Can the plane take off?

bajturner said:

"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction..."

I suppose interpretation of that statement could vary.

Sitting statically, the wheels are at rest, the treadmill is at rest. Forces on the plane fore and aft are zero.

Say the engines have available thrust of 50,000lbs. It has been shown a pickup truck can pull a large aircraft. Let's say a pickup truck has a pulling force of about 5,000lbs (approx 80% of drive axle weight is typically a good estimate, so this is generous), so we know the aircraft engines easily overcome rolling resistance (it would take less than 5,000lb thrust to get the plane moving). We also know this because aircraft accelerate under power on take off!

Power-up a little and the aircraft moves forward, causing the wheels to turn, which in turn, causes the treadmill to start. Modulate the throttle to keep the aircraft stationary relative to the ground (not relative to the moving treadmill). It would be a low throttle setting since the rolling resistance is fairly low (and decreases once not in a static state), less than 10% in this example.

Now, if you applied the other 90% thrust, the plane will accelerate forward relative to the ground, the wheel speed relative to the treadmill will increase, and the treadmill will speed-up such that its speed relative to the ground matches the wheel speed relative to the treadmill. The plane, however, is now moving relative to the ground and has airspeed.

The throttle could again be modulated to stop accelerating and maintain a new equilibrium with the plane moving forward relative to the ground and with airspeed.

Now interpretation is required or it becomes a control feedback problem.

What speed does the treadmill match? Since the plane has accelerated relative to the ground, the wheel speed must be the ground speed plus the treadmill speed in the opposite direction. However, the treadmill is trying to match the wheel speed. This would produce an endless loop and an impossible treadmill design. The treadmill would speed up indefinitely on its own and everything would self-destruct. Sure, the plane would not take off, but not for the reason I believe most are thinking.

However, if the interpretation is the treadmill is matching the equivalent wheel speed given the ground speed, then treadmill speed = -ground speed and wheel speed = 2 x ground speed. This would be a possible treadmill design and the plane would simply take off with the treadmill running at the same speed as take-off velocity (in the opposite direction) and the wheels spinning at twice their normal speed.

At twice their normal speed the wheels/tires would not likely produce enough resistance to prevent take-off, even if they self-destructed. It would depend on how loaded the aircraft was and how long the imaginary treadmill runway was.

Fun distraction this morning!

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This is the best description of what would take place, and yes of course the plane would take off. I don't remember who the OP was that started this puzzle but I'm sure he knew exactly what the answer was, he just wanted to sit back and watch as everyone got their brain tangled up in the details. It would be a good one to send to "Myth Busters" but I think building that conveyor might be just a little beyond their budget. Kinda like owning a boat.

A PhD in astrophysics could jump into this thread, state the physics behind why, and half of the people here would still not accept it as true.

The internet is a truly terrifying place. Truly.

NorCal Boater said:

Some of you guys are over thinking this. Regardless of the speed of the conveyor or the landing gear, if there isn't enough air moving across the wing surface to generate enough lift to overcome the weight of the aircraft (gravity) and drag on the aircraft, that plane, any plane, will not fly. And that speed. where lift is generated, is different for every type of aircraft from a Cessna 152 to a 747.

Without the generation of lift from the wing a plane will not fly. You can run the conveyor at 3 times the speed of sound with the plane on it but if that wing is not moving through the air to generate lift it ain't going anywhere. The engine of a plane is used to create increased air speed over the wing surface. Does a wing need an engine to generate lift....no. Think of a glider.

For another example, think about a stall in an aircraft and why it happens. A stall occurs when there is no longer enough air moving across the wing surface to generate lift. That condition can happen as a result of air speed, angle of attack (the angle the wing meets the air moving across the wing) or a change to the shape of the wing surface.

Its all simple aerodynamics.
Shawn

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The crux of the question is will the plane move forward through the air if the treadmill runs in the opposite direction in exact proportion to the planes forward movement (which, in turn, causes the wheels to rotate)?

Given the engines push against the air, and are not affected by a moving treadmill under the plane except for some added tire and wheel resistance, the treadmill is essentially a red herring. The treadmill has no fundamental impact on the engine performance for the aircraft, and limited impact to the overall forces.

So the answer is yes, it will move forward, it will gain airspeed, there will be lift, and it will take off. The added rolling resistance would add some distance to the ground-run. Certainly aerodynamics, Bernoulli's Principle specifically!

Stee6043 said:

A PhD in astrophysics could jump into this thread, state the physics behind why, and half of the people here would still not accept it as true.

The internet is a truly terrifying place. Truly.

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It is indeed!

“The conveyor belt is designed to exactly match the speed of the wheels moving in the opposite direction….”

Maybe I’m missing something, but that would result in the aircraft maintaining its relative position on the conveyor, providing the engines are producing the power to move the aircraft and turn the wheels.
There is no airflow over the wings to produce lift as its staying in the same spot on the belt.
Can the aircraft takeoff?? Sure if there was a giant fan blowing to produce airflow of 180 knots or so while the aircraft was on the belt.

Timeflys said:

“The conveyor belt is designed to exactly match the speed of the wheels moving in the opposite direction….”

Maybe I’m missing something, but that would result in the aircraft maintaining its relative position on the conveyor, providing the engines are producing the power to move the aircraft and turn the wheels.
There is no airflow over the wings to produce lift as its staying in the same spot on the belt.
Can the aircraft takeoff?? Sure if there was a giant fan blowing to produce airflow of 180 knots or so while the aircraft was on the belt.

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You mean maintain it's relative position to the ground beside the conveyor, for example in front of someone standing beside the moving conveyor?

At full throttle, where would the force come from to hold the plane back at that position? It doesn't come from the frictional force between the wheels and the moving conveyor runway.

Yes, it’s relative position to the ground or the surrounding environment…The force to hold the aircraft back is coming from the opposite direction force of the conveyor.
The fwd energy of the engines is cancelled by rearward energy of the conveyor.
The wheels are kind of irrelevant.

Will the boat get on plane?

Halfhitch said:

This is the best description of what would take place, and yes of course the plane would take off. I don't remember who the OP was that started this puzzle but I'm sure he knew exactly what the answer was, he just wanted to sit back and watch as everyone got their brain tangled up in the details. It would be a good one to send to "Myth Busters" but I think building that conveyor might be just a little beyond their budget. Kinda like owning a boat.

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That would be me… lol

I think it’s great to watch people explain their critical thinking skills. Right or wrong.

I’m also super ready for boating to resume again.

Timeflys said:

Yes, it’s relative position to the ground or the surrounding environment…The force to hold the aircraft back is coming from the opposite direction force of the conveyor.
The fwd energy of the engines is cancelled by rearward energy of the conveyor.
The wheels are kind of irrelevant.

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How does the force from the conveyor reach the aircraft?

Timeflys said:

Yes, it’s relative position to the ground or the surrounding environment…The force to hold the aircraft back is coming from the opposite direction force of the conveyor.
The fwd energy of the engines is cancelled by rearward energy of the conveyor.
The wheels are kind of irrelevant.

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The only thing retarding the forward movement of the plane is the rolling resistance of the wheel bearings and the rolling resistance of the flexing tires. At takeoff speed around 180 knots the wheel bearings and tires would be creating some additional retardation over the normal because of the doubled speed, but not enough to prevent takeoff. If you have ever ridden in a 747, you know that they have plenty of snoose. It's no different than a float plane taking off upstream in a fast river. The fact that the water is passing by the floats at a faster rate than in a lake, when the plane reaches acceptable takeoff speed it can fly. If the same plane took off running downstream in that same river the water to float speed would be less when the plane reached that same takeoff ability.

jmauld said:

What initial conditions?

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"The conveyor belt is designed to exactly match the speed of the wheels". If the treadmill can't keep up with the speed of the wheel motion, then you've "broken" the problem and that statement above can no longer be true.

mdolesh said:

If the wheels dont matter...what if they were cemented into the ground, and wouldnt break off...could the plane take off?

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Let's take this example. Let's say someone left the "parking brakes" on in the plane and fired up the four jet engines. If the "The conveyor belt is designed to exactly match the speed of the wheels" and the wheels were to try to move AT ALL because of the thrust of the engines, then the conveyor would counteract that movement, resulting in the plane being stationary, even though the engines are at full thrust.

bajturner said:

Now interpretation is required or it becomes a control feedback problem.

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You can also think of the feedback loop if the treadmill anticipates the speed of the wheel, rather than having to respond to it.

bajturner said:

Sure, the plane would not take off, but not for the reason I believe most are thinking.

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This is certainly one of those problems where you'd need to "show your work" to get credit for the right answer. If this was a question in Physics101 or Mechanical Engineering101, then the correct answer would probably be "yes, it will fly" based on the earlier discussions about the engines pushing on air.

In any more advanced class, then the answer is "definitely not" but you'd have to explain why in order to get any credit. You might get some credit for an "it will fly" answer though.

km1125 said:

"The conveyor belt is designed to exactly match the speed of the wheels". If the treadmill can't keep up with the speed of the wheel motion, then you've "broken" the problem and that statement above can no longer be true.

Let's take this example. Let's say someone left the "parking brakes" on in the plane and fired up the four jet engines. If the "The conveyor belt is designed to exactly match the speed of the wheels" and the wheels were to try to move AT ALL because of the thrust of the engines, then the conveyor would counteract that movement, resulting in the plane being stationary, even though the engines are at full thrust.

You can also think of the feedback loop if the treadmill anticipates the speed of the wheel, rather than having to respond to it.


This is certainly one of those problems where you'd need to "show your work" to get credit for the right answer. If this was a question in Physics101 or Mechanical Engineering101, then the correct answer would probably be "yes, it will fly" based on the earlier discussions about the engines pushing on air.

In any more advanced class, then the answer is "definitely not" but you'd have to explain why in order to get any credit. You might get some credit for an "it will fly" answer though.

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How advanced a mathematical proof would you like?

bajturner said:

How advanced a mathematical proof would you like?

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It's not very advanced math. The instant the plane moves then the wheels are exceeding the speed of the treadmill and therefore violates the "The conveyor belt is designed to exactly match the speed of the wheels" statement, because the treadmill just can't do that.

Q.E.D.

km1125 said:

It's not very advanced math. The instant the plane moves then the wheels are exceeding the speed of the treadmill and therefore violates the "The conveyor belt is designed to exactly match the speed of the wheels" statement, because the treadmill just can't do that.

Q.E.D.

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Well, it's a fantastical question that requires some imagination. That said, I'd be less worried about building a mechanism that can exactly match the speed of the wheels, which wouldn't actually be that difficult to do (that type of control circuit has existed for years with very good accuracy), and more concerned about the idea of building a conveyor belt the size of a runway!

I'm curious how many of the passionate "it won't fly" crowd have engineering or physics degrees...from fully accredited university's? That is a dangerously "not in my lane" question, I do get it.

The 747 on the conveyor belt dilemma solved with Simcenter Amesim
Dec 15, 2021 | Aerospace, Simcenter Amesim


With 70% of BSIM’s team being engineers, our coffee-break convo is very much on the geeky-techy side.

There’s always an engineering myth to debunk, a physical phenomenon to disagree upon. And it usually ends with one of our engineers downing his coffee and setting out on a simulation mission to prove whatever theory he had, and how the rest of us were wrong.

We’ve discussed the aerodynamics of a flying cow, argued about how to cook the perfect Thanksgiving turkey with CFD-3D simulations, how to simulate the best tennis serve – I could go on.

Our latest fixation? It’s an oldy but a goody: the 747 on the conveyor belt.

Imagine a 747 on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to move at the same speed as the airplane’s wheels, but in the opposite direction. The dilemma: will the plane take off?

Ring a bell? If you’re part of the engineering community, you’ve definitely heard of this one before. It’s intriguing because the problem involves absolute and relative reference systems, physics laws, and moving parts.

Even the MythBusters on Discovery channel spent some time on this one: check it out – once you’ve finished reading our article!

Also, there’s something about how the question is set up – it plays with your mind, am I right?! Such cunning absence of detail. It’s almost like they’re purposefully making it vague.

Anyway, what we noticed was that every engineer will go about solving it differently, depending on their background.

Our mechatronic engineer said: “So there’s an active control system closing the feedback to regulate the conveyor speed.” Our mechanical engineers were kind of annoyed: “How big can this conveyor belt even be anyway!?” Someone in the back went: “In what direction is this conveyor belt running”? “Hey, what about the wheels? Can the aircraft break?”

None of us felt we could solve this: we just didn’t have enough information. But after a while, two separate parties had formed.

Group 1 thought the airplane couldn’t take off: they believed the conveyor belt couldn’t annul the relative aircraft-air speed. There wouldn’t be any lift generation below the wings, meaning no take off.

Group 2 thought the aircraft would take off, because the engine’s thrust was mainly dependant on the interaction between the aircraft and the surrounding air, and what happened between the wheels and the conveyor was a secondary phenomenon.

But no one group was able to convince the other.

So that is when Giancarlo, one of our mechanical engineers, took it upon himself to settle the case. Off he went to set up his system simulation model, with Simcenter Amesim.

“Starting from some basic assumptions, this is how I reproduced the problem within the software:

• One 2D body representing the aircraft together with the landing gear arm
• Two 2D bodies representing the wheels of the front and the rear landing gears
• A 2D movement source representing the sliding belt surface
• A force source acting on the main aircraft body
• A contact simulating the interaction between the wheel and the conveyor belt

This is what my Simcenter Amesim sketch looked like:


At this early modelling stage, I wasn’t considering any aerodynamic forces, as I assumed the most important question we had to answer was:

“Will the plane be moving in relation to an absolute reference system?”

Let’s not forget that if speed exists in an absolute system, where we assume the speed of the air is close to zero, then we’ll necessarily have a non-null speed of the aircraft relative to the air. This means we’ll have lift and take off.

Model parametrization was based on the data from a small ultralight aircraft that was available to us. But we could have chosen any aircraft data. The contact between the wheels and the belt was modelled with Amesim’s contact profile tool, which is available in the 2D library:


Clearly, we set the wheel stiffness at a significantly lower value than the ground stiffness, to ensure increased deformability under the effect of the aircraft weight.

The simulation was also meant to prove Group 2’s theory :

“The aircraft will take off, no matter the speed and the movement direction of the conveyor belt.”

That “no matter” part of the sentence meant I had to simulate 2 different scenarios:

• the conveyor belt traveling at the same speed and in the same direction of the landing gear wheels
• the conveyor belt traveling at the same speed, but in a different direction to the landing gear wheels

But Group 2 got a bit picky, and wanted me to add in three extra simulation scenarios:

• the conveyor belt is actually off
• the conveyor belt speed is equal to wheel-edge tangent speed. According to the rolling mechanical principle, if there is no slipping at the contact point, then the maximum tangential speed will be twice the dragging speed.

I used a closed-loop control signal to represent the conveyor belt speed, based on the landing gear’s instantaneous speed, that could be employed as it is, or used to obtain the wheel’s tangential speed.

I set the expression of f(x) to reproduce various configurations inside Simcenter Amesim’s study manager: ‘x’ is a scalar speed.

I launched our 5 simulation cases and looked at the results. When I plotted the speed of the aircraft in the direction of movement, this is what I observed:

The airplane was subjected to thrust only in the 4-7 sec time range.

The aircraft is definitely moving – so we can definitely declare the null aircraft speed theory wrong. I also noticed the simulation results were different in each of the 5 cases. This proves Group 2’s theory: the aircraft will take off no matter how the conveyor belt behaves.

So, what is actually changing in our 5 simulation scenarios? To find out, we must look at the wheels’ rotation speed, the front ones.

Let’s analyse what happens in each scenario, knowing the airplane will take off:

• In the first scenario, in red, we can see the rotation speed is null, because in this case, the conveyor belt follows the dragging speed of the wheels both in terms of modulus and direction; so it’s effectively like the conveyor belt were chasing the aircraft, leaving the wheels still, when compared to the aircraft relative reference system;
• In the second scenario, in blue, we can see the relative speed is going in a negative direction. It then climbs back up to zero after 7s, because of the friction created by the wheel-conveyor belt contact.
• In the third scenario, the yellow one, the wheels have the same rotation speed we’d have on a typical runway, as this scenario presents a conveyor belt speed of zero.
• In the fourth scenario, in green, I set the conveyor belt speed at twice the drag speed and in the same direction. We are therefore looking at a self-regenerating phenomenon, by which when the aircraft exhausts its thrust and continues to accelerate indefinitely, it’s dragged along by the conveyor belt.
• In our last scenario, the pink one, I set the conveyor speed at double the landing gear wheels drag, but in the opposite direction. The plane is still moving, but it has more of a braking effect. In fact, this is the scenario where we have the smallest absolute speed values and the fastest deceleration, once the thrust is exhausted.”

So that settles it!

Group 2 won – not sure which side our colleague and article author Giancarlo was on, or if he’d admit it if he was in Group 1.

We proved Group 2’s theory with one of the simulation tools BSIM resells, Simcenter Amesim from Siemens Digital Industry Software.

Simcenter Amesim allowed Giancarlo to quickly set up a predictive model and run multiple simulation scenarios, with a few basic, simple assumptions.

While simulation tools often require a vast amount of data, Simcenter Amesim’s model-based, scalable approach allows engineers to employ simulation for new engineering products. And perform what-if analyses to assess the viability of their engineering choices long before 3D CAD model and detailed data availability.

Further developments

We could replace the 2D bodies with components from Simcenter Amesim’s aerospace library, which includes aerodynamic effects and specific models for the wheel-landing gear-ground contact.


By doing so, we’d actually be able to observe the aircraft taking off and avoid any future “court appeals” from Group 1!

Hope you enjoyed our blog, feel free to share it.

Stee6043 said:

I'm curious how many of the passionate "it won't fly" crowd have engineering or physics degrees...from fully accredited university's? That is a dangerously "not in my lane" question, I do get it.t on a simulation mission to prove whatever theory he had, and how the rest of us were wrong.

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Economics and Psychology major here, who works in IT, from a K-Mart college, who stayed at a Holiday Inn Express last night.

Where is Bernoulli????

mrsrobinson said:

Economics and Psychology major here, who works in IT, from a K-Mart college, who stayed at a Holiday Inn Express last night.

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Economics! You should be ranting about the cost of building that stupidly oversized conveyor belt, man

I am moving on to something less confusing