On 23/06/2018 18:33, Tim Streater wrote:
In article , Robin
wrote:

Well you were the one to introduce circumference into this, a value
which is irrelevant to the relationship between the 2 things measured
(the vehicles speed and the angular velocity of the wheel) and what
relates them (the rolling radius).

The irrelevance of the circumference can be seen by looking at
caterpillar tracks.Â* Ignoring slippage etc a 20m track goes round once
when the vehicle moves 20m.Â* But that's true whether it is attached to
wheels with a radius of 0.5m or 0.25m.Â* So the circumference tells you
nothing about the relationship between speed and the RPM of the
wheels. On the other hand, the (effective) radius of the wheels does.

Aren't you overlooking that, with a track, the wheel is only in contact
with a part of the track. Whereas with a flat tire, even though the
shape of the tire changes, the wheel is still in touch with the tire
all the way round (the entire tire, IOW (phew!)).

Thus TNP is right to say that, inflated or not, for one revolution of
the wheel, the whole circumference of the tire rotates once. Or, to put
it another way, any spot on the tire circumfernce will touch the road
just once.

(ignoring slippage on the road, or slippage between the tire itself and
the wheel).


Yep. But that's just another way of saying that with a tyre on a wheel
the fact that the rolling radius changes with pressure means the
"rolling circumference"[1] also changes with pressure. As TNP admitted.
So I was and am still unclear why he asked about the circumference. I
thought at first it might be because he thought that the steel
cords/belts in tyres are like caterpillar tracks. But it can't be that
when he volunteered there is an effect.

Of course I may well be missing something. But I _know_ I'm - hic -
missing the bottle downstairs, so ...


[1] TM TNP?
--
Robin
reply-to address is (intended to be) valid