From: jbrandt@hpl.hp.com (Jobst Brandt)
Newsgroups: rec.bicycles.tech
Subject: Re: building the wheels
Date: 7 Jan 1998 18:33:53 GMT

Hoyt McKagen writes:

>> Hoyt, this is apples and oranges. In the case of the wheel, the
>> spokes are shortening due to an applied load.

> That's the basic misconception: the load isn't applied to the spokes
> by the rim and tire; it is taken off by them! <=That has been our
> whole problem, I guess.

> When you inflate the tire, it stretches the rim larger, (I did the
> experiment) and it would tighten spokes which weren't already
> preloaded. Since they have a preload, though, we know they stay in
> tension when we put the weight on the tire.

Oops!  Not only did you make this up, but you just showed that you
didn't read "the Bicycle Wheel" as you claimed, because a tire
constricts when inflated and the computation of how much it does this
is in the book in equation 8.  Besides, this has been measured.  Spoke
tension decreases with inflation.  Maybe you could explain how your
wheel without tension looked before you inflated your tire and how you
determined the change, the change being less than 1/1000 inch.

> The expansion is essentially because there is more area outside the
> tire's neutral axis than inside it, and it takes the rim with it
> through the bead-notch interlocking. That rim expansion is mediated
> through the tireplies, which pull on it in response to the pressure.

Now you are just blowing smoke, so to speak.  The propensity of a tire
to blow off a rim is matched by the inflation pressure inward at the
tire to rim interface.  Thus there is no net force from that, but
there is constriction caused by the cord angle of the tire casing.
Typically an un-glued tubular tire constricts onto the rim with a
force that is proportional to inflation pressure by an amount shown in
equation 8.  That is why hose braid, visible in clear clear plastic
tubing, is at 35.27 degrees, not 45 degrees as in tires.  A tubular
tire inflated without the benefit of a rim will shorten until the cord
angle is 35.27 degrees.  A clincher would try to do the same if it
were not open and had a resilient bead.

> When you distort the tire at the contact patch, you relieve some of
> that tension and the spokes pull the rim in at the contact patch
> only (that is essentially why the flatteninig is so localized).
> That kicks off a global expansion in the rest of the rim, which
> stretches all those other spokes.  But the only element in the wheel
> which can actually stand compression is the rim.  Follow? So what
> does it actually stand on?

So now that you have brought the discussion around to what supports a
rim from the ground, pleas explain what prevents the tire from sagging
to the ground.  It can't be the air pressure because it is uniform
around the tire.  There must be a net force upward on the rim.  You
might give that concept some thought while you are at it.

Jobst Brandt      <jbrandt@hpl.hp.com>