Originally Posted by
BCRider
I'm with you up to the final total pulling force of 147 kg and that it being split between 16 pulling spokes for a linear TANGENTIAL PULL AT THE SPOKE HOLE OF 9.2 Kg. But that's where it breaks down. From there you have to consider the direction the spokes are angled at to determine the tensile load increase in the spoke. For a true tangential spoke the added tension in the spoke is at 9.2 kg. But as the angle of the spoke changes towards radial you need to get the sins and cosines out and figure out the difference. And when the spoke is not directly in line with the force there is a mechanical leverage of forces that increases the tension in the spoke to a value higher than it is when the spoke is in line with the force. Your otherwise fine set of data doesn't take that final factor into account.
And since my mind is awake now I was able to do up this vector analysis. Note that the angle isn't even close to radial in the second diagram but you can see how as the spoke angle approaches the true radial how the force in the spoke will multiply rapidly to extreme values. In fact if the spokes did not have the ability to stretch at all then a truly laced radial wheel would see the increase in spoke tension hit infinity. In real life a radial laced rear wheel would defect to some angle (as in wind up) and allow the spokes to come to an angle where they would generate the required triangle of forces. But the leverage on such a spoke at this very small angle would result in HUGE increases in tension that are way beyond what even the static tension of the spoke is. I think at that point you'd see either the spokes fail or the hub flange fail.
And this is why a disc brake or rear wheel should not be done in a full radial lacing.
EDIT- for the heck of it I reduced the spoke angle to 5 degrees from radial and 2.5 degrees. The resultant spoke tension increases at that point were 105 kgs and 210 kgs. At 2.5 degrees we're probably looking at an angle that would typically occur when our strong rider wound up the wheel and stretched the spokes from the true radial angle. I can only see very bad things occuring from such a situation.
The thing is, spokes ONLY take loads in tension. It's not a solid object where lateral forces can be broken up into two
independent vectors. The forces are translated into the direction of the spoke and are applied fully in tension. For example, if you hang a weight on a rope and push sideways on teh rope, does it increase tension on the rope at all. No, it just push the object sideways and it swings, but the tension on teh rope is always the object's mass*G.
So the initial wind-up of the hub actually results in mininal-increase in tension on teh spoke on a radial wheel. Lets magnify the results for comparison. Lets say a 3x wheel winds up 1-degrees for 5.58kgm torque at the rear-hub. You can do an integration from 0-1 degrees and figure out the tension build-up for each spoke. When all the spokes' tension increases enough to counteract the torque, the hub no longer winds up. A radial wheel would end up winding say... 5-degrees for that
same increase in tension.
A spoke, like a rope, ONLY experiences tension IN-LINE with itself. Lateral forces do not result in tension. You can test this out yourself. Clamp a rear wheel by the rim in a vise or a door. Get a long chain-whip, wrap it around a 15t cog and hang a 15kg weight from it. Measure the spoke-tension increase due to torque and you'll find that its the
same regardless to numbers of crosses or teh tangential-angle of the spoke leaving the rim.
Another way to calculate this is the actual stretch amount. Plug into Young's Modulus for amount of stretch based upon length and cross-section of spoke and you'll get the amount of lengthening and teh resultant tension. You'll find that direct tangential lacing has the least amount of wind-up angle necessary for the amount of lenghtening needed. With a radial lacing, you'll need a lot more angle of wind-up for the
exact same elongation. There's a direct relationship between tension-increase and elongation and you'll find that both tangential and radial-lacing results in the same elongation amount for the same tension-increase. Just that to generate that
same amount of elongation, you'll need to twist the hub more.
It's the emperical data that will show one way or another whether an arm-chair physicist or racer's idea is valid. How many people have actually built-up or ridden a rear radial wheel anyway? Have you guy actually ever measured the angle wind-up or spoke-tension increases? Thinking in your head without looking at the experimental data is just goofy. It's like those guys saying that generating hydrogen using electrolysis from your car's alternator and pumping it into the intake will magically increase gas-mileage. It sounds plausible, but the actual emperical data will show you something else.
