Re: Hey, Jobst, on p39 of The Bicycle Wheel the graph appears to show the ?impossibility of...

On 2008-09-15, carlfogel@xxxxxxxxxxx <carlfogel@xxxxxxxxxxx> wrote:
On Mon, 15 Sep 2008 02:30:10 -0500, Ben C <spamspam@xxxxxxxxx> wrote:

On 2008-09-14, carlfogel@xxxxxxxxxxx <carlfogel@xxxxxxxxxxx> wrote:
On Sat, 13 Sep 2008 18:05:39 -0500, Tim McNamara
<timmcn@xxxxxxxxxxxxx> wrote:

In article <4gTyk.37$MX3.133@xxxxxxxxxxxxxxxxx>,
"Philip Holman" <pholman@xxxxxxxxx> wrote:

"Ben C" <spamspam@xxxxxxxxx> wrote in message
news:slrngcnp9i.5lv.spamspam@xxxxxxxxxxxxxxxxxxxx
On 2008-09-13, Peter Cole <peter_cole@xxxxxxxxxxx> wrote:
Ben C wrote:
[...]
Here's the diagram again: http://i33.tinypic.com/2ykj9rq.jpg
[...]
Anyone who thinks that he has a substantial disagreement with Jobst's
diagram can simply sketch what he thinks it should look like, upload
it to www.tinypic.com, and post the link.

http://tinypic.com/view.php?pic=ibmomx&s=4

This is zoomed in a bit to the centre of the diagram. You can see T(L)
and the lateral force curves. T(R) is not shown. Sorry for the crappy
wobbly drawing.

The point is that I would expect the lateral force curves to have the
same absolute gradient either side of zero displacement. Then for the
left side to go half-as-stiff when it reaches the position on the x axis
at which T(L) is 0 (about -4mm).

Alternatively perhaps this diagram represents a simplified model in
which spokes work in compression, which it does seem to, but then I
would expect the left lateral force line to have the a similar absolute
gradient to the right one.

That would fail to make the point that the wheel is twice as stiff to
the right as to the left. But you can't have your cake and eat it. If
you're saying it's stiffer because it goes slack, then you have to show
that slackness on the diagram and model it at least crudely (treat the
spokes as string for example). If you're saying it's stiffer for some
other reason, then that reason isn't explained in the text.

In any case the lateral force lines on the original diagram don't seem
to show the wheel as quite as much as twice as stiff to the right as to
the left, although that's what the text says.

I really don't know where those lateral force lines come from. My best
guess so far is that they come from an FEA that allowed spokes to work
in compression. This explains the lack of a discontinuity at the
left-side-slack-point, but is at odds with the experimental results of
Damon Rinard. That itself is an interesting question.

But on what basis is the text saying "This wheel is twice as stiff for
deflections to the left as to the right"? It comes right after a
sentence saying that the left side goes slack after a small
displacement, but that slackness isn't shown on the diagram, and nothing
says directly that the slackness is what causes the stiffness
difference.

Yes I would also prefer dashing of T(L) under the x-axis and dashing of
the left lateral force line left of -4mm, but let's let that one go, I
have a much bigger problem with the lateral force lines. Where did they
come from and what exactly are they showing?

Dear Ben,

If you apply a lateral force to a rim, it moves sideways.

But it gets harder and harder to shove the rim sideways because the
angle of the spokes that resist that movement changes.

In other words, the resisting spokes have to stretch more when the rim
moves from 45 to 50 mm than they stretched when the rim moved from 0
to 5 mm, which means that more force is needed to move the rim 5 mm.

That's why the line for vertical force is curved, not straight:
http://i33.tinypic.com/2ykj9rq.jpg

Yes, I agree, that seems the best explanation of the curved shape.

As for Damon Rinard's tests, they involved only ~12 kg force and ~3 mm
displacement.

That's far less than >400 kg and >50 mm displacement in Jobst's
figure.

Yes-- Damon's tests were mostly in the range before anything goes slack,
which is only a tiny bit of the range of Jobst's figure, which as we've
said, is a theoretical extrapolation far beyond even the breaking
stress.

Here's Damon's data table for lots of wheels, which showed rim
movement up to 5 mm with the ~25-lb force:
http://www.sheldonbrown.com/rinard/wheel/data.htm

Damon's tests showed that "in every case shows that, on average, rear
wheels may flex more in response to loads from the right side than to
loads from the left. However, the range of measurements (length of
vertical lines) shows that the difference between left and right is
often smaller than the measurement error or the range of response of
one side of the wheel."
http://www.sheldonbrown.com/rinard/wheel/index.htm#3

In other words, Damon's tests support Jobst's >400 kg and >50 mm
displacement drawings, even though Damon tested only the tiny range up
to ~12 kg and ~3 mm displacement.

But Jobst's caption says the wheel is twice as stiff for displacements
to one side as to the other.

Damon didn't find a difference anything like that big.

The reason is because Damon's spokes generally didn't go slack (his
loads were too small for that). In fact when he reduced the tension so
much that they did go slack, he did get the factor of two emerging-- see
the graph at the end of section 1.

The model represented in Jobst's diagram as I understand it was a
simplified one in which spokes can compress. He said so (I think), it's
implied by the T(L) curve, and by the lack of a discontinuity in the
left hand lateral force line.

In that case, I would not expect to see much difference between the left
and right sides.

It's a fine diagram of the simplified model in which spokes also work in
compression and don't break. So far so good. But such a model would show
little or no difference in stiffness between left and right
displacements. It almost looks like the left hand lateral force line has
just been bodged to make it steeper to fit something _we_ know to be
true (but that the simplified model doesn't).
.

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