Stupid plane on a treadmill question

[Texasspilot]

I think the ice one would be better. Those planes on skies in Alaska.

the problem with those is that the surface isn't moving in the opposite direction as the skis/floats.

The problem i see is friction. Ice/water/treadmill would create a large amount of friction and heat and probably melting/exploding whatever you were on before flight.

 

[johntlewis]

I suppose my tiny brain is too small to properly comprehend all this, but it sure is fun. Although I said in a previous post that the airplane would not take off, I'm at least seeing the other side based on two of the most recent posts. I at least now see that my running on the treadmill illustration isn't as sound as I once imagined.

I wonder if an engineer could use some kind of model airplane and a custom designed treadmill to prove it once and for all?????? With enough money I'm sure just about any kind of experiment could be conducted.

 

[grassrootsflying]

http://www.avweb.com/news/pilotlounge/191034-1.html

No experiment is needed, this question is stupid. Read this article, it explains it very well.

 

[therookie]

These physics questions always pull me out of hiding, does that make me a nerd?

the problem with those is that the surface isn't moving in the opposite direction as the skis/floats.

Can't a float plane take off upstream in a river given a reasonably powerful engine?

 

[SteveC]

The plane will take off.

Picture yourself standing on a very long treadmill, wearing roller blades, hanging onto a rope that is tied to a tree at the far end of the treadmill. As the experiment begins, you are stationary, the belt is stationary, and all is well in the world. You, being the stud that you are, pull on the rope and you begin to roll forward. But hey, as you begin to move forward at the stately pace of one mile per hour, the treadmill starts running at the same speed, but in the opposite direction! The interesting thing, though, is that the roller blades that you are wearing are free wheeling, and they start to spin even faster - where they started spinning at an rpm that gives the surface of the wheel a speed of one mile per hour, now the ground moving underneath them causes the wheels to spin at two miles per hour! Amazing! Interestingly, your body is still moving forward in relation to the earth at one mile per hour, you have a one mile per hour "breeze" in your face, and your wheels are free wheeling underneath you at 2 MPH. You, feeling flush with success, begin to pull yourself forward on the rope at a faster and faster pace. Eventually you are hand-over-handing and pull yourself right off the end of the treadmill, while your wheels are spinning twice as fast as you were traveling over the ground, and the treadmill was futilely spinning in the opposite direction.

The key is in realizing that your roller blade wheels, just like an airplane's wheels, are free-wheeling. The wheels are not what drive an airplane forward, and the ground moving backwards underneath the wheels cannot stop the airplane from moving forward. Moving the ground (treadmill) underneath the plane will make the wheels spin faster and faster and faster, but they will not and cannot stop the plane from moving forward, unless you step on the brakes.


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[Flysher]

I think alot of the confusion with this question is that some people don't realize that the wheels are not tied or geared to the engine like in a car.

The post above from Texasspilot is the best description I have seen so far, Doug you should make that a sticky so people stop bringing this up every 6 months

 

[darrenf]

What I want to know is how can a message board that is geared towards pilots have so many people that don't get this? Do they think planes have propellers because it gets hot in the cockpit?? This is such a stupid question why does it always come up? Who are these people that think the plane will not move on a tread mill? What are they doing in a cockpit?? That scares me, seriously!!

 

[pullup]

Hmmm, I seem to have been mistaken by the original diagram. It shows the treadmill opposing the wheels rotation, hence locking up the wheels. If the treadmill were going WITH the rotation of the wheels then that is a different story. The problem usually says that the speed of the treadmill equals the speed of the plane. Therefore, the wheels will be going twice as fast as the plane on takeoff.

 

[bdhill1979]

What I want to know is how can a message board that is geared towards pilots have so many people that don't get this? Do they think planes have propellers because it gets hot in the cockpit?? This is such a stupid question why does it always come up? Who are these people that think the plane will not move on a tread mill? What are they doing in a cockpit?? That scares me, seriously!!

:yeahthat: This is so pointless

 

[johntlewis]

What I want to know is how can a message board that is geared towards pilots have so many people that don't get this? Do they think planes have propellers because it gets hot in the cockpit?? This is such a stupid question why does it always come up? Who are these people that think the plane will not move on a tread mill? What are they doing in a cockpit?? That scares me, seriously!!

I really I wish I was as smart as you. I came to this forum to learn more about aviation but since I'm so stupid I guess I should just sign off and not come back.

Seriously, dude, I'm trying to learn things here on jetcareers, and I for one don't prefer to have my struggle with questions called stupid. And isn't it a bit over the top to suggest that a theoretical question has anything to do with the question of if someone should be in the cockpit or not? Do you seriously believe someone can't properly pilot an airplane just because they don't yet see the proper answer to this question? Please.......give me a break.

 

[E_Dawg]

Not so quickly - if the plane was at rest it would have to overcome a certainly amount of friction to get the wheels too move, and then kenetic friction while they move. This would increase the take off distance.

It doesnt need to overcome any friction if the wheels aren't going to move anyway. All it needs to do is build up speed relative to the air, which it can do just fine.

Remember the treadmill is moving at the exact same speed as the plane and therefore has zero motion relative to the plane (and wheels) - i.e. it's going in the same direction as the plane and appearing to catapult the plane into the air.

I actually saw this exact scenario last week, they had NOTAMed the runway out of service and had replaced it with a giant treadmill.

 

[taseal]

I saw this on another forum once.. I was laughing my ass off....

my only response was "you guys are ####ing idiots"

 

[darrenf]

I really I wish I was as smart as you. I came to this forum to learn more about aviation but since I'm so stupid I guess I should just sign off and not come back.

Seriously, dude, I'm trying to learn things here on jetcareers, and I for one don't prefer to have my struggle with questions called stupid. And isn't it a bit over the top to suggest that a theoretical question has anything to do with the question of if someone should be in the cockpit or not? Do you seriously believe someone can't properly pilot an airplane just because they don't yet see the proper answer to this question? Please.......give me a break.

I'll give you a break. My comments were not directed at you personally.

My comment still stands, it scares me that someone that has trouble understanding this concept will be sharing the skies with me, or worse yet, someday piloting a tube that might be carrying my family.

I don't understand how you can have an aircraft in forward motion if it's speed is exactly matched by the treadmill. I don't know about everyone else, but when I run on the treadmill (which isn't often ), there is no actual forward motion. I don't care how fast I run on that treadmill, there will never be enough wind in my face to make me fly simply because you produce no real airspeed when you're running on a treadmill.

Have you ever seen an airplane with legs as it's source of propulsion? If so, how well did it fly??

I at least now see that my running on the treadmill illustration isn't as sound as I once imagined.

I wonder if an engineer could use some kind of model airplane and a custom designed treadmill to prove it once and for all??????

I am glad to see that you are learning, and that is what this website is here for. But this post here, where you need to see it to believe it is part of what concerns me. And a person that needs to see a demonstration with a model aircraft could then be shown a model aircraft in a hover and believe that full-scale aircraft can do the same. It is that lack of abstract understanding I find troubling. Aircraft are comprised of complex systems, and if you cannot visualize and understand how those systems work, you cannot properly and expeditiously diagnose and correct a failure of said systems. That is what scares me.

 

[TonyC]

didn't get much sleep but i've been arguing this question on another forum and then this hit me.

tell me what i got wrong here/

It is no big surprise that confusion might ensue when an answer is given, but no clear question posed. As many times as I've seen this "treadmill riddle" argued, at least the others began with a clear statement of the riddle before answers were posited. In this case, Texasspilot offered an answer before clearly stating the question.


The question, as I have seen it stated, is as follows:

A plane is standing on a runway that can move (some sort of treadmill). The plane moves in one direction, while the conveyer moves at the same speed but in the opposite direction. Can the plane take off?"

This is not as much a question of aerodynamics or physics as it is a question of reading comprehension. Sentence 2: "The plane moves ..." No, the treadmill cannot, by definition keep the airplane stationary, because the question says, "The plane moves."

The treadmill matches the plane's speed, but in the opposite direction. No reference is made to wheel speed, or the treadmill matching the wheels' speed. The treadmill matches the plane's speed. If the plane moves at 5 knots, the treadmill moves at 5 knots, in the opposite direction. If the plane moves at 100 knots, the treadmill moves at 100 knots, in the opposite direction. If you look at the wheels, not because they matter, but because you're curious, you'll see they are spinning at twice the speed of the airplane, since the airplane is moving in one direction, and the treadmill is moving at the exact same speed in the opposite direction.

The plane moves . . . and it accelerates . . . and it flies.






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[Chris_Ford]

It is no big surprise that confusion might ensue when an answer is given, but no clear question posed. As many times as I've seen this "treadmill riddle" argued, at least the others began with a clear statement of the riddle before answers were posited. In this case, Texasspilot offered an answer before clearly stating the question.


The question, as I have seen it stated, is as follows:



This is not as much a question of aerodynamics or physics as it is a question of reading comprehension. Sentence 2: "The plane moves ..." No, the treadmill cannot, by definition keep the airplane stationary, because the question says, "The plane moves."

The treadmill matches the plane's speed, but in the opposite direction. No reference is made to wheel speed, or the treadmill matching the wheels' speed. The treadmill matches the plane's speed. If the plane moves at 5 knots, the treadmill moves at 5 knots, in the opposite direction. If the plane moves at 100 knots, the treadmill moves at 100 knots, in the opposite direction. If you look at the wheels, not because they matter, but because you're curious, you'll see they are spinning at twice the speed of the airplane, since the airplane is moving in one direction, and the treadmill is moving at the exact same speed in the opposite direction.

The plane moves . . . and it accelerates . . . and it flies.
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Bzzt, wrong.

The tires spin twice as fast as "normal," yes? Can you name any plane thats max tire speed is greater than twice its rotation speed? If so, that airplane can take off, if not, the tires shred and all of a sudden we're dealing with metal rims which create tons more friction than traditional tires, and inevitably ends up with the plane losing directional control and exiting the treadmill, thus unable to complete its takeoff.

 

[ananoman]

Bzzt, wrong.

The tires spin twice as fast as "normal," yes? Can you name any plane thats max tire speed is greater than twice its rotation speed? If so, that airplane can take off, if not, the tires shred and all of a sudden we're dealing with metal rims which create tons more friction than traditional tires, and inevitably ends up with the plane losing directional control and exiting the treadmill, thus unable to complete its takeoff.

Well, I fly a Hawker 800XP. At max weight, SL, and ISA, Vr is 131 KIAS.

Max tire speed is either 190 or 210 MPH. So yes, max tire speed would be exceeded. Even at a more typical 5,000lbs under gross weight, you are still looking at a Vr of 115 KIAS.

But, you are assuming that the tires will suddenly explode if you exceed the max tire speed. I don't think this is likely. They will get hot, no question. Service life would be shorter, but I doubt they would fail. On a large airliner, you may have a problem, but most small/midsize jets and props would be fine.

Car tires are the same, they are only rated up to a certain speed, but you can easily exceed this for a short time with no ill effects. If you try to put a tire with a low speed rating on a fast car and run it on the autobahn, you will probably have a problem.

 

[TonyC]

Bzzt, wrong.

The tires spin twice as fast as "normal," yes? Can you name any plane thats max tire speed is greater than twice its rotation speed? If so, that airplane can take off, if not, the tires shred and all of a sudden we're dealing with metal rims which create tons more friction than traditional tires, and inevitably ends up with the plane losing directional control and exiting the treadmill, thus unable to complete its takeoff.

Troublemaker. I thought about just naming a few types and leaving it to you to disprove the claim. I just couldn't make myself do that.


Yes, the tires spin twice as fast as normal.



But, since they will all fail at the same time, there will be no directional control issues, and the airplane will remain on the treadmill until it reaches takeoff speed.




Or, for your particular case, we can start with metal wheels -- do away with the tires altogether. The friction with which we're concerned is not between the wheels themselves and the ground (treadmill), but the friction between the wheel's axle and the hub. Initially that friction is enough to oppose the movement of the airplane -- that's why it sits at rest. Once that initial force is overcome by thrust, the increase in friction related to increased speed is negligible.


What I want to know is how they engineer those tires to shred at the Max Tire Speed.







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[Chris_Ford]

But, since they will all fail at the same time, there will be no directional control issues, and the airplane will remain on the treadmill until it reaches takeoff speed.




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They would only shred at the same time in the perfect environment. In practice, they likely would not.

but I was just joking anyway.

 

[Realms09]

Here's the problem. Somewhere along the way the following idea entered the picture:

"If the treadmill speed always exactly equals the wheel speed, and it is moving in the opposite direction, the airplane has no forward motion and can never takeoff."

Wheel speed could mean a variety of things (how fast are the wheels spinning, or how fast is the center of mass of the wheels moving translationally?), so let's flesh it out. Define two frames: one fixed to the stationary ground, and one fixed to the moving treadmill surface. In a frame fixed to the treadmill, let's say "wheel speed" is simply the translational speed of the aircraft. Now, if the treadmill is moving at the same speed in the opposite direction, it is quite clear that the aircraft is not moving in the stationary ground frame.

Aircraft is moving +10 m/s relative to treadmill surface, treadmill surface is moving -10 m/s relative to ground surface, therefore aircraft is moving at 0 m/s relative to ground surface (airspeed zero).

If this condition is maintained at all times, then the aircraft will never take off. That's a fact, and some stop there.

The catch is, this condition will not exist in reality. Let's do a play by play with an aircraft at rest on a treadmill, which is also at rest. The treadmill is free to rotate (it is not driven at a particular speed), as are the wheels of the aircraft. Suppose the aircraft is facing towards the right.

This is sort of an expanded account where things that occur simultaneously are separated into a sort of a cause-effect chain. It also assumes rigid wheels, so rolling resistance is ignored.

1. The aircraft engines are throttled forward and develop thrust.
Forces on aircraft: thrust to the right
Forces on the treadmill: none

2. As a result of the thrust, the aircraft wants to move to the right. The wheels are attached to the aircraft, so they want to move to the right as well. At the contact point where the wheels meet the treadmill, the wheels want to slide to the right. Static friction opposes this tendency, however, and "rolling without slipping" initiates. There is now a static friction force to the left acting on the aircraft, which also acts to spool up the wheels. An euqal and opposite force acts on the treadmill to the right.
Forces on aircraft: thrust to the right, static friction to the left
Forces on the treadmill: static friction to the right

3. As a result of these forces, accelerations occur. Thrust will exceed the static friction and the aircraft will move faster and faster to the right. Only static friction will act on the treadmill, so it also moves faster and faster to the right. Note that in the condition mentioned above where there is zero airspeed, the treadmill is moving in the opposite direction. In the real case it is moving in the same direction.
Forces on aircraft: thrust to the right, static friction to the left, air drag to the left
Forces on the treadmill: static friction to the right

4a. The aircraft accelerates to the takeoff airspeed, and away it goes.
Forces on aircraft: thrust to the right, air drag to the left
Forces on the treadmill: none

4b. At a certain point drag may equal thrust on the aircraft, and it will stop accelerating. Once the aircraft starts moving at a constant speed, the wheels will no longer have a tendency to slip and the static friction will disappear. The treadmill will also stop accelerating and will move at a constant speed. Airspeed is positive as the aircraft moves in a steady condition to the right, below takeoff speed.
Forces on aircraft: thrust to the right, air drag to the left
Forces on the treadmill: none

 

[TonyC]

They would only shred at the same time in the perfect environment. In practice, they likely would not.

but I was just joking anyway.

I must be gettin' rusty. I started by calling you a troublemaker, and then by posing an equally ridiculous statement (maybe more ridiculous, whoever heard of tires all failing at the exact same time?), and you didn't know that I knew that you were joking? <shakin' head> I even used the rolleyes emoticon. Am I gonna hafta resort to using the sarcasm tag when I'm being facetious?



Troublemaker.






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