# Golf ball backspin.

Golf balls are dimpled to give the ball some grip on the air. Backspin is usually highly desirable as it increases lift and hence further distance. But why? Could it be that the friction of the ball and the air is greater on the bottom than on the top and hence heat is released under the ball causing the air to expand?

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K^2
Nope. It's simple aerodynamic lift. Very similar to what happens to the wing, but it's the spin of the ball that influences different air flow above and bellow, rather than difference in shape of the wing surface. Aerodynamic lift generated by spinning projectile is known as Maguns Effect.

turbo
Gold Member
Golf balls are dimpled, but it's not just to try to provide lift. Depending on whether you might want to play a cut or a draw, you can get the ball to curve along its path, so you can play it around obstructions. Backspin is quite helpful, too, but generally in the short game, so when you use a wedge or a short iron to get the ball to the green, the ball will "bite" and stop short instead of shooting off the back of the green.

K^2
turbo, a component of aerodynamic force perpendicular to relative wind is called lift. It doesn't matter if it's vertical or horizontal. The trajectory of a draw or a cut shot is still caused by lift.

Gold Member
Not to mention that the dimples also have nearly zero to do with the lift but everything to do with the drag.

K^2
Which I do not completely understand. I'm pretty sure I could construct equally convincing arguments for it increasing or decreasing drag. Nor can I say with any kind of certainty whether the dimples would strengthen or weaken Magnus Effect. I almost want to say neither, because I can't see how it would affect net circulation, but I'm fully prepared to be completely off.

So if somebody has good, solid understanding of this, I would appreciate some pointers.

The dimples introduce turbulence in the flow along the surface of the ball. This drastically decreases drag because it moves (delays) the flow's detachment point further back, thus inducing smaller pressure drag. The phenomenon is called boundary layer effect. Effectively, the pressure profile of the air around the turbulence is like a small airfoils'.

Interesting everyone. And sidespin, unless someone is trying to cut or draw the ball, is undesirable, as the result is an awful hook or slice, frequently into the trees.

One can read countless books on how to 'fix' a slice or hook, none of them actually work because if they did, they wouldn't need to come up with new fixes every month.

I believe science can provide a golf tip that shall stand the test of time. In order to hit the ball straight, one must close the clubface at impact such that it's perpendicular to the desired flight path. Such advice is uncontroversial. Does anyone agree or disagree?

As long as you hit it straight (as in the velocity vector at the point of impact is in the direction you want it to go) it will go that way. Even so, I believe that it is pretty much impossible to hit it with no spin, since the club will travel at a circular arc (and it is itself curved) and it will be in contact with the ball at "different points" for some fractions of a second (thus creating some tangential force component). Moreover, because of the dimples, turbulence will be formed faster on one side of the ball (in this case probably the bottom side) which will create a Magnus effect even if it had no spin to begin with. In my opinion, giving the proper spin to the ball so that it reaches its intended destination is the part the requires the most skill in this sport.

russ_watters
Mentor
Not to mention that the dimples also have nearly zero to do with the lift but everything to do with the drag.
Right. Dimples decrease drag.

Which also means they decrease lift.

Gold Member
Right. Dimples decrease drag.

Which also means they decrease lift.
That's not necessarily true at all. Drag and lift are not coupled that was. For example, consider just a flat plate at angle of attack. To a point, as you increase angle of attack, you increase both lift and drag.

Gold Member
Regarding golf tips for getting to of a slice, many to most of them work. Really, they are all just tricks to help one square up the club face and hit the ball in a part of the swinging motion where you are coming straight at the ball *** opposed to an angle. Slicing or hooking occurs due to the side spin, so even hitting it square can cause a slice if the club isn't also moving in a direction normal to the face, and that is more difficult to control than squaring up the face.

rcgldr
Homework Helper
Not to mention that the dimples also have nearly zero to do with the lift but everything to do with the drag.
Right. Dimples decrease drag. Which also means they decrease lift.
The dimples reduce drag by inducing turbulence which keeps the boundary layer attached longer, so that the boundary layer doesn't expand as much, reducing the profile drag. Note that inducing turbulence consumes energy, so the reduction in profile drag is somewhat negated by the energy required to induce turbulence.

The lift mostly occurs because the flow on the "backwards" spinning side of the ball remains attached longer, reesulting in a net diversion of air flow. I'm not sure if the dimples increase or decrease the realtive points of detachment of the flows on both "sides" of a spinning ball, and the net perpendicular diversion of air, which would increase or decrease the lift.

K^2
So why are many smaller vortices energetically favorable to few large ones? Is there a simple statement that covers that, perhaps something to do with Reynolds numbers, or is this a complicated question in itself?

I'm not sure if the dimples increase or decrease the realtive points of detachment of the flows on both "sides" of a spinning ball, and the net perpendicular diversion of air, which would increase or decrease the lift.
Well, I'm glad I'm not the only one.

rcgldr
Homework Helper
So why are many smaller vortices energetically favorable to few large ones?
There's also the issue that the transition from laminar to turbulent flow occurs later without the dimples. The delayed transtion (or larger vortice) creates a larger effective cross sectional area, which in turn creates more profile drag. Link to an article about drag, but not how this changes Magnus Effect:

golf_ball_aerodynamics.htm

At least a diagram of Magnus Effect with spin, but then the article text mentions relative surface speeds and Bernoulli effect, which considering how thin the boundary layer is, would not explain Magnus Effect. The diagram does properly show the diverted airflow at the back side of a spinning ball.

golf_ball_magnus_effect.htm

Wiki article on Magnus Effect:

it is more likely that most of the Magnus effect is due to the earlier detachment of the air flow on the forward-moving side

http://en.wikipedia.org/wiki/Magnus_effect

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Gold Member
The dimples reduce drag by inducing turbulence which keeps the boundary layer attached longer, so that the boundary layer doesn't expand as much, reducing the profile drag. Note that inducing turbulence consumes energy, so the reduction in profile drag is somewhat negated by the energy required to induce turbulence.
Well, this is almost right. The dimples do trip the flow to turbulence, and that does keep the flow attached, mainly because the greatly increased diffusion in a turbulent boundary brings momentum lower into the boundary layer more effectively which helps it resist the adverse pressure gradients that lead to separation.

It isn't the size of the boundary layer that lowers the profile drag, however. It is the presence (or lack thereof) and location of a separation bubble and thus the size of the wake. When the boundary layers separate earlier, they create the giant low-pressure regions where the flow is separated, which lead to very high drag. Keeping the flow attached simply minimizes the size of these regions.

It is very true, however, that the transition to turbulence does carry with it a drag penalty in the form of viscous drag, but that is nowhere near as large as the drag saved by reducing the separation bubble size, so you have a net gain. In terms of forces, this viscous drag penalty is because of the diffusivity of the turbulent boundary layer pulls momentum lower into the boundary layer, meaning the profiles are much more sharply curved by the surface and therefore leading to a much higher shear stress (up to an order of magnitude greater than in the laminar case).

This method of drag reduction would work just as well on a non-spinning ball as it does on a spinning ball. The flow would simply be symmetric if the ball wasn't spinning and the dimples would delay separation. For the spinning ball, the separation occurs at different points but the dimples will delay them both.

The lift mostly occurs because the flow on the "backwards" spinning side of the ball remains attached longer, reesulting in a net diversion of air flow. I'm not sure if the dimples increase or decrease the realtive points of detachment of the flows on both "sides" of a spinning ball, and the net perpendicular diversion of air, which would increase or decrease the lift.
Lift on a golf ball is a result of the Magnus effect and would occur even without separation. The backspin makes it so that, when the ball is moving, the air is essentially moving faster over the top of the ball compared to that over the bottom of the ball (relative to the ball) just like an airfoil. The flow deflection would occur, therefore, regardless of separation.

You do bring up a good point about the rotation serving to delay separation on the top and encourage it on the bottom, however. The top is spinning in the direction of the overall airflow, meaning it adds momentum to the fluid low in the boundary layer and helps it resist separation. Conversely, the bottom side rotates against the fluid motion, which removes momentum from the lower portion of the boundary layer and encourages transition.

So why are many smaller vortices energetically favorable to few large ones? Is there a simple statement that covers that, perhaps something to do with Reynolds numbers, or is this a complicated question in itself?
Not sure what you mean by this, to be honest. It is an interesting thought but what do you mean by "energetically favorable"?

There's also the issue that the transition from laminar to turbulent flow occurs later without the dimples. The delayed transtion (or larger vortice) creates a larger effective cross sectional area, which in turn creates more profile drag. Link to an article about drag, but not how this changes Magnus Effect:

golf_ball_aerodynamics.htm

At least a diagram of Magnus Effect with spin, but then the article text mentions relative surface speeds and Bernoulli effect, which considering how thin the boundary layer is, would not explain Magnus Effect. The diagram does properly show the diverted airflow at the back side of a spinning ball.

golf_ball_magnus_effect.htm

Wiki article on Magnus Effect:

it is more likely that most of the Magnus effect is due to the earlier detachment of the air flow on the forward-moving side

http://en.wikipedia.org/wiki/Magnus_effect
Generally speaking, flow separation tends to decrease lift, often quite dramatically (leading to stall on an airfoil). I need to think a little bit to try and make sense of what that means in terms of lift and the Magnus effect, however. It is an interesting question.

K^2
Not sure what you mean by this, to be honest. It is an interesting thought but what do you mean by "energetically favorable"?
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.

rcgldr said:
There's also the issue that the transition from laminar to turbulent flow occurs later without the dimples. The delayed transtion (or larger vortice) creates a larger effective cross sectional area, which in turn creates more profile drag.
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.

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rcgldr
Homework Helper
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.
It does contribute, but since turbulent flows can follow curves more easily than laminar flows (which may involve a separation bubble), the turbulent flow around the golf ball tends to be thinner, and as shown in the images, the end result is a smaller diameter wake.

One of those articles mentions that this changes at higher speeds (where tubulent flow occurs dimples or not), but well beyond what occurs in real golf. At 300 mph == 480 kph, a smooth golf ball will have much less drag than a dimpled one.

Gold Member
Turbulent flow is THICKER than laminar flow, it just doesn't separate as easily.

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.

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Gold Member
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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Gold Member
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.

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
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:
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.

Gold Member
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.

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