Why crowned pulleys and bandsaw wheels?

[tonyfoale]

.......... even though I can no longer remember as much of my math as I once had and never achieved the level that mklotz and others have. So I really appreciate these explanations found here in these forums

Except for some stuff in quantum physics and cosmology, I believe that if you can't explain something in simple non-maths terms then you don't fully understand it. Many things that I have developed everyday explanations for would be much easier for me and much more concise if explained in terms of maths but that sometimes blurs a physical understanding. Gyroscopic effects are my favourite example of that. Pick up a physics book and it is bound to have a mathematical derivation of the standard relationship between torque and spin velocities. However, even most engineers and scientists that I have discussed this with don't have a good grasp of the relationship of the simple maths to the seemingly magic reactions you get when playing with bicycle wheels. I have developed a straightforward explanation of this and those who have seen it light up like a light bulb. They finally make the connection. It is equally enlightening to those with and without the maths understanding.
I am far away from a maths-phobe. I have spend a lot of my working life developing mathematical models to simulate a wide variety of dynamic physical systems, mainly but not exclusively for land and air vehicles. Sometimes the results of such work help develop a physical understanding where none previously existed. Unless that comes I never feel that I understand anything, and I don't like that.