My next question: Swaying on a metal bridge.
I'm still "stabilizing" from the previous question . . .
This is another interesting one. I don't recall seeing any objective testing/reports about this, but I agree with the Brucey and upflying.
Tires, and the way they contact, and react to, the greatly reduced surface of the open grates (there's only the upper edges, which in total is probably down around ten percent of the tire's normal contact area), are probably the most significant factors. Others might be alignment, weight distribution, the distance between wheels (front to back and side to side) in relation to the pattern of the grate, as well as the size and shape of the grate openings, and whether or not they are all perfectly in line, and level, with each other.
The design of the tire tread, and the tire body, probably are most influential. As the others have mentioned, the longitudinal tire grooves (the ones in line with tire) would tend to follow the narrow upper edge of the grating that runs the length of the bridge. Small variations in the grating's straightness and height could cause one or more tires to move horizontally as it tries to follow the edge. Depending on the car's suspension, height, weight, and even speed, this could set up a rocking or side-to-side motion.
Also, not all bridge grates are built the same so if it is a reaction between the tires and/or the car and the grate, the same car might react differently on bridges with different grates designs (size, shape).
Someone on another forum mentioned that the rocking or side-to-side effect is greater the slower the car is moving. I haven't tried this. Also, if it is the way the tire tread follows the narrow edge of the grate, I wonder if higher tire pressure would reduce the effect.
It's not something that's caused me too much concern, although I can appreciate the probably magnified effect with a two-wheel vehicle. (Reminds me of the earthquake we had here last year -- I was standing on the concrete basement floor, and I could feel my feet moving side to side while I, that is, my head, was still. Weird, and scary, to say the least.)