As everyone knows, excessive speed is one of the main causes of traffic accidents. One of the reasons for reckless speeding is that when we think of the possible impact of a collision, our intuition fools us. We tend to assume that if we go twice as fast (say, at 80 km/h instead of 40 km/h), then the impact of a collision will be twice as large. In fact, the impact of a collision is proportional not to the speed (V), but to the kinetic energy of the vehicle (m/2 * V²), which is transformed to work as the car decelerates to zero. Here m is the mass of the vehicle, which we cannot do much about, but the other term is the *square* of the velocity. This means that the “impact” of hitting a wall at 80 km/h is four times as large as that of the same collision at 40 km/h.

To capture this intuition, the idea of this post is a speedometer design, that scales as the square of the velocity, to give the driver a more realistic view of the effects of speeding.

### Notes:

- after sketching this drawing, I found that in 1995 Goetz Kluge was thinking along similar lines and produced a similar design. There are however some differences – see next.
- besides showing the speed in the more familiar, circular layout, I also made the decision to draw the smaller lines at uniform density (i.e. they are spaced proportionally to the kinetic energy, not to the velocity). This design might make it harder to estimate the exact speed, say between 40 km/h and 50 km/h, but it makes the increased kinetic energy easier to grasp – when we speed from 120 km/h to 130 km/h, the hand crosses more “small lines” than from 20 km/h to 30 km/h.
- while I haven’t seen a similar speedometer in any real car, some of the existing speedometers are in fact nonlinear. Unfortunately, they seem to achieve the exact opposite effect to the design shown above. See this example. On the linked image, and in many other modern speedometers, the manufacturers try to put more resolution in at the lower half of the range, dilating the velocities between 0 and 80. My guess is that car makers do this,
~~because the car accelerates faster at low speeds, so dilating the lower range makes the hand movement seem more uniform at all speeds~~– this is probably aesthetically more pleasing, but it might come at a cost of an increased (false) sense of security, and in effect a reduced safety.(I got this exactly wrong – thanks Tobias for pointing it out – it is actually the opposite, on the proposed speedometer design, the hand would move more evenly – so besides being safer, it would be more aesthetical as well, the only downside seems to be the reduced resolution in the low range)