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In search of the perfect mallet

What causes a miss

What the laws of croquet say




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© Robert Fenwick Elliott 2005-2006

Fenwick Elliott Mallets


In Search of the Perfect Mallet


Alice did not have the perfect mallet. Poor dear.I started playing croquet in 2003. It was very many years ago since I had done any sport – I had not been much of a sportsman even then. It soon became apparent to me that the traditional mallets on the market do not work as well as they might. They seemed to be at about the same stage as tennis rackets were many years ago, when manufacturers took their first shaky steps away from wood and gut. A Wimbledon finalist would have no trouble at all beating almost anyone on a tennis court even if he played with an old wood and gut racket, but he plays even better with a decent graphite racket. So do we all.

And so I started making mallets for myself, and they worked much better. As a player, I have achieved rather better and faster results than I expected, or deserved, as a pretty indifferent sort of sportsman.

And then I began the search for the perfect mallet, making many prototypes. I tried many hard woods, balsa wood, soft woods, laminates, oak, beach, pine, aluminium, glass fibre, holes here, holes there, fixed shafts, removable shafts, twisted shafts, bent shafts, even two part shafts, round shafts, square shafts, moulded lead weights, resin-fixed lead weights, dynamic (loose) weights, steel weights, tungsten weights, light heads, heavy heads, thin heads, fat heads, shallow heads, tall heads, slippery faces, sticky faces. The Tudor Axe, an exercise in achieving peripheral weighting without additional materialsI even made a head with the facility to move the weights around to test the effect of different distributions of the same weights around the head. And of course the Tudor Axe. I have evaluated pretty much every variation that I could think of as making a meaningful difference to performance.

After a while, people started asking me if I would make them one as well. At first I said no, because I was not satisfied that my search had gone far enough.  I eventually came to the views that

  • Graphite was the the way to go for the shaft, not with a rounded section, but a with fatter more square cross section.  That meant incurring the cost of the CAD design and then cutting of a manufacturing tool.

  • For the head also, a graphite chassis is better than a timber one, since the removal of material from where it is not wanted in a timber head inevitably means than the structure is prone to cracking after many repetitions of hard hitting.  And the weight is better provided by embedded tungsten shot than by disc, whether of tungsten or stainless steel.

Howard Head The search for better, or even perfect, sports equipment is not new. Howard Head revolutionised both skis and tennis rackets (link to summary) by treating their design as a matter of science, not craftsmanship. Golf clubs are now hugely much better than they were a few years ago. I have tried to approach the making of croquet mallets in terms of design and analysis, rather than as a craft. Croquet mallets have, in last few years, taken a few tentative steps towards more efficiency. Many mallets have some peripheral weighting, which is good, but the steps towards good weighting have often been half-hearted. Some makers have started using graphite or other composite materials, but only in tubular form, often from stock intended for use in fishing rods (!), no doubt because the process whereby composites can be formed into tubes or cones is much cheaper than the process needed to make other shapes. 

The search path

The distribution of the weight

The moveable weight testerFor the reasons explained elsewhere on the site, a large moment of inertia is highly desirable, both to keep the mallet from twisting during the swing and to minimise the effect of off-centre hitting.  That means getting as much weight as possible to the extremities of the head; this is clear, not only from a theoretical analysis, but also by using a weight tester. Some makers use brass, since brass is fairly easily worked, and has a density of about 8.5 - much more than wood. Lead is better at 11.3, tungsten is better yet at 19.6 (see table). Depleted uranium would probably be good, but its mild radioactivity renders it unpopular. The Series 3 Fenwick Elliott Mallets used either tungsten or stainless steel; the Series 4 uses tungsten.

Given an ideal overall weight of head, the amount of weight that can be placed at the extremities depends on the weight in the middle section. In a wooden construction, this can be reduced by drilling out large holes through the head. Holes along the length of the head are bad, because they interfere with the shock wave. For a number of reasons, horizontal holes are better than vertical holes.

But a chassis made of a composite such as graphite is much lighter than any other practical alternative, and allows almost all the required weight to be concentrated at the ends of the head.  This is solution adopted in the Series 4 head.

The weight of the head

This is a matter of personal preference. The lighter the head, the more extreme the ratio that can be achieved in a stop shot (this is not the only factor, but a key one), and - for many people - the easier it is to control the mallet head at higher speeds. But too light a head can make it hard to achieve sufficeiently powerful rolls, particularly across a heavy lawn.

It seems clear from our experiments that the optimum weight depends on the power efficiency of the mallet: if the mallet transfers energy efficiently from head to ball, then it is possible to obtain the benefits of a lighter head without sacfificing the long roll.

The Series 4 head is made in 3 weights between 2¼  lb and 2½ lb.

The length of the head

For many people, this is matter of personal taste. But there is no doubt that a longer head provides a bigger moment of inertia. And lining up is more accurate with a longer head. So we recommend about 12”.  We note that many player have experimented with longer heads, and rarely retreat from a length of up to 12".  But a fair proportion of players who experiment with 13" go back to 12"; 13" seems for many to be a bridge too far.

The width of the head

A narrower head allows a little bit more nifty play around the hoops, but the real effect here is fairly marginal. So we make heads a little under 2½ inches wide. Too narrow a head seems to be off-putting to most players, and a head of around 2½ inches wide reduces the risk of mishitting rolls.

The height of the head

Our testing has suggested this makes little practical difference. We make them just over 2 inches deep.

Friction at the mallet head

Testing suggests this makes no difference.

The Shape of the Head

Some manufacturers make “boat shape” heads, such that head is deeper in the middle than at either end.

We think that this is not misguided, but counter-productive, for two reasons:

  • It puts more mass around the middle section of the head, where is not wanted, instead of at the extremities, where it is wanted.
  • It impedes the accuracy of the flat sweep shot.

We say “misguided” because some might say that a boat shape reduces the risk and effect of hitting the ground. We do not believe either. The risk point is akin to the attitude of golfers who use very tall tees to reduce the risk of topping the ball; good players do not do this, since it merely increases the difficulty of hitting the ball cleanly. As to effect, if you are going to hit the ground, and thereby pick up some twist (one side or other of the mallet bottom is almost bound to hit the ground slightly harder than the other), the last thing you should want to do is to hit it with the central section of the mallet, because if you hit it with either the front or the back the moment of inertia around that point will be up to 4 times as much as around the centre.

For work around the hoops, a flat base and flat sides are best, so that the head can be slid along the hoop leg.

And for rolls, particularly pass rolls, a flat bottom to the face reduces any inaccuracy when the bottom on the face is still in contact with the ball at the end of the impact period (a round bottom will mean than, unless the ball mark travels through the exact centre of the face - extremely unlikely - there will be some sideways force imparted by the end of the impact).Series 4 sculpture

But these constraints on the outer shape of the head do not prevent sculpture within the head, as in the Series 4.

The shock speed and elasticity of the head 

Some mallet heads feel “dead”; the ball does not spring well off the mallet head, which is bad. Others give more power for less swinging, which is good. What seems to be happening is this. The total impact time is about 1 millisecond in total. At some time around the middle of that period, a shock wave is sent from the front face of the mallet head to the back, where it rebounds. The shock speed (speed of sound) along the grain of wood varies from about 10,000 ft/sec to about 19,000 ft/sec depending on the wood (see link to UK piano page). The perfect characteristic seems to be such that the shock wave arrives back at the striking face quickly (perhaps an eighth of a millisecond or so) after it sets off towards the back of the mallet, so that the returning shock wave tends to push the ball off on its way. The length of the journey up and down the mallet head is about 2ft, so a “slow wood” will return the shock wave after about a fifth of a millisecond, plus a bit perhaps to allow for some cross-grain travel (sound travels about 3 times faster along the grain of wood than across it) and for the deadening effect of the shaft, whereas a “fast” wood will do it in about a tenth of a millisecond, plus a bit. We would like to find a way of timing the shock wave empirically, and measuring how much comes back to the face. We have experimented with various configurations and materials to “tune” the head to the perfect shock speed according to what “feels” right in the hand. Some configurations (eg placing weights directly behind a plastic of composite striking face) proved to be “dead” – probably because they are too slow. Not a perfect method yet; but under review. An inelastic configuration produces a dead feel. For this reason, we rejected the solution some makers have adopted of a metal “frame” connecting the sides of heavy plastic striking faces. What might be happening there is that the shock wave has to divide into two, each traveling first sideways to reach the metal side plate, then some of the shock will turn 90o to travel down the metal side plate, and then, some of the shock will turn 90o again to pass into the back striking face. The two waves probably then interfere with each other: little seems to return effectively.

A CAD imageThe solution of a graphite chassis, adopted in the Series 4 head, leads to a very fast shock speed, and this is particularly audible - the sound of the strike is a click rather than the dull thud associated with a wooden mallet head.  Further, we have arranged a long arc of material, not at the extremity of the chassis, but running from behind the impact point: this is designed to produce an efficient transfer of energy from the striking end and back again.

The durability of the head

The head needs to be able to withstand the shock of the big shot, including a canon played to the farthest corner of the lawn, without cracking or distortion of the striking surface. Several hardwoods will do this in the form a solid block, but for the reasons of distribution of weight, this is not perfect by any means. In our earlier Series 3 heads, we achieved the right weight distribution by drilling out holes, but after many months of hard hitting, some users were opening up cracks in the narrow areas of timber.  We dealt with this by introducing a laminate system, whereby two strips of composite were introduced, running fore and aft.  But that too carries a long term problem, in that over time, differential movement between the composite and the timber can weaken the bond with the striking face.  

Composites are good, and the prognosis is that the Series 4 will be durable. But we are having some difficulty in weaning existing Series 3 users onto the new Series 4, because they have become attached to the Series 3 characteristics, or just like the look and feel of them! 

Laser sighting

A experimental laser guidance systemPerfectly possible, as we discovered when we tried it. The trick seems to be to position the laser pointer up on the shaft, where is is away from the impact shock and can be controlled, and to reflect the beam forwards by way of a mirror set at approximately 45o just above the height of the ball. Would be a good idea, perhaps, except that it is forbidden by the Laws. So useful only for practising

The weight of the shaft

Given an optimum overall weight, the less weight there is in the shaft (where it serves no useful purpose) the better. Aluminum might have been a candidate for a perfect material, save for durability reasons (see below). Composites provide great rigidity and strength at low weights. They have proved good, not only for croquet mallets, but also for polo (see eg George Wood’s site on this point). Some shafts are fixed into the head with the aid of a metal (typically aluminum) sleeve. These add weight, and so are not perfect.

The shape of the shaft

The Fenwick Elliott lower shaftThe shaft may not be moulded with an impression of any part of the hands (see Laws) but can be octagonal, or square with rounded corners.

Round is not good, let alone perfect (see What causes a miss). This goes, not only for the top of the shaft, where it is held for drives, but for the central and lower sections of the shaft, which is held for rolls. The tradition of making wooden shafts which are round in their lower section makes no sense: it is what a wood turner might do if he has a lathe handy, because that it what he does.

The lower handle needs to fat enough to fit comfortably in the hand; some manufacturers use (and we experimented with) roll grips, but these typically suffer from being round, which is not perfect at all.

The flex of the shaft

The flex characteristics of the shaft affect several things. Traditionally, many people have disliked a shaft that is too rigid longitudinally, since it feels harsh and the "smack" can induce some discomfort in the hands and/or arms. Too soft, and it will lack feedback. It needs to be as rigid as possible rotationally, to help reduce the twist caused by off-centre hitting, and to give a stable feel. There is no way we have found yet to calculate the perfect flex characteristics as a matter of theory. So we took the one of the many experimental shafts that had the best flex characteristics for playing purposes (fairly rigid), had that flex tested on a rig, and had those flex characteristics designed into the composite shaft.

Interestingly, a very light shaft produces much less smack than a traditional shaft of the same rigidity, since there is much less material available to carry a shock wave up the shaft.

A detachable head

A detachable head is a good idea, for 3 reasons:

    * It is easier and safer for traveling

    * It allows players to experiment more freely with different shafts and different heads, until they find the combination best for them

    * It allows for off-centre alignment for players who find that useful.

Alignment splines in a Fenwick Elliott Mallets shaftBut the standard arrangement is not perfect, because, even with visual markers, it is unlikely that the shaft can be aligned to precisely the same angle each time the mallet is assembled. So we have added alignment splines to the bottom of the shaft, that create small indentations in the top of the head, designed to facilitate accurate realignment every time.

The durability of the shaft

Aluminum shafts, at least those that are light enough, appear to suffer from metal fatigue and thence fracture.  Composite materials such a graphite are much more durable.

Where has this search for perfection led to?

Series 4We have made and tested dozens of experimental mallets, heads and shafts, using hardwoods, soft woods, plastic, tufnol, G10, G11, glass fibre, brass, lead, tungsten, aluminium, resins, composites (including carbon fibre, or graphite, and glass fibre) and several other weird and wonderful materials in all sorts of shapes and combinations. We like where we have got to. But the search will never quite end.