The sixteen numbered excerpts below are from The Physics of Ball Games, by C.B. Daish. Comments of John Riches on the application to croquet follow each numbered reference in italics.
1. In the game of golf, the duration of the impact between clubhead and ball has a practically constant value of about 0.5 milliseconds. The steady value which occurs in a full shot at tennis is rather longer than this due to the 'give' of the strings of the racquet, but even so it is still very short and does not exceed 5 milliseconds.
In croquet the impact time is between these two - usually about 1 millisecond.
2. The clubhead in the golf shot might just as well have been on the end of a piece of string as far as its behaviour during impact is concerned, and the shaft has little effect on the blow. In the impact itself the shaft plays little part, and its characteristics will not affect to any appreciable extent the subsequent results.
The same would apply to single ball croquet strokes. The flexibility of the shaft may affect the amount of jarring, or the amount of control the player can exercise, but makes no noticeable difference to the power of the stroke or the distance the ball travels.
3. One direct consequence of the fact that the head of a golf club is virtually unsupported by the shaft during impact is that a shot hit off either end of the face of the club instead of off its centre will twist the clubhead during impact. Although the face of the club might be pointing squarely at the target as it comes into the ball, the twisting during impact will mean that the ball moves off a club face pointing either left or right of target, and so it will set off in the wrong direction. This is undoubtedly a common cause for missing putts.
Since a croquet ball is far heavier than a golf ball, the twisting effect is even greater when a croquet ball is hit off-centre. Other calculations have shown that a croquet ball hit firmly about one inch off centre will exert a turning force equivalent to about a half-tonne weight pressing against the mallet face at that point. There is no way such a force can be resisted. Using a very tight grip in an attempt to avoid twisting is useless, and so is using a shaft constructed so as to minimise "torque". The only answer is to either hit the ball in the centre of the mallet face, or use peripheral weighting (as explained in the next paragraph).
4. To reduce the twist produced by an off-centre shot to the minimum, the clubhead should be designed with a lot of the mass located toward the ends of the face, away from the axis through its centre of gravity. The idea of "placing the weight behind the ball" is not a good one.
This is why for more than 12 years I have been using a mallet with 'peripheral weighting'. I wrote about this idea in my booklet "Croquet: Finer Points". Peripherally weighted croquet mallets are now becoming popular in both New Zealand and Australia, and were used by some of the players in the MacRobertson Shield 2000 matches in Christchurch.
All of this seems to apply equally well to croquet. Players should be discouraged from playing roquets, take-offs, or hoop strokes with a stop-shot action.
6. The player becomes conscious of the shot having been played only some appreciable time (0.6 milliseconds for the impact to travel up the shaft, plus reaction time) after it has been completed. By this time the ball will be some two feet on its way, ahead of the club. There is no possibility whatever of a player applying any correction during impact to a shot which has not been properly made.
This also must apply to croquet strokes.
7. Increasing the clubhead mass from the normal value to a tremendously high value (say, to a mass equal to that of the Empire State building) would only increase the ball velocity by one-fifth. There is also no evidence that a more powerful player should use either a heavier implement, or a lighter one, than a physically weaker player.
In croquet also a heavier mallet does not provide additional power to any noticeable extent. That is, it does not enable the player to hit a single ball further. But it does enable him to do it by making greater use of gravitational force and less use of force from his own muscles. The negative side of a heavy mallet comes in the fact that once it starts swinging, a greater force is needed to stop it or slow it down, and this has to be done, where necessary, by muscular force alone.
8. Because the ball is deformed on impact to a much greater extent than the club, the material from which the clubhead is manufactured has little effect on the distance the ball travels.
In croquet also, the material from which the mallet head is manufactured has little effect on the distance the ball travels in a single ball shot.
9. There is little relation between the height to which a ball rebounds when dropped from a particular height onto a solid surface, and the distance the same ball travels when hit by a club.
A surprising result, and if it applies to croquet, one with interesting implications for the testing of croquet balls. [Standard tests for official certification of croquet balls are done by dropping the ball from various heights upon a metal plate. - editor]
10. So many different joints, levers and muscles are involved in the swing that the mind boggles at trying to translate them into some simple mechanical pattern or model. One is inclined to merely accept the fact that, as a machine for hitting a ball, the human body is singularly badly designed (although grudgingly admitting that it is occasionally used for other purposes) and to leave it at that.
The croquet swing is only a little less complex than the golf swing. Daish goes on to show the importance of a consistent backswing, in order to ensure that the following forward swing commences from the same position each time, allowing the muscles to coordinate consistently in the same way.
11. [Discussing the 'double pendulum' swing, pivoting primarily at the shoulders and with a second pivot at the wrists] There is evidence that, far from increasing the velocity of the implement he is wielding by the appropriate action of a couple at the wrists (i.e. by using the wrist muscles in an attempt to 'push' the implement forward and so gain additional power), a player may often inadvertently slow it down by not allowing his wrists to open out freely - he might, in fact, do better if he had a perfectly free hinge (which would provide no additional force at all from the wrists). A so called wristy shot at cricket may well be one in which there is almost a complete absence of wrist action, with the player closely imitating this free hinge. Again, the use of an overlapping grip in golf brings the player more nearly into line with the freely-hinged model, and this is likely to be one advantage of such a grip over the older two-handed grip. The latter may certainly be expected to permit more force to be exerted at the wrists, but it can also interfere with the free-wheeling of the club into impact.
In our coaching we have, for these reasons, tried to eliminate the use of wrist action as a source of power, relying instead on a higher backswing to make use of gravity. Players often tend to push with their wrists on long rushes when they feel that additional force will be needed; but as suggested above, this more often tends to reduce power rather than increase it. An overlapping grip, where comfortable, has advantages in croquet as well as in golf, for the same reasons, although total power is a far less relevant consideration in croquet than in golf.
12. A heavier body possesses a greater amount of energy than a lighter one travelling at the same speed, and it is thus of vital importance that the heavier part should be moving slowly at impact if it is not to rob the lighter, lower part of a large fraction of the energy available. Without the cocking and uncocking of the wrists in the golf shot, only about one quarter of the energy expended by the player would be fed through to the clubhead; in an efficient swing, this fraction is raised to about two thirds, thanks to the hinge at the wrists....An effective grip is necessary, but one which is so firm that it introduces a rigidity at the wrists is likely to cause a loss in power rather than a gain.
This highlights the inefficiency of the type of swing used by some players (usually Irish grippers) in which the hands are together but well down the handle, with the elbows straight, and the wrists are unable to act as a hinge. Note that the 'hinge' effect of the wrists, allowing them to be cocked and later uncocked by the natural movement of the swinging mallet, in no way implies that the wrists are being used to provide additional force. Again, although power is not the main consideration in croquet, it is better to use a fairly light grip for most shots rather than a rigid "white-knuckle death grip".
13. Once a full shot has got under way there is little that the player can do, even if he tries, to interrupt the inherent rhythm of the swing. In a full shot, the dangerous moments occur when the system is momentarily stationary and possesses no momentum: at the beginning of the backswing and again at the top of the swing. Hence the importance to the player of beginning the backswing correctly, and likewise the importance of moving smoothly into the downswing. Any errors made at these two points will inevitably be reflected in an incorrect swing and a bad shot.
If this applies equally to croquet, we may need to give greater emphasis to the beginning of the backswing. Perhaps the current fashion of taking preparatory swings over the ball partly serves to avoid any problems which may be introduced at the start of the backswing, although it does also introduce further complicating factors.
14. In the golf putt in particular, a slow, deliberate, smooth action is essential, and this is just what those unfortunates who suffer from the 'twitch' find themselves unable to accomplish. This positive accelerating movement exhibited by the professionals is in strong contrast to the weak, nervous jab characteristic of lesser mortals.
Tell me about it! The same is exactly true of hoop running in croquet, and to a lesser extent short roquets, as we are all well aware.
15. During a golf swing, the player's hands move in an arc whose centre lies somewhere between the player's shoulders. This point is kept fixed in the upswing. Then, at the top of the swing, this point in the player's body is moved slightly forward to a new position where it again remains fixed during the downswing. In spite of the usual advice given to the beginner to keep his head still during the shot, the best players do not do this. It is not the fixing of the head that is important, but the fixing in space of the between-the-shoulders pivot.
Although the body does not pivot laterally during a croquet swing as it does in golf, it is still the shoulders, rather than the head, that need to remain stationary in order to provide a fixed base for the swing. Movement of the head will matter only if it also entails shoulder movement.
16. [In explanation of what is meant by the "centre of percussion, we are
asked to imagine the mallet as stationary but free to move, and being hit
by a moving ball.] A blow directed near the bottom of the implement
[mallet] will tend -
In cricket the aim is to hit the ball in the "centre of percussion" to minimise jarring and produce a smooth, effortless stroke. In croquet you have little choice other than to hit the ball as near as you can to the centre of the end face. However, if the mallet is balanced correctly (i.e. its centre of gravity is correctly positioned), the centre of percussion will be in the centre of the end face, thus minimising jarring and facilitating the production of smooth, effortless strokes. However in recent years there has been a tendency to use materials in the shaft (e.g., carbon fibre) and its attached grip (e.g., foam rubber) which do not transmit jarring to the hands, and this makes balancing at the centre of percussion less relevant than with more traditional materials.
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