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Golf ball backspin.

by Shaky
Tags: areodynamics, golf
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boneh3ad
#19
Dec1-12, 09:00 PM
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Turbulent flow is THICKER than laminar flow, it just doesn't separate as easily.
Roy Dale
#20
Dec1-12, 09:29 PM
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Golf balls would have grip on the air without dimples but they have more grip as a result of them. A good analogy would be a spinning car tire. The more grip (friction) between the tire and the road the more linear force the spinning car tire generates. The more the spinning tire is pushed into the road the more it can grip it. A spinning ball is not pushed into the road it is pushed into air by its motion through it, the effect is not as dramatic as being pushed into the road but it does cause an effect known as the Magnus effect. The friction is greater where the ball is being pushed into the air and less where the ball is pulling on the air, this uneven friction drag around the spinning ball causes it to move more linear (Magnus effect).

Drag can move objects in any direction but even when it opposes one motion it can cause another motion. When you spin a ball the surface drag that opposes its rotational motion can cause its linear motion when the spinning ball starts to move through the air. When you pull a paddle through the water the opposition to that movement is what the boat uses for thrust. A spinning ball going through the air can turn a flow just like a wing but it does not mean the spinning ball is generating lift. The very large difference between the ball and the wing is that the ball is spinning very fast as it moves through the air and the wing is not. If not for the influence the spin has on the relative airflow influencing the ball there would be no Magnus effect (what texts call lift) yet when determining the aerodynamic force that causes the Magnus effect the fact that the ball is spinning is totally ignored. Calling it lift is bases on the false primus that the ball is not spinning.

There is another aerodynamic force generated by turning a fluid called drag. Just because an object is turning a fluid does not mean it is generating lift. A boat can use a propeller to accelerate water one way to propell the boat in the other direction as a result of the production of lift. A paddleboat can use a paddle wheel to do the same thing as a result of the production of drag. A squirrel cage fan produces a lot of airflow but no lift. If an airplane were to fall out of the sky while in a flat position it will have its weight totally supported by drag when it reaches terminal velosity. The way you can tell its drag is the high pressure on bottom and the low pressure on top. Lift and drag are very similar, by accurate definition the only difference is their direction in relation to the relative airflow that caused them. The relative airflow that causes the Magnus effect is not solely caused by its motion through the air although the aerodynamic force that causes it is.
boneh3ad
#21
Dec2-12, 10:09 AM
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Quote Quote by Roy Dale View Post
Golf balls would have grip on the air without dimples but they have more grip as a result of them. A good analogy would be a spinning car tire. The more grip (friction) between the tire and the road the more linear force the spinning car tire generates. The more the spinning tire is pushed into the road the more it can grip it.
This is actually a particularly poor example. You can't really compare friction between solids to friction in a fluid at all. They are fundamentally different. Friction in the traditional sense only does one thing in a fluid: keeps the fluid stagnant against a boundary (relative to that boundary). Any of the forces you feel as a result have more to do with the ensuing shape of the boundary layer than the friction itself.

Quote Quote by Roy Dale View Post
A spinning ball is not pushed into the road it is pushed into air by its motion through it, the effect is not as dramatic as being pushed into the road but it does cause an effect known as the Magnus effect. The friction is greater where the ball is being pushed into the air and less where the ball is pulling on the air, this uneven friction drag around the spinning ball causes it to move more linear (Magnus effect).
Furthermore, there is no analogous part of the process to the normal force into the surface. In a fluid, if you push something into the fluid, the fluid gives way and lets the object move through it. In other words, the effects of friction (in the traditional sense) in a fluid are completely independent of any kind of normal force.

The Magnus effect itself does rely on viscosity, otherwise the spinning surface would not actually be able to affect the fluid flowing over it in the necessary way, so in some sense it does rely on friction. It is not as you describe, however. It also has nothing to do with making the ball "[move] more linear". It is simply an effect that results in a lift force on a spinning body moving through a fluid.

Quote Quote by Roy Dale View Post
Drag can move objects in any direction but even when it opposes one motion it can cause another motion.
You could easily make this argument by playing around with frames of reference, but the traditional definition of drag is a forces that opposes the motion through a fluid, meaning it can't act in any direction and can't cause motion.

Quote Quote by Roy Dale View Post
When you spin a ball the surface drag that opposes its rotational motion can cause its linear motion when the spinning ball starts to move through the air.
This is not true. If you have a spinning ball in a fluid that is not moving linearly, the drag on the ball's surface, when integrated across the surface, produces a net zero force, so it will not be able to cause any linear motion. It still produces a moment, so it can slow down the spinning, but it won't cause linear motion.

If the ball is instead moving through the air, this drag still will not "cause" any linear motion. In this case, the spinning will serve to decrease viscous drag slightly on the lower surface and increase viscous drag slightly on the upper surface, but that isn't going to cause any linear motion. There is simply no means for that, especially because on a golf ball, the drag is dominated by the separation phenomenon and not viscosity.

Quote Quote by Roy Dale View Post
A spinning ball going through the air can turn a flow just like a wing but it does not mean the spinning ball is generating lift. The very large difference between the ball and the wing is that the ball is spinning very fast as it moves through the air and the wing is not. If not for the influence the spin has on the relative airflow influencing the ball there would be no Magnus effect (what texts call lift) yet when determining the aerodynamic force that causes the Magnus effect the fact that the ball is spinning is totally ignored. Calling it lift is bases on the false primus that the ball is not spinning.
It 100%, unequivocally does mean that the ball is generating lift. It matters not how the ball is generating lift, but only that it is generating a force acting perpendicular to the overall motion. In fact, the actual generation of lift between an airfoil and a spinning ball or cylinder are very, very similar. Both induce a circulation about themselves essentially be enforcing a different location of the trailing stagnation point. A wing does this with a sharp trailing edge and an angle of attack while a spinning object does this through rotation. Either way, you end up with a net circulation around the object and a downwash behind it, signifying lift.

I don't know why you are saying that determining the aerodynamic force resulting from the Magnus effect that you can ignore the spinning. You can't and you don't. The Magnus effect is actually quite nice because, by taking into account the rotation rate, you can actually construct quite accurate exact solutions using potential flow theory. Quite simply, the spinning is integral to the Magnus effect and to the lift that it generates, and lift is still lift regardless of what is generating it.

Quote Quote by Roy Dale View Post
There is another aerodynamic force generated by turning a fluid called drag. Just because an object is turning a fluid does not mean it is generating lift.
True, it must also be moving linearly through the fluid and reasonably round to generate lift, otherwise it doesn't set up the shifted stagnation point and downwash.

Quote Quote by Roy Dale View Post
A boat can use a propeller to accelerate water one way to propell the boat in the other direction as a result of the production of lift.
This is actually not the whole story about how a propeller works. A propeller's blades are actually small foils (hydrofoils in the case of a boat, of course). The propeller moves its foils through the water at great speed, resulting in a propulsive force forward that corresponds directly with the lift on an airfoil. The water accelerated backward is analogous to the downwash behind and airfoil. In other words, the force propelling a boat forward is directly analogous to lift, it just isn't called that.

Quote Quote by Roy Dale View Post
A paddleboat can use a paddle wheel to do the same thing as a result of the production of drag. A squirrel cage fan produces a lot of airflow but no lift.
The paddle boat, depending on the frame of reference used, may be described as drag reasonably correctly. The fan you mention cannot. The fan, much like the propeller, is more analogous to lift than to drag. In fact, on a fan, there will be a force on the fan blades in the direction perpendicular to the direction of travel of the blades. This is lift. A fan is just secured in place so it doesn't move that direction. Instead, we use the column of moving air it produces.

Quote Quote by Roy Dale View Post
If an airplane were to fall out of the sky while in a flat position it will have its weight totally supported by drag when it reaches terminal velosity.
Supported is a bad word to use here because the plane is still falling. When it reaches terminal velocity, the downward acceleration due to gravity is simply balanced by the drag from the fall.

Quote Quote by Roy Dale View Post
The way you can tell its drag is the high pressure on bottom and the low pressure on top.
This has nothing to do with drag or lift specifically. Consider two cases. A ball falls through the air. There is a drag force acting upward and the pressure below the ball is higher than above the ball. This is pressure drag (or form drag or profile drag as they are sometimes called). Now consider an airplane in level flight. The pressure under the wing is higher than the pressure over the wing. This is lift. In other words, what you just said makes no sense. You can tell when something is drag based on whether or not it is parallel to the direction of overall motion or whether it is normal to it.

Quote Quote by Roy Dale View Post
Lift and drag are very similar, by accurate definition the only difference is their direction in relation to the relative airflow that caused them.
You say this here, so why do you oppose it frequently in all the preceding paragraphs.

Quote Quote by Roy Dale View Post
The relative airflow that causes the Magnus effect is not solely caused by its motion through the air although the aerodynamic force that causes it is.
What do you mean by relative airflow? This isn't clear from anything in your post. At any rate, the Magnus effect is not caused by airflow alone. It is caused by a combination of airflow and rotation of the body, and the result is an aerodynamic force: lift.
boneh3ad
#22
Dec2-12, 10:15 AM
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Quote Quote by K^2 View Post
That was awfully vague of me. I'm talking about energy loss due to generation of the vortices. The mechanical energy of the golf ball becomes, mostly, mechanical energy of the vortices. What isn't immediately apparent is why few large vortices generated by a smooth ball would require more energy to produce than many small vortices due to a dimpled ball.

It just seems to me that, for a qualitative assessment, considering energy required to generate a vortex might be easier than trying to figure out the drag directly.
So which vortices are you talking about? The point of confusion to me is that there are a number of vortices in the flow in question, for example the shed vortices in the wake, the vortices generated by the dimples, the vortices that arise naturally as a result of turbulence, etc.

Quote Quote by K^2 View Post
Right. That argument mostly makes sense. What isn't clear to me is why the turbulence in the boundary layer does not contribute to the profile drag, or at least, not as strongly as the turbulence in the wake. What is so fundamentally different between the turbulence in the two regions? After all, the flow isn't strictly laminar in either.

Edit: Or is it just about the cross-section? While the turbulent boundary layer covers a significant fraction of the golf ball's surface area, the cross-section area of the turbulent boundary layer at any given slice is rather small.
It is more about the cross-section. The turbulent boundary layer is a little bit thicker than a laminar boundary layer, so it would give you a slightly larger profile drag from that effect, but it is so much more resistant to separation that this is easily balanced and then some by the smaller wake region, which means a smaller low-pressure region behind the ball and dramatically less drag. For this shape, the drag is dominated by this separation-induced drag, so the additional profile drag as a result of thick, turbulent boundary layers or the added viscous drag from turbulent boundary layers is minimal by comparison.
K^2
#23
Dec2-12, 11:01 AM
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Quote Quote by boneh3ad View Post
Turbulent flow is THICKER than laminar flow, it just doesn't separate as easily.
You are talking about just the boundary turbulent vs the boundary laminar, right?

Anyways, I understand the drag part now. I shouldn't have been trying to figure out what happens at ball's surface. The question is how much momentum the golf ball is imparts to air when it's all done and done, and narrower turbulent wake, provided by late separation, is clearly a reduction.

With lift, I still have no idea what's going on. Does turbulent boundary layer instead of laminar one have any impact on circulation?

Edit:
Quote Quote by boneh3ad
It is more about the cross-section. The turbulent boundary layer is a little bit thicker than a laminar boundary layer, so it would give you a slightly larger profile drag from that effect, but it is so much more resistant to separation that this is easily balanced and then some by the smaller wake region, which means a smaller low-pressure region behind the ball and dramatically less drag. For this shape, the drag is dominated by this separation-induced drag, so the additional profile drag as a result of thick, turbulent boundary layers or the added viscous drag from turbulent boundary layers is minimal by comparison.
Yes, that's basically what I got out of all of that. Thanks for helping me get through that.
boneh3ad
#24
Dec2-12, 11:30 AM
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Quote Quote by K^2 View Post
You are talking about just the boundary turbulent vs the boundary laminar, right?
Yes. Because of the increased momentum diffusivity in a turbulent boundary layer as compared to a laminar one, they grow faster.

Quote Quote by K^2 View Post
With lift, I still have no idea what's going on. Does turbulent boundary layer instead of laminar one have any impact on circulation?
Slightly. The thicker boundary layer associated with turbulence means that whatever shape in question will effectively be slightly thicker than its physical thickness and therefore can affect lift a bit, but that effect is usually rather small. On a golf ball the situation is more complicated than on an airfoil because of the massive separation, and at that point the interaction between it all is less clear to me at the moment. The qualitative effects should be the same, but quantitatively things are likely somewhat different.
K^2
#25
Dec2-12, 12:01 PM
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Yes, for a static surface, I can see how turbulent boundary layer would have net effect of slightly different shape. That makes sense.

But for a rotating body, it seems like things can be quite different. I mean, Magnus Effect arises because the boundary layer moves with the surface, which induces a circulation in the net flow. With turbulent boundary layer, how the actual surface moves is different than how the part of turbulent layer exposed to laminar flow moves. I'm not sure the turbulent boundary layer will be dragged as much as the laminar one would. That would suggest a significant drop in circulation due to Magnus Effect.

But on another hand, you have late separation, which all experience suggests would improve lift. At least, it does for a cambered wing. So which of the two effects would win out?

By the way, I was trying to get a better quantitative feel for Magnus Effect. Is vorticity in laminar flow zero? In other words, should circulation be be uniform in laminar flow regardless of where I draw the contour?
boneh3ad
#26
Dec2-12, 12:28 PM
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The turbulent boundary layer would be "dragged" exactly as much as as the laminar one. The surface is spinning the same way in either case, so the fluid at the surface would be moving the same in either case. I would imagine then that with the spinning, that would lead to a thinner boundary layer on the top since the Reynolds numbers would be lower up there and the bottom would be slightly thicker than the no spin case since Reynolds numbers would effectively be higher. Here, I am referring to a Reynolds number relative to the distance along the surface and referencing free-stream velocity relative to the moving surface so that it approximates the x-Reynolds number used over a flat plate.

I don't imagine that this would have any really noticeable effect on the magnitude of the Magnus-induced lift because ultimately the effect is as a result of a shifting of the rear stagnation point, and that is governed by the inviscid flowfield around the object, not the state of the boundary layers. Of course, this statement assumes no separation. When separation occurs (as it does here) then the effect this has on the lift is more nebulous other than trying to reason it out based on a wing, which probably is not a very good analogy since both sides are separated here. The separation will modify the predicted potential flow outside the region so it could modify the rear separation point, and I can't think of a good way to analytically determine how it would modify the rear separation point and overall lift quantitatively or really even qualitatively.

My gut instinct tells me that it isn't that much since experience shows that golf balls fly farther with dimples so the drag reduction must be more than enough to make up for any loss of lift. I would even bet that the lift is slightly increased since it isn't as massively separated, but again I can't think of a good way to prove that analytically.
rcgldr
#27
Dec2-12, 04:27 PM
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Quote Quote by boneh3ad View Post
Turbulent flow is THICKER than laminar flow, it just doesn't separate as easily.
I meant the net effect assuming that lamimar flow is going to eventually transition into turbulent flow, probably along with a seperation bubble on a curved surface such as a golf ball. In the articles that mention separation points, for smooth golf balls, seperation occurs at about 80 from the center of the leading edge, which would end up diverting air outwards (and I assume creation of a separation bubble, probably turbulent or at least vortice like), increasing profile drag (and wake). The same articles metion that the dimples delay the seperation to about 110 from the center of the leading edge, reducing profile drag (and wake).

In the case of some glider wings, roughing up the leading edge, using turbulator strips, or using vortex generators, can force the transtion from laminar to turbulent sooner, reducing the seperation bubble, resulting in a smaller amount of form (profile) drag with a net reduction in overall drag.

This web page article implies that the dimples increase lift, but without much explanation in the Flight Conditions section. I haven't found any other articles that mention if the net effect of dimples increases or decreass lift (only that it decreases drag) to back up this one particular article.

http://www.franklygolf.com/golf-ball-aerodynamics.aspx
Shaky
#28
Dec8-12, 06:08 AM
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I examined the Wikipedia article called "Magnus Effect", but I noticed the ball in the diagram is showing front spin as opposed to back spin. The theory, seems to argue the ball goes up because air is drawn below the ball, causing the air to compress under the ball relative to the top; the body will experience a force towards the low pressure area (i.e. up). That makes more sense than my theory that backspin causes the air under the ball to "heat up" causing the air to expand. So, the questions become, how do we determine if it's back spin, as opposed to front spin, that lifts the ball up? Then, where must the club face strike the ball such that the desired spin is obtained? I think the pros would find this kind of knowledge valuable.
K^2
#29
Dec8-12, 06:21 AM
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It has nothing to do with heat. Back spin will result in lower pressure over the ball and higher pressure bellow the ball, providing positive lift.
Shaky
#30
Dec8-12, 08:18 AM
P: 9
The diagram on Wikipedia entitled "Magnus Effect" is correct after all. I thought the contour lines, when they are closer together as opposed to apart, indicate a high pressure area. I had it the other way around. No wonder I had trouble understanding the phenomena.
boneh3ad
#31
Dec8-12, 08:34 AM
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On the Wikipedia diagram, just look at the direction the streamlines are moving after the ball. Don't worry about pressures at the moment. The streamlines are bent upward as a result of the spin. This required a change in momentum, i.e. a force. The vertical opposite and equal reaction force to the bending of the streamlines is the lift. In the case of the Wikipedia diagram, the streamlines are bent up, so the lift points down.


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