Re: What is the optimum amount of trampoline effect (deformation) of a golf clu

It is not really that there is a spring effect, but rather it is a much better transfer of kinetic energy. Coefficient of restitution (COR) is a measure of the elasticity of collision. It is measured usually by keeping one of the two objects still. For the golf club - golf ball collision COR is usually tested by launching the ball into the club face at a given speed. This is a better measure of what the golf community wants to test, namely how much energy is passed from the club face to the ball.

A perfectly elastic collision, COR = 1.0 means that there is no energy loss, while a COR = 0.0 means the two objects are stuck together after the collision. More information on COR can be found using MadSci Search with keywords: coefficient baseball or coefficient restitution. An important point is that, the club head is designed to reduce the loss of energy at collision. The effect is exaggerated between wood golf clubs and "metal wood" golf clubs, or between wood and aluminum baseball bats for hits away from the sweet spot.

The trampoline effect is difficult to gage exactly because the ball also compresses at impact. It is seen in all sorts of sports collisions: tennis ball - racket, ball - bat, foot- ball, golf ball - golf club, basketball - ground, and more painfully, body parts and ground or other people. A big part of the trampoline effect has to due with the deformation properties of the club face. In general a bigger club face will spring better, sort of like a larger bow will transfer more energy to an arrow than an equivalent shorter bow. Controlling the trampoline effect is an art form involving metallurgy, engineering, and trial and error. But a few things that must be considered in general club design can be applied:

• club face at rest must by convex so that at impact it is closer to flat and not dented or concave.
• the club face must not deform beyond the elastic limit of the material.
• golfers must be able to generate necessary club head speed, so the club cannot be too cumbersome.
• torsion effects of the shaft must be considered, so the club head cannot be too heavy but this can be corrected for with perimeter weighting.

In a very simple approximation, one can think of the club head as a spring (or a bowstring in a bow) in which the springiness is measured by the restoring force occuring to Hooke's Law :

Force = - Constant * displacement.

The Constant is a function of the material stiffness for small displacements of the club face. Note the negative sign which indicates the force is in the opposite direction of the displacement of club face. The larger the constant the "harder" the club head will be and the "harder" the hit will feel to the golfer. A club head that is too hard will not be a pleasant experience on a mishit, because the vibrations at contact will travel the shaft of the club to the golfer's arm. A club head that is too soft will not drive the ball as far. So, I am afraid the answer to your question is, "it depends." But the in general, the harder the better until the point at which the ball and club face buckle. Too much and significant energy is lost when either one is pressed beyond its respective elastic limit -- which is not going be possible in normal conditions with usual materials.

There are rules about club size/weight, material, and design that are provided by the USGA and The Royal and Ancient Golf Club of St. Andrews that can be read in published rule books. They deal mostly with club length and clubhead size and composition. For example, the clubhead must be a solid body -- no springs or loose parts. It has been a long time since I read a rules document from the USGA, but if you got a lot of patience and time to kill or if you are an insomniac, I recommend it.

I checked out the Calloway Golf homepage and was able to find the following information under the ERC driver:

NON-CONFORMING - The United States Golf Association tests for "spring like effect" or Coefficient of Restitution (COR) - the ratio between ball speed launched into the face of a driver and speed of the ball as it leaves the face. The USGA rules as non-conforming any driver that demonstrates a velocity ratio (ball rebound velocity/ball incoming velocity) which is greater than .830 when a golf ball is fired at a stationary club head. The Royal and Ancient Golf Club of St. Andrews, Scotland - which governs play for golfers everywhere outside the U.S., Canada and Mexico - has determined that extra distance off the tee is not a threat to the game and therefore does not place limits on COR.

CONFORMING - The United States Golf Association tests for "spring like effect" or Coefficient of Restitution (COR) - the ratio between ball speed launched into the face of a driver and speed of the ball as it leaves the face. The USGA rules
as conforming any driver that demonstrates a velocity ratio (ball rebound velocity/ball incoming velocity) which is less than .830 when a golf ball is fired at a stationary clubbed. The Royal and Ancient Golf Club of St. Andrews, Scotland - which governs play for golfers everywhere outside the U.S., Canada and Mexico - has determined that extra distance off the tee is not a threat to the game and therefore does not place limits on COR.

The number 0.830 is arbitrarily set by the USGA. I am not sure what the justification is for this number.

If you are interested in more physics of golf, I recommend a MadSci search or picking up the book, The Physics of Golf, by Theodore P. Jorgensen. The book is interesting but does not directly consider clubhead trampoline effect.

Tom "Ty Webb" Cull