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People who live in glass houses shouldn't throw stones. Your explanation of why golf balls have dimples [June 11] was confused at best. To say that the dimples "enable the ball to grab the layer of air immediately adjacent" is silly. Any junior fluid-mechanics student knows that a no-slip surface boundary condition applies regardless of the surface roughness. The dimples are there to ensure a turbulent (energized) boundary layer that can penetrate further than a laminar boundary layer against an adverse pressure gradient, thus reducing the size of the region of separated flow (low pressure) behind the ball. In short, the dimples reduce profile drag, contrary to your statement that they increase drag. A turbulent boundary layer does increase skin friction, but this is generally less significant than reduction in profile drag.

Lift generated by backspin on a golf ball is due to the Magnus effect. The magnitude of this lift is given by the Kutta-Joukowski theorem, which states that lift will be proportional to the circulation (amount of spin) and the free stream air velocity (how fast the ball is traveling). Bernoulli's equation is implicit in Kutta-Joukowski.

I have probably only muddied the waters and there will continue to be much misunderstanding about why golf balls have dimples and curveballs curve. If you still don't quite understand it, consult a basic fluid-mechanics text. It has been my experience that a lot of the physics gets lost in the translation to layman's terms. --Steven Lacher, MS, aeronautical engineering, Madison, Wisconsin

The reason it gets lost, Steve, is that laymen call up guys like you asking for an explanation. Another perhaps more pressing problem is that scientists just don't agree about what golf dimples do--and since Cecil can't check for himself (the wind tunnel is in the shop), he's at the mercy of whoever picks up the phone when he gives the SD Science Advisory Board a buzz. Having inquired further, I'll concede the majority view at the moment seems to be yours: the dimples make the airflow around the ball more turbulent, which paradoxically makes it follow the ball's surface more closely. That decreases the size of the "wake" behind the ball. Wakes create drag, so the smaller the wake, the lower the drag and the farther the ball goes.

Ah, but there's a minority view, and since it's a minority view that happens to be in line with what I wrote, I think it richly deserves to be heard. As eloquently expounded by Stanford grad student Craig DeForest, whose wind tunnel, let me emphasize, is not in the shop, the explanation goes like this: The main thing generating lift in a golf ball is the Magnus effect, which is related to the Bernoulli principle and arises from backspin. However, at the very high rate of backspin seen in a golf ball (as much as 8,000 RPM), the Magnus effect is actually reversed and, were it not for the dimples, would push the golf ball down. That's because at 8,000 RPM the forward speed of points on top of the ball is very low--the top surface is spinning backward at just about the same speed that the ball as a whole is moving forward. At such speeds the flow above is laminar (smooth) and does not adhere well to the ball, while below it's turbulent and does. (Physics 101 types may find that backward, but trust me.) The ball's wake is forced up and the ball itself is forced down.

The dimples eliminate this problem. They make the air near the ball's surface turbulent all over, restoring the normal lift from the Magnus effect, in which, in a manner of speaking, entrained air is carried around the ball, generating lift through the Bernoulli principle. Admittedly I skipped a few intervening steps, a not uncommon phenomenon in this column, but that's basically what I said. Admittedly also this is an alternative view, but this is an alternative newspaper. As far as I'm concerned it's vindication enough.

Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.


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