|MadSci Network: Physics|
The golf swing at first glance appears to be very simple to understand from a physics point of view. But the true swing (like many sports activities) is far more subtle than it first appears to be. The evidence of the subtle nature of the swing is demonstrated by every hacker who slices/hooks seemingly at random every round.
Theodore P. Jorgensen wrote a book called "The Physics of Golf."
He develops a simulation equation for the mechanics of a golf swing based on basic physics mechanics principles and attempts to model what is seen in film of golf swings. After reading the book a couple years ago, I had a great appreciation for the subtle difference between success and failure of a golf swing which is in agreement with my experience as an off-and-on golfer for the last 17 years. I am sure many professional or highly skilled players would take exception to some of Jorgensen's conclusions, yet his initial analysis of the mechanics is very good. To the best of my knowledge this is the only book written by a non-professional golfer that discusses the physics of golf.
The shaft of the golf club can be thought of as a whip in the extremely flexible case. The force applied to the handle of the whip propagates down the length of the whip. The handle moves first and then the part of the whip closest to the handle and then part just a bit farther away, and so on until the tip of the whip moves as well. In this way, the handle will lead the motion of the rest of the whip (sort of like a wave propagating in a string) until the handle stops it forward motion. When the handle stops the rest of the whip keeps moving. More of the whip stops moving forward and a smaller and smaller part of the whip keeps moving until just the length near the tip is moving. Conservation of momentum can be used to show (in the simplified case), that as the moving part of the whip gets smaller and smaller in length and smaller and smaller in mass too, that the speed of the moving whip component must move faster and faster. It is the claim of some, that the crack of the whip comes from a sonic boom as the tip of the whip breaks the sound barrier. While this is likely true in some cases, part or all of the crack of the whip could also come from the tip of the whip "clapping" against the whip itself much snapping your finger or clapping your hands.
It is less than obvious that the whip analogy works well with a golf club, but it gives us a good place to start. A golf club will also twist along the shaft because the club head mass is not in line with the axis of the shaft. Usually the center of mass of the club head is an inch or more off the axis of the shaft. If you have ever hit a ball off the heel or toe of a golf club you may have experienced this torque as the club twists in your hand. This is especially obvious if you hit something that will not move like a solid root or a rock during a swing.
Early steel shaft club designers produced shafts of more flexibility for women and children. The common belief was that the "whip action" was helpful for golfer's with less physical strength to hit the ball a greater distance. Also, the "whip action" was less helpful and could be even detrimental to physically stronger golfers. Whether correct or not, this information of the "whip action" is a prevalent belief held by many golfers.
How to put this sort of information to use analysing the effecct of the shaft flexibility is not obvious. The effect of the flexibilty of the golf club has usually been studied emperically (i.e. by experimenting). The bending of the shaft was measured in slow motion stroboscopic film by placing marking tape at regular intervals along the club from the grip to the club head. A couple experiments shows that the shaft of the golf club at impact actually bends so that the club head is forward of the location it would be if the shaft were perfectly rigid. This seems rather counter-intuitive to me at first.
It seems safe to assume that these measurements would be straight forward to make, even if there was plenty of variability swing to swing. The author showed a graph indicating that the club head lags behind the imaginary position in the shaft were perfectly rigid at the start of the downswing (just like a whip). The club head catches up to the imaginary spot when the club is about horizontal to the ground -- so the hands must be slowing down. And finally at impact the club head is leading the shaft (ahead of the imaginary position).
Some people claim that the lagging and twisting of the club head is a source of severe slicing for players who swing too fast. The club head lags behind the imaginary spot of the rigid shaft and because the center of mass of the club head is off the axis of the shaft, the club head twists slightly opening the face of the club (pushing everything to the right for a right-handed player).
Measurements were made of the speed of the club head during the motion of the swing taking the flexing of the shaft into account. The results indicated that the club head reached a maximum speed when the club head was forward of the imaginary rigid shaft spot. If one were to consider the club head to be a simple pendulum on the shaft then maximum speed would have been at the rigid shaft position. This aspect must have been difficult to put into the swing simulation in a reasonable manner.
Yet, having the club head ahead of the location it would occupy if the shaft were perfectly rigid would require the hands to slow down before impact with the ball. This probably happens in the swing of many golfers. Like many golfers know, a good swing (i.e. one with useful results) is all about timing. The effect of the flexibility of the shaft on the ball's trajectory is determined by the downswing speed, the speed of the club head at impact, the path of the club itself, the position of the hands, the orientation of the club face, and many other factors.
If the player can control the orientation of the club head by swing with the proper tempo then a flexible shaft will allow the player to control his/her swing by not swinging so hard. However, a more flexible the shaft will allow for more variability in club face orientation at impact for a golfer with an inconsistent swing. The more flexible the shaft the more distance the club head with move. I have played several rounds with graphite shaft metal woods and from just waggling the club around, the club head can move an easily observable amount. So when I swing at full speed, I suspect the club head will move considerable with the flexing of the shaft.
So the conclusion: The outcome on the golfer's performance based on flexibility of the shaft is not completely understood or simple to understand at all. The basic idea of "whip action" may or may not be beneficial to a particular golfer and in fact, probably is detrimental to many.
Tom "250 yards Out and 250 yards Right" Cull
Try the links in the MadSci Library for more information on Physics.