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How much does it cost to cross the road?

The guilt of pressing the button when you don't need to.

Walking home from dropping off my daughter at nursery this morning,  I came to a busy road and pressed the button at the pedestrian crossing as normal.  Then I spotted there were no cars coming so I crossed the road anyway.  I couldn't help feeling a twinge of guilt when I looked back and noticed that because I caused the lights to turn red, I forced three cars to slow down and stop for nothing.

It made me wonder: how much does it cost to cross a busy road?

I want to keep the calculations as simple as possible, so I will assume that the only cost is the waste of petrol in slowing a car and accelerating it again at the crossing.

Let's assume:

Weight of a car = 1 tonne (1000kg)

Speed of car = 30mph, call it 15metres/second.

I'll use ZZ to represent Zequals (my approximation symbol, see earlier blog).

Energy of a car in motion = ½ m v2= 500 x 225  ZZ  100kJ

According to Wikipedia, and clearly therefore a fact, a litre of petrol contains 35,000 kJ of energy.  So accelerating a car to 15m/s consumes around 1/350 of a litre.

The price of a litre of petrol is roughly £1.50.  That would suggest that the energy wasted in stopping a car is about 150/350, ZZ 0.5p. 

Even allowing for inefficiencies in the conversion of petrol into kinetic energy, wear and tear on brakes etc, it looks like the cost of unnecessarily stopping one car is less than 2p, so my three car pile-up cost around 5p.  Plus three slightly annoyed drivers, I suspect.