Originally Posted by alienator
It doesn't take wheel building experience to understand the physics of where stiffness comes from in a wheel. Moreover, there are a lot of wheel builders that aren't alfeng that understand that wheel stiffness doesn't come from spoke tension, including wheel builders at Weight Weenies.
You didn't, however, answer the question. I'll make this easier for you by using simpler language: stiffness is the measure of how much structure resists flexion, elongation, compression, or torsion. Since the topic of late is how a spoke contributes stiffness to a wheel, the stiffness of a spoke is then a measure of how much said spoke resists elongation or compression......but we ca rule out compression in the vast majority of wheels since regular spokes aren't loaded in compression. So given that how can increasing the tension on a spoke increase the stiffness that spoke contributes to a wheel? If a spoke has a stiffness, k =10, then the force to elongate that spoke by x distance is F = -10x. Tension is the force acting on that spoke so we'll call that FT = -10x. So let's take two identical spokes. One is tensioned to 50 units and the other to 100 units: FT1 = -50 = -10x1; FT2 = -100 = -10x2. That means spoke 1 elongates -50/-10 = 5 while spoke 2 elongates -100/-10 = 10. Now lets see how much force it takes to elongate each spoke 1 length unit more. 1 more unit would be -k(1) for each spoke, which means the force required to elongate each spoke by one more unit is -10. So how does more tension make a stiffer wheel when it doesn't change how much force is required to move the spoke an additional increment of distance? Further since k, i.e. stiffness, is a constant, how can more spoke tension change a constant? The simple answer is that it can't. Again, spoke tension can change the dynamics of a whelk, but that is very different situation. Nothing definite can really be said about the dynamic response of a wheel to a load without knowing more about the wheel, like the damping ratio for a wheel, since the dynamics are defined by 2nd order ODE. You could reasonably assume that a wheel is over-damped, but that doesn't help much.
Again, given that spokes with greater tension don't decrease how much a wheel deflects under a given load compared to wheels with lower spoke tension (again, as mentioned in quite a few of my other posts, the tension does have to be sufficient to prevent the spoke from going slack.) and given that the a spokes actual measure of stiffness, k, doesn't change with tension, how does increasing tension improve stiffness, klabs?
Oh!?!
Apparently,
alienator was rejuvenated by
dhk2's calculations enough so that we again have to deal with
alienator's low reading comprehension (aka "
listening") followed by a further expository bloviation where an inability to use "
critical thought" or "
reason" as they are understood in the
Real World vs. in his dystopian situational world being foisted upon us as having been supposedly derived through the "scientific method" ...
Here, once again, YOU begin your rant with a false premise as a "given" whereby you unilaterally declare "that spokes with greater tension don't decrease how much a wheel deflects ...".
Worse, yet, due to your poor reading comprehension + your inability to comprehend the data in a matrix, we see here
another example of your inability to demonstrate a "
listening" (
again, THAT would be "reading" what is in front of you in our non-oral Forum) ability beyond the voices which are apparently in your head AND we now see that you are suggesting that 'I' have been stating that a spoke's tension is the primary factor which affects the lateral stiffness which a bicycle wheel will have ...
So, in your schizophrenic confusion you are now suggesting that 'I' have been suggesting that spoke tension alone (?) has an effect on a wheel's lateral strength (
where strength is resistance to lateral deflection) when it has ALWAYS been my contention that if a person wants a "stronger" wheel (
again, one which will resist deflection) that s/he will choose straight 14g spokes laced x3 on the driveside & x2 on the non-driveside rather than a wheel laced with double-butted 14-15-14 spokes.
Of course, most-if-not-all of the followers of what I have previously referred to as the "religion of double-butted spokes" apparently believe that lacing a rear wheel x3 on both sides is a requisite part of the fore mentioned
religion ...
- Why don't ALL wheel builders use asymmetrical crossing?
- Simply stated, it (certainly) takes (me) MORE TIME to use an alternate crossing pattern on the non-driveside because you either have to have to think about it OR have a wheel which you previously laced with the alternate crossing pattern as a template ...
Your inability to understand that a double-butted 14-15-14 gauge spoke has less lateral resistance to deflection at 100 kgf than a straight 14g spoke fabricated from the same material at 100 kgf speaks volumes to your lack of "
critical thought" with an incorrect belief that 'I' am saying that a spokes tension, alone, affects a wheel's lateral strength.
OR, are you
now going to say that "of course a thinner spoke is more easily deflected" despite your repeated bloviationg about Hooke's Law?
Because, as you have been presenting Hooke's Law in a linear analysis in the wrong Axis, you have been addressing a straight 14g spoke to be the same in a wheel as a double-butted 14-15-14 spoke (
which is presumably of the same material) ...
And, extrapolating YOUR statement would logically suggest that a piece of rebar (
if it were made of the same material) would have the same ability to resist lateral deflection.
What say you, now?!?
Your insistence that Hooke's Law is directly applicable to analyzing the lateral stiffness which a bicycle wheel will have via an analysis in the wrong axis reaffirms that ...
alienator apparently doesn't know the difference between Hooke's Law and Captain Hook.
Regardless, if you are going to pretend that Hooke's Law is applicable, then you would need to base your calculations on the Conic cross section of the different spokes ...
BUT, while the
length of the spokes might vary by a small enough percentage to be negligibly different, if the double-butted 14-15-14 spoke's cross-section is approximately only 90% of the that of the straight 14 gauge spoke's cross-section, then the resultant calculation will not be a small amount....
The Park Tool tensiometer's matrix suggests a difference of roughly 76+ %.
If you don't like the precision of the Park Tool & matrix, then at the very least, THAT minimally suggests a difference of 81% ...
81% is hardly a small amount in the
Real World.
Regardless,
YOU are absolutely incorrect when you bloviate that a spoke merely needs to have enough tension so that it does not go slack ...
And, if one allows that your suggestion of "50 units" vs. "100 units" is translatable to "50 kgf" and "100 kgf" then it is really, REALLY TOO BAD that you don't still live in the Tucson-area-and-environs because if you were able to convince your AZ wheelbuilder (
or, if you were to finally venture to actually build a set of wheels) to lace a set of wheels for you which were only tensioned to 50 kgf and then ride up to the summit of Mt. Lemmon (
if you ever did so in the past ... OR, as far as you can go where you encounter switchbacks or curves which are taken in excess of a modest 20mph) then I'll bet you have a different song to sing after the descent on bicycle wheels whose spokes are laced at only 50+ kgf.
Hey, why don't you detension your current wheels ...
then see how you subsequently feel about a wheel's
lateral strength [
resistance to lateral deflection] on a roadway which you are familiar with that has some moderately high speed left-right turns in succession!