Word. 
Oh, God, for the first time in this thread I am truly laughing! 
Thank-you, you two!!
You are just as inconclusive as you claim Cecil to be, to determine that friction of the wheel bearings will provide enough force against the plane to keep it from taking off.
It is absolutely feasible and probably true that there are engines stong enough and ball bearings efficient enough that a plane will still obtain enough air speed to take off on a runway that is moving twice as fast against the plane as the plane is moving through the air.
I agree with a couple of the other posts when I say: Sorry, Cecil, but this plane’s going no where.
I have an Associates in Aviation Maintenance Technology, as far as credibility goes.
Let’s look at Cecil’s answer:
First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt–if the conveyor moves backward at the same rate that the car’s wheels rotate forward, the net result is that the car remains stationary.
An aircraft in the same situation, they figure, would stay planted on the ground, since there’d be no air rushing over the wings to give it lift. But of course cars and planes don’t work the same way. A car’s wheels are its means of propulsion–they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane’s wheels aren’t motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing).
This mostly looks good… The statements about lift are the problem. We’ll see why.
What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground–and more importantly the air–regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane’s wheels spin madly.
Here’s where we run in to trouble. Four forces act on an aircraft: lift, which overcomes gravity, and thrust, which overcomes drag.
http://library.thinkquest.org/2819/forces.htm
Forward airspeed indirectly enables the aircraft to take off (and to continue to fly once airborne). Thrust is provided, yes, by the powerplant and propeller. But in our model the aircraft is producing thrust but is not gaining forward airspeed. And what actually enables the plane to gain altitude is lift, which requires forward airspeed.
Lift is generated by the relative wind (motion of air in relation to the aircraft) passing over the wing, which is shaped like a venturi
on its upper surface. As the air passes over this surface it must increase its velocity, thereby decreasing pressure above the wing, in accordance with Bernoulli’s principle.
http://library.thinkquest.org/27948/bernoulli.html
It is this difference in pressure (low pressure above and high pressure below an aircraft wing) that generates lift and causes an airplane to climb. This same principle generates lift in a helicopter’s main rotor; hence, helicopters are often referred to as “rotary-wing aircraft”.
In most applications, the sole purpose of the powerplant and propeller is to provide thrust, where lift is provided solely by the relative wind acting on the surfaces of the wings. In the thought experiment, we concede that the aircraft has no forward airspeed, quite a bit of wheel speed, and that somehow it is still able to take off. But without airspeed, no air is moving over the wings to provide lift. Without lift, our aircraft is an extremely expensive sidewalk ornament.
Because if all we needed was the thrust (not lift!) produced by the engine, then as has been mentioned in some other posts, a pilot could pull his plane out of the hangar, set his brakes, “clear prop!”, start her up, and take off from position. Obviously this is not the case; an aircraft taxis to the runway and must gain a certain forward airspeed (it’s even marked on the instruments!) before the wings generate enough lift to take off.
Earlier I mention that this is the absolute reality in most applications. Take a look at the Mythbusters answer to this question.
http://mythbustersresults.com/episode97
Sorry, but their conclusions are also wrong, and their experiment is flawed.
An aircraft’s propeller is also a type of rotary wing and its thrust is provided in the same manner that a wing provides lift (the Bernoulli principle). If you ever have a chance, look down a propeller from tip to root. Then look down the wing from tip to fuselage; it’s the same shape (although the prop’s angle varies to compensate for the additional air that the tip passes through in comparison with the root).
Your average single-reciprocating-engine, propeller-driven Cessna, Piper, Mooney, or what-have-you will generally weigh between 1000 and 2000 pounds. A propeller can certainly roll this much weight on wheels or pull this much weight through the air, but does not provide the amount of lift necessary to “pick the plane up” as a helicopter’s main rotor does.
But anyone who’s been to an airshow has probably seen an aircraft “hang on its prop”.
Well sure, it’s possible. If the force exerted by gravity (the weight of the aircraft) is less than the lift being generated (in this case, by the propeller), then upward acceleration is achieved. The aircraft in the link above, chances are, is a stunt or light-sport aircraft (exceptionally light) with a high-performance engine (enhanced thrust). But note that this aircraft is already airborne, and that the pilot had to angle it perpendicular to the ground so that the prop’s thrust would be vectored completely opposite to gravity’s pull (unlike the aircraft in our thought experiment).
The problem with the MythBusters conclusion is that they used a 400-lb ultralight aircraft (significantly less than typical lift is needed) and that the “conveyor belt” still allowed the aircraft to gain forward airspeed. And plenty of it, as you can see in the video, which makes their experiment unacceptable as a solution to this riddle.
But believe this: The plane takes off.
— Cecil Adams
My apologies, Cecil, but I must respectfully disagree. 
- Skyler Hart
No, it’s a perfectly acceptable solution. The whole point of the experiment was to see if the aircraft would gain forward speed. And it did, thus allowing the wings to generate lift.
When this question came up, I argued as you do: that the treadmill would not allow the aircraft to move forward, and thus there would be no lift. But I was operating on a false assumption: that the treadmill could keep the aircraft from moving forward. It can’t. Unlike a car, there is no relationship between the thrust being generated and the landing gear. The wheels do not transmit energy to the treadmill.
Why not? What exactly is stopping the plane from moving forward due to the engines throwing air backwards? The wheels on the treadmill rotate faster than they would if the plane was on solid ground, but that is the only difference from a normal takeoff.
No it’s not. Lift is provided by the air hitting the underside of the wing, in the same way as when you put your hand out a car window flat then tilt it slightly upwards. The Bernoulli theory demands that the air rushing over the top of the wing move faster than that below the wing, ie that the air “knows” that it needs to move faster over the longer distance over the top of the wing. Obviously it doesn’t do that.
Cite from NASA site.
I believe an image macro is in order:
The wheel speed is irrelevant. The plane could be on skids scooting along the ground and it’ll still take off. The Mythbusters test was conclusive. I don’t see why we’re debating this any more. I was in the ‘the plane won’t take off’ camp until I saw the video and it clicked for me. Now I can’t unsee it.
Not goes: gone.
Can anybody tell me why this zombie is walking again? Have I missed something?
I’ve had it with these motherfucking zombies on this motherfucking plane!
No one is (or should be) suggesting that a plane can take off without forward air speed (or, in the absence of that, air directed backward at sufficient velocity). The question is whether the plane will have forward air speed given the conveyor belt beneath it.
You assume prima facie that the plane will have no air speed. Everyone else – Mythbusters included – say “wait a minute, who said the plane wouldn’t move relative to the ground? Look here, the physics says it will.”
So why are the experiments invalid? They show that the plane will have airspeed – and as you admit, a plane with airspeed will take off. So what’s the problem?
Powers &8^]
I suppose I should repost this once again, because it’s easier than referring back to the older post, and I’ve also gotten a lot of mileage out of it already.
For reference: In case you didn’t know, Cecil has two columns on this subject: An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off? (03-Feb-2006) and “A plane is standing on a runway. . .” No, it’s not. Here’s why. (03-Mar-2006)
Now, with this particular problem, you have to be aware of a couple things. First is the physics: In order to take off, the plane requires an airflow over the wing, which means the problem reduces to: Does the plane move with respect to the air around it? Next, in order to prevent the plane from taking off, the treadmill has to stop the plane from moving with respect to the air around it. Preventing motion takes force. That means the problem reduces to: Can and does the treadmill transmit enough force to the plane to prevent it from moving with respect to the air around it?
Second is the semantics: there are different wordings of the problem and different assumptions that can be made about how it’s set up. Some wordings refer to the speed of the plane, some to the plane’s wheels. Speeds can be measured relative to different objects: relative to the treadmill, relative to the ground, relative to the air. What type of plane are we talking about, and what are the limitations of the system? Different people can and do make different assumptions about what the problem means, and that’s perfectly fine.
But–and here’s the real key to the problem–when people argue about what the “answer” to this problem is, it’s usually not because one person is right and one is wrong, it’s because people start with different assumptions about the question, and too often don’t bother to state what those assumptions are. So what looks like a physics question becomes a comedy-of-errors semantics question. So if you disagree with someone else about the “answer” to this problem, it’s usually because your assumptions are different. It’s not that they’re “wrong,” or you’re “wrong,” it’s just that you each have differnt assumptions. Asumptions, assumptions, assumptions, assumptions, assumptions. Assumptions. Check them.
Now, on to the analysis:
There are plenty of answers to this question, because the key to the question is the wording and your interpretation and what you assume from the beginning. And these answers can all be correct, but the assumptions are the key. Let’s start off at the top:
A. Suppose we actually built a treadmill and put a 747 on it, and had the treadmill match the speed of the plane. Would the 747 take off? If the treadmill matches the plane fuselage speed with respect to the ground, then yes. The treadmill simply accelerates in the opposite direction that the plane does; the plane moves in one direction relative to the ground and the treadmill moves in the other. The wheels wind up rotating twice as fast as they normally would, but the plane will take off, leaving a treadmill behind that’s rotating in the opposite direction.
B. Let’s reword the question. Suppose we actually built a treadmill and put a 747 on it, and had the treadmill match the speed of the wheels. Would the 747 take off? Depends. If “exactly matching the speed of the wheels” means that the treadmill matches the hub speed of the wheels (the speed of the wheel center, which is the same as the fuselage speed), then yes. Just like in the last scenario, the treadmill accelerates in the opposite direction that the plane does, the wheels rotate twice as fast as they normally would, and the plane takes off.
C. But that problem is trivial. Let’s assume that “exactly matching the speed of the wheels” means “matching the outer diameter surface velocity”–the velocity with respect to the hub, or the “speedometer” speed. Would the 747 take off? Almost certainly it would, but only because we can’t build a treadmill capable of keeping up with the thrust transmitted to the plane by the engines, and not enough force is transmitted to the plane to keep the speeds matched–in other words, we violate the *spirit *of the question, because the treadmill *isn’t *matching the wheel velocity.
D. OK, that’s stupid. It’s a thought experiment. Posit a magic treadmill that can accelerate as fast as desired. And it doesn’t break. It’s possible the wheels will skid on the treadmill, because the friction won’t be able to transmit the necessary force. In that case, we again violate the spirit of the question, and–
E. It’s a thought experiment, smart guy. Assume there’s enough friction to rotate the tires. All right; that’s quite possible in the real world. When the engine lights off, the treadmill will accelerate until the force transmitted through the wheel hub to the plane exactly balances the thrust. The plane would stay stationary as the thrust power was dissipated in the wheel bearings (as friction), tires (hysteresis), and in accelerating the wheel to ever-increasing speeds. Since all the power is dissipated in the wheels, eventually either the bearings would overheat, the tires would blow, or the wheel would rip itself apart due to inertial forces. After that, the plane crashes and burns. Then you’ve destroyed a rather expensive magic treadmill.
F. Thought experiment, I said! Let’s posit ultra-strong and heat resistant tires. All right. It turns out the real world is rather complicated. If the treadmill is a long, runway-sized treadmill, it will eventually, running thousands of miles an hour, pull in air at high enough velocity that the plane will lift off at zero ground speed (but substantial air speed). However, now you’re running into trans-sonic compressibility effects…
G. No speed of sound effects! And assume magic air that doesn’t become entrained with the treadmill motion. And don’t throw in any other crazy stuff, either. In that case, the treadmill speeds up (still balancing the plane’s thrust force) and the plane stays in place until the engines run out of fuel. I imagine the treadmill goes pretty fast at that point. The plane stays put until the fuel’s gone, at which point the magic treadmill whips it backwards.
H. Backwards, shmackwards. Now we’re getting somewhere. What if we had infinite fuel? Then the wheels keep going until they’re running near light speed, and relativistic effects take over. The wheels get smaller, I suppose…
I. None of that! No relativity-- Hey, wait a minute. Back up. Suppose we have zero friction bearings and tires. That doesn’t seem so unreasonable for a thought experiment. Well, zero friction tires would mean they just skid on the runway, since nothing turns them. So the plane will take off, tires motionless, and the treadmill won’t move.
J. Hey! Quit it! I already said the tires don’t skid! Sorry. Just friction on the tire/treadmill interface, then, but none in the bearing or sidewall. With zero friction in the bearing, you lose the friction coupling between the treadmill and the jet. But you still have inertial coupling. The wheels accelerate, and that acceleration takes force. Now you have the same case as you do with friction. The jet stays stationary as the wheel accelerates; the wheel just accelerates faster.
K. Well, how about the other way around? Massless wheels, but you still have friction? Here it starts to get complex: friction is a funny thing and hard to extrapolate. As you accelerate the wheels, the bearings will change shape and heat up and so forth, so the “friction coefficient” goes up with increasing speed, meaning it takes more and more force to keep the wheels rotating. In that the case, then when the engines start, the treadmill accelerates up to whatever speed will give enough friction to balance the thrust. The plane stays stationary, wheels rotating at some reasonably constant (but large) velocity, dissapating the engine power through friction, and the bearings become incandescently hot.
L. But I want massless wheels and a constant coefficient of friction. Indestructable wheels, remember? None of this hand-waving “it’s gonna get bigger” crap. OK. It is a thought experiment, and determining the friction coefficient requires a pretty substantial extrapolation of “real” bearing behavior. With a limited “friction coefficient,” only a limited amount of energy can be absorbed by the friction. When the engine lights off, the treadmill instantly accelerates to infinite speed. It’s never able to counteract the thrust force, and thus plane takes off, leaving the infinite-speed treadmill behind.
M. Ah. OK, one last step. What if we had no bearing friction and massless tires? What happens then? Pretty much the same thing. There’s now no energy losses in the wheels and tires, no coupling between the treadmill and the plane–no bearing friction, no inertial effects, no air resistance, and no way for the treadmill to affect the plane’s motion. The same thing would happen as above, with the plane taking off, leaving the infinite-speed treadmill behind. However, there’s one added interesting thing: This is now an unstable runaway system. There’s no resistance to treadmill motion, and a positive feedback circuit. Imagine the poor mechanic who bumps a wheel, setting it in motion. A very slight roll by the tire is sensed, and the treadmill luches forward. The tire goes faster, the treadmill goes faster, the tire goes faster… Since we’ve posited an instantly-accelerating treadmill and no relativity and no air resistance and no wheel inertia, the treadmill goes from zero to infinity in no time flat. Try to keep your balance on that.
Pick your scenario–they’re all correct.
Kill me now.
For the benefit of poster #164:
There was one way in which the plane could be kept stationary; only if we presume a magical treadmill which, because of frictional effects in the wheels, will go as fast as necessary to overcome the thrust of the plane. Reason it needs to be “magical” is because the treadmill will rather quickly be forced to increase its speed into Ludicrous territory, where any normal treadmill will blow apart from the stresses. [I believe Cecil addressed this in a followup column] I, like you, due mainly to ambiguous & unclear premises by those who put forth the problem, thought that it was telling me the plane was taking off while stationary, but that’s not what will happen in the normal world with “normal” treadmills.
Edit: I see Zut beat me to it. Thank you Lord.
Every time this comes up I think of Eve 6
I want to put my little
Plane on a treadmill
Wheels spin around 'til they’re blown to oblivion?
Into the blue
Is what it will do…
You’re welcome, my son.
I realize this is probably pointless but to those who wish to argue:
You are not a genius who has reasoned the obvious solution to the problem and need to educate the moronic masses. Everything you’ve thought about the problem (and more) has been considered. There is no obvious solution.
Before you give your opinion, read zut’s post. If you don’t fully understand it read it again until you do, or ask questions until you can. If you still feel the need to argue you haven’t understood the post.
For zut’s post is the Word, and His Word is Good.
SkylerHart said:
I have bolded the problem with your statement. You are assuming the bolded statement, that the airplane does not have forward airspeed. Cecil did not make that assumption. Instead, Cecil looked at the physics and found that the treadmill would not keep the plane from moving, just make the wheels spin faster.
Different assumptions, different answers.
Once again highlighted for clarity. You may concede that, but not everyone does. Cecil did not. Different assumption, different answer.
No, they conducted an experiment to see if the treadmill could prevent the plane from moving forward, not to see if the plane could take off when held stationary.
If you want to hold the plane stationary, tie the landing gear to the ground. Then no matter how hard the engine pulls, the plane will not roll forward.
I’m reluctant to flog this old bird, but I’m a bit confused about one point.
Nearly everyone seems to be assuming that, if the plane has no groundspeed (relative to the real ground, not the treadmill,) then it has no airspeed. It seems to me that a stationary engine, whether prop or jet, will create a tremendous area of moving air around itself. That moving air has to be generating lift on the stationary (relative to the ground) wings. The zone of airspeed won’t be very wide, so a long-winged plane is unlikely to leave the ground. Would a short-winged sport plane make it?
Would it be enough to lift the plane? I don’t know. Irishman proposes tying the wheels to the ground, but that’s only halfway to a good test. The plane would crash on its nose. If you want to know if a plane with no groundspeed will get off the ground, tether it from its center (center of effort? center of drag?) on a horizontal axis. You’d want to allow the pilot to control the angle of attack if it lifts. Again, you don’t want to crash the thing. :eek:
I feel a little foolish stepping into the ring with this zombie, but I felt this detail had been overlooked.
This is only true if the engine is a propeller which is in front of the wings. For obvious reasons, you don’t put jet engine exhausts in front of the wings. And not all propellers are made to “pull” the airplane; some are set to “push” the plane, and thus don’t push wind over the wings.
Having said that, I cannot believe that the wash from a plane’s prop(s) would provide anything like sufficient lifting force. And IIRC, if you do a good search through the various threads on this question from the last two or three years, someone will have addressed exactly this point. Good luck finding it. 
Actually, both pusher props and jets would entrain a certain amount of flow over the wings. Not enough, realistically, to give decent lift, but this crazy business left realism behind long ago.