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Dr Ian Plummer

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Technical
Measuring Bias in Croquet Balls by Floatation

If the centre of mass of a croquet ball is not coincident with the centre of the sphere then a ball will have a bias. This could be caused by an off-centre air pocket or a variation in the density of the ball material. A bias will cause a ball to curve in its track as it slows down.

One method used to quantify bias in croquet balls is to float them in a strong salt solution and add peripheral weight until the ball shows no preference in floating in any orientation.

Result: A test was done on a Sunshiny ball and it was found that a 4.49gm peripheral weight was required – this is marginally more than a sugar cube weighs. This is ~1% of the weight of the ball.

Method

Ball floating in Salt SolutionThe hardest part of the exercise is finding a vessel which will take the croquet ball and have sufficient depth to completely cover the ball without requiring gallons of solution. Salt is about 25p/1000gm from a supermarket (2008).

To get approximately the right concentration add 30-40gms (a level tablespoon) of salt to 100ml of warm water (a cup full), scaled up as necessary for the volume you need. You will need less solution than the volume of the vessel since the ball will take up ~400ml. Alternatively the same concentration can be made by pouring salt into, say, an empty tin can until it is ~1/5th full and then top up with warm water.

Put the ball in the vessel and top up with solution. If the ball fails to lift off the bottom once just covered you will need to add more salt to the solution. You could use excess salt but it then starts to crystallise out of solution – all over the ball and vessel.

With the ball left floating in the solution it will eventually stop moving with the lightest part of the ball uppermost, if it is disturbed with the lightest stroke and returns with the same area uppermost then it has bias.

Blu-tack blob ~4.5gmTo remove the bias a small blob of Blu-tack or similar putty is applied to the uppermost point and the ball left to see if it still floats with a preferred orientation.

If the putty blob swings to the bottom it needs reducing (snip off a bit with scissors), but if it remains uppermost more putty needs adding.

If the putty rises to the near the uppermost point again then the weight needs increasing and the blob wants moving slightly towards the new top.

Once you are close to the correct position and weight the ball will take a long time to settle. After you have got the correct weight the putty can be removed and weighed.

Very approximately a 13mm diameter sphere of Blu-tack is weights ~4gm.

Background

The density of a croquet ball can lie between 1.066 g.cm-3 and 1.158 g.cm-3 given the variations allowed in diameter and weight.

For a ball to float it must be in a solution of higher density:

Percent by Weight in Solution

Density of Sodium Chloride (Salt) Solutions

 

0°C

10°C

20°C

25°C

30°C

40°C

50°C

60°C

80°C

100°C

20

1.157

1.153

1.148

1.145

1.143

1.138

1.132

1.127

1.115

1.102

22

1.173

1.169

1.164

1.161

1.159

1.154

1.148

1.143

1.130

1.117

24

1.190

1.186

1.180

1.178

1.175

1.170

1.164

1.158

1.146

1.133

26

1.207

1.203

1.197

1.194

1.192

1.186

1.180

1.175

1.163

1.149

Data from the Salt Institute.

In the table above densities less than the maximum density of a croquet ball have been greyed out. A sensible temperature will be between 20-25°C, hence a solution of 22-26% by weight is required.

Example

30gm of salt in 100gm of water yields 30/(100+30) as the weight fraction of salt = 0.23, i.e. a 23% by weight solution in water. Water weights 1gm per ml at standard temperatures.

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Updated 28.i.16
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