. If the axis did precess, that definitely will lead to a helical trajectory like that observed in 114. Thinking about this one gives me serious nightmares of bouncing air molecules, energy transfer, and shearing boundary layers. Note by the way that this is still a Magnus effect. I really have not invoked another completely different mechanism to explain the data. Anyone better in this stuff want to jump in here? HELP!
As for the latest proposal by Hitech that Von Karman street vortices may be the cause of the broad shot patterns, I have a problem understanding its impact on a paintball. As others have noted, paintballs are definitely well into the Reynolds region where the effect is unstable or aperiodic. A random walk model may be a bad choice for this as a rationale for the paintball shot patterns. Take another look at the 114 data. If a random walk model was dictating the results you are going to have to deal with explaining why the ball's trajectory is not randomly oscillating in all directions. The only way I see to do this is to say that you only can get a few big kicks while the ball is in flight. Otherwise, as the random walk model shows the effect averages out to zero. If there were only a few kicks, then you should see big discontinuities in all ball trajectories. I don't think this is supported by the 114 or similar data, or watching any ball go down range. It would jump all over the place. Now one could invoke chaos theory which can be tamed to produce a periodic variation by imposing another force on the chaotic motion.
I know this is long. Sorry. I just hope it is reasonably coherent to follow.
First let me try and summarize and verify facts and strong beliefs by at least the majority on this thread to this point:
*Paintballs do spin. Most paintballs will have a spin. This applies even to nylon balls that do not have any seams or protuberances (I hope paint marks on the balls in the pictures do not qualify them as rough nylon surfaces.)
*The spin rate is moderate, and probably under 5K for a barrel in good condition and with a good barrel/ball fit.
[quotes]
[5x5] Did all shots show the balls spinning or were there a large fraction that did not spin at all?
[from hitech]
AGD: most were under 5k and a small percentage had no spin
*The paintballs do not seem to drop their spin rate much throughout the trajectory. This comes from the analysis of the pictures. (However, that the spin rate does not decrease dramatically for baseballs is also known, )
*Shot patterns are even random for nylon balls where no seam is found. [obvious from the photos]
One of the questions asked is whether the Magnus effect explain the issue. Well, the conclusion that has been reached is yes and no.
bjjb
Based on tests 101 and 114, I think that the Magnus effect is not what causes the shot-to-shot inconsistency seen in modern markers; the spin resulting from a barrel not specifically designed to induce spin (i.e. Flatline, etc.) is not sufficient to deflect the ball from its normal course. The inconsistency may be the result of nonuniform release of air behind the ball as it exits the barrel. In normal gameplay, pockets of air turbulence may be a factor.
AGD:
----------------------------------------------------------
The next claim is that maybe the ball is kicked sideways right out of the barrel. If this were true you would expect to see it deviate in one direction and that direction would be significantly increased in the second camera trap. If you look at the picture called "3D interpretation" you will see the balls position plotted as relative movement from one pic to another. If you look at the first position in the second trap (flash #6) you will see that the ball trended LEFT from the #5 flash postion but it hits WAY RIGHT at the final target backdrop.
So if we interpret the data correctly the ball "S" curved in flight. This is not consistent with a ball knocked off course at launch.
--------------------------------------------------------
More AGD:
Importantly we see it overcoming the slower spin WHILE THE BALL IS IN FLIGHT. This is the next point of debate so I will start. If the X force happened in the barrel or say a foot from it, then the spin no matter how small should affect the flight path in a direction consistent with the axis of rotation as it flies down range. To state it another way, if the ball in flight was not being affected by X then spin should be the major factor causing deviation. From another point of view, the force X has to be happening while the ball is in flight because in 114 it pushes the ball in two different directions while its going down range. So in order to argue against this you have to explain how something in the gun or barrel can affect the ball down range as we see in 114. The one thing the barrel can do is impart spin to the ball and that affects it down range but since we have that under control you have to come up with something else. Fire away.
Paladin
---------------------------------------
Since the ball seems to have a rotation to the right, it makes sense that it would have "S" curved in flight even if it had gotten a little "kick" to the left as it exited the barrel. Based on the orientation of the seem of the ball to the line of flight, as seen in test #1:01 any muzzle blast could easily move it to the left a bit and then allow the rotation to move it back to the right
-------------------------------------
AGD rebuttal to Paladin:
You have to explain the muzzle blast effect in context of the smoke pictures. It is not apparent to me that there is a pressure jet exiting the barrel right when the ball leaves
AEGIS
One thing that I have yet to see in ANY discussion on any forum is reference to the crown of the barrel. I shoot for accuracy with anything from a .17 hornet to a 6BR and I can state without a doubt that the condition of my barrel crown is vital to accuracy, due to the effect that the expanding gases can have on the departing bullet. If that is true for a bullet leaving the muzzle at >4000FPS, I would think that a paintball at <300 FPS would be affected greatly
So we have two schools of thought: One promoted by the AGD Group is that there is another force in addition to the Magnus effect that must be causing the behavior in a case like 114. How else can we explain the strange "S" shaped trajectory curve!
On the other hand, we have the Paladin Group which believe that something, possibly a asymmetric blast of gas from the barrel kicks the ball first to the left, and then the Magnus spin aerodynamics mechanism kicks in.
First, I, like Glenn Palmer, aka Paladin, am not convinced that we have to invoke another mysterious force to explain the random shot pattern in well formed rigid spheres. After thinking about this for the last week or so off and on I have decided I am more confused then ever, and will transfer my confusion to the group. Maybe you all can help me out.
I am of aware of an entire bunch of forces that are often considered small, that must come into play such as the coriolis effect and the gyroscopic effect between the gravity and the spinning ball. In addition, maybe part of the problem is definitional as well. Once you start looking at these forces beyond drag and gravity, you find that with one exception, spin is related to all the other effects. The one exception has been identified so far is the Von Karman street for non spinning balls, but more on that later.
As background I urge you to take a look at this thesis I just located while thinking about all this stuff again. The thesis has to do primarily with prediction of baseball trajectories, but there is a lot a stuff mentioned that is pertinent to quite a few of the discussions and questions that have come up in this thread - http://www.geocities.com/baseballdocs/ Even better, because it is a thesis, it tends to discuss issues in a more easily understandable and detailed form than found in published aerodynamics papers - Including detailed derivation of the trajectory differential equations.
As we have seen, the single argument that would seem to counter the idea of spin alone being the cause of the deviation is the 114 image and data where we see a nylon ball do two curious, counter-intuitive moves. The ball rises in flight throughout the entire region from muzzle to final target. Second, the ball veers left of the barrel axis starting nearly right out of the muzzle and continues going left some 40 ft down range. However, at the final point, which I believe is 60 ft down range, the ball hits the target to the right of the barrel axis. Keep both of these conditions in mind, they are critical.
Whatever is causing the trajectory change in114, it produces a force higher than the force due to gravity, otherwise the ball would certainly not climb through the entire 60 ft range.
Can the Magnus effect help us explain any of this? At first I thought it could. As I hope I can bring out here, what it ends up showing is that things are indeed more complicated, but it is possible we do not need to invoke any other forces.
What I want to determine first is whether a relatively modest spin can account for the shot patterns we observe. This partly goes to AGD's comments about the magnitude of the effect being out of whack. I am going to concentrate on 10027 shot patterns data. As far as I am concerned, the nylon ball data is critical for getting to the bottom of this type of discussion. From measuring the actual center points of the circles, the mean of the cluster is 0.12" to the right of the center and 3.4" down. However, a drop of only 3.4" at the stated velocity and suspected target distance of 60 ft is hard to reconcile. Even completely neglecting drag, the drop in a vacuum would be 8.4" at 60 ft. (You only need your good old high school physics to show this. How far will a released ball drop in 60/286.9 = 0.21 sec?) What am I missing here? If the target center was coincident with the barrel axis, then there is a consistent factor that is causing all the balls to rise. Or the target distance was about 30 ft away.
Well lets stay with the 60 ft and hope that the targets were off-axis. What about the dispersion of the shots? The only way I have to look at this in detail is with my trajectory calculator. By no means am I willing to make it the final authority, but it least gives us something to start with, and can give at least a feeling of whether an idea is on the right track or not. Now the first thing to keep in mind is that my calculator will only provide a value for the maximum deviation from a "normal" trajectory when a ball spins. This is because the calculator only considers the spin axis to be able to rotate in a plane perpendicular to the ball velocity.
First, some data to crunch. Based on the fact that the circles in 100027.tif represent ball diameters, I was able to get a good idea of the scatter. Each target tic mark appears to represent two inches. What we see is that ~90 % of the shots are within four inches of the center of the cluster.
Now for the calculation: Ball speed was 286.9 ft/s. The ball diameter used was 0.679 and the ball density (mass) was assumed to be similar to a regular paintball, which is 1.18 g/cc. (I did find a density for one type of nylon at 1.1 g/cc.) I assumed a gun angle of 0 degrees (horizontal) and used a spin of 3000 rpm. This is a relatively low spin and is not at all out of keeping with the speeds seen in the photos. The spin angle axis was set at 90 degrees which means side spin only. Air temperature was set at 25 C. At 60 ft the ball dropped 11.9" and had a side deflection of 2.95" from the straight line trajectory. This amount of side deflection is just about the right amount to allow spin to explain away all the deflection we see in the figure. So the Magnus effect can at least explain the data. The random pattern produced does not bother me. All that is needed to create a scatter pattern (ignoring linear velocity variations) is to change the spin axis and the spin rate
As I already stated, the bad news is the actual balls where not dropping anywhere near the expected amount due to gravity and drag. (This assumes the target center was indeed co-linear with the laser and the laser was exactly co-linear with the gun barrel. This difference is particularly disturbing since the air temperature was lower than I used for the calculation which would have increased the drag even more. This could mean that the drag coefficients I used are too high. If this were true this would reduce the spin deflection I calculate a bit because it is related to the ball's linear velocity. About all that can be said at this point is that even with the discrepancies the data is in the right range for being the dominant effect.
Next problem, the 114 data:
As I indicated above there are two elements to consider in the 114 data. The ball does not drop, and the "S" curve. Is it possible to predict a trajectory that changes from a negative to positive deviation from the barrel axis? The answer is - yes. A specific example of exactly this happening can be seen on my website here: http://home.attbi.com/~dyrgcmn/pball....html#sidespin
This occurs because of the shape of the lift coefficient for smooth spheres: From my website: http://home.attbi.com/~dyrgcmn/pball/pballphys1.html or in case the graph does not show up - http://home.attbi.com/~dyrgcmn/pball/pballCalc.html
CdCl.gif
It shows the drag coefficient and the Magnus lift coefficient used in the trajectory calculator. These values are a combination of data that was found in the literature for smooth spheres. For a paintball, the values above 0.4 are most important. Such values will result in lift. There are two ways to get into > 0.4 region. The initial paintball spin can be very high at the muzzle throwing the V/U into the positive CL region at time zero. For moderate or low spins, as drag decreases the paintballs velocity the V/U value will slowly increase. The value of CL will first be negative and then go positive. This is one reason why balls can S curve. Finally, at very low spins only a negative value will be observed. Now people don't really like the idea of a negative lift coefficient, but there at least two studies on smooth spheres which both observe the effect in the same Reynolds number region of paintballs which is indeed about 10^5. (The value varies depending on air density and air viscosity so temperature, pressure, and humidity are important.) Balls with rough surfaces do not show this negative behavior.
So we can get an "S" shaped curve, but there are problems compared to the numbers relative to the 114 data. Such effects only become pronounced at high spin velocities of 25K or higher. There already has been a good discussion with respect to the images and their faithfulness in showing the spin rate. I believe the data and the observed rates are much lower than 25K. So even though an "S" shaped trajectory is possible the spin rates seem quite low.
How about the second problem of the trajectory rising continually over the 60 ft range?. Again, it is easy to produce a trajectory even at distances close to the muzzle that can fairly well match the "gravity defying" vertical increase in distance we see along the 114axis.tif data. But again the problem is that very high spin rates on the order of 40-50K rpm are necessary to have this occur as early in the trajectory.
If hard pressed one could say that maybe the CL data for smooth paintballs is not the same as for much larger smooth spheres even though the Re is the same. Certainly, if the CL values were much higher and/or the curve shifted to the left this would fix the high spin rate problem relative to the 114 data. However, there is another bigger problem. As mightily as I try there is no way for any CL curves of the form shown in the diagram to predict both an S curve in the horizontal plane (lateral, yaw or side motion) and a rising ball in the vertical plane AT THE SAME TIME. This is an indication that indeed some other degree-of-freedom is missing from the calculation. I guess the mysterious force "X" is the nomenclature used here.
So what is going on? I think the AGD Group would say that there is another force, probably related to spin and vortices down range. The Paladin Group would say that the problem occurs because of an initial asymmetry in the pressure field near the muzzle. I have what I believe is a third possibility. One problem is that we may have trapped ourselves into thinking two dimensionally about the Magnus force. (I am definitely in this group.) All the calculations on ball trajectories that I remember having seen and every example of the Magnus effect for balls assumes that the ball spin axis is restricted to a plane perpendicular to the balls motion (including my own calculator). Basically, there is no consideration of a spin axis that points to the front or back of the ball. There are several reasons for this limit. One is that it simplifies the math. Second, think about how most sports balls like a golf ball are sent into a spin. The axis would most likely lie very close to the perpendicular plane to the forward motion. So it makes some sense to allow this assumption. The question is whether the same is true for paintballs. I suspect that there may be somewhat more variation than for other sportballs. And we do know the spin axis for the114 and 101 data is indeed not perpendicular to the down range axis. Why may this be important to consider this? Because I believe once the axis is no longer restricted to a single plane, we find ourselves with a new spin aerodynamic effect to worry about. To be quite honest, I don't know if this is the answer. At first I thought that maybe the only thing that would happen is that the amount of off axis ball deflection would be attenuated. Now I am not so sure. The reason is that the air flow now interacts with the spinning boundary layer at an angle and the layer does not see the air "head on" and flow completely with or against it. So now what happens to the region where the boundary layer separates from the ball and forms the wake or vortex region? The separation line or point will no longer be in the line of the ball motion since the boundary layer will now see different asymmetric air pressures on all sides. Could the ball corkscrew because of this? I hope some of you can help shed light on this possibility. I have this nagging suspicion the effect may also fall in the category with gyroscopic action. In this case, the spin axis could precess like a gyroscope does against the earth gravity field. Except in this case instead of the force of gravity, we have the force of the ball moving through the air. If the axis did precess, that definitely will lead to a helical trajectory like that observed in 114. Thinking about this one gives me serious nightmares of bouncing air molecules, energy transfer, and shearing boundary layers. Note by the way that this is still a Magnus effect. I really have not invoked another completely different mechanism to explain the data. Anyone better in this stuff want to jump in here? HELP!
As for the latest proposal by Hitech that Von Karman street vortices may be the cause of the broad shot patterns, I have a problem understanding its impact on a paintball. As others have noted, paintballs are definitely well into the Reynolds region where the effect is unstable or aperiodic. A random walk model may be a bad choice for this as a rationale for the paintball shot patterns. Take another look at the 114 data. If a random walk model was dictating the results you are going to have to deal with explaining why the ball's trajectory is not randomly oscillating in all directions. The only way I see to do this is to say that you only can get a few big kicks while the ball is in flight. Otherwise, as the random walk model shows the effect averages out to zero. If there were only a few kicks, then you should see big discontinuities in all ball trajectories. I don't think this is supported by the 114 or similar data, or watching any ball go down range. It would jump all over the place. Now one could invoke chaos theory which can be tamed to produce a periodic variation by imposing another force on the chaotic motion.
I know this is long. Sorry. I just hope it is reasonably coherent to follow.
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