Wheelbuilding / Wheel Building / Wheel build help

A above middle C

I don't get this standard 440Hz theory. It seems to imply that all spokes of the same length should be placed under the same stress and strain, as if the material limits of the spoke are what determine its appropriate load.

But if the limit is set by the rim then there is a budget of tension to be shared among however many spokes there are. Even assuming equal numbers of spokes, thinner butted spokes require higher stress (so higher notes) to generate the same tension*.

If you look at changing wheel size the theory gets even worse: larger diameter rims can withstand less tension, but tension would have to rise with square of spoke length to maintain the same note!

(The frequency of the fundamental note of a string is f = v/2l, where l is the length and v is the velocity of transverse waves on the string. v = sqrt(T/da), T tension, d density, a cross-sectional area. Solve for T = da(2lf)^2, or write stress o = T/a, then v = sqrt(o/d), f = sqrt(o/d)/2l )

• I think it's slightly misleading that (e.g.) Sapim advertise the strength of their spokes in Newtons/mm^2, not Newtons. Newtons/mm^2 tells us how clever they are at getting more strength out of steel. Newtons would tell us how strong their spokes actually are. Just for kicks, i did the sums:
  [code]
  spoke strength dimensions area strength
  / N/mm^2 / mm / mm^2 / N
  cx-ray 1600 2.0, 2.3x0.9 ellipse, 2.0 1.63 2600
  cx 1200 2.0, 2.8x1.3 ellipse, 2.0 2.86 3430
  laser 1500 2.0, 1.5, 2.0 1.77 2650
  race 1350 1.8, 1.6, 1.8 2.01 2710
  2.0, 1.8, 2.0 (standard?) 2.54 3440
  strong 1400 2.3, 2.0 3.14 4400
  leader 1080-1180 1.8 2.54 2750-3000
  2.0 (standard) 3.14 3400-3700
  2.3 4.15 4490-4900
  2.6 5.31 5730-6260
  2.9 6.61 7130-7800[/code]
  Although the N/mm^2 values are more closely linked to how much strain (stretch) the spokes can take which might be a more important consideration. And fatigue life should matter a lot too.