RM> This is the linchpin of your argument, and it's got a huge hole
RM> in it: it's true only for a circle!! For the umpteenth time, a
RM> flattish tyre is NOT a circle. The axle is locked to the tyre,
RM> *not* to a circle.

BL> It has nothing whatever to do with circles. Do you understand
BL> calculus? Even vaguely?

RM> Yes. I understand it clearly enough to see the faulty
RM> assumptions you've made applying it. d0/dt is nice and steady
RM> right round for a circle, but varies like mad across the
RM> distorted shapes we're talking about. Your approach is grossly
RM> oversimplified.

 Jesus, Roy... you are telling me that the axle is jumping up and
down as the wheel goes around! Are you Sirius, or just thick? It does
not matter a rat's arse what shape the wheel is. We are only
interested in the tiny little bit of tyre under the axle, and that's
always going to be the same as the wheel goes around. I agree that the
tyre is going to be a funny shape, but who gives a shit?

RM> Your approach is grossly oversimplified.

 ROFL! Your approach is grossy stupid. I keep telling you... it can't
be anything else but the linear movement of the tyre under the axle
divided by the axle height.

 Perhaps you could get your brain to work if you tried to turn your
assumptions upside down. Okay... assume that the circumference does not 
vary. Let us assume that the tyre is perfectly round. What is the axle 
height?

 Now. Let all the air out of the tyre. The circumference is the
same. Can the axle height be different?

... the correct answer is no.

 If the axle height varies, then the tyre passing under the axle goes 
slower, and the tyre would wind up on the sheel.

RM> Of course it can. You haven't read what I've said at all. Take
RM> a rigid rim, give it an axle with elastic spokes. Push the axle
RM> down 5%, turn the wheel. The axle must rotate at the same speed
RM> as if it was still at the centre, because one rev of the wheel
RM> still carries the axle one circumference forward. If the axle
RM> rotated faster, the spokes would wind up around it.

 Yes... that is what would happen. The spokes would wind up, and the 
resulting force would lift the wheel to its original axle height (less 
the bit needed to create the force in the spokes).

RM> Don't just say "this is INARGUABLE", tell me what is wrong with
RM> the above para.

 Who cares? You are an idiot if you think you can keep a constant
circumference with a variable axle height.

 I'm serious. Try and turn you mind around. Ask yourself how it can
be. Don't propose pins in the wheel and elastic spokes, just stick to
the facts. If the circumference is constant, then how can the axle
height be different? Like all small minds, you can only see a problem 
from one end. Equations have two sides. Look at the other side.

 And btw, don't say "constant". In engineering, everytrhing varies. 

Regards,
Bob
 

--- BQWK Alpha 0.5