The only real question is about the wording of the original question. It could go either way but it needs to be specified…Does to plane move relative to the air or not?
If it does move relative to the air it will take off, but then the conveyor belt is just a red herring (as is wheel rotation speed, conveyor speed, direction) and doesn’t matter to the question. The plane might as well be on a regular runway and pulling itself along normally with it’s engines.
If it does not move relative to the air then it does not take off and might as well be tethered in place.
Seems pretty simple. There is no lift unless there is movement relative to the air. Lift requires the overall upward force (or lack thereof) of air on the wing. Alternatively you can tilt the engines relative to the ground to provide that force. They have to be pushing up againstthe ground not along the runway.
Put your hand out the car window when you drive. We’ve mostly all done it. You are moving forward with respect to the air going the other way and you can feel the lift. Now put your car on blocks. Gun the engine all you want and stick your hand out the window. Is there lift? -No.
The only question is whether or not you are moving forward through the air. Nothing else matters.
I appreciate your post - I was one of the first people in this thread who took the position that it should be theoretically possible for a conveyor to hold back the plane, based on acceleration and rolling resistance. I was assuming that it would increase with speed because of how the tires are deformed under load, but when others strongly stated that rolling resistance is constant, I quieted down.
I think we all pretty much agree with that, notwithstanding the occasional hit-and-run poster to this thread. The discussion has settled into a question of whether a conveyor could prevent the plane from achieving forward speed. The consensus seems to be that there is no way this could happen with a real plane, because the speeds would blow out the tires, and this even assumes that you have a magical conveyor belt. But as long as you’re assuming impractical material properties to make the conveyor belt, you can use those same materials for the tires and axles, and maybe it could be held back.
Right. So… No the conveyor has nothing to do with the planes forward speed. Again it would just be the engines pushing on air to go forward. The conveyor is just there to hold the plane up. Ideally a planes wheels can revolve almost without friction and therefore that force would be minimal compared to the force of the engines pushing backward on the air and moving the plane forward. Planes are not wheel driven so the conveyor is still a red herring here.
Planes can take off on ice without much difference in their forward thrust for example. The wheel friction is irrelevant other than holding the plane back slightly until the push backward on the air can overcome the planes inertia. Once that inertia from the planes mass has been overcome the plane will move forward.
The friction may eventually cause the tires to blow if they can’t spin fast enough but even that would not cease the forward movement with enough engine thrust.
It pretty much depends on your assumptions. If you interpret the meaning of the problem to be that the conveyor matches the fuselage speed, then the plane moves forward and takes off (which is pretty much what you said). If you interpret the meaning of the problem to be that the conveyor matches thetangential wheel speed (and thus keeps the plane stationary with respect to the ground) things get more dicey.
In that case, as CurtC said, whether the conveyor is able to transmit the required force depends on your original assumptions about the problem. I list all the cases I could think of way back in post 106 of this thread.
OK, so my opponents were right. The belt does exert a backward force on the plane. Go ahead and have your fun. You’ve earned it.
First a writeup to detailwhy the rotating mass needs a physical connection to the pivot. I’ll tell you straight. This mea culpa stuff gets old in a hurry. However I don’t mind too much being wrong about the mass spiraling out without the physical connection. Finally figuring out that 1332 was right was my key to what I believe is the right answer.
My analysis is for the case where the belt matches the speed of the plane. There seems to be the feeling in the air that in this case the plane will take off. I don’t see any reason to do the other case because I agree with Cecil that this results in an unstable system. No matter what periferal velocity you pick for the wheel, it’s too low. 10 mph, sorry should be 20, 20 mph, sorry should be 40 until either the wheel speed increases beyond any limit or something blows up, whichever occurs first. Anyone who thinks otherwise is of course free to present an analysis of that case.
At the end of the rotating mass writeup you were told to come back here and go to the next link. That was it that you just passed. Unfortunately the writeup was so long that I had to break it into three parts so there is alsoanother next link.
When I wrote in a previous post that the problem wasn’t difficult it seems that was an overoptimistic assessment. It’s a feedback system and I haven’t been able to formulate an open-loop system function. That makes analysis quite difficult. In fact I was forced into an approximation that I think is valid. Still another link explains why I think so.
In the original GQ thread I did make it clear that there was a backward force on the axel as a result of friction and tire resistance. I don’t believe that was done in any of my posts in this thread.
In the posts here I assumed the wheel to be lossless and a simple reminder, “Hey buddy, aren’t you forgetting about the force needed to accelerate the wheel?” would have been a lot more useful than hypotheticals about cylinders skidding on ice or cement blocks swinging around poles. That would be on topic and not give the impression, even though erroneous, that the topic was being converted to some other problem.
In any case, we are on the same page of the music now.
Well, seriously, it’s not really about being opponents or making fun. It’s about exploring an interesting problem. I admit to feeling a certain level of, um, frustration at being inadequately able to explain concepts, but all’s well that ends well.
Mmmm…not speaking for treis here, but your first post on this topic quoted a post of mine that covered the relationship between force and acceleration in some detail. It appeared to me that you were simply rejecting that relationship outright. Thus the roundabout discussion.
Because in calculating the decimal for my username it looks like you started with 2^1, not 2^0… effectivley shifting the digits to the left.
10100110100 = 1332, not 1330
1010011010, my username, != 1332.
Forget the wheels and any related forces. Wing are what makes plane fly - without meaning to sound rude - that is planes have wings.
Air passing under the wings gives the plane lift. Take kite and look at the conditions in which it will life:
If you pull it through the air (you create lift)
If you place it on the ground in high wind, (the wind create lift).
A plane flying creates its own lift by virture of the speed. A plane on the ground needs to move fast to move air under the wings, again, theat is what the wings are for.
On a conveyer belt there is no air rushing under the wings. So no lift. so no flying.
Forget the wheels, the wheels are there to move the plane forward to get the air rushing under the wings; if the wings are not moving forward is doesn’t matter what speed the wheels are rotating.
If the wind was blowing fast enough it could lift the plane up, as with a kite (think of a roof in a hurricane).
If anybody still believes it is possible to fly the plane from the conveyer belt, perhaps they can explain what part the wings play. No air movement means they have part to play, which means you have invented a wingless plane.
As for the Harrier jump jet - it turns its engines 90 degrees, so the thrust diwn (like a rocket. In this case the engines create the lift - the wings play no part (infact the are a hinderance), but the harrier can only maintain this mode of flying for a very short time - the fuel needed is too great. In this mode it is not a place but a rocket.
I’m reasonably certain everyone (or almost everyone) posting in this thread understands that airspeed is what’s necessary for the plane to take flight. What most of the discussion in this thread has revolved around is a couple other things: the interpretation of the problem and the assumptions you start out with.
You’ll note that in Cecil’s column, there are two different phrasings of the problem which imply different circumstances. The first implies the conveyor matches the plane fuselage speed: the plane does move forward with respect to the air, in other words. The second implies that the conveyor matches the wheel speed: the conveyor attempts to keep the plane stationary with respect to the ground.
In the first case, it should be obvious that the plane will take off, since it’s allowed to move forward. In the second case, the problem is more subtle: is it possible for the conveyor to stop the plane’s forward motion? The answer depends on what your assumptions about the problem are. I outline all the scenarios I could think of way back in post #106 of this thread.
If you believe there’s no air movement, explain to us why thousands of pounds of thrust from the jet engines will not impart forward motion to an airplane resting on properly functioning free-turning wheels. If you believe there is no air movement in this scenario, what you have invented is a wheel-less plane.
Well, rolling resistance could hold the airplane in a nice steady-state situation. Don’t confuse rolling resistance with bearing friction. Rolling resistance is the total of bearing friction (small) and tire deformation (large).
RR is substantial. For a car at freeway speeds RR accounts for 30%, or so, of total resistance. I have been searching like mad for the numbers to plug into the equation I quoted earlier to see where resistance = thrust. I’m also trying to find out tire failure speeds. Just in the pursuit of fun, of course.
I understand that, I was just trying to explain the situation to Johnny-come-lately.
Essentially this exercise is very similar to the question “Can an airplane take off in a tailwind?” And of course the answer is “yes”, assuming that the runway is long enough and that the tailwind is not strong enough to destroy the airplane.
Well, to be fair, it’s hardly reasonable to expect someone with a comment to wade through ten fairly meaty pages worth of discussion before posting what seems like a good point.
