this post was submitted on 26 Jun 2024
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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)?
That’s the thing - it is not prevented from accelerating. The wheels are functionally frictionless. That’s why planes have brakes. The plane pushes on the air to move, & the treadmill could accelerate backwards until the plane’s tires explode.
so, every wheel or ball or any other kind of rolling-thing has rolling resistance, which is how we sum up the total drag on the system. A steel ball bearing on a steel plate will have a significantly lower rolling resistance than, say, a steel cube on that same plate. Tires have some- but not a lot- of rolling resistance.
You can see that in a car, just put it into neutral and watch as you slow down, even on flat ground. Plane wheels also have rolling resistance. it's just the way our world works. But it's generally ignored because it's hard to model perfectly and in any case pretty negligible relative to the amount of acceleration being put out by modern aircraft engines.
A treadmill will only push an aircraft or whatever else along, with an acceleration that is equal to, or lower, than the rolling resistance. If you try to accelerate the plane faster, it'll 'slip', and the plane will remain largely stationary- like the dishes in the tablecloth trick (if you want to try that at home... make sure the tablecloth doesn't have a hem, heh.)
But, keep in mind you're thinking about the plane relative to either the ground, or the treadmill's belt.
the plane's wings and it's engines are 'thinking' about the plane relative to the air it's moving through. It's the airspeed that generates the lift, and the engine isn't coupled to the wheels, they're just rolling along doing their thing. (aircraft engines work by taking a volume of air and accelerating it. newton's equal-and-opposite does the rest.)
Oh wow thank you. This is genuinely excellent and immensely helpful. I think this bit:
As well as this video that I found where a pilot explains how under specific but unrealistic conditions you could construct a treadmill that does indeed prevent an aeroplane from taking off,
Really helped solidify my understanding of the problem. So you end up with a situation where the wheels are going to be slipping, just like the slippage created when your hand pushes a toy car on a treadmill.
Thanks!
So, another way to think about it is with Kites.
The air flows around it the same way it would any other kind of aircraft, though they have effectively zero ground speed.
They do differ in that, being tethered, they’re pulled through the air, with the wind providing the energy to stay up.
But they’re still moving through the air, and the airfoils are inducing drag to convert some of that energy into lift.
In both cases, the important speed is relative to the air, not the ground and not the treadmill. The wheels might impart some drag while they’re on the ground, but they’re never going to impart enough to overpower the engines- 747s typically take off at about 75% of their rated take off power, which means a longer take off roll, but less wear and tear.
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.
The tricky bit is that the air within a few millimeters of the treadmill will move with the treadmill. The air slightly above that will be slightly disturbed and also move a bit in the direction of the treadmill. If you had an extremely long and extremely wide treadmill (say the length and width of a runway) it's possible that the air at the height of the propeller would be moving along with the treadmill, rather than staying still, or moving with prevailing winds.
But, even in that case, the plane could still take off. All the plane needs to do is move the body of the plane through the air at enough speed to allow the wings to start generating lift. If the air at propeller-height is moving with a treadmill that is moving at take-off speed, the plane might take off with zero forward speed relative to the non-treadmill ground. But, as long as you're not somehow preventing the propeller from moving the plane through the air, the plane will always be able to take off.
There are videos of planes taking off by themselves in high wind, and videos of VSTOL (very short take-off and landing) planes taking off and landing using only a few metres of runway.
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.
The point it occurs at is when the plane uses the air to propel itself.