Plane On A Treadmill

Gillette

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An Jet aircraft is on a runway that is also a conveyor belt. The conveyor exactly matches the aircrafts movement BUT is going in the opposite direction of the aircraft. Will the aircraft be able to get airborne?




The problem as posed says nothing about the wheel. The treadmill moves in one direction at exactly the same speed that the airplane moves in the other direction (as I interpret the wording). There's no requirement that the airplane even be touching the runway/conveyor for the postulated conditions to be met.

DC_DEEP's summary of the physics is entirely sound. Airplanes fly by virtue of air speed, not ground speed.

The use of the word on rather than over denotes that they are in fact touching.
If you assume the two aren't even touching then doesn't that mean the plane is already airborne, making the entire question moot?

If the treadmill is moving backwards at speed V, the plane must be moving forwards at speed V. That was how the problem was stated. When the plane V equals the takeoff speed, up she goes. What the treadmill is doing in the meantime doesn't enter into it.

If you're only focusing on sentence structure the use of the word movement in place of thrust, speed, power or momentum does imply that the plane is in actuality "moving". That may mean that there is 400km/hr thrust of the engines vs 200km/hr speed of the conveyor but that would provide each with a directional speed of 200km/hr. So yeah, if you nit-pick the sentence structure this is the answer. She flys.
 

Gillette

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SpeedoGuy,
Your analogy breaks down because the plane is applying thrust against the air, not against the ground or the treadmill. Your analogy does have some use, though. Suppose there was a rider on a bicycle on a treadmill, and there was also a person standing on the ground next to the treadmill.

The standing person's job is to push the bike forward and bring it up to his walking speed. With the rider just coasting, how much harder is it for the pusher guy to get the bike to walking speed in the case of the treadmill moving, vs the treadmill not moving. The answer is that the pusher guy will hardly notice the treadmill moving or not moving. Since the rolling friction of the bike on the treadmill is very small, the action of the treamill will pose very little additional resistance to the forward motion of the bike.

Now the pusher person is analogous to the jet engine, which is also not applying its thrust to the wheels and the ground (or the belt). Just like the case of the bike on the treadmill and the pusher, the backwards motion of the treadmill beneath the plane will offer very little resistance to the forward motion of the plane in comparison to the very strong thrust of the engines.

In either case, the vehicle will start moving forward at almost the same rate with the treadmill either running backwards or not running at all.

Assumes zero friction.

If you were to try this on a moving sidewalk at an airport you would see this isn't true. There is a significant difference in the force required.

You say "hardly notice" and "little resistance", so you do acknowledge there is resistance. If the question posits that the resistance is equal to the force regardless of how weak or strong you still get a net forward motion of zero, hence zero airflow, and zero lift.

I'd say Speedoguy's assertion stands.
 

DC_DEEP

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Again, speed or velocity is relative to something. If the plane is on a runway (fixed or treadmill-type), the speed of the plane is still going to be relative to something. There is no such thing as "absolute speed." If you are driving on a freeway at 80 miles per hour and another car goes past you (same direction) at 85 miles per hour, to a road sign the other car appears to move at 85 mph, while to you, the other car appears to move at 5 mph. This same phenomenon applies to the original post.

For an airplane to become airborne, its forward speed has to be relative to the air, not relative to the ground or the runway or the treadmill. It does not matter if the plane is moving at the speed of light relative to the treadmill runway; if the plane does not have sufficient speed relative to the air, it will not take off. If the conveyor is moving the plane backward at the same rate the jets move the plane forward, the vectors cancel out to zero. The lift is not generated by the jet engines nor the wheels nor the runway, it is generated by the wings moving through the air.
 

kamikazee_club

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The problem as posed says nothing about the wheel. The treadmill moves in one direction at exactly the same speed that the airplane moves in the other direction (as I interpret the wording). There's no requirement that the airplane even be touching the runway/conveyor for the postulated conditions to be met.

Unless I'm mistaken the word ON in the title does imply contact or it would have been Plane in the general vicinity of a treadmill. But I agree it's net forward motion that matters and not wheels or magic treadmills.:rolleyes:

DC_DEEP's summary of the physics is entirely sound. Airplanes fly by virtue of air speed, not ground speed.

Well, strictly aircraft fly due to force (lift) induced by a pressure differential between the top and bottom surfaces of wings/blades, which is generally (but not necessarily) a result of their forward motion through a fluid.

My initial post was not thought through, it had been a long day and two mins later I realised this and re-posted. In essence if there is no net forward motion there can be no lift, thus no take off.

Now, if you had read what I initially posted, rightly cited by DC_D as incorrect and stopped being your usual horses ass contrary self you'll see I agree with you in the 'how aircraft fly' regard.

In real life, all tires have a maximum sustained speed rating, and if the plane rolled on the conveyor without taking off for an hour or so, the tires could conceivably overheat and consequently fail. But that's not part of this particular problem.

Let's not bring real life into it.:smile:
 

B_big dirigible

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If you're only focusing on sentence structure the use of the word movement in place of thrust, speed, power or momentum does imply that the plane is in actuality "moving".

Focusing on the sentence structure is the only way to determine what the problem is. If one doesn't bother with that step then one is likely to solve the wrong problem - as witness the analogies with bicycles, above. Entirely different problem, and not an analogy at all.
 

B_big dirigible

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Unless I'm mistaken the word ON in the title does imply contact or it would have been Plane in the general vicinity of a treadmill.

Yes. My construction was meant to emphasize the fact that the transition from travel via rolling to travel via flight is continuous. When the airplane speed V is a speed at which lift over (or under, if you prefer - in real life, a bit of both) the airfoils equals the weight of the airplane, it can roll or fly. The problem as posed doesn't become discontinuous at that point. In real life the pilot keeps the aircraft on the ground until a slightly higher speed is reached, then "rotates" the aircraft, which changes the airfoil's angle of attack and increases lift. The aircraft then flies. It's still in the ground effect region, but fortunately that's not part of the problem.
 

DC_DEEP

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Is she required to solve physics problems? How about someone with a mere physics degree?
Even a degree is not needed. Problems such as this are covered in any Physics 101 class at any reputable university. I got a 4.0 in Physics 101 and in Physics 201. It's all about understanding the fluid dynamics and being able to add vectors.
 

B_big dirigible

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Even a degree is not needed. Problems such as this are covered in any Physics 101 class at any reputable university. I got a 4.0 in Physics 101 and in Physics 201. It's all about understanding the fluid dynamics and being able to add vectors.

Nor is a pilot's certificate needed. This problem should be eeeeeaaaaasssssyyyy. But as we see in this thread, to some it's not.

It's also about reading the problem as posed, and that's just plain ol' English. Also not as easy as it should be.
 

Gillette

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Focusing on the sentence structure is the only way to determine what the problem is. If one doesn't bother with that step then one is likely to solve the wrong problem - as witness the analogies with bicycles, above. Entirely different problem, and not an analogy at all.

Cripes, I expect you to browbeat me when we're in disagreement but not when I've agreed with you.

Is she required to solve physics problems? How about someone with a mere physics degree? Even better, someone with a physics degree who's flown an airplane or two himself?

Cool, fine, thumbs up, okay. I mention Claire only because she's the only one I knew to be a pilot and an engineer to boot. I hear loads about your veiws but precious little about you so how am I to know your experiences.

Lighten up grumpy, I agreed with you.
 

DC_DEEP

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Nor is a pilot's certificate needed. This problem should be eeeeeaaaaasssssyyyy. But as we see in this thread, to some it's not.

It's also about reading the problem as posed, and that's just plain ol' English. Also not as easy as it should be.
Right. I viewed the OP as something like a problem in a physics textbook - where the problem usually has a codicil like "disregarding friction of the wheels and runway, and assuming no wind..."

Some of the posts are adding variables not in the original question, rather than disregarding those variables.
 

DC_DEEP

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"What is the airspeed velocity of an unladen swallow?"

"What do you mean? An African or European swallow?"

"A five ounce bird cannot carry a one pound coconut!"

"Of course he can, if he grips it by the husk and is launched by a treadmill moving in the same direction."
 

JustAsking

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"What is the airspeed velocity of an unladen swallow?"

"What do you mean? An African or European swallow?"

"A five ounce bird cannot carry a one pound coconut!"

"Of course he can, if he grips it by the husk and is launched by a treadmill moving in the same direction."


"Its simply a question of power to weight ratio."

"Are you saying Coconuts migrate?"
 

JustAsking

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Assumes zero friction.

If you were to try this on a moving sidewalk at an airport you would see this isn't true. There is a significant difference in the force required.

You say "hardly notice" and "little resistance", so you do acknowledge there is resistance. If the question posits that the resistance is equal to the force regardless of how weak or strong you still get a net forward motion of zero, hence zero airflow, and zero lift.

I'd say Speedoguy's assertion stands.

Yes, I have to agree with you there, Gillete. It demonstrates quite clearly that I sold out as a physicist years ago and became an engineer. But as Big_D says, the problem is under-specified. It implies that there is rolling friction greater than zero, but it doesnt say anything else about the other practical aspects. If one assumes that it is an engineering problem where typical values should be used for everything (except the magical, very fast belt), I maintain that the wheels would burn up or fly apart long before the belt could move fast enough backwards to counteract the thrust of the engines.

The reason for that is that any force on the plane due to rolling friction must be dissipated as heat. This means that at full throttle, and with the belt moving fast enough to prevent the plane from moving forward, all of the power of the engines is being dissipated as heat in the sources of the rolling friction (tires, bearings, etc).

If you ignore that problem, then you are right. If the rolling friction is non-zero, the wheels are magically indestructible, and the belt is magically able to go extremely fast, and the windspeed is zero in respect to plane and surrounding ground, then the plane will achieve no forward motion in respect to the surrounding ground and will achieve no lift.


The same goes for your bicycle on the airport people mover belt. The amount of effort needed by a person standing next to the people belt who is trying to keep the bike from moving backwards due to the moving belt is trivially small compared to a person's strength. How fast would that belt have to move backwards to prevent a person from pushing the bike forward? In the ideal physics problem, the answer is very fast. In the engineering version of the problem, the bike flies apart before that condition is achieved.

The difference between the "Physics" version of the problem and the "Engineering" version of the problem is related to how much is specified or in absence of that, it is related to what assumptions you make.
 

B_big dirigible

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The problem isn't as well-framed as it might be. It has mutated a bit as it's made the rounds of various boards, and the wording has suffered. The basic constraint is given only as

"The conveyor exactly matches the aircrafts movement BUT is going in the opposite direction of the aircraft."

This isn't very specific and has to be interpreted. The only interpretation which seems to make sense is that the aircraft is free to move forward at some velocity V with respect to .... what? Certainly not the conveyor itself, or the problem would reduce to a trivial case - obviously the airplane would never take off if the wheels were stuck to the conveyor. The most reasonable notion is that V is measured with respect to the ground - what Officer Friendly would measure with a radar gun if he was hiding behind a nearby tree. As no prevailing wind is mentioned in the problem, V is then also the airplane's airspeed - its speed relative to the air. That's the speed which we rely on to generate the lift needed to support flight. V is also the conveyor's speed, but in the opposite direction. That constraint means that any scenario demanding very high speed of the conveyor but zero speed of the aircraft is RIGHT OUT!

The conveyor actually exerts no force on the airplane, except to support its weight. Any postulated friction is not a major factor in the situation, that being the great attraction of wheels in the first place. We can safely assume that the airplane is going to take off in the normal way that airplanes do when they aren't sitting on conveyors, and in that case the friction of the tires is not one of the major load which has to be overcome to get the thing airborne - those loads are air drag of various sorts and the craft's weight and inertia (and of course dilly-dallying by those Federal lard-asses in the control tower). These major factors are all the same whether or not there's a conveyor involved.

Then all we have to do is realize that the conveyor speed has no effect on the aircraft's motion, except to spin the wheels faster. Since the aricraft isn't driven by the wheels, that's inconsequential.
 

JustAsking

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Now here is a well framed problem with a small but sufficient amount of information for it to be solved:

An air bubble rises from the bottom of a fresh water lake, doubling its volume when it reaches the surface. How deep is the lake?