Carl Fogel wrote:
> Dave Lehnen <
[email protected]> wrote in message
> news:<
[email protected]>...
>
>>jim beam wrote:
>>
>>>>Titanium spokes won't feel as tight as steel, so other than that make sure that they're properly
>>>>tensioned in the normal way?
>>>
>>>
>>>if you have two springs, one rated at 20lbs & the other at 10lbs, the 20lb spring is going to
>>>deflect half that of the 10lb spring for each lb of load. a ti spoke has roughly half the modulus
>>>of an identically sized steel spoke so is roughly twice as elastic.
>>>
>>>
>>>>I'm guessing that this means that "feel" isn't what you consider the proper, normal method of
>>>>tensioning spokes, but I'm not sure that I'm right.
>>>
>>>
>>>it's nothing to do with tensioning method. it's purely a function of the modulus. easy!
>>>
>>
>>The force you feel when deflecting a tensioned spoke is not purely or even primarily a function of
>>modulus. It would be for a spoke with zero initial tension, but not for a tensioned spoke. At
>>small deflections the additional elongation is negligible, and the resisting force comes from the
>>sines of the deflection angles and the initial tension. At high deflections, additional elongation
>>becomes significant and modulus does matter.
>>
>>Dave Lehnen
>
>
> Dear Dave,
>
> I suspect that what you're saying is said quite clearly for the engineering crowd, but I'm so far
> behind here that I'm not even certain that I'm on the same page as you and Jim.
>
> By "deflecting" do you mean plucking or pushing the tensioned spoke sideways to get a "feel" for
> the "tightness," a sort of seat-of-the-pants tension-measurement that a tensiometer would measure
> far more slowly and accurately?
>
> If so, are you and Jim discussing whether this sideways "feel" would be noticeably different
> between steel and titanium spokes, given the small sideways movement involved, with Jim suggesting
> that the twice-as-elastic titanium spoke would bend or deflect further, while you suggest that the
> elastic difference doesn't actually matter much for a tensioned spoke that moves only slightly
> sideways?
>
> Sorry if I've completely missed what's being said.
>
> Carl Fogel
After re-reading the original post, I'm not sure what he meant when saying the wheels didn't feel
tight. If he meant the wheels had too much lateral (sideways) flexibility, Jim was correct in saying
tightening the titanium spokes would not do any good. If he meant that the spokes seemed to be too
loose when pushed sideways by hand, or perhaps plucked like a guitar string, tension will matter.
The possibly irrelevant point I was trying to make in my last post was that if you push a tensioned
spoke sideways, but only a small distance, the modulus of elasticity of the material has very little
effect. Modulus of elasticity is a measure of material stiffness.
As an example, suppose you have two spokes, one stainless, and one titanium, tensioned to 250 lb
each, between two perfectly rigid supports. Each spoke is 1.8 mm diameter. The titanium spoke has
elongated about 1.074 mm from the tension, but the stiffer stainless spoke has elongated 0.632 mm.
Now push each spoke 2 mm sideways at mid-span. From triangle geometry, each spoke elongates an
additional 0.028 mm. The tension in the titanium spoke goes up to about 257 lb, and the tension in
the stainless spoke to about 263 lb. It takes about 7.3 lb of force to deflect the ti spoke, and
about 7.5 lb for the stainless spoke. For bigger deflections the modulus matters a lot more. If you
push each spoke 10 mm sideways at mid-span instead of 2 mm, the additional elongation is 0.713 mm.
Tension in the ti spoke goes up to about 416 lb, and in the stainless spoke to about 532 lb. The
deflection forces are now about 59 lb for the ti spoke and about 76 lb for the stainless spoke,
probably now enough to feel the difference.
The above calculations ignore bending stresses in the thin wire spokes, and assume neither spoke
starts to yield. I mixed English and metric units only because not many people have much feel for
how much force a Newton is, but spokes are sold in mm.
Dave Lehnen