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

On Tue, 16 Sep 2008 07:01:01 -0500, Ben C <spamspam@xxxxxxxxx> wrote:

On 2008-09-15, carlfogel@xxxxxxxxxxx <carlfogel@xxxxxxxxxxx> wrote:
On Mon, 15 Sep 2008 16:37:05 -0500, Ben C <spamspam@xxxxxxxxx> wrote:

On 2008-09-15, carlfogel@xxxxxxxxxxx <carlfogel@xxxxxxxxxxx> wrote:
[...]
Dear Ben,

As the quote pointed out, Damon's tests _did_ show a difference in the
direction that Jobst predicts.

But of nothing like the magnitude.

For only 12 kg force and ~ 3 mm movement, Damon's test should not be
expected to show anything very clearly about an FEA carried out to
+400 kg and +50 mm.

The tiny red circle shows the section of Jobst's drawing that Damon's
test covers:
http://i34.tinypic.com/mae4nb.jpg

I realize that, but in that tiny red circle, the left hand line is
almost twice as steep as the right hand one. Why?

Dear Ben,

On a drawing with the scale of Jobst's figure, how would you draw the
curve within the tiny red circle?
http://i34.tinypic.com/mae4nb.jpg

The same. As pm's illustration shows, the lateral force line has a
non-zero second derivative at zero-displacement (its second derivative
is at zero when the rim is centered between the flanges). Because of the
very zoomed-out scale of the diagram, that's making the left hand line
look shallower nearer zero than the right hand one.

If you plotted the contents of the tiny red circle much bigger, it would
be more obvious that the slope of the line is very nearly the same for
small displacements either side of zero.

What's confusing about the diagram is that it's showing a different
effect from the one (I still think) the text is describing. But because
of the scale, and because the left lateral force line is drawn
"rectified", it almost looks as though the left line is demonstrating
the effect described in the text.

If you look at the rim displacement for lateral forces of 1000N left and
right, it's about 50mm on the right and about -100mm on the left. The
text says "This wheel is twice as stiff for deflections to the right as
to the left". So naturally you put two and two together. But the text is
talking about a completely different effect-- the abrupt roughly
factor-two change in stiffness that happens at small left displacements
because the left side goes slack. The diagram doesn't show that change
at all because it isn't in the model it's using.

At least I assume that's what the text is talking about, but that isn't
100% clear.

But 1000N is a huge force. The effect of bracing angle is very small at
realistic forces, and the practical factor-of-two stiffness change comes
from the left side going slack.

It might be better to have two diagrams: the one as it is, but with
dashed lines in the places where spokes compress and a note saying that
that is what's happening. Then to comment on the effect of the different
bracing angle but to point out that it's not significant at realistic
forces.

Then a second zoomed-in diagram that only goes from displacements of
about -5mm to 5mm, showing the lateral force line as effectively
straight for that region, but marking the discontinuity where the left
side goes slack.

Better still might be to use a slightly less simplified model in which
the spokes are like string-- so they provide absolutely no support in
compression. That's reasonably accurate and would show better what was
going on. You could superimpose the original model with dashed lines,
because it's quite interesting to see the shapes of the curves.

I would also draw the left hand side "un-rectified", as in pm's
illustration, because that makes the lateral force line much clearer.

I'm not suggesting Jobst should do any of these things-- that's his
business. It's just how I would draw it because I think that would be
clearer.

Now you're probably going to challenge me to actually draw these
diagrams :) Well I might actually see if I can reproduce the model on a
computer to confirm what's going on.

Nothing's bodged or inaccurate on Jobst's diagram, but I do think it's
confusing because the lines are showing a different effect from the one
the text is describing. It's taken a while to sort it out, and the penny
only dropped when I saw pm's flipped version and explanation.

Dear Ben,

Why not just stop after you wrote "The same" in reply to my question
of how you'd draw the diagram?

Cheers,

Carl Fogel
.

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