There are many reasons why you should never be a referee, but the reason I’ve never become a referee is fear of being cooked if I make a decision the home side don’t like. That’s right, cooked. I’m about to do the maths for those of you who don’t believe me.
The average man weighs about 70 kg. Now I reckon the average ref weighs less than this, but we’ll count that as slack.
On a cloudless day (the ideal kind for a football match) the earths surface receives approximately 942 Js-1m-2. More when the earth is closer to the sun, and less when it’s further away.
Now the human body consists mainly of water, which has a specific heat capacity of 4.2x103Jkg-1oC-1. This is generous, as the human body would probably be easier to heat than 70kgs of water.
So the amount of heat energy required to raise a mans body temperature by 35 degrees (way more than we need – to kill we only really need about 10 degrees) all the way through is 70 x 4.2x103x35 which is 10290000 Joules.
Now lets say we give the home side audience reflective programs that fold out to be about a half metre square. If we allow that they are going to be tilted at on average 30 degrees to the vertical in order to focus them then the area of sunlight they are each catching is the width * (the height * sine 30), which works out at 0.125m2 each.
Now there’s the matter of time. That is, how long will it take for the ref to work out whats going on and come up with a strategy to counteract it? Well, on the roads, they allow 2 seconds thinking time, but I think that refs are a little stupider than average folk so I reckon about 3 seconds.
Over 3 seconds, we only need 10290000 / (942 * 3 * 0.125) people focussing these programmes on the ref for three seconds to raise his whole body temperature by 35 degrees. That’s only 29129.5 people. Well, lets call it 30,000 people.
Wembley stadium can hold over 126,000 people (according to Britannica), and its not even the biggest stadium by a long shot. So a home side in Wembley is going to be well over 30,000 people. Even if only half of the home side (say three quarters of capacity – 94,000 people) are organised to do this, and only three quarters of them got it right, you’d still kill the ref with a bit left over.
So a survival tip in case you are ever compelled to referee a football match - ensure it's on a cloudy day, or be blatently biased in favour of the home side.
I may have got the idea from this node from A slight case of sunstroke by Arthur C Clarke, but it's so long ago, I can't remember.