You’re railing that descent, nailing every line and feeling like a world champ, when suddenly you smash a wheel into a big square-edge rock. Quite literally, you can feel the air go out of the ride.

Having spent the better part of a year installing tires at the Pep Boys in Fredericksburg, Va., I thought I knew a thing or two about how a tire is mounted to a rim. It was my first job after ...