## Reply To: 2012 Hub Review: Information overload?

Very comprehensive review and wonderful archive of the current state-of-the-art in hub design and construction; thanks to all of you who put in the long hours to assemble this. I have a few comments:

1) In the the section headed, “Notes on bracing angle,” I staunchly disagree that “Bracing angle (or flange offset) is the most important factor effecting the lateral stiffness and stability of the wheel,” unless you meant to include the word “hub” between “important” and “factor.” Yes, it matters, but it’s no more than the second most important factor for any reasonable hub design. The most important factor is the rim! The rim bending stiffness (second moment of inertia) is proportional to the cube of the section depth for rectangular or triangular rim sections in either the x- or y- (radial or lateral, let’s say) axes, so a small difference in section depth makes a big difference in bending stiffness. Just going from a 19 mm wide rim to a 22 mm wide rim, all else being equal, increases the stiffness by (22/19)^3=1.55, or 55%, while the difference in bracing angle between the narrowest front hub (Soul-Kozak Aero) and the widest (Alchemy ELF) is 7.9/5.7=1.38, or 38%. See my point?

2) You go on to say, “The lateral stiffness imparted by the spokes goes up with the *square* of the bracing angles, while using more or heavier spokes only results in a linear increase in stiffnessâ€¦ and an increase in weight.” How is it proportional to the square of the bracing angle, unless you mean to imply that it’s squared because it’s linear on both sides so the combined effect is quadratic? The lateral spoke force is proportional to sin(bracing angle), and sin(x)/sin(y)=x/y for small angles, but Hooke’s law says the force is directly proportional to the displacement. That’s a simplistic view, though, as a stiffer rim also spreads the load out over a larger region, so perhaps the square law is appropriate for linear spoke and cubic rim proportionality on each side of the wheel? The full answer, of course, is FEA analysis, and Henri Gavin, Prof. of ME at Duke University, did that years ago.

3) I agree with those who say that narrow hub flanges afford no aerodynamic advantage vs. wider flange spacing. Jobst Brandt addressed this generic issue years ago in _The Bicycle Wheel_, where he points out that radial lacing affords no aero’ advantage over crossed lacing, since the spokes in either case still see the wind, only at a slightly different apparent angle relative to vertical: the spoke cross section into the wind is the same in either case. Same goes for hub flange spacing. Thus, I would never recommend a Soul-Kozak hub Aero front hub for a wheel build since there’s no aero’ advantage and lateral stiffness is compromised compared to other high-quality hub offerings.

Keep up the good work, and ride on!

Dave Walker

PAKETA CYCLES