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Discussion: Sorry, the math is wrong!

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941nmb

941nmb
Sorry, the math is wrong!
May 2 2008, 11:47 PM EDT
The plane's take-off speed is a red-herring.

In general principal, when lift plus thrust equals or exceeds load plus drag, flight will occur.

The true calibration lies in the maximum ground speed obtainable by the plane. Let's say the plane needs a take-off speed of 40 MPH and has a max ground speed of 85 MPH. If the conveyer is travelling at 50 MPH, the plane will not be able to take off because 85 minus 50 is 35. The plane will still move forward but will not take off because there's not enough lift. If the conveyer is going 80, then the plan will stand still, removing virtually all of the lift. (A propeller rotating quickly speads a lot of air over the plane's body and very little over the entire wingspan, where lift occurs.)

The max ground speed was never calculated in any of the televised experiments and the math above is incontrivertible.
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TrueThanny

TrueThanny
RE: Sorry, the math is wrong!
May 3 2008, 12:54 AM EDT
All they did wrong in the episode is not explain clearly what the nature of the confusion over this issue is.

And that confusion is all about the way cars measure their speed. They use the rotational rate of the wheels to calculate the linear motion of the car, on the assumption that the wheels are rolling on stationary ground.

A car in gear on jacks, with the engine gunned, will show something on the speedometer. That's an artifact of the normal means of measuring speed. The car isn't moving, and the speedometer has been turned into nothing but a wheel tachometer (without useful measurement units).

That same car with the wheels turning at a rate that indicates 60 miles per hour normally, but on a conveyor belt going backwards at 60mph, is not moving. It has a ground speed of 0 miles per hour, even though the speedometer says its going 60mph. Instead of measuring the car's speed, it's been tricked into measuring the conveyor belt's speed.

The whole thing no longer works when you're not using the wheels for power distribution. If the car has free-spinning wheels and a jet engine, it'll accelerate almost completely normally, as if the conveyor belt weren't there, but the speedometer will be incorrect - it will show the sum of the car's actual ground speed and the conveyor belt's speed.

Stick in an airplane instead, which probably won't even have a speedometer attached to the wheels, and you don't even get that. You just get an airplane taking off with a conveyor belt uselessly running underneath it. The only way to make any sense of this "myth" is to rig the plane so that it distributes all its power through the wheels until takeoff (using a wheel-based speedometer), then switches on the propeller. And even then, the speedometer would be measuring only the speed of the conveyor belt, not the plane.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 3 2008, 6:02 AM EDT
Comparing apples to oranges (cars to airplanes) is flawed logic as cars were never really intended to become airborne.

Look at the four components of flight. Lift + thrust >= load + drag. (A+B >= C+D) Lift is generated by air passing over the entire length of the wings. Thrust is generated by the rotating propeller, Drag is caused by the friction generated when tires contact the tarmack plus the air travelling over the hull. (Hulls generally don't provide lift) Load is caused by gravity (G) A plane on the ground will always have 1 G-force applied to it.

To simplify the flight equation, let's say lift = 1, thrust = 1, load = 1 and drag = 1.

If the conveyer is moving to the left and the plane is stationary, then the thrust must be exactly equal to the drag. (B=1 and D=1) A stationary plane generates zero lift yet still has one g-force on it, (A = 0 and C = 1) In this equation, a+b =1 and c+d = 2. The plane will not leave the ground.

If the conveyer is moving to the left and the plane is moving to the right then the thrust generated by the propeller MUST* be greater than the drag. (B = 2 and D = 1) If the amount of lift is equal to or greater than the amount of load (A = ! and C =<1) then the following equation exists (1+2 > 1+1) The plane takes off and flies.

* A plane will move only if the propeller generates more thrust than load+drag.

Your calculations are flawed because wheels on a plane never generate thrust, they cause drag and you totally ignore the lift component needed for flight. Even if you attached a drive train to the wheels, the essential formula remains the same: A + B >= C + D.

Again, my original point remains uncontested. At no time in the televised experiments did anyone calculate the maximum ground speed of the plane. If the plane is exerting maximum thrust and the conveyer is moving in the opposite direction at the same speed, the plane will never be able to take off.
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TrueThanny

TrueThanny
RE: Sorry, the math is wrong!
May 3 2008, 7:02 PM EDT
You have missed the point entirely. The ground speed of an airplane is a measure of how fast it is moving with respect to the ground. How fast the wheels are spinning is irrelevant. If you re-read what I wrote and try to understand, perhaps you can dig yourself out of this mental rut. But I'm through trying to help.
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 3 2008, 8:38 PM EDT
"Again, my original point remains uncontested. At no time in the televised experiments did anyone calculate the maximum ground speed of the plane. If the plane is exerting maximum thrust and the conveyer is moving in the opposite direction at the same speed, the plane will never be able to take off."
Nonsense. The only way the plane doesn't take off is if it's airspeed is held to be less that it's takeoff airspeed. Ground speed means nothing to a plane.

The speed at which the conveyor is moving under the wheels means nothing to the airspeed of the plane. Only the conveyor's ability to exert a force on the plane matters. Since the wheels of the plane exist to minimize the friction between the conveyor and the plane, the conveyor's ability to exert a force on the plane is negligible.

Your formulas above show a good attempt at analyzing the problem, but you have made a critical error in assuming that the drag is equal to the thrust. It's not - the thrust is much greater than the drag.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 3 2008, 11:24 PM EDT
Perhaps I could explain my use of the word "gound speed" to help make my point. Take the wings off the airplane and let it taxi down the runway at full throttle. Let's say someone with a radar gun points it at the wing-less plane and gets a reading of 100 MPH. Under my formula, this is what I've been calling ground-speed. (Yes, I know the removal of the wings will mess up the drag and the load coefficients, but humor me for a moment on this scenario and pretend it doesn't.)

The next step is easy. Bolt the wings back onto the airplane and put it on a conveyer that's calibrated to run at 100 MPH. Since the plane's maximum thrust now equals the speed of the conveyer, the plane remains stationary creating insufficient lift for flight.

Now look at the two experiments they conducted. They calibrated the MINIMUM speed and distance needed to get airborne then set up a treadmill to run at the same MINIMUM speed but in the opposite direction. The airplane ruined the experiment by adding more thrust. If you want to test the theory, then run everything again at Max speed. If it works at the bottom end of the speed curve, then it should also work at the top end.

And while we're setting up the equipment for this, could we please make sure that the conveyer is smooth enough to prevent any jarring of the wheels. Bouncing a plane on a conveyer causes the wheels to loose contact. This isn't a true representation of lift, it's a reaction to an inconsistent surface. The moment the wheels unfairly break contact, the plane gathers air-speed and the scales tip giving a manufactured result.
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TrafficCone
TrafficCone
RE: Sorry, the math is wrong!
May 3 2008, 11:37 PM EDT
THWAP!THWAP!THWAP!

Do you guys hear that? It sounds like...why, it sounds like someone's beating a dead horse! Lol.
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 3 2008, 11:52 PM EDT
"Since the plane's maximum thrust now equals the speed of the conveyer, the plane remains stationary creating insufficient lift for flight.
"
No, it doesn't! The maximum SPEED of the conveyor matches the maximum SPEED of the plane, but the FORCE exerted on the plane by the treadmill does NOT equal the FORCE exerted on the plane by the engine!

All the contact with the treadmill is doing is making the wheels spin faster, it's not exerting any appreciable force on the plane itself!

You are mixing up speed and thrust, using them interchangeably, when they are not the same thing and cannot be used interchangeably.

I agree with TrafficCone. You might think this horse is up and running, but it's been dead for a good long while.

The plane flies. Deal with it.
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wrbryan

wrbryan
RE: Sorry, the math is wrong!
May 4 2008, 12:22 AM EDT
"
You are mixing up speed and thrust, using them interchangeably, when they are not the same thing and cannot be used interchangeably."
Ask any pilot what the difference between groundspeed and airspeed is. The Wright brothers understood this principle when they raced Glenn Curtiss. They both had comparable planes with comparable engine thrust. Curtiss, not truly understanding the principles of aerodynamics, took off with a stiff wind at his back and could hardly leave the ground. Wilbur Wright, knowing that airspeed is what makes a plane fly, and not groundspeed, took off into the wind and easily beat Curtiss' race time with that advantage. Just because the plane is traveling a certain speed on the ground, it does not mean it will take off. What matters is the speed of the air the wings are travelling through.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 4 2008, 2:42 AM EDT
"No, it doesn't! The maximum SPEED of the conveyor matches the maximum SPEED of the plane, but the FORCE exerted on the plane by the treadmill does NOT equal the FORCE exerted on the plane by the engine!

All the contact with the treadmill is doing is making the wheels spin faster, it's not exerting any appreciable force on the plane itself!

You are mixing up speed and thrust, using them interchangeably, when they are not the same thing and cannot be used interchangeably.

I agree with TrafficCone. You might think this horse is up and running, but it's been dead for a good long while.

The plane flies. Deal with it."
wrbryan is right!

If a plane is going down the runway at 100 MPH and the wind is travelling the same direction at the same 100 MPH then the amount of air flowing over the wings is zero and the plane will not lift off. The wind at your back is very much like the conveyer under your wheels. The conveyer robs the plane of forward movement (thrust > load + drag = motion). If it's going fast enough, it robs the plane of all thrust. Without positive forward thrust, there is no air going over the wings, ergo, insufficient lift. The mechanics of wind vs. coveyer may be different but the net result is still the same. The movement of the conveyer is expressed mathematically as a negative number where solid ground has a value of zero. That negative number must be factored to the four principals of flight . The number doesn't correlate to load or drag. (by the way, your use of the word "force" hints that it's does.) Given that thrust always comes before lift then the negative must be a component of the thrust variable.

The premise of the experiment was the conveyer would be rolling at a rate sufficient enough to keep the plane stationary at whatever rate of thrust the propeller was producing. Zero forward thrust equals zero lift. The plane won't fly.
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TrueThanny

TrueThanny
RE: Sorry, the math is wrong!
May 4 2008, 2:53 AM EDT
"The next step is easy. Bolt the wings back onto the airplane and put it on a conveyer that's calibrated to run at 100 MPH. Since the plane's maximum thrust now equals the speed of the conveyer, the plane remains stationary creating insufficient lift for flight.
"
OK, I lied. I'll try one more time to help.

The quoted statement is completely and utterly incorrect. The airplane does not distribute power through its wheels. It uses thrust from an engine, and the speed of the conveyor belt is almost entirely irrelevant (all it can do, by spinning the wheels, is take a miniscule amount of the engine's power through friction in the wheel bearings). You can leave the wings off, and the crippled airplane will still accelerate down the conveyor belt until air resistance prevents it from going any faster. Just like a car that uses a jet engine instead of a driveshaft.

I've explained it perfectly clearly (and I'm sure others have as well, in numerous other threads). If you persist in raising zombie equines just so you can pummel them again, you will be willfully ignoring the truth of the matter, and hence officially stupid.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 4 2008, 4:33 PM EDT
I'll stick to my deceased equine for as long as it takes you to present a supported mathematical formula that correctly and numerically expresses the value (negative or positive) of a conveyer rotating contrary to forward motion.

For you to say the number is small is to infer that the number exists. If the number exists, it must be reconciled within the entire the flight equation.

Again, here are base numbers to assist in your logic. Flight occurs when lift + thrust >= load + drag. If all four components have a value of 1, the plane will fly where solid ground has a value of zero. For this scenario, the propeller rotating at maximum output has a value of 1.

Your task is two-fold: First, determine the accurate numeric value created by a conveyer rotating in a fashion that will cause all forward motion of the craft to end. (Hint; the number will be a negative value) Second, determine which of the four main components will be impacted most by the new variable and factor it into the flight equation. State your findings numerically then verbally describe the flight capabilities of the plane based on those numbers .

Please always bear in mind your debate, no matter how stupid, is no longer between you and I, it's between you and the numbers.
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 4 2008, 5:02 PM EDT
"I'll stick to my deceased equine for as long as it takes you to present a supported mathematical formula that correctly and numerically expresses the value (negative or positive) of a conveyer rotating contrary to forward motion.

For you to say the number is small is to infer that the number exists. If the number exists, it must be reconciled within the entire the flight equation.

Again, here are base numbers to assist in your logic. Flight occurs when lift + thrust >= load + drag. If all four components have a value of 1, the plane will fly where solid ground has a value of zero. For this scenario, the propeller rotating at maximum output has a value of 1.

Your task is two-fold: First, determine the accurate numeric value created by a conveyer rotating in a fashion that will cause all forward motion of the craft to end. (Hint; the number will be a negative value) Second, determine which of the four main components will be impacted most by the new variable and factor it into the flight equation. State your findings numerically then verbally describe the flight capabilities of the plane based on those numbers .

Please always bear in mind your debate, no matter how stupid, is no longer between you and I, it's between you and the numbers. "
I'm not sure why you say the number will be negative, maybe trying to indicate direction?

I disagree with your formula, by the way. Motion is dependent on thrust > drag, flight is dependent on lift > load. Since lift is dependent on motion, and its magnitude depends on the airfoil, it cannot be simply calculated in this manner.

Given that the thrust is normalized to 1, then I say the drag generated by the conveyor is in the range of 0.05 to 0.10. Evidence for this can be seen by observing the throttle settings of planes taxiing at your neighborhood airport.

Since thrust > drag, the plane will accelerate and gain airspeed. Once sufficient speed is obtained to render lift > load, the plane will take off.

But as you said, this isn't between you and I, it's between you and the numbers. Disprove that drag <= 0.10

Good luck.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 4 2008, 7:43 PM EDT
What tests did you conduct to proove drag is 0.05 to 0.1? none? Science is either theory or fact. Myself, I'd prefer fact.

Perhaps there's neither a problem with my logic or yours but in the execution of the premise as done on TV.

Ignore everything for a moment except for the drawn illustration that they used to explain the premise. It showed a plane on a conveyer and (critical point) the plane was stationary..

Now look at the two experiments and ask one question. If the goal of the conveyer was to keep the plane stationary and the planes moved forward in the experiments, did the conveyer accomplish it's goal? I'm guessing you answered yes to the question while I said no. I further assert the wrong types of tests were performed to see what speed the treadmill would need to obtain.

Now consider an alternative experiment. (I ask forgiveness twice in the following, One, the following will probably never take place and, Two, the example of our fishing trips is the best I could think of to help in the description.)

I love to go fishing with my daughter it's a great pasttime. There's a weight restriction, however, on some of our catches so we carry a small gravity scale to make sure we don't break any rules.

Consider then the proposal where a plane is sitting on a large conveyer. Attach a rope to the tail of the plane and attach a large gravity scale to the end of that rope. The other end of the scale is attached to an anchor capable of withstanding whatever force might be generated by the pull of the propeller. Turn on the motor and advance it to full throttle.

Now turn on the conveyer and advance it's speed to where the gravity scale reads zero pounds. At this point, the experiment mirrors the premise and the conveyer obtains it's goal. If you now release the rope, the plane will not fly because there's no air flowing over the wings to create lift.
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 4 2008, 9:07 PM EDT
"What tests did you conduct to proove drag is 0.05 to 0.1? none? Science is either theory or fact. Myself, I'd prefer fact.

Perhaps there's neither a problem with my logic or yours but in the execution of the premise as done on TV.

Ignore everything for a moment except for the drawn illustration that they used to explain the premise. It showed a plane on a conveyer and (critical point) the plane was stationary..

Now look at the two experiments and ask one question. If the goal of the conveyer was to keep the plane stationary and the planes moved forward in the experiments, did the conveyer accomplish it's goal? I'm guessing you answered yes to the question while I said no. I further assert the wrong types of tests were performed to see what speed the treadmill would need to obtain.

Now consider an alternative experiment. (I ask forgiveness twice in the following, One, the following will probably never take place and, Two, the example of our fishing trips is the best I could think of to help in the description.)

I love to go fishing with my daughter it's a great pasttime. There's a weight restriction, however, on some of our catches so we carry a small gravity scale to make sure we don't break any rules.

Consider then the proposal where a plane is sitting on a large conveyer. Attach a rope to the tail of the plane and attach a large gravity scale to the end of that rope. The other end of the scale is attached to an anchor capable of withstanding whatever force might be generated by the pull of the propeller. Turn on the motor and advance it to full throttle.

Now turn on the conveyer and advance it's speed to where the gravity scale reads zero pounds. At this point, the experiment mirrors the premise and the conveyer obtains it's goal. If you now release the rope, the plane will not fly because there's no air flowing over the wings to create lift."
Regarding the picture - of course they didn't show it moving, it's a still picture :)

Tests: None performed by myself. Instead, I have made observations based on real world examples. Specifically, planes taxiing at the airport use almost no throttle setting to maintain their taxi speed. Double that since the wheels are spinning twice as fast, and I guesstimate at 5%-10% throttle. Double that if you want, it's still less that 100%. This guesstimate is backed up by experience in flight simulators, again taxiing with less that 10% throttle.

Regarding your proposed test: I have suggested such a test many times, using the same type of fishing scale. Here's my setup:

1. Tether the plane at the rear to a fixed anchor. Throttle up to 100% and measure the force, i.e. the thrust.
2. Put the plane on a conveyor with it's engine off. Tether the plane at the nose to a fixed anchor. Turn on the conveyor to its maximum setting. Measure the force, i.e. the drag.

If thrust > drag, the plane moves forwards. If thrust = drag, the plane should be stationary. If thrust < drag, the plane should move backwards.

My hypothesis is that the thrust will be an order of magnitude greater than the drag.

In your version, however, you are disallowing the plane from applying full power and TRYING to take off. You are matching forces, when the myth specifically says to match speeds.

I would love to meet in real life and make this experiment happen, just to get people to stop doubting, but somehow I don't see that happening. Oh well.
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941nmb

941nmb
RE: Sorry, the math is wrong!
May 5 2008, 12:50 AM EDT
Aaaahhh!

I didn't see your proposed experiment until now and I agree; under most of these open-ended conditions, flight is possible.

There are a few propositions under these terms, however, that, as a matter of fairness, should be considered:

If the plane is capable of infinite thrust and the conveyer is limited to a set maximum, then the plane will always get airborne and the myth is true.

If the plane has unlimited thrust potential and the conveyer also has infinite potential, then the myth is plausible but impossible to research.

If the plane has limited thrust and the conveyer is also limited on potential, then the myth is both plausible and possible to research. It really comes down to how much bigger one item is over the other and your hypothesis hints that I'm allowed to get a bigger, more powerful conveyer.

If the plane has a set limit on thrust and the conveyer has infinite potential, then the plane will never fly. Eventually, the wheels will be unable ward off all of the drag force and the myth is busted.

Under these sets of values, You're right at one end of the scale and I'm right at the other.

If we're talking abount an all-or-nothing proposition where plausible is not an acceptable outcome, then, under the Scientific Method of Investigation, the myth must be busted because one set of variables exist that negate the hypothesis.

Either way, I appreciate the friendly sparring. My hats off to a worthy opponent!
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martiandrifter01
martiandrifter01
RE: Sorry, the math is wrong!
May 5 2008, 1:11 AM EDT
TO ALL PARTIES: There's a number of people who don't want to admit defeat on both sides of this ridiculous argument.

I HAVE A SOLUTION.

Having seen a string of proposals on how to conduct the test, most of which alter the airplane, test conditions or belt unfairly in favor of the conveyor, I propose one more change: alter the airplane. Fair, as they say, is fair.

Let's make the airplane one with 3-axis, 360-degree thrust vectoring and 360-degree laminar-flow airfoil. No matter which way you pull the plane it will generate lift and take off. Plus, you'll have an airplane that looks like something out of a 1950s sci-fi flick (Forbidden Planet, anyone?).

You'd think someone that calls himself MartianDrifter would've thought of Yew-Eff-Oh's sooner. (I was holding out.)
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 5 2008, 8:26 AM EDT
"TO ALL PARTIES: There's a number of people who don't want to admit defeat on both sides of this ridiculous argument.
"
http://xkcd.com/386/

;)
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EnderGT

EnderGT
RE: Sorry, the math is wrong!
May 5 2008, 8:47 AM EDT
"Aaaahhh!

I didn't see your proposed experiment until now and I agree; under most of these open-ended conditions, flight is possible.

There are a few propositions under these terms, however, that, as a matter of fairness, should be considered:

If the plane is capable of infinite thrust and the conveyer is limited to a set maximum, then the plane will always get airborne and the myth is true.

If the plane has unlimited thrust potential and the conveyer also has infinite potential, then the myth is plausible but impossible to research.

If the plane has limited thrust and the conveyer is also limited on potential, then the myth is both plausible and possible to research. It really comes down to how much bigger one item is over the other and your hypothesis hints that I'm allowed to get a bigger, more powerful conveyer.

If the plane has a set limit on thrust and the conveyer has infinite potential, then the plane will never fly. Eventually, the wheels will be unable ward off all of the drag force and the myth is busted.

Under these sets of values, You're right at one end of the scale and I'm right at the other.

If we're talking abount an all-or-nothing proposition where plausible is not an acceptable outcome, then, under the Scientific Method of Investigation, the myth must be busted because one set of variables exist that negate the hypothesis.

Either way, I appreciate the friendly sparring. My hats off to a worthy opponent!"
The problem I have with your argument is in the application of the force exerted by the conveyor onto the plane. The conveyor might be powerful enough to move tons of steel, but if there's not enough friction between it and the plane, that force will never effect the plane. Because the wheels of the plane are free-spinning, almost all of the friction is removed, and so the plane never feels the force of the conveyor. The only impact is that the plane's wheel spin faster.

Back to the experiment.

Take any real-world fixed-wing aircraft that you might see in operation at a civilian airport. This excludes helicopters and military aircraft, such as the Harrier or any other that might have VTOL capability.

Take any real-world conveyor or treadmill, with a belt of sufficient length and width to fully support the chosen plane. If you feel that its drive motor is inadequate, feel free to replace it with the most powerful drive motor in the world.

Perform the experiment as I described it. Measure the thrust generated by the plane with the conveyor off, then measure the force exerted on the plane by the conveyor with the plane off. Use maximum speed or power settings for both.

I *guarantee* you that the thrust will be greater than the drag.

Looking back at your argument one more time, you are stipulating that the plane is not allowed to generate more thrust than the conveyor is exerting on it. This constraint is not what is required by the myth, as the myth specifies matching speeds, not matching forces. What you are saying is that the plane isn't allowed to apply full power, and thus *try* to take off.

I do admit that if the conveyor moves fast enough, there is risk of damage to the tires and wheels, which could severely impact the plane's ability to take off, much less land again (should it manage to survive long enough). But since the speeds should be matched, I suspect the plane would be airborne by then.
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