A mechanical analog speedometer works by magnetic drag. There is a little gear in the transmission that is turned by the transmission output shaft (that’s the one connected to the road wheels). A flexible cable is attached to that gear, so that as the car moves faster down the road, the gear is spun faster which spins the cable.
The cable runs to the dash and into the back of the speedometer. There, it is attached to a magnet which spins. Then, a metal disk is placed near the magnet. As the magnet spins, it will “drag” or pull the metal disk along with it, and the faster the magnet spins, the more it drags on the disk. To the disk is attached the speedometer needle, and a return spring tries to keep the needle at zero. So the faster you go, the metal disk overpowers the spring, and the needle climbs.
This system had an unfortunate side effect that the cable would require lubrication, and would wear out. On my ’88 VW Fox for example, on winter mornings the speedo would make an awful squealing sound as the lube in the cable had solidified in the cold.
An electronic “analog-style” needle gauge takes a digital signal from either the transmission or from the road wheels themselves, and a [stepper motor](https://en.wikipedia.org/wiki/Stepper_motor) moves the needle to the appropriate position calculated by the computer. Although these are becoming rare and the speedo is starting to become simply a display, just like your smartphone screen.
calculations for tire size (rolling diameter), transmission internal speed, and speedometer internal gearing, and demarcations on the speedometer are all calculated to ensure the needle points at the proper mark on the gauge face. The needle is usually driven by a cable that runs directly to the transmission, or in some cases a wheel hub assembly. It doesn’t ‘count’ like newer cars with an electronic speed sensor and an electronic speedometer, but it is precisely designed to display a certain point on the gauge when the cable is driven at a particular speed.
It counts the rotations of the drive shaft, taking the diameter of the wheel for granted.
Fun fact: As with many other sensors and instrumentation, a digital speedometer is basically just an analog speedometer with an analog-to-digital converter. In other words, the thing that’s measuring the shaft speed is the same old analog sensor as ever, putting out the same old analog electrical signal as ever… just, eventually being converted to digital for the instrument cluster.
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