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Dr Ian Plummer

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Technical
Frequently Asked Questions

This section collects responses to questions I have received. Some of the material may now be dated. Caveat Emptor! Please note that questions about the rules/Laws will not be included here


How much does it cost to lay a croquet lawn?

I was reading your article on the specs for a Croquet Lawn. I'm working for a new residential community and we are looking to build our own croquet playing area. I have the guidelines of how to build the area, but can you tell me the cost, approximately?? I know it will depend on cost of sand and etc., but it would be very helpful if you can give me a rough estimate.

Without much more information this question equates to `how long is a piece of string?´ The answer you probably are looking for is from ~£6K - £35K depending on initial conditions and final quality.

£6K - For a flat site with ~20cm of good topsoil (not acid or alkaline or too stony), the site can be harrowed, the stones removed and then flattened using a laser guided machine. It is then over-seeded to produce the turf. Wait a year for the grass to establish.

£30K+ - The site is levelled, the entire site is excavated to a depth of ~50cm and the content scrapped. Membranes, drainage and irrigation are installed; imported layers of stone, sand, ash, and topsoil are individually applied and levelled. Quality turf is then applied to the surface. The surface ready to play on in a handful of months. [2005]


What are Wharrad Turns?

On your excellent pegging down sheet, there is a line, "Wharrads Left:" what are Wharrads?

Lionel Wharrad suggested an alternative method for concluding timed games. After, say, 2hrs of play "time" is called and the players are each given 'n' more turns. These turns are the Wharrad turns. Their principal benefit is that they discourage 'time management' by a player playing deliberately slowly to deprive the opponent of the opportunity of playing (and winning) before 'time' runs out.

This concept has been embraced in the UK Tournament Regulations as an option:

"T3 LIMIT ON NUMBER OF TURNS

APPLICABILITY. As an alternative to a one-hour time limit imposed under Regulation T1(b), or to the final hour of a time limit imposed under Regulation T1(a), the Manager may limit instead the number of further turns to twelve (exclusive of any bisque turns) to be played by each side. The general procedure is as described in Regulations T2(a)(1) and T2(a)(2), with the following provisions.

START. The additional turns shall start after the end of the extension period defined in Regulation T2(a)(2). Regulation T2(b) will not apply.

END. If the game has not ended before these turns are completed, the side which has scored the greater number of points is the winner. If each side has scored the same number of points, play continues and the side for which the next point is scored is the winner (any points scored subsequently in the stroke are ignored). "

http://www.croquet.org.uk/tournament/regulations.html#T3 [2006]


Why isn't croquet a commonwealth sport?

Clearly the Croquet Association has attempted to raise the profile of croquet with respect to the Commonwealth games. I found the following references in their archives:

  1. "While researching worldwide numbers for our application to the Commonwealth games in 2001, the association secretaries in .."
  2. In the committees' review of 2002 it was said: "The Commonwealth Games Federation Committee will include croquet in their next review of recognised sports. "
  3. http://www.croquet.org.uk/tech/croquetintro.html starts by saying "This introduction to croquet is modified from one prepared in support of an application to become a Recognised Sport by the Commonwealth Games Federation." This seems to have been done in 2003.
  4. The Croquet Association minutes of that time have the single entry: "J Ruddock's e-mail referred to pressing for Croquet to be played at the Commonwealth Games in 2010. This was passed to JK (International Committee)."

The Croquet Association seems to have passed on the task. The World Croquet Federation, have 'getting involved in the Commonwealth games' in their business plan.

Croquet was played in the 1900 Olympics in France however! [2006]


How can I improve my hitting-in accuracy?

You may wish to think about your swinging technique: If you use Mechanical Advantage then your muscles do less work. A long pendulum stores more energy than a short one; think of knocking in a nail by grasping the hammer head or holding it well down the shaft!

** You should swing from your shoulders **

This gives you the longest pendulum. The wrists can flex at the start of the stroke and/or at the end of the follow through.

A weight at the end of an arm is difficult to deviate due to its momentum; try balancing a hammer upright in the air, with either your finger on the bottom of the shaft or, flip the thing over, with your finger under the head with the shaft sticking up. If you use a long pendulum it is more difficult for your wrists and arms to deviate the path of the head.

** You should grip the shaft lightly **

** For a normal stroke draw the mallet back slowly and then allow it to come forward under its own steam to hit the ball for moderate strokes. **

To play different strength strokes change the length of the back swing. For hard strokes you have no option but to gradually increase the speed of the mallet on the forward swing; it is important that your impetus does not twist the mallet.

** If you tighten your grip, it should not rotate the shaft **

If you get tense or try to 'muscle' the mallet forward and the tension in your grip twists the mallet all is lost. Try to find a grip which, if clenched, does not twist the mallet. [2005]


What sort of sight line is best on a mallet head?

I have tried various forms of sight lines, from none through arrow heads, tram lines to thick ones. I trialled them using strips of white insulating tape cut with a rule and razor blade on a mirror.

'None' can be effective because it causes you to be critical about mating up the mallet face perpendicular to the ball. I prefer a single narrow, high contrast stripe.

How do you use a sight line? For me I cast the mallet as I stalk the ball and the image of the sight line is a test of whether my mallet points forward. If the streak of the sight line is narrow and of high contrast - fine, if it is wide and blurry then the mallet head is twisted. For that reason I would always prefer a high contrast (highly visible) single sight line. I do not swing the sight line through the target - the line is set by my stalking. Others likely differ on their use of the sight line. [2005]


How perfect should mallet faces be?

I have worried a lot about the perpendicularity of mallet faces. I have produced my own mallet heads out of both wood and metal on high precision workshop (metal) milling machines. On the heads I produced I milled the faces, after assembly, to be perpendicular to the body.

A crude calculation says ... length of lawn 33 yds (excluding yard lines), say ball leaves at ½ degree off true ...

Tan (theta) = opposite / adjacent; adjacent (in inches) = 33yds x 36"; tan (½) =8.73e-3; GIVING A 10.3" DEVIATION of the centre line of a ball all other things being perfect.

I would make the case that the ball is deviated through twice the tilt of the mallet face (think of light beams bouncing off mirrors - although real experiments for large deviations do not show this). This means that a mallet face with a 1/4° degree tilt could lead to a 10" miss over the length of a lawn. I am amazed anyone ever hits!

Consider a laminate face being glued on to the head with a nice gungy layer of glue ... the likelihood of it ending up parallel to the underlying face is not high. Mathematics aside, world-class players play with wonky, worn faced mallets and are amazingly accurate. [2005]


How can I straighten my swing?

  1. The idea that you have to swing the mallet straight back is an **absolute fallacy**.

    Provided the mallet face returns to the position it addressed the ball before the swing it does not matter (a touch of a simplification). Robert Fulford has a beautiful hooked swing and is amongst the best shots in the world.
     
  2. The line from the shoulder to the mallet head on the back swing can/should be essentially straight; I do not propose a compound pendulum where you take your arms right back and then cock your wrists. A little wrist movement at the furthest extreme is of course natural.
     
  3. To increase the available backswing you can drop back the foot corresponding to the side of the lowest hand of your grip. My right hand is under my left so I drop back the right foot. This should be used for all shots - so that you have consistency. There is a correlation for me between how far that foot is back and the line the ball takes.
     
  4. Provided you are swinging from the shoulders with a reasonable backswing, the ball can be struck firmly. You are using a long pendulum which has a lot of energy due to the radius of the swing. On heavy lawns however the mallet needs additional force applied gradually as the mallet approaches the ball.
     
  5. Use small backswings to hit a ball softly, etc.

    Work = Force times Distance = Energy Expended

    If you try to hit a ball the length of a lawn by holding the shaft 6" above the head you have a short pendulum, hence a short (available) radius and thus need a large force.

    Angular momentum L = m * v * r

    Let the mallet do the work not your wrists!
     
  6. When I hit firmly I accelerate the mallet on the forward stroke (gradually) to achieve more powerful strokes. I feel that I am pulling against the weight of the mallet head when I am doing this.
     
  7. If you desire to literally straighten your swing then there are 'swing trainers'. The Bamford design consists of two parallel vertical arcs of wood. The player stands over the arcs with the mallet between the arcs. These constrain the mallet head to always point forward. There have been reports of a swing trainer incorporating electronics which make a beeping noise if it deviates from a straight swing. Currently I cannot find the reference. [2005]

What are your views on the Pidcock 2001 mallet?

What are your current views on the Pidcock 2001 mallet?

Alan P. has achieved two very clear goals in the scientific design of a mallet: a lightweight shaft and a head where the weight is concentrated at the faces. (footnote 1). These are the same design parameters I have worked on with my prototypes - he can afford fancier materials than I was able to! There is no doubt that it is a top-flight mallet. It has no known faults that I have heard of, e.g. it does not fall to pieces.

How do you now feel about the faces? Are they damaging balls? Has Pidcock changed the faces over time, to address such issues?

Since my early Pidcock metal-faced prototype he has modified the profile of the grooving to be more of a sinusoidal channel rather than like an engineers thread. Lacking any abrupt corners the grooves do not seem to be harming the balls. There was an article in the UK Croquet Gazette recently reporting tests by Bernard Neal and another on whether the edges of metal-faced mallets (they used the Pidcock 2001 mallet) would nick modern balls. Their conclusion was that they did not. They did not however comment on the nutmeg grater aspect I had found with my prototype.

Do some players put, say, Tufnol on the faces, etc?

I have seen no adulteration of Pidcock 2001 mallet faces.

Have you heard discussion about, say, using tungsten instead of brass to get the ultimate Moment of Inertia? (I am assuming depleted-uranium might be a bit too hot for some).

Robert Fenwick Elliot has used tungsten in his prototypes - expensive and difficult to work unless you commission someone to sinter a batch for you. Depleted uranium is a viable product and a waste material. I suspect that you would not get your mallet very far into an airport however since it is still mildly radioactive.

A large Moment of Inertia head will favour a straight swing and provide a large sweet-spot. For someone like Robert Fulford, who has a hooked swing, the heavy head would cause the mallet to twist against his grip, which I suspect would be undesirable.

Are there any 'options' for the Pidcock 2001 mallet you see of merit?

One thing that I do not recall Alan offering was a choice of weight for the head of the Pidcock 2001 mallet. I have not have looked deeply into ordering one. The basic options are head length and shaft length. It is possible that some variation in shaft whippiness may be available through the choice of rod or tub and external diameter. Unless you can get your hands on one you are pretty much under his advice. My experience with the carbon Pidcock 2001 mallet shafts is that they are stiff - at least as stiff as wood. The foam grip deadens any smack to the hands however. The black foam is pretty robust but at the start of the season it sheds its dry outer layer and will blacken the hands for a couple of games. That is assuming you do not play all year!

I have no worries about the carbon shaft tube getting damaged - I have thwacked it into the crown of hoops with considerable force. The only evidence was white paint on the tube.

RPM (Ray Puckett Mallets) Premier has an optional weight for the top of the shaft interior, to change the balance - I do not use it as I like the mass to be in the head, not the shaft (at this stage). I only found out about this option by accident, as Ray does not push it (even though he uses it). So I wondered if such might be the same with the Pidcock 2001 malletS?

Alan does not offer any adornments to the shaft apart from your choice of length and position for the main grip and roll grip. I personally see no benefit at the moment for any additional weight in the shaft. It is possible that for a specific grip and mass distribution the mallet would feel 'sweet' when hitting a ball (see footnote 1 again). It would have no benefit for any other grip/stroke-type. Working out where to put the weight would be complete trial and error.

Additionally, I would appreciate your advice on head length. My RPM is 9in, & I was feeling that I should now consider 10in the minimum, and possibly 11in. ...

These days I would consider a 9" mallet too short "for me". I have gradually evolved to longer mallet heads. Conversely I built a 12.25" head (the stainless one on http://www.oxfordcroquet.com/equip/mallets/index.asp) and was not comfortable with it for roll shots. My current one is ~11" and I am fine with it. There can be a teething time whilst you learn that you need to lift the mallet a little more off the ground before swinging it! I would suggest the going from 9" to 10.5", or 11"; it should not cause a major upheaval in your play.

The faces of the Pidcock 2001 mallet are of reasonably small diameter (? 1.5") and a careless swing will catch the edge. It is however a good tutor for making sure that you swing into the centre of the ball (I did make a small-faced mallet ... my swing was not that good!).

I want the best mallet to take me to the next stage of development, and will then buy another mallet for the stage beyond that, and so on.

I do not believe that a mallet alone will hold back your development. A new mallet is extremely valuable for getting you to analyse all aspects of the way you hold and swing it. It's a new toy; you are excited, encouraged and focussed. As such it is worth every cent - you are likely buying confidence; excellent value

I suspect that Robert Fulford could take your current mallet and after a brief practice do a sextuple!

Are there any other mallets you would consider if you were in my position now?

Robert Fenwick Elliotts are worth a thought but are yet unproven. Apart from the RPM all the others I know of (USA excluded) are 'traditional'

Aside

I would probably have a Pidcock 2001 mallet were it not for three things: 1) they look ghastly, 2) they will not stand up unsupported, 3) they do not have a square head.

None of these is a killer complaint, and just down to my preferences. Only the square head argument could have a smidgen of justification - it allows more mass ever so slightly further from the turning point and hence could increase the moment of inertia. A round-headed mallet will topple over onto wet grass and be disgusting to hold ...

Footnote 1

Robert Fenwick Elliotts has similarly pursued the same goals (his mallet as yet unseen by the world) and has further considered varying the flexibility of the shaft. He is starting to think about the moment of percussion, but I think that that is a red herring, since croquet players have different grips for different strokes and different player hold the mallet individually for the same strokes. [2005]

Alan P. responds (April 2006):

Ian,

Thank you for the opportunity to respond to your analysis. My comments/corrections are of course subject to your editorial discretion and my tongue has occasionally ventured into my cheek....

Ball damage

Initially faced with composite, the faces were changed to brass with milling fairly early on. Milling is now very shallow and has not been found to damage balls. The tests on the edges were extreme and no damage to balls has ever been authenticated.

Addition of Tufnol

My composite is glass fibre/epoxy and I can supply 2001s with this facing if desired. Retro fitting has not been attempted to my knowledge - the rounding of the edges on the brass would perhaps limit the quality of fit.

Tungsten etc.

The centre of gravity of a tungsten face would lie only about 1/4" further from the shaft, so it would hardly be cost-effective in the 2001 design. Depleted uranium is not released for dispersal in small items. The authorities like to know where it is!

Options

The weight of the head can be increased by lengthening the brass ends inside the carbon tube; a lightweight mallet (2 lbs 4 oz) is available for golf croquet in which brass is bored out behind the face. An alternative, more flexible, shaft will be available in 2006 as a result of collaboration with David Barrett; the hybrid mallet will be called a Barcock. When a Hobbs shaft is fitted, a Hobcock results.

The lack of smack to the hands is also partly due to the lower centre of percussion - the energy goes into the balls instead of into shaft vibration.

Variable weights

Altering the head weight alters distance ratios in croquet strokes. I think it better to adapt the use of a single mallet to varying conditions.

Head length/width

Available at 9" only to special order. Otherwise, 10/11/12" are stocked, of which 11" is by far the most popular.

The diameter of the 2001 is 2.3" (5.8 cm), but as your guess shows, there is an optical illusion - it appears to be much narrower and to 'point' better.

Aside

The majority view is that the 2001 looks the business, they can be brought to hand when prone by simple footwork, and how often do you hit the ball with the corners of a square face(!)?

Finally, I too believe that lowering the centre of percussion is valuable - it always increases efficiency and reduces vibration.


Our lawn slopes - is it worth levelling it?

[Note this information is given without prejudice]

The corners of our playing area lie at (x,y,z) in metres:

(0, 62, 0.072)
(72, 62, 0.136)
(0, 0, 0)
(72, 0, 0)

What will be the effects of accepting a 1:1000 slope versus a perfectly flat lawn in term of drainage and ball deviations?

Volume of wedge = integral from 0..62 of 1/2* 72*(x*((0.136-0.072)/62)+0.072).dx = 232.128 m3

Soil Calculations

I calculate that the wedge of soil described by the four corners' elevations you give approximates to a cubic volume of 232 m3 un-bulked soil (I took the 0mm-0mm edge to be the 62m one). As a sanity check if all this soil was re-spread to a uniform depth over the 72 x 62m area it would be 52mm high - which would be your cut and fill depth for moving the minimum amount of soil, which I guess is half 232 m3 = 116m3.

Provided that you are happy for the final surface to be 52mm above your datum (0mm), then the work can be reduced: you would not want to rotary hoe any land lying at or around the 0mm level as 50mm of soil will be added on top, and you move the minimum amount of soil.

It does presume that at the high points there is a sufficient depth of topsoil remaining once you have skimmed off 84mm (136-52mm).

Slopes

My enthusiasm for doing a further integration to work out the volume of soil for the sloping proposal has dwindled but ... Assuming a 1:1000 slope is acceptable (as it is convenient since the 72m edge elevates 72mm over its length, if I have the corners the right way around!) the wedge of excess soil in question has corner elevations 0,0,0,(136-72), i.e. 0,0,0,64mm, lying on top of a wedge 0,0,72,72.

This wedge has a cubic volume of 72m3 and all of it will have to be smeared over the whole lawn surface 16mm deep.

You have to shift 60% more soil for the cut-and fill method.

Flatness

The only really flat lawns I have played on were the 12 laser-levelled courts in Palm Beach, Florida. They were lovely! Although I have seen really heavy rain there, since the courts are *very* sandy I cannot comment on whether flat lawns present any particular drainage issues.

Apart from short lived surface water, most lawns drain by percolation which can be fast or slow depending on the porosity of your soil. Hence you can control drainage with slopes or soil type. The mental picture of a sheet of water whooshing down a hill carrying soil with it is likely inaccurate. A slope of 1:1000 is 1mm per metre. I doubt whether the water will even notice that, with surface tension and clumps of grass. For smooth vitreous drainpipes the recommended fall is 1:80 to 1:120.

I would doubt that the proposed slope has any effect on drainage.

Drainage

You express a concern about drainage - is this a real problem? If it is perhaps now is the time to consider either installing drains, sand filled slit trenches or similar.

Stones

Unless your courts were deliberately laid, then I would guess then the rotary hoe will pull stones to the surface. These will either need to be riddled out of the soil, a stone-burying machine used or a team of volunteers found with strong backs.

Deviation of Trajectory

I appear to be making the same assumptions as you have as to calculating the sideways force due to the slope and hence get the same deviation. Given this pure figure, is it realistic? A 'thousandth of a gravity' does not sound much to me and wonder how it compares to a gust of wind, or constant wind. How significant is the straightening influence of gyroscopic forces (I have no clue as to how to start with that one!)? Eccentricity of balls, off axis centre of gravity? Is the slope on a billiard table more or less than 1mm in a metre (I scanned the web without success!)

A typical transit time for a ball to travel the length of a lawn is ~10 seconds; using s = u.t + ½.a.t2 + c for the transverse motion, assuming a = 1/1000 g, gives ~50cm deviation. This ignores the friction of the grass, etc. which would reduce the value.

The final issue is the tolerance of the laser leveling machine. I was unsure about what +/- 5mm means. It seems to be missing a characteristic length; otherwise a lawn with a 1cm square-wave finish might result. Is the +/- 5mm the pointing accuracy of the alignment laser? [2005]


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