Golf balls and dimples
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?
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.
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
Click here to return to the Physics Archives
Update: June 2012