There’s nothing wrong with Cecil’s answer, per se, but, unfortunately, it just doesn’t explain things very well.
Now, he’s clearly correct when he agrees that “the question is often worded badly, leading to confusion, arguments, etc.” But that’s part of the problem: Cecil himself doesn’t clearly state exactly what question he’s answering.
Poor Analogy
Case in point: his use of the car analogy. Cecil states: “if the conveyor moves backward at the same rate that the car’s wheels rotate forward, the net result is that the car remains stationary (my italics).” Completely true–nothing wrong with that. However, note this very important fact: in the situation described, the car’s engine is essentially doing no work. It’s providing only enough power to overcome bearing friction.
Then Cecil compares this situation to that of a plane with the engines at full thrust, and notes the different result. This shouldn’t be surprising: Of course things are different when you start with different circumstances. If the analogy were truly parallel, he’d compare the case where the car engine provides only enough power to overcome bearing friction with the case where the plane engine provides only enough power to overcome bearing friction. In that case, the plane would remain stationary, as there’s no thrust left over for acceleration.
Begging the Question
Next, Cecil simply begs the question. Remember the situation is one where “the conveyor moves backward at the same rate that the … wheels rotate forward.” In answer to this situation, Cecil baldly states the following: “Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground–and more importantly the air–regardless of how fast the conveyor belt is moving backward.” Again, not precisely wrong: the answer here depends specifilcally on the assumptions that you make. But Cecil doesn’t state his assumptions, and, more tellingly, violates the condition of the thought experiment.
It’s clear that if you interpret the condition that “the conveyor moves backward at the same rate that the… wheels rotate forward” as meaning that the conveyor speed match the speed of the exterior of the tire, the plane/car will remain stationary (like the car analogy specifically states). There are a number of reasons why this condition might not reasonably hold, but Cecil needs to state those reasons, not just ignore it with no explanation.
Ignoring Physics/Not Stating Assumptions
Finally, Cecil serves up this, calling it a paradox: “If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward… Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed.” Again, not wrong, necessarily, but it depends on your assumptions.
If you assume massless wheels and no friction, then Cecil’s analysis is correct. However, those are large assumptions, and should be stated. The fact that they’re not stated at all leads me to believe Cecil simply didn’t account for them, in which case his conclusion is misleading at best, and flat-out wrong at worst. If the plane has wheels of any mass, the treadmill will rotationally accelerate them, speeding up at a rate governed by the engine thrust. No infinite speeds required.
Conclusion
Let me sum up:
[ul][li]Not actually wrong, but:[/li][li]Piss-poor analogy[/li][li]Begging the question[/li][li]No statement of assumptions[/li][li]Violation of the conditions of the experiment[/li][li]Ignoring rotational acceleration[/li][/ul]
Did I forget anything?