Solar Heating of Croquet Balls - II
It is well known that dark objects absorb more heat than light ones. It is often whispered that the black ball expands most when it is hot. This paper reports on a series of experiments carried out to investigate radiant heating (via direct sun) of croquet balls.
A previous paper on solar heating a thermocouple was used on primary coloured Sunshiny Balls. Measurements for this paper were made using a non-contact infrared thermometer and expands on those previous results. The thermal conductivity of croquet balls is also considered. There is an accompanying paper which investigates the effect of near uniform heating and presents the thermal coefficient of linear expansion for Dawson and Sunshiny balls.
This investigation was done in two parts:
Dawson 2000 (secondaries) and Sunshiny Tournament (primaries) balls were left under hot direct sun and their surface temperatures measured on the part of the ball facing the sun:
An additional temperature measurement was made of the 'back' of the ball, away from the sun:
The experimental detail is given in the appendices.
As might have been expected the darker ball colours have higher surface temperatures in direct sun than the lighter colours. The Black ball's surface temperature in direct sunlight is 20 ºC warmer than the Yellow's, and the Brown ball's surface is ~24 ºC warmer than the White's.
The measurement from the back as well as the face of the balls shows that the whole ball is not heated to the same temperature - it is a poor conductor of heat. Only the sun-facing side is heated appreciably.
As has been shown in an accompanying paper we can expect a Dawson ball to expand by 1/64th inch when the whole ball is heated by ~22 ºC. Taking the Black ball, if we crudely assume half the ball is 30 ºC warmer than the rest we will get 1/2 * 30/22 * 1/64" ≈ 0.7 x 1/64" = 0.0107" overall expansion in the diameter. Not a great amount for a large temperature rise.
The conclusion is that direct solar heating does not increase the diameter of a ball appreciably.
Why Might Heating Affect Balls?
The solar heating is only on the part of the ball facing the sun. This would create a small expansion on the heated area, potentially making it slightly 'less spherical'. Probably more significant is that it will affect the surface properties of the ball.
Elastic substances become softer as they get warmer. (Consider a soft pencil eraser which has been put in a freezer). Consequently a hot ball may grip the uprights more than a cold ball (higher coefficient of sliding friction).
Some plastic materials become more rubbery and more bouncy as they are heated, however previous experiments on the change in bounce with temperature of Jaques and Barlow croquet balls showed a negative temperature coefficient of resilience, i.e. the balls became less bouncy as the temperature increased.
The feeling is that the Dawson balls certainly do not 'become like bars of soap' as they become hot, as was the case with Barlow balls. This will be a topic for future investigations.
In the first experiment a non-contact infrared (IR) thermometer was used to measure the temperature of sets of balls (Dawson 2000 secondaries, Sunshiny Tournament primaries) which had been left in direct hot sun for a couple of hours. Measurements were made on the part of the ball facing the sun (corresponding to 'A' in a later diagram). The horn of the IR thermometer (15 mm diameter) was held nearly touching the ball's surface to eliminate outside sources of heat, restrict the area of measurement and to prevent reflected IR entering the instrument. Two readings were made on each ball and averaged. The readings were made on the balls in the sequence 1-8, 8-1 to reduce any memory effects, drift or background temperature changes.
The grass temperature was taken again with the IR thermometer adjacent to the balls and it was also in full sun. The air temperature was taken from my nearby weather station; it probably uses a semiconductor or thermoelectric temperature sensor. As an observation if you point the IR thermometer straight up, away from the sun, it gives a temperature of -13 ºC. There are no sources of infra-red radiation that it can see!
Appendix B: Experimental - Thermal Conductivity
Further experiments were done to investigate how well croquet balls conducted heat and what the effect of ambient thermal radiation was.
On another hot day (5/7/17) selected balls were left in the sun for an hour (14:00-15:00) to reach equilibrium. E.g. like leaving the balls in the sun over lunchtime. Temperatures were measured at different locations on the balls, as indicated below, with the non-contact IR thermometer.
Taking the case of the Black ball, it was able to maintain a 30 ºC difference between the sun-facing side of the ball (A) and opposite side (C) during an hour's heating. The 'base height' temperatures were similar irrespective of the colour of the ball (see second figure above).
To determine how much the air and ground temperature affected the readings, balls were left out overnight and in the morning (~9:30) with the balls in shadow from the sun, corresponding measurements were made. The results below are the average of two readings scanning L-R, R-L whilst the air temperature increased from 24.1 to 25.2 ºC.
All the ball temperature measurements above are close to each other (13.8 - 16.3 ºC). Again the temperatures follow Black-Brown-Yellow-White where the balls are not in contact with the ground. This could be differential absorption of general radiation or different emissivities affecting the reading of the IR thermometer. Emissivities however are investigated below and are shown to be extremely similar.
Next consider colour choice - under direct sunlight all the balls heat up above the air temperature. In direct sunlight the balls' surface temperature can range between 50 ºC (Yellow) and 70 ºC (Black). (OK it was the hottest June day in the UK for 40 years when I made the measurements). Measurement on the sun-facing side of the ball, and that in shadow, shows that there is a temperature distribution, even after some hours under the sun. This makes calculation difficult. One side of the ball is at 50 ºC or 70 ºC and the underside at possibly 35 ºC.
For the sake of argument say that the entire half of the black ball facing the sun is at 70 ºC; it is 55 ºC hotter than when the hoops were set in the morning at say 15 ºC. 55 ºC ≈ 2 x 27.7 ºC for which we know the expansion (see accompanying paper). We have half the diameter heated to twice the temperature difference thus we might expect the heated side of the ball to expand by the original amount, 0.015" ≈ 1/64". Suddenly we have no clearance on the hoop and we have not yet added in the expansion of the second half of the ball which is likely to be approaching air temperature i.e. 30 ºC. Ok this is likely to be 1/256" but that is added to a ball which is already jamming. The affects of expansion is covered in the accompanying paper.
The take home here is that you should avoid the dark colour balls in direct sunshine when it is hot! In direct sunlight you have radiative heating which is directional. No problem when it is overcast as all balls will gradually reach air temperature by conduction and a little radiation from their surroundings. Radiant heating increases the temperature to a much higher level than the air temperature.
Appendix C: Experimental - Emissivity
The IR thermometer used in this and the companion experiments on the thermal expansion of croquet balls had a fixed emissivity calibration. The displayed temperature depends on the similarity of the test surface to a surface which has an emissivity of 0.95. Shiny surfaces have a very low emissivity as demonstrated by pointing the IR thermometer at a very shiny pressure cooker on heat; the temperature recorded was 38 ºC, however droplets of water would boil on its surface - it would have been at some 121 ºC.
Unfortunately no further information was available about the internal working of the thermometer from the manual, e.g. did it compensate for the temperature of its sensor, or did it simply indicate a scaled version of the signal from the sensor? In the case of the latter the temperature of the thermometer body becomes an issue.
To do a simple emissivity check both sets of Dawson and Sunshiny balls had patches of thin black carpet tape stuck to them and they were left indoors overnight with no direct radiant sources of heat. It is assumed that the tape stuck to a ball would be at the same temperature as the ball.
The temperatures of the tape and adjacent ball surfaces were measured across the range of balls using the IR thermometer. The horn of the IR thermometer was pressed close to the surfaces to eliminate any reflected IR reaching the sensor. Whilst it would be hoped that the tape and balls' surface temperatures were the same; there is however no reason for the temperatures between balls to be the same - they may have different properties, e.g. heat capacities and IR absorption/radiation which would lead to temperature variations.
The data below was obtained first thing in the morning after the balls had been left indoors and out of view of the sky:
Two readings were taken on each ball - the first taken moving from left to right through the balls and then repeated from right to left. This hopefully would average out any drift in the IR thermometer's reading due say to it being warmed by the hand or heated by constant use. Adjacent cooking and precision mercury thermometers gave the room temperature as 21.7 ºC and 21.9 ºC respectively.
The temperatures and hence the emissivities are (amazingly) consistent. As a further sanity check the same black tape was stuck on the side of a stainless steel kettle containing boiling water and the reading was 97.7 ºC
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