Originally Posted by
FLYcrash
Tension does not balance torque. Tension is a force, and a force must be multiplied by a distance (the "moment arm") to make a torque. To revise your statement:
What happens is ALL hubs will wind-up until the increase in tension, multiplied by the moment arm (perpendicular distance from the axle), equals the applied torque. (Perpendicular distance means perpendicular to the spoke.)
There we go. Now the radial has a tiny perpendicular distance from the axle, generated solely by the wind-up, so a huge tension increase is needed to equal the applied torque. The tangential has a healthy perpendicular distance built into the structure, so only a modest tension increase is needed.
Please put the first part into numbers and equations and you'll see that you have exactly the same equation I presented earlier.
As for the 2nd part, compare the "perpendicular distance" from the axle between the radial and 3x and tell me what that distance is in numbers. You too are assuming that the force that's increasing the spoke-tension is being applied at the nipple. It's not, it starts at the hub.
The thing here is that we need emperical data to see if the model in our heads fit with reality. I'll conduct BCriders rope configuration with real physical structures and measure some real data. Then we can continue the discussion with common assumptions and workable models.
1. The mistaken assumption BCrider and you have is that there is some sort of mechanical-advantage going on with the angle. In reality, there isn't, and the empirical data on the rope-experiment will borne that out. Spokes and ropes work only in tension and do not have lateral force components. Tension-A in the upper rope-section will be exactly the same as the vertical section directly attached to the weight.
2. Vector-analysis is incorrect. What vector diagrams show is how to divide a larger diagonal force (hypotenuse), into two X-Y right-angle vectors. It can break up the diagonal into two smaller right-angle components. But it doesn't work the other way around with a smaller lesser component multiplying into a bigger diagonal. We'll deal with that in a different topic.
BTW - regardless of your credentials, does the airplane on the conveyor belt take off or not? You'd be surprized at how many people with "credentials" got that one wrong.
While you're waiting for me to conduct the experiment, I suggest you read this article:
Dean's World - The Brainteaser That Changed My World