Nuclear Physicist Enrico Fermi (1901-1954) described the solving of problems with imprecise data when there is no need for an exact answer (it‘s called a Fermi problem). If you wish to estimate the speed of a vehicle passing you on the road, or one which you are passing, you can use this easy method to estimate the relative speed of the two vehicles.

 Now the average car is about 15 feet long.

 If a car is passing you, when the two front bumpers are aligned, start counting, one thousand, two thousand, etc to estimate the number of seconds that pass (count quickly). Stop counting when the other car’s rear bumper is aligned with your front bumper. Dont use “one thousand AND ONE, one thousand AND TWO, etc which gives a more accurate estimate for the time passed. We need this over-estimate of the time, as described below.

 Now divide 15 (feet) by the number of seconds that passed. Say it took 3 sec for the car to pass as described. So 15/3= 5 feet per second is the answer. To make it easy, if the time were four seconds, use 16 ft, so you can do it in your head, i.e., 16/4=4 ft/sec.

 Now 60 miles/hour equals 88 feet/second, but driving we dont have a calculator in hand, so just say one foot/sec= one mile/hour. So the result in the stated problem is 5 mph. Of course the answer is not exact, it is off by 47%, (88-60)/60=0.47, but we dont care, we just want a rough estimate we can do without a calculator, and by over-estimating the time elapsed, we just about compensate for the under-estimate of the ft/sec to mph conversion.

 Now an 18 wheeler’s tractor part (forget the trailer) is also about 15 ft long, so you just count for the tractor part of the 18 wheeler and ignore the trailer. So the same scheme works for 18 wheelers. Now if a very tiny car passes you, use 10 ft, not 15 ft.

 If you are passing another car, start counting when your front bumper is aligned with the other’s rear. Stop counting when you have both front bumpers aligned. Try it, it’s very easy. All you have to remember is 15 ft, and divide that by the number of seconds.

 If you see a car pass you at very high speed, and that car has an accident that you see, you will have some very important information to give to the police, if you choose to do so.

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This site written and copyright 2002-2004 by Richard L. Field, BA, BSME, MSME, PhD. Field holds a doctorate in Mechanical Engineering (Math minor) and worked in the Space program for 20+ years before retirement. He also taught four years at Texas A&M Unniversity.  

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