# Aeroplanes & Conveyor Belts

d2tw4all

## Main Question or Discussion Point

I hope there are some physicists here, an argument has been going on for many years between myself and someone else, anybody who has any insight, please answer the following question and you will help to resolve this debate!

A 747 jetliner weighing 163844 kg (the empty weight of a 747) lands on a treadmill that is 500 meters long running in the opposite direction of the plane and doesn't apply any brakes whatsoever, relying only on whatever friction is in the bearings of the wheels to slow it down. The speed the aircraft lands is 200kph, and the speed that the treadmill is moving in the opposite direction of the plane is 200kph. Assume the tires and landing gear withstand the impact, remember, little to no brakes are applied at any time. Also, it's autonomous so there is no margin for pilot/human error, assume it's a "perfect" landing onto the treadmill. WHAT WILL HAPPEN.

Thanks!
Tom Lavoie

Related Other Physics Topics News on Phys.org
The wheels rotational speed would accelerate to twice the speed of the treadmill and the plane would continue to move toward the far end of the treadmill till it goes off if it. Sort of like taking a friction car and moving it against the ground which is staionary gives one speed to the wheels, but to get an even higher speed to the wheels push them against a piece of wood that you are dragging in the oposite direction.

That is my opinion of what would happen.

d2tw4all
Ok, just so I am clear, what's your physics background, for the record.
Thanks a lot for replying, anyone else have an opinion?

Tom Lavoie

enigma
Staff Emeritus
Gold Member

Originally posted by d2tw4all
please answer the following question and you will help to resolve this debate!
If you don't mind me asking, what are the points the two of you are arguing?

A 747 jetliner weighing 163844 kg (the empty weight of a 747) lands on a treadmill that is 500 meters long running in the opposite direction of the plane and doesn't apply any brakes whatsoever, relying only on whatever friction is in the bearings of the wheels to slow it down. The speed the aircraft lands is 200kph, and the speed that the treadmill is moving in the opposite direction of the plane is 200kph. Assume the tires and landing gear withstand the impact, remember, little to no brakes are applied at any time. Also, it's autonomous so there is no margin for pilot/human error, assume it's a "perfect" landing onto the treadmill. WHAT WILL HAPPEN.
Well, you've got a big qualifier in there when you say that the tires and landing gear withstand the impact. If that is the case, then, just as Artman described,the plane will slow down a little bit by the time it gets to the end of the runway... maybe a little bit more than if the plane landed on a normal runway without applying brakes.

The problem is that the wheels and landing gear are not designed to sustain a 400kph landing. My SWAG factor tells me that the bearings would overheat, locking the wheels, and causing them to overheat and explode. Big mess.

For the record (since you asked): senior year aerospace engineering major.

Last edited:
For the record, my physics background is mostly practical and not academic. I've been doing Mechanical Engineering for about 20 years.

I drew the situation out to arrive at my guess.

d2tw4all
I kind of want unbiased opinions to the question and that's why I didn't identify the two opinions, I just need the most reputable people I can find to answer the question as best they can, assuming the landing gear can withstand the landing and have bearings that don't sieze up. Thanks a lot for your answer, I hope others will or if anyone knows a physics professor who could comment, that would be even better.
Thanks!
Tom

enigma
Staff Emeritus
Gold Member
Originally posted by d2tw4all
Thanks a lot for your answer, I hope others will or if anyone knows a physics professor who could comment, that would be even better.
While others are more than welcome to comment, if you assume that everything with the landing goes smoothly and safely, there really isn't much to the problem. Definately not enough that would need a PhD to answer it (not to mention that you'd probably get a better answer from an engineer for any 'real-life' type question).

Assuming the landing gear works at the higher speed it's feeling, the only thing which I can think of which would differ between an airplane on a normal runway would be the potential for a higher coefficient of friction in the bearings due to the higher velocity. That would translate into a small decrease in the plane's speed relative to a normal plane's speed at the end of the runway.

My \$.02

LURCH
Agree with the answers already given. Although I am not a physics professor, I have been a pilot. One fo the first things they start drilling into your head in flight school is that the plane "feels" airspeed, NOT ground speed. The exceptions heve already been stated; the gear would be subjected to more friction, I would add that the inertia of the gear would be a greater factor. The mass of the landing gear would have to go from stationary to whatever rpm's they spin at 400 kph, rather than zero to 200. This would make the instant of touchdown quite a jolt, and the plane would lose slightly more speed than it would on a stationary runway. Not enough to make much difference in the rollout distance, though.

Now if, rather than a treadmill, you used a wind machine, that would be a different story. Generate a 200kph wind above a stationary runway, and land your 747 with its nose into that wind, and you can actually get it to hover, and then make a vertical landing!

stipulation. Are you saying that
the planes "autopilot" or whatever
it operating it, refrains from
applying the brakes after touch-
down?

d2tw4all
Correct, no brakes are applied. The general consensus seems to be that the plane will undoubtedly roll off the runway, and that the speed of the wheels will be the sum of the forward velocity of the plane plus the speed of the treadmill in the opposite direction. To me this seems logical but the other party involved does not see this. Instead, he believes that the aircraft landing on the treadmill presents an "infinite plane" for the aircraft to roll on, thus significantly reducing the landing distance required. Obviously if you used brakes the treadmill might provide an advantage in that regard, but resulting in doubling the stresses on the landing gear and it would have the same net effect of doubling the braking capacity on the plane. You have all thus far confirmed my belief, and I thank you!
Tom

By reversing the direction of the treadmill to match that of the plane and varying the speed that it moves as the plane slows to a landing, you could land the plane without the wheels turning much at all and save stress on the landing gear.

russ_watters
Mentor
Originally posted by Artman
By reversing the direction of the treadmill to match that of the plane and varying the speed that it moves as the plane slows to a landing, you could land the plane without the wheels turning much at all and save stress on the landing gear.
Yeah. You could land, set the parking break, and use the brakes on the treadmill to slow and stop the plane. It would stop faster and wouldn't wear down or heat up the brakes on the plane.

With the treadmill going in the opposite direction, all you do is overheat the tires and wheel bearings. The plane won't stop any faster than if it were on a regular runway with no brakes (which is to say it won't stop). The primary force slowing the plane down before the brakes are applied is aerodynamic drag.

d2tw4all
I definitely see how running the treadmill in the same direction as the plane would allow you to essentually "set it down" on the treadmill and then bring it to a stop. You would still have to decellerate it over the same relative distance as you would landing it on a runway, to maintain the same stresses on the plane and it's contents though, so I see no advantage in that from the distance to land aspect...
Tom

Whenever I ride in a jet I hear
a fairly sudden change in the
sound of the engines that happens
after touchdown but before coming
to a complete stop. I've always had the impression they were
reversing the direction of the
turines to help bring the plane
to a stop.

What is this noise, in fact?

d2tw4all
It's called "reverse thrust" and it's pretty much as you said, they are making the engines blow forwards instead of reverse. They can't run the engines in reverse, however, so for jets they usually deploy thrust reversers which are basically pieces of metal that redirect the air coming out of the engine forward instead of backwards.
Tom

Thanks Tom,

Very cool info. Every time I stop-
ped to think about my assumption
they were reversing the direction
of the turbine something told me
it was insane to think they could
do that without the engines coming
to a full stop first, but then I'd
leave the airport and forget the
whole question.

So if they did not engage reverse
thrust, or flaps, or brakes,
how far off the treadmill runway
would the plane go and how bad
would the crash be?

d2tw4all
I would say the crash would be pretty bad, but that wasn't the basis of my argument... No problem on the info... On a side note, propeller driven planes also employ reverse thrust, however usually they actually alter the pitch of the blades to achieve negative thrust, just so you know...
Tom

We are having a heck of a discussion on a board I am a member of. Maybe you guys can provide some insite?

---------------

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?

G01
Homework Helper
Gold Member
No it wouldn't. Because the plane will move with a velocity equal and opposite to the conveyor belt. It will stand in place with respect to the air. Because of this, the plane will not be able to move throught the air, and the pressure under the wing is equal to the pressure above the wing. Since a plane takes off because the pressure under the wing is greater than above, (because it is moving through the air -look into the Venturi Effect), the plane will stay on the ground.

This is a quote from NASA. The Venturi effect is based on Bernelli's theory.

When a gas flows over an object, or when an object moves through a gas, the molecules of the gas are free to move about the object; they are not closely bound to one another as in a solid. Because the molecules move, there is a velocity associated with the gas. Within the gas, the velocity can have very different values at different places near the object. Bernoulli's equation, which was named for Daniel Bernoulli, relates the pressure in a gas to the local velocity; so as the velocity changes around the object, the pressure changes as well. Adding up (integrating) the pressure variation times the area around the entire body determines the aerodynamic force on the body. The lift is the component of the aerodynamic force which is perpendicular to the original flow direction of the gas. The drag is the component of the aerodynamic force which is parallel to the original flow direction of the gas. Now adding up the velocity variation around the object instead of the pressure variation also determines the aerodynamic force. The integrated velocity variation around the object produces a net turning of the gas flow. From Newton's third law of motion, a turning action of the flow will result in a re-action (aerodynamic force) on the object. So both "Bernoulli" and "Newton" are correct. Integrating the effects of either the pressure or the velocity determines the aerodynamic force on an object. We can use equations developed by each of them to determine the magnitude and direction of the aerodynamic force.

Hope that helps. There must be flow/velocity in order for the plane to lift off.

I understand the whole lift aspect.

The main part i'm concerned with is if the plane would have the ability to move in the first place. Here is a quote from someone on the board...

"There are four forces that govern an airplane at any given time: lift, weight, thrust and drag. Lift and weight oppose each other but can be disregarded in this question because all we are talking about it whether or not the airplane can accelerate in reference to the surrounding air. Once we get acceleration and airflow we can get the lift and weight but we don't need to talk about that now.

The throttle of the airplane is advanced and propeller/jet of the airplane produces thrust. We now have a forward vector, say 500 pounds of force, for a small cessna. In order for the plane to remain stationary an equal and opposite force needs to be introduced. Everybody follow? This opposite force would be drag.

We need to account for 500 pounds of drag. Right now the only drag is the force of friction in the wheel bearing. Has anyone here ever tried to push a cessna? It's not very hard...maybe 50 pounds of force at the most. So now we have 450 pounds of force acting in the forward direction. The conveyor belt itself does not impart any friction or drag to the airplane. It will accelerate, gain airspeed, and take off

Let's think of it a different way. Let's say the plane is landing. It approaches the runway at 100 knots and is 1 foot above the ground. As posed in the original question the conveyor belt is moving in an equal and opposite direction. So it's moving 100 knots backwards. As soon as the plane touches down, what happens? nothing...it continues its rollout as if the runway were stationary. It doesn't just automatically come to a stop. The airspeed indicator of the plane would read 100 but the wheel speed would be 200. (apologies to Youens at flightinfo.com)

People cannot separate a car/bike/walking on a treadmill with an airplane. Same thing would happen if you put the airplane on ice and hit the throttle, it will still accelerate at the exact same rate as on a runway (not a safe operation however). Try that with a car/bike/your foot and you'll get drastically different results."

brewnog
Gold Member
G01 said:
No it wouldn't. Because the plane will move with a velocity equal and opposite to the conveyor belt. It will stand in place with respect to the air. Because of this, the plane will not be able to move throught the air, and the pressure under the wing is equal to the pressure above the wing. Since a plane takes off because the pressure under the wing is greater than above, (because it is moving through the air -look into the Venturi Effect), the plane will stay on the ground.

Sorry, this is not right. The aeroplane's wheels are not powered, - the forward motion of an aeroplane on takeoff is produced by thrust from the engines. For these purposes, it makes no odds what speed the runway is moving relative to the plane, since the undercarriage wheels are free to spin at whatever speed they're being driven at.

sm0ke said:
I understand the whole lift aspect.
The main part i'm concerned with is if the plane would have the ability to move in the first place.
To answer your orignal question, No - there wouldn't be forward movenment. If the conveyer offsets any increase in trust... So no matter if there's 500# or 1K# of trust, it won't move if the conveyer can keep up.
In a common situation is the differential relationship between air-speed and ground speed. If an aircraft has a set speed of let's say 75knts and it [hypothetically] hits a head wind of 75knts, it's ground-speed would be 0. Even though the lift + trust is present, the plane isn't moving forward.

James R