Originally Posted by
DannoXYZ
....So lacings with exactly 90-degree spokes relative to flange will have the least amount of wind-up......
Agreed. If I didn't make that part clear then I said it wrong.
Originally Posted by
DannoXYZ
.....Note that this force on the spokes at the hub is the same regardless of the lacing. That's because the force at the hub comes from the force at the pedals, through the crank, through the gearing, to the flange. .......
It was all great up to the bolded part. That bit just doesn't wash. For a given torque in the hub radial spokes will see a much higher torque related rise in tension compared to tangential spokes due to the geometry of how the tension in the hub is applied to the spokes. Due to the radial nature the hub has a lot more mechanical advantage due to the angle the radial of the hub meets the spoke at. That mechanical advantage means the hub torque is going to be able to pry on the spokes with a better leverage ratio so the tension buildup in the spokes from the torque will be a lot higher than for the tangential setup.
A great way to show this is with a vector analysis of the forces. But it's late and my brain is mush at the moment. I'll see if I can remember enough of my Grade 19 geometry to figure it out tomorrow. But in the mean time if you've ever used an over center cam lock you'll remember how easy it is to move the cam when the rod is moving up closer to the center and then over center point. That's the same principle I'm trying to describe that will result in torque in the hub being able to generate a lot more force in the spokes with radial lacing vs tangential.
For the same reason a full radial drive wheel will suffer from a lot more wind up. When the force stretches the spokes that little bit more that little bit of stretch translates to a lot more angular travel in the hub compared to the same amount if the spoke is tangetial. So the radial lacing will feel sort of rubbery at the pedals to the rider vs the tangential lacing. That part I can show you. For the sake of the demonstration lets assume the rider's torque can stretch the spoke by 1/16 inch. It makes the diagram easier to see because you're not trying to work with lines that are visually too close together to see. So we get this sort of effect that's going to make the wheel feel more rubbery at the pedals. At least my brain was this awake....