B
Benjamin Weiner
Guest
Tim McNamara <[email protected]> wrote:
> Jasper Janssen <[email protected]> wrote:
> > It can't expand, no, but that doesn't mean it can't contribute to load.
> Not an engineer here. So bear with me.
> A rim weighs, what, 400 grams. Imagine it spinning in space, all by itself. How fast does it have
> to spin before it expands along the major diameter from centrifugal force, which would require the
> the metal of the rim to stretch? 1,000,000 rpm? More?
Awright, you two, break it up.
The rim has a non-zero modulus of elasticity - about 70 GPa (10000 ksi) for aluminum. So if you spin
it, it stretches under the centrifugal force, the question is how much? If I did the calculation of
hoop stress correctly, in order to stretch by 10^-3 of its diameter, it would have to spin at 31,000
rpm. That's a bicycle velocity of 1100 meters/sec. About Mach 3. Superman travels that speed all the
time, but a factor of 10^-3 elongation is not very significant.
A concern for fast-spinning parts is that they not break up,
i.e. centrifugal force/area must not exceed tensile strength. One might ask how Superman's bike is
going to keep the tires on. Remarkably, it seems that he would have to go above 800,000 rpm in
order to rip off the rim flanges (I assumed a typical 400 g tire+tube and an MA2 rim with 1mm
thick flanges). Even Superman probably doesn't descend that fast. I don't know the tensile
strength of tubular glue, so can't say whether he should ride tubulars. Sorry, tubie adherents.
Anyway, I would worry about the tire holding together at those speeds.
The HPV record crowd deals with bicycle-like vehicles at high speeds. Most of their problems seem to
have to do with steering mechanisms and stability, and crosswinds.
> Now, with an elastic and heavy item, such as pizza dough, you can easily see this happening. But
> an aluminum rim is a light and relatively inelastic structure. It doesn't stretch under rotation
> like pizza dough does, therefore the major diameter doesn't increase, and therefore it contributes
> no load to the spokes from centrifugal force. My contention is that the rim's tensile strength is
> such that at any realistic speed, it contributes nothing to spoke tension load.
This we can certainly conclude.
Ben
> Jasper Janssen <[email protected]> wrote:
> > It can't expand, no, but that doesn't mean it can't contribute to load.
> Not an engineer here. So bear with me.
> A rim weighs, what, 400 grams. Imagine it spinning in space, all by itself. How fast does it have
> to spin before it expands along the major diameter from centrifugal force, which would require the
> the metal of the rim to stretch? 1,000,000 rpm? More?
Awright, you two, break it up.
The rim has a non-zero modulus of elasticity - about 70 GPa (10000 ksi) for aluminum. So if you spin
it, it stretches under the centrifugal force, the question is how much? If I did the calculation of
hoop stress correctly, in order to stretch by 10^-3 of its diameter, it would have to spin at 31,000
rpm. That's a bicycle velocity of 1100 meters/sec. About Mach 3. Superman travels that speed all the
time, but a factor of 10^-3 elongation is not very significant.
A concern for fast-spinning parts is that they not break up,
i.e. centrifugal force/area must not exceed tensile strength. One might ask how Superman's bike is
going to keep the tires on. Remarkably, it seems that he would have to go above 800,000 rpm in
order to rip off the rim flanges (I assumed a typical 400 g tire+tube and an MA2 rim with 1mm
thick flanges). Even Superman probably doesn't descend that fast. I don't know the tensile
strength of tubular glue, so can't say whether he should ride tubulars. Sorry, tubie adherents.
Anyway, I would worry about the tire holding together at those speeds.
The HPV record crowd deals with bicycle-like vehicles at high speeds. Most of their problems seem to
have to do with steering mechanisms and stability, and crosswinds.
> Now, with an elastic and heavy item, such as pizza dough, you can easily see this happening. But
> an aluminum rim is a light and relatively inelastic structure. It doesn't stretch under rotation
> like pizza dough does, therefore the major diameter doesn't increase, and therefore it contributes
> no load to the spokes from centrifugal force. My contention is that the rim's tensile strength is
> such that at any realistic speed, it contributes nothing to spoke tension load.
This we can certainly conclude.
Ben
