Yes, the wheels are free-spinning, but not friction-free. If the treadmill could go fast enough, the wheels would experience enough friction to hold the airplane in place.
Yes, but in the original scenario, the treadmill is only going as fast backwards as the plane is going forwards.
S^G
At no constant speed would the frictional force be sufficient to do this. But if the treadmill is allowed to accelerate at will, it can produce a force that’s limited only by wheel skidding (i.e. about equal to standing on the brakes). But the acceleration required would be enormous - in a matter of seconds the wheels would be turning so fast they’d be destroyed.
Note that all this was pretty well covered by zut’s excellent summaries in old threads.
I checked at the MB fansite. Since the episode aired there are about 20 more pages of arguments. I didn’t read through them all, but there are still people arguing about it, saying they did it wrong.
Can one of you physics experts answer this?
To me, the question raised about this stunt is all about airflow over the entire span of the wings. It would sem the thrust of a propellor directly backward would not generate sufficient airflow to provide lift across the whole of the wings.
In a normal takeoff, the single propellor thrust would be sufficient to drag the plan the though the air up to a speed where air passing around the wings would be at a high enough velocity to generate lift across the whole wing.
But that doesn’t happen on the treamill. Only a very narrow portion of the wings, directly on either side of the cabin and in the “wake” of a nose-mounted propellor, will get airflow of a sufficient speed to generate lift. The outer portions of the wings will be basically sitting in still air.
Which is why it would seem to me that the experiment mght work with a multi-engine plane, say with two engines mounted to each wing, but fail with a single engine plane with a nose mounted propellor.
Yes, it does. The treadmill has no significant effect on the motion of the plane. Why would it? The plane’s wheels are not powered.
Read the extensive literature linked above.
Maybe I am visualizing this wrong? Is the episode available online?
If I were standing on solid ground next to the treadmill, would the plane be moving horizontally relative to me?
Ok, it’s time to overcome the first part of the difficulty with this: the assumption that the propellers push air over the wings and that makes the plane fly.
We will dispense with this stupidity by noting that planes can fly when PUSHED by propellers. That is, put the propeller in the back, behind the wings, and the plane STILL FLIES.
The plane flies because the action of turning the prop causes the prop to force air backward. This results in an equivalent force by the air on the prop, pushing the prop forward. The prop being connected to the plane, the whole plane moves. As it moves, air flows over and under the wings, and the effect of the forces involved in the air hitting and flowing over the wings causes the wings to be forced upward (PLEASE let’s not debate how this happens here!!!). The wings being attached to the plane, the plane lifts up too.
Yes, it would be moving relative to you.
Your post above seems to be postulating a scenario in which the engines are providing lift simply by blowing air over the wings, which is incorrect. The engines pull the plane forward regardless of what any real-world treadmill apparatus could do. This movement of the wings through the air produces lift, and the plane takes off. (And if you can postulate an ideal treadmill, I can assume ideal wheels, which will still result in the plane taking off.)
The plane flies. Get over it, people. (Not directed at you Jim, just at stubborn naysayers.)
I understand all this. The point I was trying to get to was that either the wings need to be moving through the air, or the air needs to be moving over and under the wings, to generate lift. I think everyone agrees on this.
My assumption is, and this is the point I may be visualizing incorrectly, is that putting the plane on the treadmill makes the plane horizontally motionless relative to the ground, and to the (relatively) still air in the vicinity of the plane – except for whatever air is being sucked through the propellor and flowing over the wing in the immediate vicinity of the propellor. So over most of the span of the wing, there is no airflow.
Since the plane takes off, I accept that I am getting something wrong here. What is it?
No, I am not postulating that, I’m saying that does NOT happen, except for a very small portion of the wing immediately behind the propellor, and the way I am envisioning the experimental setup leaves my scratching my head as to how the other airflow over the rest of the wings are happening.
Is the treadmill itself being towed along the ground, so the only difference between this and a normal takeoff is that the plane’s wheels are not turning? That would make sense to me from an aerodynamic viewpoint, but it would seem to be such an obvious “of couse that would work” question that it’s surprising any one would feel the need to prove it.
What you’re getting wrong is that the treadmill does not prevent the plane from moving forward. Single prop, multi-prop, pusher, puller, jet, it doesn’t matter - the plane moves forward on the treadmill.
That’s the assumption of the vast majority of those who believe the plane will not take off. This assumption is incorrect.
It is quite true that if any normal plane were held “horizontally motionless” it would not take off. But (unless you make a far-fetched assumption*) the treadmill is quite incapable of doing this.
A typical airplane’s engine can generate thrust equal to something like 10% to 20% of its weight. The force necessary to roll a plane on normal pavement (or the surface of a treadmill) is probably around 1% to 2% of its weight. Since the thrust far exceeds the force the treadmill can exert through the wheels, the plane accelerates, air flows over the wings, and it takes off.
The action of the treadmill simply means the wheels are turning faster than for a normal takeoff. The small additional resistance means the time from start to takeoff is slightly longer.
*The far-fetched assumption (not allowed by any statement of the problem I’ve yet encountered) is that the treadmill can rapidly and continuously accelerate. Assuming the wheels of the plane have some mass (as all real wheels do) the maximum force exerted on the plane by the treadmill can then be about equal to what it takes to skid the wheels. For nearly every real airplane, this is greater than the maximum engine thrust, so the plane would not move forward and thus not take off.
A big problem with this is that the wheels would quickly spin up to a rotational speed that would exceed the limits of any known material - wheels would be destroyed, no doubt badly damaging the plane as they flew apart. Which means the plane would not take off.
What Xema said,
the only way the plane doesn’t take off is if we have a constantly accelerating treadmill that accelerates to infinity or if there is a giant wall at the end of the treadmill.
Cecil also does a good job of explaining all of this (I added the wall bit).
Slowly for the cheap seats, please. I swear that this has been driving me crazy(er) since it first appeared and the consensus was that it’s obvious the plane take off. Clearly I am framing the experiment wrong in my mind, and I am still hoping for that AHAH! moment.
If I had wings, as was capable of generating enough speed for takeoff by running on the ground and reaching a velocity where lift and thrust overcame lift and drag I’d take off, correct?
Now I get on a treadmill, I walk on the treadmill, I jog on the treadmill, I sprint on the treadmill. I don’t go forward because the treadmill can match my speed. No lift and thrust, no takeoff, correct?
Is it just that a treadmill cannot be constructed that can move fast enough to overcome the forward speed of a plane?
I am really trying to understand this.
ETA: I think that’s what Xema just said.
Your legs are the source of your power which are generating speed by moving on the treadmill so to move forward on said treadmill you need to move faster than the treadmll moves.
The difference between you and the plane is that the plane isn’t powered through the wheels, it uses a propeller or a jet engine which pushes against the air. The wheels are simply there to decrease friction and they will spin as fast as they need to for the plane to move forward. If the treadmill moves 100 mph in reverse and the plane uses it’s thrusts forward at 100 mph, all that would happen is the wheels simply spin at 200mph and the plane moves forward relative to he air and takes off.
Having said that, if the other ridiculous assumption that the treadmill can continuously accelerate is what we are talking about here then the plane would accelerate up to it’s 100 mph and the wheels would follow suit. The treadmill then accelerates in reverse to match the spin of the wheels rendering the plane motionless. The main problem with this is that the wheels continuously accelerate forward because the plane wants to move forward and the treadmill continuously accelerates in reverse to match the spin of the wheels. This would continue until infinity or the wheels broke down. (noone ever has the treadmill breaking down for some reason).
That’s probably a little convoluted, but I think it’s generally right.
Thanks to everyone for their patience in this.
It’s all starting to make sense. Yes, I was seeing the conveyor belt/treadmill as continuously accelerating and I see that introduces the error. I don’t see it as a ridiculous assumption though. From a materials standpoint, it’s impossible, but I remember many math and science problems in school that were not framed any worse. The ability to match the speed of the wheels indicated to me it was “magic,” like so many items in thought problems.
So, the plane DOES move forward relative to the ground and surrounding air… does this mean the plane simply pulls itself off the front end of the treadmill, or that the treadmill is like a quarter mile or so long, or that the tradmill is being towed along the ground at approximately the same forward speed the plane would be rolling if there were no treadmill?
The problem isn’t always explained very well, and it’s only interesting if the treadmill is long enough for the plane to stay on it. What we’ve been calling a treadmill, Mythbusters called a conveyor belt, which suggests much greater length. For the full-scale experiment, they rolled out a 2000-foot-long tarp and connected one end to the trailer hitch on a pickup truck. It’s not an inifinite looping belt like most conveyors, but it did what they needed; a long, thin, moving flat surface.
Imagine you’re a worker in a car factory. You work at the very end of the assembly line, where the cars are finished and a big clamp picks them up and carries them over your head so you can inspect the bottom. But you’re a bad worker and the line is going too fast, so you want to slow it down a little. You reach up and put your hands on the bottom of the tires and start pushing backwards. What’s going to happen? The wheels will spin and you won’t slow the car down in the slightest.
Same thing with the airplane. The treadmill makes the wheels turn, but it can’t slow the plane down because what’s pushing it forward has nothing to do with the wheels.
I think an error some people may be making is that they’re envisioning a small treadmill - say, twice the length of the plane - and trying to figure out how it’s taking off.
In case it’s not clear, we’re actually talking about a treadmill long enough to provide a takeoff distance for a plane - in our hypothetical it can be arbitrarily long.
If the plane ordinarily needs a quarter-mile runway, then yes, you need to have a quarter-mile long treadmill. If you had a normal runway right next to the treadmill, with another, identical plane on it, and started both at the same time, then the two planes would stay right next to each other, and take off at the same moment. This is true no matter what the treadmill’s motion is, barring the insane-acceleration scenario.