Speedometers and GPS units

I’ve noticed that the speedometer in my car says I’m going faster than the speed reported by my GPS.  On reflection, this makes a lot of sense, and the GPS is almost certainly right.

First, one very good way to compute speed is to have a very good clock and to know more or less exactly where you are at time₁ and at time₂.  You then compute the distance from where you were at time1 to where you were at time2 and voilà! S = D / T where S is speed, D is distance and T is time.  To do all this you need the ability to make a few simple but reasonable precise measurements, including knowing the (more or less) exact time and your more or less exact location (Heisenberg be damned!) and the distance from one point to another.  All of this is what a GPS does for a living, and it is absurdly exact; able to detect your location within a radius measured in a small number of feet and able to detect the time to an absurdly accurate degree.

Your car, on the other hand measures your speed quite differently.  It measures the number of rotations of the tire over a set amount of time.  The clock involved is none-too-accurate and the computed speed can be thrown off by any number of mechanical factors (not least is using the wrong size tire).

Thus, I speculate, the GPS, by its nature, is more capable of finding the correct speed.

What is more, I think car engineers know this and they allow for it.  Their thinking must go something like this: “if the car shows a speed that is higher than its actual speed, then the worst that will happen is that you will not get that speeding ticket and if you crash the impact will be slightly less, but if the car shows a speed that is lower than it actually is, then you are more likely to get a speeding ticket and more likely to get hurt in an accident than might otherwise be expected, all of which is likely to come out in court in a very expensive law suit.”

Thus, I suspect, as a matter of good engineering, the automobile manufacturers make up for the inherent inaccuracy of their speedometers by tooling them up by a couple miles an hour  — better to be going slower than you think than faster.

And this fits with my experience; the speed measured by my car is not only consistently different than the speed measured by my GPS, but the car’s measured speed is typically 2-4 mph faster than that measured by the GPS.  This is across a couple dozen rented cars and both my family cars. 

Your mileage, speed and experience may differ. 

I note all of this because I think GPS navigation systems are the most magical devices that I use on a regular basis; including computers, dvr’s, cell phones, etc.  We are surrounded by the science fiction of a previous generation, but the GPS totally blows me away.

More on GPS soon.

Trivia question of the day: how far away are the satellites used with GPS? and for extra credit, who was that area of space named for?