Physics of the Golf Swing

Ok, for all you "engineer geeks" out there (like me), feast your hungry golf brains on a powerful physical force generated in the golf swing..."The Conservation of Angular Momentum".

What is this force you ask?...

Simply stated; "The principal that states angular momentum of an object remains constant as long as no external force or moment acts on that object."

Lemme explain...

If the object (club head) is brought closer to the axis (formed by the golfer's stable spine), it speeds up. If the club head is moved further out, it slows down. In a golf swing, as the player rotates the club, the hands move farther from the body or axis and slow down. This reduction in momentum feeds into the much lighter club and increases the speed of the club head in the last part of the stroke, in a whiplash type of effect, increasing the force of impact on the ball.

Any attempt to speed up the club head as it approaches impact with any hand action will only slow the club head down...based on this principal.

Once I fully grasped this principal I was able to start my downswing from the bottom up (feet, knees, hips) as opposed to throwing the club from the top with my arms and hands.

I quickly learned the late hit by holding the angle formed by my left arm and the club till the last minute before impact, then let angular momentun release it's powerful fury through the golf ball.

This is how I learned to maximize the positive effects of angular momentum in my golf swing...

Hope this helps.

--John

Thanks.
It's called clubhead lag.
Most of us know how to start the downswing.

Maybe most of the 3.8's.

You've done a good job of explaining it. Thanks! Although in theory I've known that one should lag the club head, your explanation helped me tie it to another phenomenon: tucking your legs in while you spin on an office chair. Or maybe an ice skater tucking in their limbs to spin really fast.

Lynchjo,

IMHO, your theory is indeed correct.

1) The golf swing, including the golfer, club shaft, and club head, is the system.

2) The spine angle, and later the posted leg & spine angle are acting as the centers of rotation.

3) The golfer's body is the large center mass.

4) The golfer's arms, club shaft, and club head comprise the smaller mass body that rotates around the large body of mass.

5) The system requires an initial angular force to initiate the swing. This is an inside force, not external to the system. If these internal forces were not considered, there would be no torque present in the system, thus no rotation.

The supply of this force depends on the skill level of the golfer. The high handicapper will use a combination of hands & upper torso action, gravity, and upper body uncoiling to supply this impetus. The scratch player will use gravity and the lower body to generate it.

6) Granted, the better golfers will accelerate in the downswing, efficiently adding force and maintaining lag until later.

7) Angular momentum equals the distance between the two mass bodies times the linear momentum of the small mass body. L=r x p.

8) It is when the golfer winds up at the top that the system mass (all bodies) is closest to the center of rotation. From the top, the high handicapper coverts his potential energy (torque, gravitation energy, etc.) into kinetic energy immediately by activating the wrists/hands, as well as lunging down with the shoulders in order to hit the ball. Except for point #6 mentioned above, remember that the system is closed to any significant external forces. As the HH swings, the club head arcs out away from the golfer, the distance "r" increases, and momentum is transfered to it because it's the farthest point away from the center axis. The body and arms decelerate while the club head accelerates, and swings ahead of the hands. So this golfer will likely hit fat. If he misses the ground, the club will ascend up and probably skull the ball.

Hi Erik...please expand on what you mean by "

forces ARE being applied "???

It is the conservation of angular momentum that explains the angular acceleration of the club head. A good analogy is to think of an ice skater as she brings her arms and legs closer to the vertical axis of rotation. By bringing her body closer to the axis she decreases her body's moment of inertia. Because the angular momentum is constant in the absence of any external torques, the angular velocity (rotational speed) of the skater has to increase, just like the clubhead.

You are not turning on an axis free of outside forces though. A golfer does not posses a level of angular momentum, he is applying force to build it. The swing is not an example of constant momentum but of rotational acceleration.

You can apply elements of angular momentum in your understanding of the swing, but it fails to express the fact that the golfer is constantly applying force which change momentum.

I just purchased a book "The Physics of Golf" by Theodore P. Jorgensen. I don't have a strong physics background, so it will probably take me a while to get through it.

The reason I purchased the book is to reserach a formula for estimating, based on several variables, the distance a ball travels when hit. So far it seems that appendex 3 is promising. We shall see.

If anyone knows such a formula, it would save me some time. Thanks.

Jorgensen's book is excellent, and explains the physics of the swing about as well as it can be done. Cochran and Stobbs "The Search for the Perfect Swing" also delves into the physics of the swing.

It's hard to comment on what anyone is saying here because these are hard things to put into words, people can misunderstand what you mean, etc. It's also hard to talk about physics of a human body, with two arms, two legs, a spine that can rotate and tilt and stoop and stand, etc., so what both books do is construct theoretical models of the swing, and then compare the predictions of the model with measurements of an actual golfer's swing.

Both books' models are the same: A two lever system. One lever represents the golfers' arms, the other represents the club/club shaft (the issue of the rotation of the club face is left out of the basic models). The first lever (arms) rotates around an axis (spine), and the second lever hinges relative to the first (wrists).

Torque is applied by our muscles to move the first lever back and set the wrist angle, and then another torque must be applied to reverse the direction of the club and swing down.

I'm not a physicist, but it's intuitive that if you have the wrists cocked and swing down with the arms, the force you apply to the arms is eventually going to make it's way to the wrist hinge, opening up that angle, and accelerating the club into impact (like cracking a whip, or playing that game of "crack the whip" that kids play). What happens when you photograph the swing confirms this. The hands accelerate early in the downswing, but late in the downswing, they actually decelerate and almost stop moving as the wrist angle opens and the club head accelerates. This slowing of the hands and speeding up of the club is an example of conservation of angular momentum.

Is there "no" force applied to the club, by the hands and arms? Of course not, there MUST be force applied. The key is when and where the force is applied. If a golfer was actually succesful at accelerating his hands at or near impact, after the wrist joint had begun to open up, this would definitely, by the conservation of angular momentum, decrease the club head's acceleration. Maybe this is what the original poster meant.

However, Jorgensen definitely believes golfers apply an active torque to the wrist hinge at some point during the swing. His calculations suggest that in order to explain the speed of the club head and it's actual pattern of acceleration, in measurements of pros' swings, there must be a torque/force applied to the wrists... at some point in the downswing (in addition to the torque generated by the swinging/rotation of the arms). But certainly it couldn't be at the very bottom, when the club head is accelerating the most. If the club head is accelerating, and you were able to consciously accelerate the other end of the lever (the wrists), by the conservation of angular momentum, the club head would HAVE TO slow down (sorry for repeating myself...). However, earlier in the downswing, the hands are moving much faster than the club head--during the lag phase, the hands may be accelerating and the head actually moving in the opposite direction.

Whether or not we sense it as such, any force we apply to the wrist hinge in the golf swing probably occurs EARLY in the downswing or even during the transition. According to laws of physics I don't think it could be any other way.

That's in a good swing, of course. Violating these principles is probably why you can have 200 lb., muscular guys who struggle to generate 90mph club head speed with a driver, and why 150 lb. David Thoms probably swings the driver about 105 mph.

Anyone who is interested should really consider buying Jorgensen's book, as well as "The Search for the Perfect Swing." They're really interesting books for golfers.

Ok, lets see if i know anything here and correct me if i'm mistaken (starting junior year ME:)):

if anything, you would want the club head to be as far away from the instantaneous center of rotation (which I'm picturing to be somewhere near your shoulders based on the intersection of the lines of action perpendicular to the club head's tangential velocity and your hands tangential velocity at impact) at impact for the greatest club head speed possible.

Tangential velocity = angular velocity * radius

Hence the reason why longer clubs (longer radius) have the potential to generate more club head speed.

And if any sort of momentum is conserved, it will be linear momentum (mass * velocity) at the moment of impact with the club head and the ball which where the coefficient of restitution (COR) is derived from for drivers. The higher the COR, the more elastic the collision between ball and club and hence the more kinetic energy is conserved between the two and the further you hit the ball. This is the reason why there is a limit on COR values.

How about gravity, for starters?

I don't think gravity plays a role because it is a conservative (non-impulsive) force and does not affect whether momentum is conserved in a system.

Try spinning around in your office chair. Do you spin forever? Guess why not?

Angular momentum is never really conserved in a real life system. Besides, a golf swing starts with no angular momentum at all, so there is no constant momentum to be conserved. Here's my way of consolidating all of the physics going on here. If you keep the club close in as you begin the downswing, you can spin your body faster (angular momentum). When you extend your arms and the club towards the ball, the club head picks up speed because it's farther from your body (centrifugal force). Creating lag in the club head also produces an acceleration in angular momentum of the club relative to an axis through your wrists, as you un-hinge them. A combination of the three provides the highest club head speed. It seems to me that it's all about acceleration, not conservation.