How about a seaplane on a river with a really strong current going in the opposite direction. How easy will it be for the seaplane to take off? How much more power does the plane need to overcome the river current? Any seaplane pilots out there to give a definitive answer and put this whole matter to rest?
It's true that the plane on a tarmac needs some way to thrust it forward. Whether with a propeller or jet engine, it doesn't really matter. The thrust moves the plane on a regular tarmac. It can roll, like on wheels, or it can slide/skid, like on pontoons. Either way, in normal circumstances, the plane moves forward.
As it moves forward, with constant thrust, we get constant acceleration so that we go from zero speed to a critical speed that allows the plane to take off.
We all agree on that, I think. So on to the controversy with the conveyor belt.
Now let's say we have a thrust that normally allows for an acceleration of 1 m/s^2. Starting from rest, in 1 second, the plane would have traveled 0.5 meters (that's from x = x0 + v0t + (1/2)at^2). The conveyor belt, in that time, also travels 0.5 meters in the opposite direction (say to the right).
Result: To someone standing on the tarmac, the plane is in the same position it started with and has not moved. To someone standing on the conveyor moving to the right, the plane just moved 0.5 meters to the left.
After the next second, the plane would have normally moved a total of 2 meters. But so did the conveyor. Again, to an observer on the tarmac, the plane still has not moved; to an observer on the conveyor, the plane moved 2 meters to the left, with an instantaneous speed of 2 m/s. (That's from v = v0 + at.)
So, depending on who's doing the observing, the plane is either moving or it's not.
The key then is the air flow around the plane. On a still day, an observer on the tarmac will see a wind speed of zero. To a guy on the conveyor belt moving to the right, the wind speed (after 2 seconds) will be 2 m/s to the left.
What about the plane? 2 seconds after we started the exercise:
To an observer on the tarmac, the plane is not moving. The wind is also not moving. So the plane sees no motion of the wind.
To an observer on the conveyor belt, the plane is moving to the left at 2 m/s. The wind is also moving to the left 2 m/s. Since the plane and the wind are moving with the same speed, in the same direction, then an observer on the plane sees no motion of the wind.
We can keep incrementing time, we can change the values of the acceleration, and we'll still get the same result. There is no relative motion between the plane and the wind.
If there is no wind, as far as the plane is concerned, there is no lift. No lift, no takeoff.
With the MythBuster guys, the "conveyor belt" did not match the speed of the plane. What they should have done, to approximate the hypothetical, is to have the "conveyor belt" - which looked like just a very long piece of cloth - hooked up to a similar plane with the same engine as the test plane, but going in the opposite direction. Then, with the equal thrust, one can probably get similar accelerations. That would have been far more convincing to me than using a truck and a plane.
It's true that the plane on a tarmac needs some way to thrust it forward. Whether with a propeller or jet engine, it doesn't really matter. The thrust moves the plane on a regular tarmac. It can roll, like on wheels, or it can slide/skid, like on pontoons. Either way, in normal circumstances, the plane moves forward.
As it moves forward, with constant thrust, we get constant acceleration so that we go from zero speed to a critical speed that allows the plane to take off.
We all agree on that, I think. So on to the controversy with the conveyor belt.
Now let's say we have a thrust that normally allows for an acceleration of 1 m/s^2. Starting from rest, in 1 second, the plane would have traveled 0.5 meters (that's from x = x0 + v0t + (1/2)at^2). The conveyor belt, in that time, also travels 0.5 meters in the opposite direction (say to the right).
Result: To someone standing on the tarmac, the plane is in the same position it started with and has not moved. To someone standing on the conveyor moving to the right, the plane just moved 0.5 meters to the left.
After the next second, the plane would have normally moved a total of 2 meters. But so did the conveyor. Again, to an observer on the tarmac, the plane still has not moved; to an observer on the conveyor, the plane moved 2 meters to the left, with an instantaneous speed of 2 m/s. (That's from v = v0 + at.)
So, depending on who's doing the observing, the plane is either moving or it's not.
The key then is the air flow around the plane. On a still day, an observer on the tarmac will see a wind speed of zero. To a guy on the conveyor belt moving to the right, the wind speed (after 2 seconds) will be 2 m/s to the left.
What about the plane? 2 seconds after we started the exercise:
To an observer on the tarmac, the plane is not moving. The wind is also not moving. So the plane sees no motion of the wind.
To an observer on the conveyor belt, the plane is moving to the left at 2 m/s. The wind is also moving to the left 2 m/s. Since the plane and the wind are moving with the same speed, in the same direction, then an observer on the plane sees no motion of the wind.
We can keep incrementing time, we can change the values of the acceleration, and we'll still get the same result. There is no relative motion between the plane and the wind.
If there is no wind, as far as the plane is concerned, there is no lift. No lift, no takeoff.
With the MythBuster guys, the "conveyor belt" did not match the speed of the plane. What they should have done, to approximate the hypothetical, is to have the "conveyor belt" - which looked like just a very long piece of cloth - hooked up to a similar plane with the same engine as the test plane, but going in the opposite direction. Then, with the equal thrust, one can probably get similar accelerations. That would have been far more convincing to me than using a truck and a plane.
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