This isn't nearly done, so check back later for pictures and better descriptions and the like.

The styrofoam cup analogy doesn't work, because styrofoam cups are rigid (mostly) and tires aren't. if it did work that way, when you leaned the bike over at all it would tumble.

A roling cone (or segment of one, like a cup) describes a circle with a radius as big as the height of the cone. In the case of a cup, the center of the circle is where a line through the center of the cup touches the table/ground. In the case of a motorcycle the center of the circle would be where a line through the axle touches the ground. Now, imagine a bike going 100 mph, leaned way over so the pegs are almost scraping. A line through either axle would touch the ground about a foot and a half from the bike. We know for certain that the turning circle of a bike at 100 miles per hour is more than 3 feet. a *lot* more than 3 feet.

Countersteering works because when you push on the bar, it leans the bike over, and when the bike leans over, the steering geometry turns the front wheel in the appropriate direction. That is caused by the trail. just to be pedantic, the trail is the distance between the contact point of the tire and where a line through the steering head touches the ground. the contact point of the tire is behind the line through the head tube, so when you lean a bike over, the wheel turns in the same direction. Try it on a bicycle sometime. Hold the bicycle by the seat, vertical, on a flat surface. Now, lean the bike to one side or the other. The wheel points in the direction you're leaning the bike. Now push down (through the centerline of the bike) on the seat and lean the bike, the wheel turns less, but still turns.

When you put a motorcycle into a turn, centripital force is the same as pushing down on the seat, preventing the wheel from just flopping over and tossing the rider off.

When you push on the right bar, the front wheel turns to the left for a very very very small time, so small you can't feel it unless you're going slowly, and then all of this is more obvious. but at non parking lot speeds the wheel turns the left, putting the contact patches a very tiny amount to the left of the line of motion of the bike , or more accurately, to the left of the line inertia wants to take the bike. this leans the bike to the right. When the bike is leaned to the right, the steering geometry takes over and puts the front wheel so the contact patches are in line with the center of inertia. I don't know if "center of inertia" is a real phrase, but I mean the line described by the center of mass of the bike and the combined forces of gravity and centripital force.

To a lot of people it *feels* like when you push on the right bar, the wheel turns left, but that's just because your body is made up of flexible things like flesh and cartalidge, and our joints are flexible and move when we do things. Also, I have seen many people push on the right bar, and at the same time move their torso to the left, which feels a lot like the wheel moving to the left if you don't know you're moving your torso.

I'm going with Tim's idea that it's probably a not quite symetrical riding position causing the bike to turn left, and not some wierd fan effect or camber in the road. The camber in the road would make the bike turn right too, because gravity wants the bike to turn right, and when the tires are on a slant like the camber of the road, the center of gravity is to the *right* of the contact patches, not left.