"Greg Neill" wrote in message news:...
"Spaceman" wrote in message ...


Length dilation is along the direction of
motion. An observer would see a foreshortened
wheel, apparently elliptical, with the height
remaining the same but the width contracted.

If the wheel were stationary its diameter would
be measured to be D = Circumference/pi = (1 mile)/pi.

The wheel is doing 0.5c linearly, so it's front to
back diameter (minor axis) is D*sqrt(1-v^2/c^2).
Its height remains unchanged.

Actually, upon further reflection I take this
back. The observer stationary in the frame of
the ground will see the top of the wheel moving
forward more quickly than the center, which
in turn will be moving more quickly than the
bottom which is instantaneously at rest where
it touches the ground. So the shape will be
more complex than a simple ellipse. More of
an ovoid I'd guess.

Relativistic velocity addition and length
contraction always applies, so it's possible to
work out the shape (and hence the circumference).
I'll have to give it a go.