car speedo and sat nav discrepancy

Richard53

There was a long discussion about how much a gradient will alter a GPS speed reading over at one of the bike forums last year. The agreement was - not very much, but there is a small effect.

Imagine a 1 in 4 (25%) gradient. Going up the hill, the car travels 4 units forwards (which is the speed the GPS understands relative to the satellites) and 1 unit upwards. Pythagoras gives you the actual length of the road you travel (the hypotenuse of the triangle) as sqrt(17), which is 4.123, which represents roughly a 3% increase. In other words, you are travelling at an actual speed of 4.123 units, but your GPS is recording your speed as 4 units.

A 3% under-read of your speed is not massive, and that is on the steepest roads in the UK, so a long gradient on a motorway would be a lot less, a fraction of 1%. In other words, nothing to get excited about. But I am sufficiently nerdy to find this kind of thing interesting.

(This is assuming that the GPS calculates speed based on movement in two dimensions. If it's clever enough to include your altitude as well as horizontal movement, then the effect would be zero.)