# Speedometers

by Chris Woodford. Last updated: May 23, 2021.

Excuse me, sir, have you any idea how fast you were going? That's the question every motorist dreads being asked by a police officer at the side of the road. If you were staring straight ahead, not looking at the dashboard, you might have only a vague idea what to say. If you were looking at the speedometer, on the other hand, you'll know the answer exactly, possibly to within one or two kilometers or miles per hour. Have you ever stopped to think how a speedometer actually works? It's a really ingenious use of electromagnetism!

Photo: Speedometer and instruments on the dashboard of a restored 1949 Plymouth. Photo by Christina Russo courtesy of US Air Force.

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## How to measure speed

If you've read our article about motion, you'll know that speed is very simply defined: it's the distance you travel divided by the time you take. So if you go 200 kilometers and it takes you four hours to do it, your average speed is 50 kilometers per hour. Measuring your average speed after you've traveled is not actually that much help, especially if a police officer is asking you questions. How fast were you going sir? Erm, pull me over again in a couple of hours, when I get to my destination... and I'll divide the distance I've gone by the time it took... and then I should be able to give you some kind of an answer. Okay?

Artwork: To find your average speed from A to B, you could divide the distance between them by the time it took you. But that doesn't tell you anything about your speed on the way, because you might have traveled by different routes or paused your journey. Only a speedometer can tell you your actual speed at any given moment.

What we're talking about here is average speed; what you need to know as a motorist is your instantaneous speed: the speed you're going at any given moment. Figuring that out is a lot harder than you think. If you've seen traffic cops (or speed cameras) by the side of the road, you'll probably be aware that they use radar beams to check speeds. The radar gun (handheld or mounted inside the speed camera) shoots an invisible electromagnetic beam at your car at the speed of light. Your car reflects the beam back again, modifying it very slightly. The gun figures out how the beam has been affected and, from that, calculates your speed. Now in theory we could all have radar guns mounted in our cars, shooting beams out at lamp-posts and buildings and waiting for the reflections to come back—but that's an awful lot of bother! Isn't there a simpler way of finding out how quickly we're going?

Photo: Measuring speed with a radar gun. Some speed guns use LIDAR (reflected laser light) instead of radar (which uses reflected radio waves). Photo by Lek Mateo courtesy of US Air Force.

What we really need is a way of figuring out how fast the car's wheels are turning. If we know how big the wheels are, we can then figure out the speed fairly easily. But how do you measure a wheel's rate of rotation? Even that problem isn't simple. Imagine how much harder it must have seemed in the early days of motoring, back in 1902, when German engineer Otto Schulze invented the first practical solution: the eddy-current speedometer.