A little lightbulb turned on for me a couple of weeks ago. I left campus to go to work in the usual manner. I traveled through the roundabout onto Thompson Drive, and as usual I found the big curve to be a bit slick. (I've long thought that this curve is banked the wrong way, it is scarier than it should be) The back end of the car slid sideways, so I turned the wheel to correct for it. I only moved a few feet when the car tried to slide sideways again, and I again corrected it. I had control, but it didn't take much to lose it. It occurred to me that if I had more space, a gentler curve would keep me on the road without sliding. Hmm, I pondered, do I need a greater arc length? Maybe, but it needs to be less rounded... redrawing it in my head I realized that I needed a larger radius. It also occurred to me that the car was sliding away from the curve, in a straight line, maybe? <blink, blink> Is the line tangent to the curve? That sounds familiar...

"wait a second!", I thought. I am sliding because the road is icy. Friction is what should be holding me in my intended curve (that thought would not have crossed my mind a few months ago), so there must not be enough of it. Aiming for a slightly larger curve is OK, I can hold that arc. Does that mean that my speed is somehow related to both the radius of the curve and the amount of friction between the road and my tires? Holy spherical cows! I know how to calculate that!

I mentally ran through the whole thing several times while driving to work. I then told my coworker all about it, and although she smiled at me, I really don't think she was as excited as I was. I couldn't quite work through the equations in my head, so had to check my notes when I returned home, and yup - speed is related to both radius and friction.

Amazing. It really does work.