An Application of Mental Arithmetic to Highway Safety

While preparing my latest column for the MAA Online I had to visit the Rutgers Math Library to copy a paper on Morley's Triangles by W.J.Dobbs. The paper appeared in 1938 in The Mathematics Gazette where it took approximately 7 and 1/3 pages. On the last page, the remaining space was used by a letter from a judge concerning traffic safety. The letter (reproduced below) serves, in my opinion, as a finest example of the utility of mental arithmetic in everyday life.

How do you figure out the speed of a car in feet per second when what is given is the speed in miles per hour? Nowadays, one can use almost any calculator to easily convert between miles per hour and feet per second. But this is besides the point. Can you imagine yourself taking your eyes from the road while driving at 60 mph just to check with a calculator your speed in feet per second? The device suggested in the letter can be used "by any child," and "any child" big enough to drive a car should be able to carry out this kind of calculations.

Judges are conscientious when trying cases, and I always felt that in order to understand any motor case it was necessary that I work out the respective speed of each vehicle in a measure that would tell me their respective ground speeds. The only measure that would give me any mental picture of the speed at which a vehicle covered the ground was the measure of feet per second. That involved me in a lot of arithmetic. Sixty miles per hour works out at 87.9 recurring feet per second, and every time I converted miles per hour into feet per second I got a result in recurring decimals. So then I had to look for simple formula, and this in how I got it. Instead of calling 60 m.p.h. 87 odd feet per second, I called it 90 f.p.s. and that gave me the simple formula of adding half to my miles per hour to obtain speed in feet per second correct within 2 per cent. Ever since then I have driven cars, and tried running down cases in feet per second. Now what I say to all motorists is that they try doing what I do, that is, always to drive and think of speed in feet per second instead of in miles per hour, and you will at once become a hundred per cent better and safer driver. All you have to do is to add one half to the figure of your speed in m.p.h. and you will get your speed in feet per second. Any child can do that.

The other aspect of road safety touches what is called kinetic energy, which means the moving force possessed by a vehicle in motion. I can't give you a more detailed explanation, but another way to put it is to refer to kinetic energy as the kick possessed by a moving vehicle. A small motor oar weighing about a ton and moving at a speed of 40 miles per hour strikes the same blow as eighteen ten-ton steam rollers travelling at their highest speed, which is 3 miles per hour. That is the force you axe handling when you speed up a light oar to 40 miles per hourly feet per second. If you are driving a big seven-seater two- ton car at 60 miles per hour (90 feet per second) its kinetic energy is more than that of 100 ten-ton steam rollers moving at 3 miles per hour. The Listener October 1937, p. 892.

[Per Mr. R. M. Wright; Mr. F. Ayres; Mr. W. G. Faires.]

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