Plane on a Treadmill

[N Harmon]

Yes I did ask before, but I have to admit that your answer did not actually answer my question. I really want to know how the forces can be exerted by the treadmill in such magnitude and direction to counteract the force provided by the propeller.

It would be simple mechanical advantage, where the force of friction is multiplied over the huge distances developed by the treadmill to create a huge amount of work. Since there is a limited amount of mechanical advantage available to the propeller, and by definition of the problem, an unlimited amount of advantage available to the treadmill, the treadmill at some point should be able to counteract the force produced by the propeller.

Of course, this assumes all sorts of things in the problem that could be perceived differently by different people, thus the problem of ambiguity.

[lordmonar]

Okay......Simple machines.

The axle and wheel.

The Wheel works in two ways.

One it reduced the amount of friction between the load and the surface.  Say a 10'X10' load weighing 2000lbs sitting on the tarmack.....you can push all day and it will not budge.

But put it on 6" wide tricycle gear wheels and the area in contact with the ground is GREATLY REDUCED.

They also reduce friction by transferring it to the axle.

The weight of the load is not sitting on the rough ground....but on the ultra smooth surface of the axle bearings.  The bearing have an even smaller surface area then the outside of the tires....again greatly reducing friction.

The other way wheels work is by acting as a lever.  The longer the lever the less force it takes to move a particular load a set distance.

This is how you can get those iron men who can move 747's!

Now.....with this in mind.  If you want specific numbers we would have to know a whole lot of details that are just not provided.

We would have to know the resistive properties of the tradmill....it is Teflon, rubber, concrete, glass, polished steel?  The make up of the surface material has a lot to do with this problem.  Teflon is specifically designed to be low friction. but we use rubber mats in our bath to keep from slipping on the porcelain tub.

Then we would have to know about the properties of the wheels themselves.  Some tires are designed to have a lot of grip.  Take drag racing.....lots of surface area with very soft rubber.....they WANT a lot of traction between the road and the tire......airplanes tires are ususally designed with two things in mind.  Reducing friction on taxi and take off.....but having enough friction to stop the aircraft on landing or during an abort. 

We also need to take into account the size of the tires. The larger the diameter of the tire the less force it take to move the load. But larger tires weigh more too. Big Fat tires are good in very rough terrain...that is why bush planes has like the husky and cubs have big fat donut tires.  These tires are not so good on asphalt as they are too soft and get eaten up by the tarmac and they add additional weight to the aircraft.

Next we have to look at the efficiency of the axle/bearings.  The bearing/axle interface is critical.  Seize a bearing and you can lock up a wheel.

The next issue we would have to look at is the power plant and propeller....how much static thrust do they generate and how much total thrust do they generate at take off speed.

So.....to answer your question....we cannot answer specific questions about the total induced drag because we don't know any of the many, many, many variable in the problem. (I did not even go through things like density altitude, head winds, tail winds, crosswinds.  gross take off weight, ramp weight etc ET AL.)

My GUT tells me that unless I am missing something very basic.....the treadmill can't generate enough drag to counter act the thrust of a 182's engine/prop combination.  The wheels are too efficient.

[davidsinn]

Let's go back to the original post shall we?

Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

Picture the airplane sitting on the conveyor 36/18 if it were a runway. Advance the throttle and the thrust of the engine moves me forward to the north at one knot and the conveyor matches my speed at one knot to the south so the wheels are spinning at the equivalent of two knots. Let's say my lift of speed is 60 knots so at 60 knots forward speed on the aircraft the conveyor is moving at 60 knots in the other direction and the wheels are spinning at 120 knots. I now lift off and leave the conveyor. There is nothing that will stop me from moving. If the airplane's speed is zero then the conveyor is at zero as well because I haven't caused the wheels to spin yet. I can only cause the wheels to spin by moving the aircraft and I just demonstrated that the conveyor will not exceed my forward speed and the amount of friction in the system should not come anywhere near the amount needed to keep me from moving forward. The reason the hypothetical conveyor is the length of a runway is because it assumes the aircraft is moving forward to gain airspeed.

[AirAux]

Where do you get to intercede that the wheels are moving at 2 knots and not at 1 knot as the premise states??  The thrust of the engine (as measured by the speed of the wheels)  and the speed of the conveyor belt match so you are not moving anywhere and you will not fly.  No air moving over the wing and no lift..No Flying..  The only way would be "if" the engine could create enough power to move enough air over the wing to lift it straight up, ie, creating airspeed while stationary...   

[N Harmon]

Picture the airplane sitting on the conveyor 36/18 if it were a runway. Advance the throttle and the thrust of the engine moves me forward to the north at one knot and the conveyor matches my speed at one knot to the south so the wheels are spinning at the equivalent of two knots.

Stop right there. Your situation violates the premise of the original post. Here it is again (emphasis mine):

Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

[Major Lord]

The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

[lordmonar]

Where do you get to intercede that the wheels are moving at 2 knots and not at 1 knot as the premise states??  The thrust of the engine (as measured by the speed of the wheels)  and the speed of the conveyor belt match so you are not moving anywhere and you will not fly.  No air moving over the wing and no lift..No Flying..  The only way would be "if" the engine could create enough power to move enough air over the wing to lift it straight up, ie, creating airspeed while stationary...

If you can explain how you can acheive this I would listen to it.

How can you move the conveyor belt in a way that is exactly matches the speed of the wheels......with out affecting the speed of the wheel.

The treadmill either moves in the same direction as the aircraft......keeping the wheels stationary.....but the plane still has forward motion and will lift off.   Or....the treadmill moves in the opposite direction.....INCREASEING the speed of the wheels....which violates the premeis of the problem......and again not inducinging enough drag to prevent flight.

[davidsinn]

I just spent the better part of two hours drawing some pretty pictures and another 30 min typing this post, to put this one to bed once and for all.

First let's review the four forces at work on an aircraft: Money, red tape, politics...

Seriously: Lift, Drag, Thrust, and Gravity.

If Thrust>Drag and Lift>Gravity then the bird will fly. There is no denying that.

Let's set up our scenario. The observer(you) is on the ground. All velocity's are relative to the ground not the treadmill.


The aircraft is static. No thrust, no drag, 1g of gravity and 1g of lift due to the treadmill pushing up on the aircraft.

There are two possible ways for this to work. The treadmill can move to the right or it can move to the left. I will address a right moving treadmill first.



Case one. I apply power and Sir Newton says that unless my aircraft is tied to the ground the thrust of the engine will move it to the right. At this point I have 10 kts of velocity relative to the ground. Since the treadmill is matching my wheel speed exactly and for this one I decided the treadmill is moving to the right it's velocity is 10 kts and my wheels have zero RPM. I have a little drag due to aerodynamics. Lift=gravity.


A little while later my aircraft is at 60 kts relative to the ground which gives me 60 kts of airspeed. My treadmill is still matching my wheels so it's at 60 kts and my wheels still have no rotation. Lift>gravity so I lift off. Drag is higher but still well below my thrust.

Case 2 Treadmill moves to the left.

I apply power and Sir Newton says that unless my aircraft is tied to the ground the thrust of the engine will move it to the right. At this point I have 10 kts of velocity relative to the ground. Since the treadmill is matching my wheel speed exactly and for this one I decided the treadmill is moving to the left it's velocity is 20 kts and my wheels have 200 RPM. I have a little drag due to aerodynamics and a little drag due to wheel bearing friction. Lift=gravity.

A little while later my aircraft is at 60 kts relative to the ground which gives me 60 kts of airspeed. My treadmill is still matching my wheels so it's at 120 kts and my wheels are at 1200 RPM. Lift>gravity so I lift off. Drag is higher but still well below my thrust.

Any questions?

[N Harmon]

The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

Take a wheel with a circumference of 4 feet. If it rolls on a stationary treadmill at 5 RPMs, then it's speed is ( 4 feet * 5 RPM ) 20 feet per minute. Now, if the treadmill is moving backward at a speed of 20 feet per minute, then the wheel will appear to be stationary from an observer on the ground. If the wheel is not stationary, then it's speed is not the same at the treadmill. If it is moving forward in relation to the ground, it's speed is greater than 20 feet per minute. If backward, it's less than 20 feet per minute.

Can we agree on that?

Any questions?

How did you arrive at your force figures? And did you multiply them over the distance to find the amount of work they performed?

[davidsinn]

The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

Take a wheel with a circumference of 4 feet. If it rolls on a stationary treadmill at 5 RPMs, then it's speed is ( 4 feet * 5 RPM ) 20 feet per minute. Now, if the treadmill is moving backward at a speed of 20 feet per minute, then the wheel will appear to be stationary from an observer on the ground. If the wheel is not stationary, then it's speed is not the same at the treadmill. If it is moving forward in relation to the ground, it's speed is greater than 20 feet per minute. If backward, it's less than 20 feet per minute.

Can we agree on that?

Yes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

Any questions?

How did you arrive at your force figures? And did you multiply them over the distance to find the amount of work they performed?

The g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

[N Harmon]

Yes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

I'm not missing that fact at all. What makes you think that?

The g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

You didn't say why you only calculated forces and not work.

[ßτε]

You didn't say why you only calculated forces and not work.

Because work is irrelevant. It is the force that leads to acceleration to speeds at which the aircraft can take-off.

[tsrup]

This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

[davidsinn]

Yes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

I'm not missing that fact at all. What makes you think that?

The g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

You didn't say why you only calculated forces and not work.

I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

[Major Lord]

This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

Dude! I suggested that anyone who thought it could not lift off should turn in their Yeager too! I also offered a wager of $100.00 to Nathan, but he has not bit......I don't think there is any way to convince the people who believe in magic that it will fly. I guess we are just going to have to build one great big treadmill and find a pilot willing to "risk" his life with a daring, high wheel RPM, normal speed takeoff! Where do they find such men?

Major Lord

[CadetProgramGuy]

I still believe that the aircraft will not fly.

In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

Now can someone tell e how much relative wind is moving over the airfoil (wing) with a relative speed of Zero?

The premise of the question in my understanding is that the treadmill speed was matched by the wheels of the aircraft.  Equal forces applied, Does the aircraft move anywhere? No it does not.

I'll take the $100, and keep my Yeager.

[tsrup]

In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

I fail to see how a treadmill has anything to do with a propeller.

[N Harmon]

Major Lord isn't interested in any serious conversation on the subject and is just trolling.

I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

This is the second time you have said the wheels will spin faster than the treadmill, which is NOT what the original problem said the treadmill is designed to do. The original problem said the treadmill will "exactly match the speed of the wheels, moving in the opposite direction". It doesn't say it will match them "once the airframe starts to move", or at half of the speed of the wheels. It says it will MATCH the the speed, EXACTLY.

I would appreciate if you, and some of you others tone down the condescending "you are completely failing to grasp the concepts at work here". I do grasp them. You are violating the conditions of the original problem by saying the velocity magnitude of the wheels and treadmill are unequal.

I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

[tsrup]

This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

Dude! I suggested that anyone who thought it could not lift off should turn in their Yeager too! I also offered a wager of $100.00 to Nathan, but he has not bit......I don't think there is any way to convince the people who believe in magic that it will fly. I guess we are just going to have to build one great big treadmill and find a pilot willing to "risk" his life with a daring, high wheel RPM, normal speed takeoff! Where do they find such men?

Major Lord

Yes, I believe it was your post that I was referencing

I'm sure I would be fine "risking" life and limb in this daring pursuit of science.  I better check my POH first to find out what published max wheel speed is. 

[darn] me for even mentioning it, I can see the new AD now..

"As per CFR XXX-XX wheels on the cessna 182T aircraft are limited to XXRPM.  Placard shall be placed in the middle of the windscreen in Bright neon pink on brown background no smaller than 3" by 8" "   

[N Harmon]

I would like to point out that the conditions of the original problem are impossible to replicate in the real world. That might be the biggest impediment to understanding here.