Impact shaft loading - any good?  Let's see for ourselves

There are some who believe firmly that 'loading' the shaft and sustaining this 'loaded' condition against the ball will help to avoid deceleration of the clubhead during the collision time interval. One can find this theme expressed in various ways in several golf books (7,8,9,10). Let's have a look together to see what it is really all about and try to get some idea on the validity of this idea, quite persistent through time.



Fig1 depicts the situation. The club approaches the stationery ball with a velocity V1 . They collide and travel  a small distance δx together. A force Fs acts during this interval. At separation the clubhead has a reduced velocity V2 and the ball flies away with a velocity U2. The purpose of our analysis is to establish only an order of magnitude hence launch angle of ball and approach angle of club are immaterial.

The collision between clubface and ball can be treated very conveniently using 'principle of linear impulse and momentum' and 'conservation of linear momentum'. This results in the expression

where Fs represents the force exerted by the shaft.                

Since the ball is initially at rest, U1=0, we can simplify,

Usually during impact some energy is lost. This is expressed through the coefficient of restitution e,

Combining  2 and  3 results in

Let's assume that Fs is constant during  impact.

Let's take some realistic values

Substituting into  5 gives

Let's assume for the clubhead speed for a driver,    V1=50m/s (112miles/hour).

Substituting gives,

Hence,

We have obtained a very simple and elegant relation relating the ball departure velocity U2 to Fs, the force exerted through the shaft onto the ball during the impact interval δt.

Let's see what relation (8) can teach us. For a relatively small increase of only 10% in the departure ballspeed U2 , one can see from (8) that an extremely large force Fs is required,  i.e., 4594 N (1033 lbs).  Even for only a tiny 1% increase in U2 a very large force Fs is required : 459 N (103 lbs).

The analysis is now conclusive as it allows immediately a limpid conclusion  to be drawn: a golfer can not, in any appreciable way, influence the departure ball velocity, using the shaft to exert force during impact.

The above analysis is totally sufficient in itself, but let us look at some other ways to support the conclusion above.

- About 20 years back a team of scientists lead by Dr. Alastair Cochran and John Stobbs did scientific experiments wit a driver  fitted with a free hinge just above the clubhead.  Their published photographic evidence shows that the clubhead despite being completely free  hinged hardly bent back at all at impact and behaved as if a perfectly normal golf club.

Their driving tests showed negligible difference between the distance obtained with the test club and a similar ordinary club. This conclusively confirmed that the clubhead behaves as a freely moving object, as if it were not connected to the shaft.  

- The impact forces at work during the very short time of the collision are extremely large in magnitude and very much larger than any force a golfer could possibly exert through the shaft onto the ball. Hence the latter can be neglected.

-There is ample evidence that the shaft of a driver bends forward at impact. How does this possibly fit with bending the shaft backwards, required to be able to exert force?

Is there something we can add to the various arguments above ?

- Take your driver and clamp the handle to a table. Attach a small weight, eg, a 2lb dumbbell, at the hosel and notice the considerable deflection of the clubhead even for this tiny load. Since we know from photographic evidence that the bending at impact is very small, and moreover forward, even this very crude simple experiment should convince anyone that evidently we are not exerting any appreciable 'loading' force on the ball during impact with the shaft.

Conclusion

We have looked above at the problem from different angles and have come up in each case convincingly with an identical conclusion. There is however nothing new with these conclusions. This is well known in the scientific golfing community, but alas completely overlooked still by many. It is one of those persistent conflicts between feel and real. The believe that one can influence the ball departure velocity by using the shaft to exert a force on the ball during the impact interval, is one of those persistent myths in golf.

References

-1- 'How Golf Clubs Really Work And How To Optimize  Their Designs' -   F. D. Werner  &  R. C. Greig

-2- 'The Physics Of Golf' -  T. P. Jorgensen

-3-  'Search For The Perfect Swing'-  Dr A. Cochran  et all