We touched the tire at perhaps 1mph, probably less. The dock is wood. I think there would have been nothing to do if the tire wasn't there. It's more of a problem than a help.
Pool noodles, as recommended elsewhere in this thread, are a better and also cheap solution.
Those pool noodles would not work at my location. My dock already is fully lined with marine dock bumper edging. The edging is fine for very light hits (as a pool noodle would be), but would provide no protection when the surf gets up. Here in HI with the UV being in the extreme category nearly every day the pool noodle would being falling apart within two months, and then dropping into the water and causing pollution. Now I would be equal to the guy using old boggie boards as fenders (as I previously posted). Note the poole noodles and insides of cheap boogie boards are made out of the same closed cell foam.
At my dock there are two large catamarans (40 - 50 feet). One uses about $2,000 dollars worth of fenders tied end to end to protect his cat. The other cat uses old tires covered with carpet. The gel coat of both cats looks great. Now which way is the best way to go? If the tires work, I would save the $2,000. And I would assume, due to the constant wear the fenders get, the fenders will need replaceing every 5 years (these cats are at an end pier so they must be tied tight to the dock).