Solar Heating of Croquet Balls
The following experiments were carried out to answer the question "How hot does a black croquet ball get on a hot English summer's day". The result was to be used in setting a sensible temperature range for testing the coefficient of restitution (bounciness) of tournament standard croquet balls. Leaving aside the scarcity of hot summer days the next issue was how to measure the temperature. Two methods were considered: a). using a surface thermocouple and b). using a non-contact infrared thermometer. Unfortunately an IR thermometer was not available. Sunshiny tournament standard balls were used.
The basic result is shown on the following bar graph. Primary colour croquet balls were left out on a very hot cloudless, windless July day and their surface temperature measured after 2 hours exposure at ~3pm.
The Black ball's surface temperature was 17.8°C (32.2F) above that of the Yellow ball. The method is presented later.
The difference in temperature of the balls will have two significant effects: on size through thermal expansion, and 'bounce' (coefficient of restitution) due to the change in properties with temperature.
On size, we still have to make suitable measurements - currently I have no data on the thermal expansivity of these balls. If they are made from filled polyurethane as were the earlier Dawson balls then a random coefficient of expansion grabbed from the web for rigid polyurethane is 3.5e-5 in/in/F which would result in a size difference of 0.00406" for a 32.2F temperature difference on a 3 5/8" ball. Given that 1/32" = 0.03125", this coefficient would suggest that the size changes insignificantly for these assumptions.
Dawson reported for an early ball (1989 Patent 4,872,677) that although it rebounded 45" when dropped from 60" at both 0°C and 20°C, its rebound height had decrease to 35" at 100°C. If the Sunshiny balls follow the same trend then the Black will be less bouncy than the Yellow. Measurements awaited!
There will also be other effects - the surface texture could become more rubbery with temperature affecting the contact in croquet strokes and binding with the hoops, etc.
Equipment and Method
A thermocouple thermometer was constructed based on an integrated circuit with cold junction compensation. This demonstrated an accuracy of 0.5°C when tested in ice and steam. The thermocouple itself consisted of a 4mm silver-soldered twisted region of J thermocouple wires (~0.5mm each). This produced stable readings in a couple of seconds and had a low heat capacity. Measurements were made by pressing the thermocouple into the milling of the balls using the spring of the thermocouple wire, with the wire held a couple of inches from the twisted region. Additionally a small drop of PEG (polyethylglycol - an inert clear treacly liquid which does not evaporate) was placed on the contact area to improve thermal contact. The measurements were influenced by the strength of the sun during measurement.
The reading was taken once it had stabilised to within ~0.3°C. Ground temperature was taken by tucking the thermocouple under the ball (in a shadowed region) and the air temperature by waving the thermocouple in free air away from other surfaces.
A number of measurement runs were done all showing the same trend. The listed measurement above represents that single run during which the maxiumum temperatures were measured.
The surface temperature of a ball will depend primarily on the heat flows below:
The temperature of the bulk will depend also on the last three factors and heat gained or lost through contact to the ground. Whilst attempts could be made to quantify all of these, the real interest is what the final temperature is and things which affect it.
Solar intensity is approx 1kW/m2. Ball area = pi*r2, where the radius is ~.046m, hence area is 0.00665m2, yielding a maxiumum heat input of ~ú6.67 watts in bright sunlight.
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