How a car’s differential works

In the old days, cars could be called ‘one wheel drive’ vehicles since a car’s engine powered just one of its four wheels. The problem was that in such cars, if the powered wheel ended up in a place with low or no traction, say because of snow or ice or mud or dangling over a ditch, you were literally stuck. The development of two-wheel drive vehicles that sent power to the two rear wheels improved this situation since if one wheel lost traction, the other could pull you out of it. But this created a new problem in that when you turn a corner, the outer wheel on the axle has to rotate faster than the inner wheel since it traverses a circle of larger radius.

It was to solve this problem that the differential was invented that enabled two wheels connected to the same axle to both receive power and yet rotate at different rates. Via Mark Frauenfelder, I came across this 1937 short video that gives a remarkably lucid explanation for how the differential works its magic. The first part is a long set up involving some synchronized motorcycle riding and the real explanation starts just after the 1:50 mark

With four-wheel drive vehicles (sometimes referred to as 4×4) power is sent to all four wheels and there is a differential for each of the front and rear axles. This causes some jerkiness when taking corners on dry surfaces since the front wheels travel slightly longer distances than the rear wheels and thus the four-wheel drive should be engaged only when necessary. The newer all-wheel drive cars have an additional differential between the two axles to take care of that problem.

So we have come full circle, since the four-wheel or all-wheel drive cars, like the old one-wheel drive cars, can move even when only one wheel has traction. But the major difference is of course that with the new cars, any wheel can serve that purpose.

Differentials are expensive. When it comes to trains, they have many axles, each one having two wheels rigidly connected to it, and no differentials. So how do they take corners? The ingenious solution to that lies in the design of the metal wheels that have a slight conical shape. This article explains how they work and below is Richard Feynman’s explanation of how it works, that I linked to four years ago.

Here’s a simple explanation and demonstration of how the conical shape of the train wheels also help the train stay on the track and here is a more detailed explanation.

This solution for trains only works for a limited range of curves which is why the curves on train tracks have to be much more gentle than for roads.

These are quite ingenious solutions.

Engineers. You gotta love ’em.


  1. Ogvorbis: A bear of very little brains. says

    The other reason for tapered treads on train wheels is to save lots of energy. When a train rolls through a corner, if the corner is tight enough, there is a delightful squealing sound — like fingernails going down the worlds largest chalkboard — as the flange of the outer wheel rubs the inside of the outer rail. Of course, any time a machine is screaming in pain, you are losing lots of energy — it takes a lot of power to make annoying noises.

    You can’t do much about that on a corner, but on a tangent, that squealing is money disappearing. Fast. So, by tapering the tread, the wheel set centers itself and neither flange rubs.

    By the by, those treads — that nice profile — is only good for about 30 to 40 thousand miles. At that point, if there is enough steel left in the wheel (or tyre, on some), it can be recut on a big lathe. If not, the tyre or wheel gets replaced. They can be recut three to five times unless the wheel has been flat-spotted by an emergency stop or hung brake gear.

  2. raym says

    Fascinating -- thank you! Now for some arithmetic to see if I can work out the required angle for those cone-shaped wheels.

  3. A Crawford says

    Not sure if Alfred Hitchcock understood how differentials work. In North by Northwest the Mercedes Ponton cabriolet driven by Cary Grant stops just shy of going over a cliff. He guns the engine but one of the rear wheels is barely touching the ground so spins ineffectively. Then, magically, traction is restored and the car takes off. It would have been much more believable (and dramatic) if he had stretched his body out to redistribute weight in the car allowing that one wheel to gain enough traction to move the car to a more favorable position.

  4. Ogvorbis: A bear of very little brains. says

    1:40 is standard in the United States. Doesn’t take much.

  5. jrkrideau says

    Re the differential.
    I’m on my way out so only watched up to 3:20 but did the film mention that the differential was invented by the Starleys (a famous bicycle manufacturing family) before the end of the 19th C? They were faced with the same problem with 3 and 4 wheeled cycles.

    I’ll have to come back for the railway info. It looks interesting

  6. DonDueed says

    There’s one error in your description, Mano. With a standard differential, if one wheel spins, the opposite wheel does not move at all. Anyone who ever got stuck in a snowbank can verify that (I’m looking at me right now). That’s why it’s a good idea to carry some sand in the winter: you can toss some under the slipping wheel and (with luck) get enough traction to pull free.

    What you described is a different beast: a limited slip differential. Those are more complex and expensive than the standard type, but they’re pretty common these days.

  7. Mano Singham says


    Thanks for the correction.

    If you don’t happen to have sand, another method is to take one of the car’s floor mats and wedge it under the wheel that you want to get traction.

  8. John Morales says



    But this created a new problem in that when you turn a corner, the outer wheel on the axle has to rotate faster than the inner wheel since it traverses a circle of larger radius.

    The radius is larger, but that’s not what’s traversed; what’s traversed is the arc.

  9. DonDueed says

    There are a couple other subtleties about the train-wheel scheme.

    First, because the outer wheel is riding on a larger radius than the inner, the axle has to tilt slightly. The trucks (which hold two axles / four wheels) likewise tilt, and these are connected to the cars on flat pivots. Therefore the cars also tilt inward when rounding a curve.

    In other words, even though the track is completely flat, to the train the curve is banked! It’s a small effect but real.

    Another thing that many people don’t realize about trains is that every axle on every car is braked, using a compressed air system that is connected from the engine back through each car. That wasn’t always true. In the very early days of railroads, trains were short and only the engine had brakes. As trains became longer, this no longer worked -- there was just too much mass for the engine to stop. So brakes were installed on the cars.

    But at first, there was no system to apply the brakes from the engine. Instead, men were employed to manually apply the brakes, but one man had to cover many cars. When braking was needed, the brakemen would run along the top of the train, turning the wheels that applied the brakes before dashing along to the next car.

    Needless to say, this was tricky and dangerous, and there were many crashes and fatal accidents (especially in bad weather) until Westinghouse developed the air brake system.

  10. John McElhinny says

    Thanks--very interesting.

    Completely unrelated to the content, how would one have viewed a film like this in 1937? Were they shown before or after feature films in theaters, or were there other venues that specialized in short educational/commercial films like this, or something all together different?

  11. Mano Singham says

    I’m guessing that these were produced to be shown in theaters before films and in schools. Short films and newsreels were important educational tools back before TVs became common.

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