Re:speedo accuracy

[Joe Elliott <jee@domain.elided>]

At 12:59 PM -0500 1/29/02, alfa-digest wrote:
>Now, suppose you find yourself with an electronic speedo and a good
>conneciton at the sender on a nice open stretch of road in a place where it
>is OK to drive like a maniac, such as Germany or Italy.  As you approach the
>speed of light, will the speedo be more or less accurate?  You won't be able
>to use the watch and road markings technique as time will slow down.  How can
>you calibrate it?


Well, the speedo's electrical systems will still be 100% accurate, 
because both the sender and the gauge will be stationary in your 
reference frame.  As for measuring the accuracy of the gauge at these 
speeds, I think this is where fancy GPS toys come in handy.  If your 
GPS isn't programmed to compensate for the weird stuff that happens 
at slightly subluminal speeds, just have your wife stand on the side 
of the road and measure the length of the car when it goes by at a 
given indicated speed on the speedo.  Your actual speed can be 
determined by the percentage difference in the real length of your 
car and length observed by your wife.  The car will appear shorter by 
a factor of the square root of (1 - B^2) where B is your speed as a 
factor of the speed of light.  So just solve (1 - B^2) = [(observed 
length) / (proper length)]^2 for B and multiply B by the speed of 
light (299,792,458 m/sec last time I checked) and see if it matches 
the speedo.  But you might want to check my math first.  All I know 
for sure is that it's not worth investing in clear taillight lenses 
for your Honda because at those speeds (assuming your Honda has a big 
enough Wal-Mart spoiler to allow it to reach those speeds) they'll 
just appear red to stationary observers and slower traffic anyway, 
due to the Doppler shift of the light waves.

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