What determines the range of spokes that lose tension under the axle
when the wheel is loaded?
I know of only two FEA models, Jobst's and Ian's.
Here's Ian's:
http://www.astounding.org.uk/ian/wheel/index.html
Jobst uses a 50 kg load and a simplified radial wheel, while Ian uses
102 kg (1,000 Newtons) and a cross-3 lacing.
But both models show the same 40-degree arc of 5 of 35 spokes losing
tension, with the middle spoke centered on the contact patch:
//|\\
What happens when the spokes shift so that there's no middle spoke,
meaning that two spokes straddle the center of the contact patch?
Do six spokes lose tension over a 50-degree arc?
///\\\
Or only four spokes over only 40 degrees?
//\\
My guess is six spokes, but it's just a guess.
***
What happens as the load increases on a real wheel where spokes can go
slack and the radial stiffness of the wheel varies, with modern deep
low-spoke-count rims being stiffer than their ancestors?
That is, what happens if the load and spoke tension combine so that
all 5 spokes under the axle of a 36-spoke wheel go slack?
Do the spokes next to them change behavior and start losing tension?
Or do the other 31 spokes all continue to gain tension?
Does the wheel deform so that only the bottom 5 can lose tension?
My guess is that the other 31 spokes continue to gain tension, instead
of the tension-loss range expanding from 5 to 7 spokes.
***
What happens with lighter loads?
Do the same 5 spokes immediately lose tension on a 36-spoke wheel, no
matter how small the load is?
Or does the wheel deform so that first just the central spoke loses
tension, then the two on either side of it as the load increases, and
then the next two?
I haven't even got a guess about this.
***
What is the range of spokes that lose tension on an 18 spoke wheel,
with half as many spokes as the 36-spoke models?
Do only 3 of the 18 spokes lose tension like this over a smaller arc?
/ | \ possible 18-spoke 40-degree arc for tension loss
versus
//|\\ FEA 36-spoke 40-degree arc for 50 and 102 kg
Or does the range broaden so that 5 of 18 spokes still lose tension?
/ / | \ \ possible 18-spoke 80-degree arc for tension loss
versus
//|\\ FEA 36-spoke 40-degree arc for 50 and 102 kg
With only 16 spokes, spokes are spaced 22.5 degrees apart. If three
spokes lose tension on a 16-spoke wheel, then the arc of tension loss
_must_ increase to at least 45 degrees versus the 40 degrees of the
36-spoke model. (Maybe only the single central spoke loses tension?)
To turn things around, what happens with a 72-spoke wheel? Do only 5
spokes lose tension in a 20-degree arc, with 67 other spokes gaining
tension? Or do 10 spokes lose tension?
(Substitute 40 or 48 spokes, if you want to do trickier arithmetic.)
Again, I don't even have a guess. We have only two FEA models for 36
spokes. We don't have one for 32 spokes, much less 18 spokes.
***
In a 3-spoke model, things may become very strange.
If the single spoke is pointing down, it seems likely that the single
lower spoke loses tension when the wheel is loaded, since it must be
in the arc where the rim flattens and moves closer to the hub:
\ /
|
lose
But what happens when the single spoke points up? Do the two lower
spokes lose or gain tension when the wheel is loaded?
|
/ \
? ?
If the two lower spokes are outside the rim section that flattens
inward, then they should _gain_ tension, and we have a pre-tensioned
wheel that in some positions doesn't lose tension (assuming that the
_top_ of the wheel doesn't do something sneaky and flatten toward the
hub).
And what the hell happens when the 3-spoke wheel is loaded in these
positions?
_ / \ _
\ or /
The wheel would deform, but probably asymmetrically.
***
A 6-spoke wheel may raise similar questions:
A spoke pointing down at the center of the contact patch probably
loses tension. But the spokes on either side may not lose tension,
since they may lie outside the flattened rim section:
\|/
/|\
In the position below, do the two spokes 60 degrees apart lose
tension? Or are they so far apart that they just gain tension?
_\/_
/\
***
You could ask the same questions about an even simpler 4-spoke model,
where the arc between two bottom spokes increases to 90 degrees:
_|_
|
lose
versus
\/
/\
? ?
Interestingly, if the lower spokes do indeed lose tension, then the
upper spokes may gain impressive tension after the lower spokes have
lost all tension.
If so, then low spoke count rims would be more prone to cracking at
the spoke holes because the spokes _gain_ so much tension when loaded.
***
Again, I'm just guessing about most of this. It would be nice if there
are much simpler answers.
Cheers,
Carl Fogel