On 2007-10-04, Peter Cole <[email hidden]> wrote:
[...]
Quoted message said:Quoted message said:If so you would need to put in a bit of energy to snap it into a taco
(easily done when you hit a bump etc.) but once it starts to go, it will
"want" to sink towards the local minimum of a taco shape.
I think you mean force, not energy. I'm not sure it "snaps" into that
shape. It's just a buckling beam, forced into a saddle shape by the spokes.
But why a saddle shape rather than any other shape?
Quoted message said:"Local minimum" of what?
Of energy. The wheel consists of spokes which are all stretched out a
bit and a rim that is in compression. It's a bit like a jack-in-a-box.
The shape it adopts can be predicted by working out what shape minimizes
its energy subject to the constraints every component is under.
I thought that was roughly how FEAs worked.
Here we are, I've found Michael Press's explanation:
http://groups.google.co.uk/group/rec.bicycles.tech/browse_thread/thread/fdac1b666bd5c5ed/59ff11c0efe8f451?hl=en&lnk=st&q=&rnum=1#59ff11c0efe8f451
or
http://tinyurl.com/32szvf
Yes some of the configurations between a true rim and a
potato-chipped rim have longer spokes, more highly tensioned spokes,
and higher energy than the starting and ending configuration. The
true wheel and the potato-chipped wheel are both local energy
minima. The latter has lower energy than the former because the
spokes are shorter, hence have given up mechanical energy that was
stored in their elastic deformation in the true wheel configuration.
And a couple of posts up:
A potato-chip wheel is in a lower energy state, even starting with
equal tension on all spokes. A potato chip is a surface with
negative Gaussian curvature. A sphere is a surface with positive
Gaussian curvature. Cut a disk out of a sphere such as a basketball
then try to flatten it. The outside portion is not big enough around
and wants to tear as you flatten the disk. A surface of negative
curvature is different. It wants to fold over at the outside as you
try to flatten it. A Lettuce leave is another example of a surface
with negative curvature.
A potato-chipped wheel has the same circumference as when it
started, but the spokes are shorter. Hence, the energy is much less.
[...]
Quoted message said:Quoted message said:I also wonder if it might be easier to achieve even tension with a lower
spoke count, since the low-spoke-count wheel is less over-constrained:
uneven tension means out-of-true and therefore easily corrected when the
wheel is built.
I don't understand this argument. I don't understand your use of the
term "over-constrained".
I just mean "more redundancy". It's easier to build a 36 spoke wheel
that is true and round but with uneven tension than a 16 spoke wheel.
This is because if tension is wrong in one spoke of a 16 spoke wheel you
are likely to see a wobble in the truing stand. There aren't so many
other nearby spokes around to make up for it.
Quoted message said:You seem to be trying to build a case for beefy rims and few low tension
spokes.
I'm not building a case for anything, just curious what the pros and
cons are.
It's just possible that the the changes to wheels over the years weren't
solely driven by a conspiracy between jim beam, George Bush and the
Solomon Ski company. That's a very sound theory of course, but I think
it's OK to consider alternatives.
Quoted message said:Sounds beam-ish. I'd rather not play that game, thank you. I'd
also rather not quibble over semantics, that's unfortunately beam-ish,
too.
I've got nothing against beam but I don't take sides.
