Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Golf Ball Trajectory Question



Several weeks ago I posted a question regarding the flight path of an arrow
shot in a vacuum. I would like to thank all those that responded.

I have a similar question regarding the flight of a struck golf ball. Would
a struck golf ball fly farther on Earth, or in a vacuum (everything else being
equal)? Intuitively, and using the bow-and-arrow example as a model, it
would seem that the ball should fly farther in a vacuum.

The physics of struck golf balls appears to be terribly complex.  Perhaps I'm
mistaken, but it doesn't appear that any simple equations can be applied to
find out the initial speed of a struck golf ball.  It depends, I think, on the
speed of the clubhead, the type of club, where on the face it is struck, how
it is struck, the spin on the ball, the type of golf ball, and probably several
other things as well.

After literally a few hours on the Web, things didn't get too much clearer. 
I actually found "authoritative" sites that I'm certain were completely
incorrect.  For example, one site stated that the speed of a struck ball could never
be greater than the speed of the clubhead.  ???????  If that were true, then
shouldn't you be able to throw a golf club at least a good percentage of the
distance you can hit the ball (a golf ball benefits from the dimples, which
keep it aloft for a longer period of time).

At any rate, there did seem to be some reasonably similar figures that
compared the initial clubhead speed to initial ball speed.  One Website
(http://www.wishongolf.com/indepth_traj_bf_software.html) has developed software relating
to this question.  I'm assuming this software was developed by using actual
experimentally determined values.  If it were really "off the mark," equipment
merchants would quickly realize this and it would be useless.

Anyway, one set of numbers indicated that a typical amateur golfer with a
swing speed of 85 mph would launch the ball with an initial speed of about 127
mph.  The ball would stay aloft for about 5.29 seconds and would carry 191
yards.  These number certainly seen consistent with what one observes when actually
playing the game.

My intuition told me that with an initial speed of 127 mph, a golf ball
struck in a vacuum should travel farther, because of the lack of air resistance.

So I decided to do some simple calculations.  I assumed an optimum launch
angle of 45 degrees.

Here's what I got.

Initial ball speed = (127 miles/hour)(5280 ft./mile)(12 in./ft)(2.54 cm/in)(1
m/100 cm)(1 hr./3600 s) = 56.77 m/s

If launched at a 45 degree angle, the vertical component of velocity will be
28.387 m/s.  The ball will take 28.387/9.8, or 2.897 seconds to reach the top
of its trajectory and the same amount of time to return to the ground, so the
ball will be in flight for (2.897)(2) or about 5.79 seconds.

Since its horizontal velocity is also 28.387 m/s, the ball will carry a
distance of (28.387 m/s)(5.79 s) or 164.45 m, which is about 180 yards.

This seems to indicate that the ball struck in the atmosphere will actually
fly farther, the reason being that it stays aloft for a similar period of time,
but its launch angle is less than 45 degrees, so its horizontal velocity is
greater.

This doesn't "seem right" to me.

What, if anything, have I done wrong here?