for the 5 millionth time, the thrust from the engines.
I predict this will satisfy all readers and this thread will quickly die.
Propeller. 
But yeah, you’re right.
in the ideal world the plane’s wheel bearings have no drag or friction, and the tires have no rolling resistance. in which case the wheels are irrelevant. the treadmill could be going eleventy billion miles per hour and it would have no effect on the plane.
This is the pattern for a lot of thought experiments. You start from some set of circumstances which naively seem possible, and ask what would happen. You follow through on that, and reach a contradiction. Therefore, you conclude that that that set of circumstances isn’t possible after all, even though it seemed like it at first.
And then you stop. You don’t keep on saying “but what if it happens anyway, even though it’s impossible?”. Once you ask that question, you’re talking about magic, not science, and literally any answer is possible. You can literally logically conclude “then the sky turns green, and Santa Clause takes back all of the presents he’s given away over the years”.
…sigh… I feel like at least one of you could actually answer the question but maybe you are unsure yourselves. There could be a real-world experiment where the treadmill always moves faster than the plane’s wheels. For example, in the real world the plane has limited thrust, so the speed of treadmill is always at the plane’s maximum ground speed + 1 ft/sec. How does the wheels’ axles move forward referenced to ground? Even if there is zero rolling resistance, infinite friction between the wheel and belt what force prevents the plane from moving forward? I can’t think of any, but at the same time it doesn’t make mechanical sense to me that the plane, with all of its weight on the wheels, the wheels have to turn for the plane to move forward, and they do, but for all the distance 1 revolution covers, the new starting point for the next revolution is actually behind this initial starting point (w.r.t. ground) due to the belt moving backward at a higher speed.
Just saying the plane moves due to thrust from the jets is not explaining the above. Like me wearing roller skates on a treadmill, if my wheels are not allowed to turn as fast as the treadmill is moving, I’d quickly fall off the back, regardless of my arms (the jets) pulling myself forward.
Yeah, imagine the roller skates have brakes. They can’t turn as fast as they need to to keep up with the treadmill. But if you’re pulling yourself forward by a rope attached to the wall, you’ll still move forward, and the wheels will just skid. It will require a little more force to pull yourself forward, but not an infinite or insurmountable force.
If that is the case, then the wheels will skid until the plane either lifts off, or they explode.
Forget about the wheels and treadmill, they do not act of the plane. The plane propels itself through the air without friction with the ground like a boat in water.
The wheels only support the plane off the ground long enough to achieve enough lift to take-off.
we’ve answered it multiple times. You not liking the answer you were given doesn’t change that.
the force pushing the plane forward (thrust) is far greater than whatever force the treadmill can apply to the wheels to try to hold the plane still.
The plane doesn’t have a maximum groundspeed. It has a maximum airspeed. And if you set the treadmill to a speed greater than the plane’s maximum airspeed, then when the plane reaches that airspeed, the wheels are turning twice as fast.
Cecil answered this question as well:
Alright, this is what I would imagine would happen. I feel like I’m getting somewhere with understanding this. The skidding part is left out of the common explanations I’ve seen.
But if there is no slippage allowed, the plane would never move forward, right? The force that is enforcing the no slippage policy obviously would be much greater than the plane’s thrust.
Wait, why would the wheels need to travel @ 2x the treadmill speed for the axle to remain stationary? If the “treadmill” was just a copy of the wheel rotating in the opposite direction, they would rotate at the same speed to keep the axle stationary, right? Like a 1:1 gear?
Sure.
But that force doesn’t exist. So the plane still takes off.
Because the axle isn’t remaining stationary. The plane is moving forward, the treadmill moving backward, the wheels are spinning faster.
Again, I’m aware this topic has been beat to death, and I swear I’m not trying to assert that I’m right, I’m genuinely trying to understand where my logic is wrong. Sorry that it’s taking so much effort.
Can you describe how you think this works? The plane starts, so the wheels are moving at 0.001 m/s. So, the treadmill immediately moves to 0.001 m/s in the other direction, causing the wheels to move at 0.002 m/s. Now what? Does it go to infinity immediately?
Did you see the last paragraph of Cecil’s explanation where he says that A cannot equal A+5?
Are you positing a world where there are frictionless bearings but treadmill surfaces with infinite friction?
wheels convert rotational/angular velocity to linear velocity (and vice versa.) All you are doing by increasing the linear velocity they’re experiencing (by speeding up the ground surface e.g. treadmill) is increasing their angular velocity (e.g. making them spin faster.) that doesn’t translate directly to a linear force capable of counteracting the engine thrust.
Toys on a real treadmill have been mentioned before, but I think thinking about that is the best way to understand this intuitively.
If you put a toy car on a treadmill with your finger against the back of it and set the treadmill speed to 1 mph, the car stays in place and presses against your finger with a minimal force. Crank up the treadmill’s speed as high as you can and the car becomes no harder to hold in place. And it takes the same amount of effort in both cases to push the car forward. Your finger is the plane’s engine.