[cc438]

Gyroscopes accumulate error with time, they make sense for an application with a short range but they're useless over long periods of time without a reference standard to crosscheck and recalibrate. That's one part of The Martian the author got entirely correct despite the criticism. The mechanical odometer in your car is only accurate to +/-3% of reading and the best mechanical calibration standards are only 0.25% of reading, that puts the trip described in The Martian off by ~90km.

[stephentmcm]

Thanks, I was being mildly sarcastic in my post but having the math laid out is great.

[cc438]

NASA has the brains to design a better odometer but navigating by stars and GPS makes more sense.

Also, remember the +/-3% next time you're comparing a used cars. Worrying about 5-6,000 miles on a car with 100,000 is pointless since the odometer itself lies by up to 3,000 miles. Then you have further error introduced by new sets of tires which wear down 6-15mm depending on their tread depth and can vary several mm in diameter despite having the same nominal size as the OEM tires.