What happens to spoke tension on a motionless wheel when a normal load
is placed on the axle?
This page uses FEA to calculate spoke tension changes in newtons for a
36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
newton (225 lb) load:
http://www.astounding.org.uk/ian/wheel/index.html
Here's an extrapolated graph of the spoke tension changes that Ian
predicts, in pounds rather than newtons and for a more reasonable 95
pound load, with the spokes re-numbered from 1 at the bottom at 6
o'clock:
http://i16.tinypic.com/47ca8fm
How well does Ian's theoretical wheel match a real wheel?
Here's a rig to load a front wheel with 95 pounds on a bathroom scale,
just an old frame with its seat post trapped in a bench vise and a
pole and board attached to the top tube to hold weights over the axle:
http://i9.tinypic.com/4p97ur7.jpg
First, I measured the tension changes in 36-spoke cross-3 aero rim
from a bike used by visitors. The wheel came nicely trued from the
factory.
Here's the graph of how spoke tension changed from that real wheel
with a tire inflated to 110 psi, first in the air and then standing on
a scale showing 95 pounds:
http://i8.tinypic.com/52at279.gif
Oops!
Obviously, twanging spokes on that wheel would not confirm the theory
that only the lowermost spokes change tension significantly when the
axle is loaded. It doesn't match Ian's predicted graph very well.
Instead of staying at about 3 pounds of increased tension, spokes are
jumping up and down between 30 pound gains and 20 pound losses.
What's the explanation?
A) Gross incompetence at Fogel Labs must account for some of the wild
variation--the pay is scandalously low and attracts only workers
unable to find more rewarding jobs.
But if the discrepancy was just the result of inaccurate measurements,
then the bottom spokes probably wouldn't match Ian's FEA prediction.
And a 50-pound variation where the graph is supposed to be nearly
level at a 3 pound gain would be amazingly inaccurate.
B) Theoretical wheel models don't include inflated tires constricting
the rim and lowering the spoke tension about 10% to 15%.
But I'm damned if I can see how that would change things. I just put
tires on the wheels to make them as real as possible.
C) Theoretical wheel models do not include one effect of cross-lacing,
namely that lowering the tension in any spoke must lower the tension
in the other spoke around which the first spoke bends at the crossing.
But this effect, however large it might be, should be fairly even and
diminishing, without one spoke gaining and the next spoke losing lots
of tension.
D) Theoretical wheel models assume absolutely uniform initial spoke
tension that real wheels never achieve.
In fact, many real wheels show very uneven tension. Significant random
variations in initial spoke tension on a true rim might lead to
significant random variations in spoke tension changes under load.
So I tested another 36-spoke cross-3 wheel, one that had more evenly
tensioned spokes than the first wheel, though nothing to boast about:
http://i12.tinypic.com/67n6o1c.gif
Aha! The more even the initial spoke tension, the more the spoke
tension changes resemble the idealized FEA prediction on Ian's page.
Here's a graph with all three spoke-tension changes:
http://i13.tinypic.com/4qro8qx.gif
And here are graphs showing how even the initial spoke tension was,
with a level line showing Ian's idealized wheel set to the average for
the two real wheels:
http://i11.tinypic.com/4lp55cl.gif
http://i15.tinypic.com/4zxw03t.gif
http://i6.tinypic.com/4u1lesl.gif
A few conclusions . . ..
A) Pay cuts may not be necessary at Fogel Labs, but workers should
still strive to improve accuracy. Marginal employees may be given more
suitable tasks, such as cleaning up after the guard dog.
B) On real wheels, spokes with uneven initial spoke tension may indeed
twang in very unexpected ways, even though the wheels are true.
Anyone sinfully proud of his evenly tensioned spokes can arrange to
have his wheel tested--you pay to ship it, I'll pay to ship it back.
C) Uneven initial tension may be a bigger problem than expected.
A real spoke that gains or loses more tension than expected as soon as
you sit on the bike may lead a very exciting secret life when the
wheel starts rolling, with more or larger tension changes per
revolution than an idealized spoke.
D) Real testing often produces curious results. I wonder what spokes
do on rear wheels, which have inherently uneven tension? Maybe someone
will email me about testing a really beautifully tensioned rear wheel?
Cheers,
Carl Fogel