They will result in some drag because their bearings are not totally frictionless. But wheel drag will be negligible next to the thrust of the engines, or the aerodynamic drag on the aircraft resulting from forward motion. So the wheels will have little effect whether it is rolling on the treadmill or a concrete runway.
The rated speed of the tires are a concern. Airplane tires, like car tires, have a rated speed. Putting the plane on a treadmill will cause them to roll twice as fast as normal and likely exceed rated tire speed. I don't know how long they will last and whether they will survive one complete take off run. But I don't think this kind of detail is what the original puzzle was getting at. The original puzzle was about pulling the leg of people who don't much about how aerodynamic flight work in principle.
The rated speed of the tires are a concern. Airplane tires, like car tires, have a rated speed. Putting the plane on a treadmill will cause them to roll twice as fast as normal and likely exceed rated tire speed. I don't know how long they will last and whether they will survive one complete take off run. But I don't think this kind of detail is what the original puzzle was getting at. The original puzzle was about pulling the leg of people who don't much about how aerodynamic flight work in principle.
