Monday, September 12, 2011

Techie Tuesday - Optimal Wheel Spoking

This is a post I have wanted to do for months and months, and never seemed to find the time. I was motivated to do the post now because disk brakes are taking off for Cyclo-Cross racing, and Johan Bruyneel has been calling for at least rear disk brakes being used in the TDF to cut down on crashes caused by carbon wheel lockups. I happen to agree there.

While a rear-only disk wheel will not impact road wheels that much, front and back disk wheels would make radial spoked wheels disappear in a heartbeat. It would also introduce all of the torque-bearing considerations to the front wheel as are present in rear wheels.

Mid-1980s 36 hole low-flange hub with very little tear-out protection. Even laced 3X, the spokes have a significant concave path across the wheel. Note that on all 3X lacing, adjacent spokes pull in the opposite direction, offsetting each other's stresses on the flange.
Mid-1980s rear low-flange hub. The larger flange, relative to the front hub, creates a flatter, more optimal spoke path across the wheel.

Ultegra 6700 32 hole low-flange front hub laced 2X. The spoke path is even more concave than the 36 hole 3X spoking above. Better than radial, and with extra material to prevent tearout, it nevertheless is NOT warranted for radial spoking.
Ultegra 6700 32 hole low-flange rear hub laced 3X. Spoke path is very close to straight across. If they're ever made available in Ultegra 6700, 28 hole hubs should produce optimal 3X spoking.
Mavic Aksium: Drive-side spokes run perfectly straight across the wheel, the optimal 90-degree pulling angle for a torque-bearing spoke, from LR corner to UL corner here. Well done.
Mavic Ksyrium: A tribute to pig-headed stupidity and marketing arrogance. The beautiful convex spoke path on the non-drive side is completely negated by the use of radial drive-side spoking. The decision to use aluminum spokes, with no fatigue limit, guarantees failure.
These two wheels, identical in all other respects, show the difference a larger diameter rim makes on spoke path. As you can see, the 29r (~700c rim) spoke path isn't quite as optimal against tear-out as the 26r's is, although both are very good.
WTB Mtb 26r: Convex spoke path on 3X spoking, from LL to middle R on drive side and LL to UR on disk brake side here.
WTB Mtb 29r: Slight concave path from LL to UR on drive side, and LR to UL on brake side here.
The 24 hole drilling and 3X spoking creates straight-across path on the drive side. Uses a Hi/Lo flange strategy to make the wheel respond more symmetrically
Perfect straight-across spoking, which Mavic calls R2R (rim to rim) on their Cosmic Carbone all-carbon wheels. They must have fired some marketing people and hired some engineers.
  A few notes on ferrous (steel) and non-ferrous (aluminum) metals. The curves look like this. Note that 6061-T6 fatigues down to only 10% of original strength with symmetrical, oscillating, mean-zero stresses, and to only 4% with maximum asymmetrical stresses.

This textbook on metal fatigue spells it out much more starkly - non ferrous metals have no real fatigue limit. They fatigue to zero strength. Still think those Ksyrium spokes broke because you abused them?

As I remarked on before, drive-side spokes are tightened to about twice the tension of those on the non-drive side in an attempt to shore up the drive side's lateral strength. There are several strategies available to mitigate the resultant asymmetrical way the wheel responds to axial and lateral loads. In general, the goal is to have the spokes of the two sides yield equally with any applied stress, such that the effect on rim movement and deflection is symmetrical.
  1. Radial spoking on the ND. This shortens its spokes, making them less elastic. Ironic that NDS radial lacing is used by mfgs who lace the front wheel radially to make it stiffer. The NDS is already too stiff visa-vie the drive side.  It also makes for a harsher ride, and precludes it from bearing any torque.
  2. Use of a larger flange on the drive side. This moves the spoke bed outward, improving its angle, and can be helpful. It also bears torque better. It will also improve the spoke path, shorten those spokes, and thereby, stiffen them. 
  3. Low (or very low) flange on the NDS. Effectively moves the spoke bed inward, and lengthens the spokes. Most helpful when combined with 3X lacing and thinner spokes to increase elasticity. 
  4. Using more spokes on the drive side. This is rare, but it has the potential to soften up the NDS so the wheel responds more symmetrically to loads. One interesting option here is to use radial lacing and only populate every other hole. Fewer spokes would be more aerodynamic.
  5. Heavier gauge spokes on the drive side. This was my personal choice, as I used 14/15 on the drive side, and 14/17 on the NDS. This makes for a rock solid wheel that is also supple.
  6. Using a smaller freehub body, as found on Hope and Chris King single-speed hubs, and mount only 6-7 gears of a cassette. You'll have fewer gears, but a much stronger wheel. This idea is getting some traction in the mtb community. With a triple crank adequate gears are still available.
  7. Off-center spoke drilling. Velocity's O/C rims can move the spoke bed over 4mm. It should help, especially if combined with other strategies. This directly attacks the problems of dishing a wheel.
  8. Move the NDS flange inward. Disk brake rear wheels do this routinely. It usually results in a wheel that is laterally weak on both sides. Measure the flange to flange distance and buy accordingly.  Wider is better.
  9. Use heavier spokes only where they are pulling torque. These would be trailing spokes on the drive side, and with disk brakes, leading spokes on the NDS. With caliper brakes and 28 hole drilling, only 7 spokes would have to be 14/15, all the other spokes could be 14/17. This should keep spoke weight to ~ 100 grams.
White Industries H3 road hub with titanium freehub body. 252 grams. Note the hi/lo flange strategy.
Tune MAG 150 weights only 150 grams. Note straight-pull zero-flange on NDS and large flange on drive side.

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