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Question:
One of my students is researching golf balls and how dimples affect their flight. Does any one have a formula for computing the distance with a given initial velocity? Secondly, does anyone have some ideas or formulas that would adjust this distance based on the number or shape of the dimples?



Replies:
There is no such formula, except perhaps something that a private company might use for rough guessing at how their balls should work. The dimples create a subtle interplay between the spin of the ball and the air around it - I do not know the details at all. Also, anybody who has played golf knows there is a lot more than just the initial velocity that goes into the distance. There is the quantity of various kinds of spin as well - and remember the velocity needs to include both horizontal and vertical components. And then there is the air pressure, wind speed, quantity of dirt on the ball, etc...
Try looking up golf balls in a local library business index.

Arthur Smith


Howdy Judith:

I also do not think that there are any such formulas. After checking my fluid mechanics textbook, I found values of drag coefficients for spheres. It turns out that the drag force is proportional to the square of the velocity over a fairly large range of the velocities (or actually over a large range of the Reynolds number). However, there was no information regarding the drag coefficient for spheres with dimples. Therefore, I do not think you will find a simple answer to this rather complicated question. I may be able to help further with an explanation of why the dimples are there in the first place, something that was probably discovered in Scotland when golfers realized that some of the old (beat up)balls flew further than the new ones (originally, I think they were all balls with a smooth surface) 14What happens to reduce the drag on a ball with dimples is that you push the point of separation of the boundary layer further toward the "back" of the ball thus reducing the area on which the low pressure region is acting. There are really two components of drag force at work when objects fly through a fluid. One component is due to friction (related to viscosity of the fluid) and the other is due to pressure. The dimples actually promote turbulent flows, which increases the friction drag but reduces the pressure drag (because of the separation phenomenon). Since the pressure drag phenomenon is more significant than the friction drag, there is an overall reduction in drag for the ball with dimples. This type of disc discussion can be found in many textbooks on Fluid Mechanics. You might try the one entitled, Fundamentals of Fluid Mechanics by Munson, Young and

david r munoz



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