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A PHYSICIST WRITES . . .

(April 2006)

Letís start with a reminder of last monthís look at energy: we motorists fill the tank with fuel, which the car then converts into all sorts of energy. We make grossly inefficient use of this and then it all disappears wastefully into the environment as heat. We can, however, prevent a modest amount of the wastage by adopting driving habits such as avoiding unnecessary speeding thatís followed immediately by braking.

You could of course save more fuel by reducing your top speed and by always being in the right gear for getting the greatest efficiency out of the engine. But what should this maximum speed be? And how can you tell which gear is best ó after all, it will depend on the gradient of the road, your actual speed and whether you are accelerating. I fear that you can only optimize your driving like this if you happen to have an instrument panel that displays a reliable readout of instantaneous miles per gallon. But while concentrating on the mpg as you compared different gears, you would be at some risk of losing your attention on the road ahead!

Thinking still about all the energy that you extract from fuel (when driving) and then throw away as heat: doesnít this contribute to global warming? A little, perhaps, but the main cause of global warming is the slow build-up of carbon dioxide in the atmosphere, increasingly blocking the escape of heat ó nearly all supplied originally by the sun ó from the earth back into space. So itís the CO2 from your exhaust that does the damage.

I want to focus now on kinetic energy (KE). This is the energy that your car possesses by being on the move. As you accelerate, more KE is given to the car by the engine. Then when you decelerate the energy has to be taken away again, by whatever it is thatís slowing you down. This might be air drag and engine braking if you just lift your foot, or the brakes if you apply them, or something that you might unfortunately collide with...

I would say that itís more important to understand kinetic energy than to know almost any advanced-driving technique. Why? Well, for a start, a car moving at just 30 mph possesses more than 100 times the KE of a big-game rifle bullet! Obviously, someone in the road has more time to get out of the way of an approaching vehicle than if it was replaced by 100 high-speed bullets, but if he or she failed to do so the consequences would be much the same.

Then thereís the fact that kinetic energy is proportional to speed squared. Think of it this way: at double the speed, your car has four times the KE to be disposed of somehow if you slow down in a hurry ó thatís four times the heat to be dissipated by the brakes, or four times the vehicle-crushing if thereís a full-speed collision ... not to mention the much reduced probablility that the accident will be survivable. In France, Iím told, this message is (or used to be) driven home by occasional road signs saying simply: E = Ĺmv 2.

If youíre wondering whether KE is linked to Braking Distance, which also goes up in proportion to speed squared (see the Highway Code table of Stopping Distances ó click here), youíre right: it is. But is the average driver really aware that the overall Stopping Distance extends four times further ahead (or very nearly) at 60 mph than it does at 30? I doubt it very much.

And I challenge any driver, however advanced, to guess the answers to the following questions, even though they are based on the HC table and its steady rate of braking (which is about 15 mph lost per second):

Q1 ó You are driving along at 30 mph and are being overtaken by another car at 40mph. As it draws level an obstacle appears ahead, at exactly your Stopping Distance, hence you can stop safely. If the other driver also reacts as assumed in the HC table, at what speed will the car hit the obstacle?

Q2 ó Again you are driving at 30 mph, but with less care: you suddenly notice an obstacle ahead at half your Stopping Distance. If you react as assumed in the table, at what speed will your car hit the obstacle?

Is the answer to Q1 ten miles per hour? Fifteen? Twenty? Surely not 25? No indeed ó the colliding speed of the other car will be thirty miles per hour. Why so high? Partly itís the greater Thinking Distance at 40 mph, but mostly itís E = Ĺmv 2 again and a curious fact hidden within this formula: in Ďsteadyí braking you actually shed most of your speed only in the last few (life-saving) metres.

You still wonít guess the answer to Q2, Iím sure: it is 27 mph! Here your downfall is your own Thinking Distance, which leaves you almost no space for braking. Now imagine the obstacle is a person, remember the 100 bullets and resolve never to drive so that you cannot stop in the space thatís clear ahead.

Peter Soul

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