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Technical
How to Determine Lawn Speed During a Game

By Louis Nel

Nowadays all sporty wrist watches are equipped with timers and hand held calculators are inexpensive. So it is within easy reach of a spectator to make a fairly accurate estimate of the lawn speed during a croquet game – while remaining seated. How this can be done is explained below. And why would any spectator want to do that? Aside from personal curiosity, this information is sometimes of interest in a game report, especially when the speed is unusually fast or slow. A triple peel on a fast lawn is a greater achievement than one done on an easy paced lawn.

The lawn speed of a court is defined as the time in seconds it will take a ball to roll 35 yards (the length of a full court) before coming to rest. For brevity people sometimes just say “12.5 seconds”. Brevity is better achieved by saying “12.5 Plummers”, as done in “Further Lawn Speeds Calculations”.

Let me begin by describing the two needed measurements. When you see a player is going to hit a ball for a long stroke without colliding or going out of bounds, you need to note the start position and the end position of the ball. That enables you to measure the distance, s, travelled by the ball. You also need to measure the time, Ts in seconds, that the ball takes to roll that distance s. Suggestions are given below for doing these measurements.

For the moment let us assume you have obtained the experimental data

s = 21.5 yards and Ts = 10.4 sec.

(1)

Then the lawn speed, P, (in Plummers) is obtained via the calculation

P = 10.4 * √(35 / 21.5) = 13.27 sec.

(2)

(i.e. 10.4 times the square root of 35 / 21.5). In general terms,

P = Ts * √(35 / s).

(3)

Background

Validity of this formula (3) rests on the application of Newtonian mechanics to a rolling croquet ball done by Ian Plummer in his article “Lawn Speeds”. According to that theory, the distance, s, that corresponds to a travel time, t, is given by the equation

s = -½ * a * t2

(4)

where a is a constant which reflects the court conditions that cause the ball to decelerate. Putting t = Ts and rearranging, this equation becomes

-½ * a = s / Ts2.

(5)

In particular, when s = 35 the corresponding time P = T35 satisfies the equation:

-½ * a = 35 / P2.

(6)

Equating the two expressions on the right, we obtain

s / Ts2 = 35 / P2.

(7)

Solving P from (7) gives the above formula (3). You could use feet instead of yards throughout if you prefer. Instead of 35 / 21.5 you will then use 105 / 64.5 (same thing).

Underlying assumptions include flatness and levelness of the court, uniformity of surface and no wind. So the accuracy of the computed lawn speed will be reduced to the extent that these assumptions fail to hold.

Practical Suggestions

It is a good idea to take the average of several calculated estimates. If the estimates are typically within 1/2 second of the average, you might report the speed to the nearest 1/2 second e.g. 13 1/2 sec. If they are merely within 1.0 second of the average, report to the nearest second e.g. 13 sec. Don’t report it with two decimal digits (e.g. 13.27) because your accuracy will never be within 1/100 of a second.

The main problem about timing the roll is to know exactly when the ball stops. It is a good idea to measure only rolls that end within close view. Rolls close to 35 yards in length are preferable. Avoid shots which may have caused the ball to become partially airborne.

Here follow two ways to facilitate distance measurements.

  1. Make use of known distances. For example, if on a full court a ball in corner 4 is struck directly northward towards corner 3 (to roquet a ball there) and comes to rest 2 yards short of the target ball, you can conclude it traveled for a distance of 33 – 2 = 31 yards. Another example is the known distance from hoop 2 to hoop 4 (25.25 yards), which comes into consideration quite frequently in the split shot after hoop 2 is executed.
  2. Use a plan of a croquet court, drawn to a convenient scale e.g. ¼ inch to a yard. The start and end positions could be marked by two little crosses for comfortable later measurement in inches, which is converted to a distance in yards according to the scale.

Another Use

When lawn speed is determined by direct experiment, the ball will normally refuse to come to rest exactly 35 yards away, opting for s yards instead. People have been using plots to then convert the experimental data (s, Ts ) to Plummers. The plots for one court do not apply to another court. From now on the conversion can conveniently be done via the formula P = Ts * √(35 / s). Thus this formula addresses one reason why the Standard Ramp Method was introduced. The ramp remains convenient in special situations e.g. when no second person is available to strike the ball or when the lawn speed of a relatively small untypical patch is to be determined.

8 March 2008

Author: Louis Nel
All rights reserved © 2008


Updated 28.i.16
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