Which is insane as it’s not that difficult to understand
I found it hard to understand because neither they nor any of the other sources I’ve seen explaining this even attempted to answer what I thought was an incredibly obvious question: at what point does this become true? A stationary aeroplane on a treadmill will obviously move with the treadmill. I assume an aeroplane moving at like 1 km/h still gets pulled backward by the treadmill. At what point does the transition occur, and what does that transition process look like? Why can’t a treadmill prevent the plane from taking off by pulling it backwards by never letting it start getting forward motion? Where does the lift come from?
I can understand how a treadmill doesn’t stop a plane that’s already moving, but how does it get lift if it is prevented from accelerating from 0 to 1 km/h of ground speed (relative to the real ground—relative to the ground it experiences, it is moving forward at the same speed as the treadmill is moving backward), since until it starts getting lift, airspeed and ground speed are surely effectively equal (wind being too small of a factor)?
The key insight is that the force a plane uses to move is independent of the ground, because planes push on the air, not the ground.
Imagine you put a ball on a treadmill and turn it on, what happens? The ball starts to spin and move with the treadmill. Now take your hand and push the ball backwards against the motion of the treadmill, and the ball easily moves in that direction. The force your hand put on the ball is exactly what planes do, since they push on something other than the ground (the treadmill) they have no problem moving, no matter how fast the treadmill is moving.
A stationary aeroplane on a treadmill will obviously move with the treadmill
What do you mean? The plane has its parking brakes on and moves with the treadmill surface? If you don’t have parking brakes engaged and start up a treadmill under a plane, the plane’s wheels will spin and the plane will stay pretty much in one place. Because the wheels are free to spin, initially that’s all that will happen. The inertia of the plane will keep it in place while the wheels spin. Over time, the plane will start to drift in the direction the treadmill is moving, but it will never move as fast as the treadmill because there’s also friction from the air, and that’s going to be a much bigger factor.
I assume an aeroplane moving at like 1 km/h still gets pulled backward by the treadmill.
Moving at 1 km/h relative to what? The surface of the treadmill or the “world frame”? A plane on a moving treadmill will be pulled by the treadmill – there will be friction in the wheels, but it will also feel a force from the air. As soon as the pilot fires up the engine, the force from the engine will be much higher than any tiny amount of friction in the wheels from the treadmill.
but how does it get lift if it is prevented from accelerating from 0 to 1 km/h of ground speed
It isn’t prevented from accelerating from 0 to 1 km/h of ground speed. The wheels are spinning furiously, but they’re relatively frictionless. If the pilot didn’t start up the propeller, the plane would start to move in the direction the treadmill is pulling, but would never quite reach the speed of the treadmill due to air resistance. But, as soon as the pilot fires up the propeller, it works basically as normal. A little bit of the air will be moving backwards due to the treadmill, but most of the air will still be relatively stationary, so it’s easy to move the plane through the air quicker and quicker until it reaches take-off speed.
I found it hard to understand because neither they nor any of the other sources I’ve seen explaining this even attempted to answer what I thought was an incredibly obvious question: at what point does this become true? A stationary aeroplane on a treadmill will obviously move with the treadmill. I assume an aeroplane moving at like 1 km/h still gets pulled backward by the treadmill. At what point does the transition occur, and what does that transition process look like? Why can’t a treadmill prevent the plane from taking off by pulling it backwards by never letting it start getting forward motion? Where does the lift come from?
I can understand how a treadmill doesn’t stop a plane that’s already moving, but how does it get lift if it is prevented from accelerating from 0 to 1 km/h of ground speed (relative to the real ground—relative to the ground it experiences, it is moving forward at the same speed as the treadmill is moving backward), since until it starts getting lift, airspeed and ground speed are surely effectively equal (wind being too small of a factor)?
The key insight is that the force a plane uses to move is independent of the ground, because planes push on the air, not the ground.
Imagine you put a ball on a treadmill and turn it on, what happens? The ball starts to spin and move with the treadmill. Now take your hand and push the ball backwards against the motion of the treadmill, and the ball easily moves in that direction. The force your hand put on the ball is exactly what planes do, since they push on something other than the ground (the treadmill) they have no problem moving, no matter how fast the treadmill is moving.
It’s always true.
What do you mean? The plane has its parking brakes on and moves with the treadmill surface? If you don’t have parking brakes engaged and start up a treadmill under a plane, the plane’s wheels will spin and the plane will stay pretty much in one place. Because the wheels are free to spin, initially that’s all that will happen. The inertia of the plane will keep it in place while the wheels spin. Over time, the plane will start to drift in the direction the treadmill is moving, but it will never move as fast as the treadmill because there’s also friction from the air, and that’s going to be a much bigger factor.
Moving at 1 km/h relative to what? The surface of the treadmill or the “world frame”? A plane on a moving treadmill will be pulled by the treadmill – there will be friction in the wheels, but it will also feel a force from the air. As soon as the pilot fires up the engine, the force from the engine will be much higher than any tiny amount of friction in the wheels from the treadmill.
It isn’t prevented from accelerating from 0 to 1 km/h of ground speed. The wheels are spinning furiously, but they’re relatively frictionless. If the pilot didn’t start up the propeller, the plane would start to move in the direction the treadmill is pulling, but would never quite reach the speed of the treadmill due to air resistance. But, as soon as the pilot fires up the propeller, it works basically as normal. A little bit of the air will be moving backwards due to the treadmill, but most of the air will still be relatively stationary, so it’s easy to move the plane through the air quicker and quicker until it reaches take-off speed.