The great conveyor belt

[Richard]

Jesse's drawing are spot on. Think of it this way: the conveyer belt is simple a mechanism which results in increased rolling friction. It's no different than bad bearings in the wheels or a significant reduction in power settings. Merely idling along will not produce the required thrust. You need that thrust to carry you aloft. As long as thrust is greater than friction there will be a forward movement which will result in airspeed and achieve flight. Just like a any normal takeoff.

You land your ski equipped a/c uphill on a glacier. You roll out and shut down. Gravity wants to pull the a/c downhill so you stake the a/c in position. Now, ready to depart you fire up and unstake the a/c. You're gliding backwards. Can you still takeoff uphill as you glide backwards downslope? Yes, as soon as thrust overcomes gravity (more precisely, as soon as thrust required for rotation is achieved).

You land your float equipped a/c upstream on a fast moving river. You idle down and then begin a takeoff upstream. Is is possible to takeoff heading upstream against the fast moving river?

Both scenarios remove the problematic question of the wheels. Having done that the only question which remains is one of required thrust.

 

[gibbons]

The problem I had was the way I read the question (gee, that takes me back to High School).

It does not state that as the aircraft moves forward the belt rotates fast enough in the opposite direction so as to keep the aircraft stationary relative to the air mass (which is how I read it to begin with).

The belt simply moves backwards as fast as the airplane is going forward - the same speed - which is virtually irrelevant as has been pointed out many times in this thread.

"In the future I will read the question more carefully."
"In the future I will read the question more carefully."
"In the future I will read the question more carefully."
"In the future I will read the question more carefully."

 

[jesse]

The belt simply moves backwards as fast as the airplane is going forward - the same speed - which is virtually irrelevant as has been pointed out many times in this thread.

Yup. Either way though. It does not matter how fast you move the belt backwards.. The plane can omve forward. If your wheel bearings could take 1000 mph backwards, your thrust could overcome it ..accelerate forward and take off

 

[Bill]

That description works for a drivetrain powered system where the powerplant drives the wheels that are in contact with the surface - such as a car, motorcycle, truck, bicycle, Saturn V crawler, puppy on a leash, etc.

OTOH: Airplane wheels are for all practical purposes free rotation unless the brakes are applied or the velocity is high enough to blowing out tires and/or bearings. IOW airplane wheels are simply surface friction reduction devices that work in a forward/aft direction and nothing more.

Yup, I've confessed to my sins elsewhere in this thread.

It does not state that as the aircraft moves forward the belt rotates fast enough in the opposite direction so as to keep the aircraft stationary relative to the air mass (which is how I read it to begin with).

[AOL] Me too! [/AOL]

 

[Michael]

See attached photo

 

[Skip Miller]

For example, you start your takeoff roll. The conveyor belt, being tuned extremely sensitively, feels the wheels moving at one knot per hour, and so starts moving in the opposite direction at 1 knot. Assuming no wind, you now have zero airspeed.

What would stop the plane? Force = Mass*Acceleration. Some force would have to act on the plane. The moving runway may be able to roll the wheels but assuming the brakes are not set, no force is applied to the plane.

to quote Jackie Gleason: "...and away we go!"

-Skip

 

[gismo]

The question, then, is just designed to be clever, but is actually annoying. How could a conveyor belt know how fast the aircarft were moving? More likely, it could adjust to wheel speed. In that case, the airplane would never move (much). For example, you start your takeoff roll. The conveyor belt, being tuned extremely sensitively, feels the wheels moving at one knot per hour, and so starts moving in the opposite direction at 1 knot. Assuming no wind, you now have zero airspeed.

As the propeller tries to move the aircraft forward, the conveyor belt instantly adjusts so that it moves in the opposite direction of the wheels at the same speed. In this manner, the aircraft never moves forward. If the aircraft can't move forward through the air, there is no airspeed. If there is no airspeed, there is no takeoff.

While obviously just a thought experiment, the scenario as originally proposed is phyically possible given a sufficient budget. Your idea of controlling the conveyor speed so that it's speed is equal to the plane's wheel speed would require infinite speed assuming frictionless wheel bearings. Even with real bearings, the tires would explode very soon after you started as the only thing really resisting the acceleration of the conveyor is the polar intertia of the wheels and tires plus a small amount of friction in the wheel bearings and tires. You'd basically have the plane engine's horsepower being applied to the spinning of the wheels and nothing else. Taking a wild guess, with a 100 HP engine I'd expect the wheels to reach 200 mph in about half a second.

 

[Nav8tor]

Now here's a guy that's really trying to get to the bottom of this debate! Except the skate board doesn't take off.

 

[drhunt]

Well Michael, I had hoped that my Socratic questions would illicit a different response...so you see it must be hemlock, not hanging

 

[spiderweb]

What would stop the plane? Force = Mass*Acceleration. Some force would have to act on the plane. The moving runway may be able to roll the wheels but assuming the brakes are not set, no force is applied to the plane.

to quote Jackie Gleason: "...and away we go!"

-Skip

I have already been convinced. (See post #39)

While obviously just a thought experiment, the scenario as originally proposed is phyically possible given a sufficient budget. Your idea of controlling the conveyor speed so that it's speed is equal to the plane's wheel speed would require infinite speed assuming frictionless wheel bearings. Even with real bearings, the tires would explode very soon after you started as the only thing really resisting the acceleration of the conveyor is the polar intertia of the wheels and tires plus a small amount of friction in the wheel bearings and tires. You'd basically have the plane engine's horsepower being applied to the spinning of the wheels and nothing else. Taking a wild guess, with a 100 HP engine I'd expect the wheels to reach 200 mph in about half a second.

LOL--so I am right after all, but not for the original reason. This experiment would turn out just as you say. Since the aircraft has to have real bearings, and therefore will experience some friction, and since the conveyor belt is automatically and immediately adjusting to wheel speed, the undeniable result is that, as you say, ". . . the tires would explode very soon after you started. . . ."

LOL! After the tires blow, the airplane is stuck on the conveyor belt (just as if you had landed with all flat tires and screeched to a stop on a runway). The airplane stops moving; the conveyor belt stops, and once again NASA gets crticized for another failed experiement.

Where is Burt Rutan when you need him?!

 

[jesse]

I have already been convinced. (See post #39)


LOL--so I am right after all, but not for the original reason. This experiment would turn out just as you say. Since the aircraft has to have real bearings, and therefore will experience some friction, and since the conveyor belt is automatically and immediately adjusting to wheel speed, the undeniable result is that, as you say, ". . . the tires would explode very soon after you started. . . ."

LOL! After the tires blow, the airplane is stuck on the conveyor belt (just as if you had landed with all flat tires and screeched to a stop on a runway). The airplane stops moving; the conveyor belt stops, and once again NASA gets crticized for another failed experiement.

Where is Burt Rutan when you need him?!

Really the question sucks as far as that goes. Basically what it's saying is that you can build a belt that could detect thew heel speed and instantaniously match it. Well I'm sorry. Things don't work like that. Everything takes time.

So yeah. Basically the thrust would pull the airplane foward, making the wheels turn. THe belt of course matches this speed magically and the wheel speed continues to increase with this belt. They are perfectly equal. It would take a..very short time before the bearings failed..the wheels failed.. and you looked like an idiot.

Really though the question requires you to build several things that would just plain be impossible. It's just something that gets you to think is all.


What really suprised me though on some other forums were people who were comparing it to ice and saying how an airplane would accelerate slower on ice due to a loss of traction, when in all reality an airplane would accelerate quicker on ice due to less friction.

You can argue aerodynamics all day, Doesn't really make you a better pilot though..just something fun to talk about.

"Beware the lessons of a fighter pilot who would rather fly a slide rule than kick your ass!"

 

[Missa]

See attached photo

Michael,

I see a problem with your tree. It's not long enought to hang the treadman on... He's just wandering on, and on, and on, and on, and on, and on under the tree, just like this thread.

Missa

 

[drhunt]

You said that this would bring a good debate and indeed you were so correct.

Rather than responding to all the individual posts, I’ll try to consolidate here. Unfortunately, the fan/skateboard video posted by Nav8tor is not a very well controlled experiment (Nav8tor just offered it without comment pro or con). If you keep matching the speed of a treadmill to a walker or runner, they don't leave the treadmill. So if the paper under the fan/skateboard were really pulled at the proper speed, the fan/skateboard would remain stationary, right? A better experiment would be to set this up on a treadmill and match the speeds...then no motion...no airspeed, no lift, just propwash or in this case, fanwash. Anybody see your airspeed indicator move during a runup from propwash? I can't say that I have but suspect if so it is very small. I usually don't notice it coming off the peg until I've gone a few hundred feet down the runway (call out - airspeed alive). The thrust from the prop begins the acceleration, but if a treadmill continually matched my speed I would have no forward motion, I'd still only have propwash and thus no airspeed/lift/takeoff.


In Chuck's example of the matchbox car on a treadmill, the force on the string balances the rearward force of gravity/friction of the car. If you measured the force on the string, you'd see the force increase as you turned up the speed of the treadmill. It is not a frictionless situation. The only time it would be frictionless would be when lift offsets the weight of the plane and then the wheels could spin freely. Until then, you’ve got a lot of friction from the weight of the plane. In his example of pulling the car forward, that only happens if you don't increase the speed of the treadmill to produce an offsetting force in the opposite direction, the same as running faster on a treadmill to stay on it if the speed is increased. So in theory, (and that's all this whole deal is) any forward thrust could be offset by increasing the rearward speed of the treadmill. No forward motion...no airspeed/lift, hence you need a fan to keep cool while running on a treadmill but not out on a track


Sorry to repeat from my post #40 but I’m trying to consolidate my points. If you start the treadmill backward first, say at 10 kts, you could add just the right amount of power to offset the backward force and keep the plane stationary. Now if the treadmill was going backward at 20 kts you could still add the right amount of power to remain stationary but that amount of power would be greater than when the treadmill was only going 10 kts, right? Now how about 30,40,50,60 kts? Any backward movement I set on the treadmill you can set the right amount of power to remain stationary and like running on a treadmill it takes more and more power as the speed of the belt increases. Eventually, you run out of throttle. So in this hypothetical scenario, I can always set the belt speed to match your power and vice versa, hence you never move forward through the air…no airspeed/lift/takeoff. Notice that this requires no wiz/bang computer driven machinery other than the BHT (big honking treadmill), just me on the treadmill speed control and you on the throttle.


Jesse, thanks immensely for launching this thought provoking topic which will undoubtedly remain quite divided. Obviously, I seem to be in a minority camp but have tried to illustrate the logic behind my position. The value is in the thinking…not the answer.

 

[EdFred]

Well Michael, I had hoped that my Socratic questions would illicit a different response...so you see it must be hemlock, not hanging

Maybe that's a hemlock tree he's hanging from.

 

[jesse]

Rather than responding to all the individual posts, I’ll try to consolidate here. Unfortunately, the fan/skateboard video posted by Nav8tor is not a very well controlled experiment (Nav8tor just offered it without comment pro or con). If you keep matching the speed of a treadmill to a walker or runner, they don't leave the treadmill. So if the paper under the fan/skateboard were really pulled at the proper speed, the fan/skateboard would remain stationary, right? A better experiment would be to set this up on a treadmill and match the speeds...then no motion...no airspeed, no lift, just propwash or in this case, fanwash. Anybody see your airspeed indicator move during a runup from propwash? I can't say that I have but suspect if so it is very small. I usually don't notice it coming off the peg until I've gone a few hundred feet down the runway (call out - airspeed alive). The thrust from the prop begins the acceleration, but if a treadmill continually matched my speed I would have no forward motion, I'd still only have propwash and thus no airspeed/lift/takeoff.

Wrong.

Your wheels / bearing / tires would fail before you would run out of thrust to overcome the very minimal amount of friction caused by the tire on the belt.

Your wheels serve one purpose on an airplane, to hold your plane off the asphalt so you don't grind away the bottom and strike your prop. They have absolutely nothing with providing motion.

If you take a look at the video of the skateboard and fan, He pulls that piece of paper back WAYYY faster then that fan moves forward. It doesn't matter HOW fast he'd pull that piece of paper back the fan's thrust would overcome the tiny amount of friction cauesd by the tires. Up until the point to where the wheels exploded.

THE FRICTION OF THE WHEELS IS NOT LINEAR WITH THE SPEED
Think of it this way. You stand on the skateboard on the treadmill and your friend takes the treadmill up to 5 mph. You are holding onto the handle o nthe treadmill so you don't fall off. Then your friend takes it up to 15 mph, That is 3 times higher. How much harder do you think you'd have to hold onto that handle to not fall off? I doubt you'd notice much of a difference. All you'd notice is the wheels are spinning MUCH faster.

The value is in the thinking…not the answer.

Exactly.

 

[drhunt]

Clever guy Ed

Hey, are you flying that Bo yet?

 

[Greebo]

And to add to that: the amount of thrust force generated by the propeller is much, MUCH higher than the amount of friction force applied by the conveyer belt to the wheels.

drhunt: Your "walk on the treadmill" comparison is not applicable. Walk on treadmill = drive on treadmill with car. In both cases, motive force is coming from force applied against the treadmill. Legs move feet, feet press against treadmill, body moves forward, treadmill moves backward at same speed, equal forward force and reverse force are applied. Feet are held to treadmill by friction of the surface of the feet, and are physically attached to the rest of the body and so the whole body stays in the same place.

Car wheels turn, mechanically geared to the engine, giving forward thrust, but the wheels are held on the treadmill by their surface friction, and the moving treadmill imparts equal thrust in reverse. In the cars case, the wheels CAN not turn faster freely, they can only turn as fast as the torque from the engine/linkage allows. Wheels rotate at 20 mph, treadmill moves at 20mph, car stays in one place.

In the airplane example, the tires stay on due to surface friction but are not mechanically linked to the planes motive force. They are only connected to the axle, and are free to spin at any speed (minus the negligible friction of the rotation on the axle).

Planes motive force is the reaction to the movement of air. Propeller moves air backwards, plane moves forward. When plane moves forward, conveyer belt moves backward, and wheels, being not mechanically linked, simply revolve at twice the speed of the forward motion of the plane. There is no linking force between the rotation of the wheels and the forward motion of the airplane. The wheels rotate around the axle with uniform friction, which has a net effect of 0 force on the axle. Just generation of heat.

 

[EdFred]

Clever guy Ed

Hey, are you flying that Bo yet?

Nah, looking at Arrows now too. It's my plane with retract. All I gotta do is worry about a blue knob thingy and checking the gear. I'm thinking I may just stick with the piper line.

 

[drhunt]

..snip...

In the airplane example, the tires stay on due to surface friction but are not mechanically linked to the planes motive force. They are only connected to the axle, and are free to spin at any speed (minus the negligible friction of the rotation on the axle).

Planes motive force is the reaction to the movement of air. Propeller moves air backwards, plane moves forward. When plane moves forward, conveyer belt moves backward, and wheels, being not mechanically linked, simply revolve at twice the speed of the forward motion of the plane. There is no linking force between the rotation of the wheels and the forward motion of the airplane. The wheels rotate around the axle with uniform friction, which has a net effect of 0 force on the axle. Just generation of heat.

OK, hang with me Chuck, I'm really trying to understand this and your input is great. Let's take an airboat in Florida. It floats but has propulsion from a prop just like our airplane example, hence we don't need to get hung up on motive force. Lets put the airboat in a fast flowing stream with the boat facing upstream. The moving stream is now like the treadmill. The airboat would initially move downstream at the same speed as the stream...let's say 10 kts. We start the engine, engage the prop and head upstream. Our groundspeed would gradually change from a negative value to zero if we applied just the right amount of power to stay in one place with respect to the shoreline, right. Now imagine we can increase the flow of the stream to 20 kts. We have to apply more power just to stay even...no breeze blowing in our face as we stay in one place. Now we boost the stream to 30, 40, 50 kts, etc. We have to add more and more power just to stay in one spot right? Still no breeze blowing in our face, thus no airspeed. OK I took the wheels off the problem so we don't have to worry about tires exploding, etc. I'll grant Jesse that the friction is not linear but we still have to add more and more power if we keep increasing the flow of the stream, albeit incrementally less. Help me understand why is the airplane problem any different?

 

[jesse]

OK, hang with me Chuck, I'm really trying to understand this and your input is great. Let's take an airboat in Florida. It floats but has propulsion from a prop just like our airplane example, hence we don't need to get hung up on motive force. Lets put the airboat in a fast flowing stream with the boat facing upstream. The moving stream is now like the treadmill. The airboat would initially move downstream at the same speed as the stream...let's say 10 kts. We start the engine, engage the prop and head upstream. Our groundspeed would gradually change from a negative value to zero if we applied just the right amount of power to stay in one place with respect to the shoreline, right. Now imagine we can increase the flow of the stream to 20 kts. We have to apply more power just to stay even...no breeze blowing in our face as we stay in one place. Now we boost the stream to 30, 40, 50 kts, etc. We have to add more and more power just to stay in one spot right? Still no breeze blowing in our face, thus no airspeed. OK I took the wheels off the problem so we don't have to worry about tires exploding, etc. I'll grant Jesse that the friction is not linear but we still have to add more and more power if we keep increasing the flow of the stream, albeit incrementally less. Help me understand why is the airplane problem any different?

There is LOT more friction/drag of the airboat over the water than the tires over the belt. A lot more surface area touching it, and down into it.

tires have a fairly small footprint over the ground, they also have very efficent bearings.

 

[Matthew]

Hey, I want to jump in!

Try the treadmill example - If you run and increase speed, you are exerting force on the treadmill. You and the treadmill must match forces, cancel them out, and you remain stationary (no airspeed).

Now, don't exert force on the treadmill. Tie a rope to the front bar and wear roller skates. Set the treadmill for as fast as you want, and pull on the rope. You will move forward (increase airspeed). If you could pull hard enough (like a propeller pulling into the air), and reach whatever your Vx would be, you'd be flying.

This must assume that the friction (drag) in the roller skates (wheel bearings) is less than the thrust the propeller is able to generate. The airboat example would work better if it were a hovercraft and had no friction between the hull and the water. In an ideal word, the current could be as fast or slow as you desire, you could still move against it. The airboat still has to overcome all the additional drag of the water.

It took a few (OK, more than a few) minutes for me to see this.

edit - It looks like somebode else beat me to these examples - what I get for joining in late.

 

[jesse]

edit - It looks like somebode else beat me to these examples - what I get for joining in late.

Yeah. I broke out some really cool crayola drawings. I put them in my portfolio for some art schools.

 

[fgcason]

If you keep matching the speed of a treadmill to a walker or runner, they don't leave the treadmill.

Correct. The reason that the runner/walker/car/bicycle will not accelerate in relation to the outside world is that it is applying thrust through the wheels/feet themselves directly to the moving surface. It's a closed loop energy dissipation system. There is no thrust connection to the external world. Thus: 100lbs thrust applied, 100lbs thrust dissipated through the surface. +100-100 = 0. No net change in velocity.

An airplane is open loop propulsion in this situation and there is no connection between imparted thrust and the surface. None beyond minor rolling friction. The wheels are simply a friction reduction device. Nothing more, nothing less. The thrust being applied in the aft direction to move the airplane forward is coming from outside the otherwise closed loop system. Thus: 100lbs thrust applied, 1 lb thrust dissipated through the low friction bearings into the surface. +100-1 = +99lbs excess thrust available to change velocity forward therefore acceleration forward allowing airspeed to build for takeoff.

Side note: Your airboat in a moving river comparison is a good thought process however it does not take into account that in the real world the airboat is partially sunk in the river to displace the weight of the boat itself. That is a lot of frontal surface area for the river to grab onto. It is a very high drag environment. That is the equivalent of holding the brakes in the wheeled airplane.
Think of it this way: Would the airboat accelerate upriver if there was an air cushion between the surface and bottom of the boat like a hovercraft has? Remember that the wheel bearings are friction reduction devices that works similar to lifting the airboat out of the water on a cushion of air plus a bit more drag than a clean air cushion would have..say a water rudder in the river, not the entire bottom of the boat shoved down 6 inches. The correct answer is yes, it would accelerate upriver at the same thrust setting that would just stationkeep if the boat was in the water with all the excess hydrodynamic drag.

Anybody see your airspeed indicator move during a runup from propwash?

Side note: The pitot tube is outside the prop arc at an adequate distance to avoid propeller air flow getting to the pitot hole under reasonable conditions (airshow octoflugerontwistysidewayspitchroll excluded for obvious reasons)

In Chuck's example of the matchbox car on a treadmill, the force on the string balances the rearward force of gravity/friction of the car. If you measured the force on the string, you'd see the force increase as you turned up the speed of the treadmill. It is not a frictionless situation.

True. It is not frictionless. However in a real world scenario with wheel bearings on say a Cherokee in the 0-60mph range, the resistance of the bearings is not going to be high enough to counter the engine thrust. The matchbox car string force is considerably less than the weight of the car, even at double or triple the velocity. It is being held in place by the string pulling on an external device. (eg: your finger, or the wind in the case of the plane)
Think about this: Using free turning wheels on the matchbox car, can you pull the string (thus the car) forward in relation to the outside world without exceeding say 10% of the weight of the car in pull force? The answer is yes, you can because rolling friction is very very low in relation to the weight of the vehicle and in relation to the thrust being imparted into the vehicle. The excess force comes from outside the closed loop energy dissipation system. (an example of the forces involved in rolling friction: on a flat surface, in netural, I can Q.E.D. hand push my multi thousand pound all steel grand wagoneer jeep all the way across the parking lot with one hand with very little force - rolling friction is relatively very low friction. It takes two hands and a good shove to overcome the stationary static friction then it's a one handed operation because rolling friction is far less than static friction)

So in theory, (and that's all this whole deal is) any forward thrust could be offset by increasing the rearward speed of the treadmill.

Correct. You forgot the conditional modifier though: rolling friction of the bearings and tire contact is not linear in relation to velocity. I refuse to pull the physics book out right now however to counter takeoff thrust of say 2000lbs at 60mph, you're probably talking 1000+mph of rearward belt velocity at which time you'll probably be into air cushion hydroplaning. As the conditions of the experiment we're discussing here is stated, forward belt velocity is countered by a 1:1 ratio of rearward velocity, not a 1:10 or 1:100 or 1:1000 ratio.

Sorry to repeat from my post #40 but I’m trying to consolidate my points. If you start the treadmill backward first, say at 10 kts, you could add just the right amount of power to offset the backward force and keep the plane stationary. Now if the treadmill was going backward at 20 kts you could still add the right amount of power to remain stationary but that amount of power would be greater than when the treadmill was only going 10 kts, right? Now how about 30,40,50,60 kts? Any backward movement I set on the treadmill you can set the right amount of power to remain stationary and like running on a treadmill it takes more and more power as the speed of the belt increases. Eventually, you run out of throttle. So in this hypothetical scenario, I can always set the belt speed to match your power and vice versa, hence you never move forward through the air…no airspeed/lift/takeoff. Notice that this requires no wiz/bang computer driven machinery other than the BHT (big honking treadmill), just me on the treadmill speed control and you on the throttle.

That's takes us back to the low friction realm of rolling friction with an axle and wheel. A 1:1 velocity ratio at relatively low velocities won't allow the engine to run out of throttle in a garden variety simple airplane until after it lifts off. To make the thrust/drag issue work out, the brakes will have to be applied or the belt will have to be moving much much higher than 1:1 velocity ratio's.


Don't think of this in terms of surface movement or aircraft movement. Think of it in terms of total system energy. Where is the energy coming from? Where is the energy going to? What are the energy gain/loss ratio's?

Jesse, thanks immensely for launching this thought provoking topic which will undoubtedly remain quite divided. Obviously, I seem to be in a minority camp but have tried to illustrate the logic behind my position. The value is in the thinking…not the answer.

Agreed. This is fun.
From this side, we have to justify our logic or you won't come over to our side. Everyone is having to think and make valid connections to the opposing side of the issue.
It's all fun in the name of scientific research theory.


Happy flying...even off the runway conveyor belt from hell.

 

[Missa]

Help me understand why is the airplane problem any different?

Simply put it's in the wording of the question.

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?

The only way for the "plane" to have a speed is for it to be moving. As long as the "plane" is moving it is developing airspeed and therefore will be able to take off.

The problem we have in this debate is that 'speed' is open for a bit of interpertaion. On the plane there are several things that can have 'speed': the angular speed of the engine, the angular speed of the wheels, the indicated air speed of the airframe as measured by the diffrence is static and ram air preasure, the true air speed of the airframe through the air mass, the airframe speed over the ground... So what speed are we talking about here?

I think most people think of speed as it is measured in a car, which is the angular speed of the tire multiplied by the circumfrence of the tire. In most cases this directly reates to the forward motion of the car. So now on the big treadmill in your BMW you can be showing an indicated speed of 40MPH but have an actual speed of zero because the treadmill is moving at -40MPH, but this would mean your treadmill control would be based on the indicated not actual speed of the BMW. If your control is, as stated in the plane question, controled by the speed of the BMW then when the BMW has a speed of 40MPH and the treadmill has a speed of -40MPH the BMW will indicated a speed of 80MPH. This means that even the BMW will make it off this scyopath's runway with a loud squeal and some whiplash as we go back to the real pavement.

Even if you assume that the control of the covyer is by the indicated speed, the plane will still take off even though the BMW is going nowhere. A plane measures speed by the differance between ram and static air preasure, the only way you can have this diffrence is if you have forward motion through the air.

Missa
[/geak off]

 

[Eamon]

If the plane is not moving in relation to the ground there is no airspeed (calm wind situation) & therfore no flight even if the wheels & belt are both turning 200 kts.

Where is "Relative wind" coming from? There is none!!!!!

 

[RotaryWingBob]

That was well put, Missa...

It's really no different than the situation where you have a headwind greater than your airspeed. The aircraft is happy because it's moving through the air at a speed at which the wings can generate lift, but it moves backward with respect to the ground because the air mass that it's in is moving backward faster than the aircraft is moving forward through the air mass.

That's fun to try, BTW

 

[gibbons]

If the plane is not moving in relation to the ground there is no airspeed (calm wind situation) & therfore no flight even if the wheels & belt are both turning 200 kts.

Where is "Relative wind" coming from? There is none!!!!!

EAMON!!! Where ya been?

OK. Here's another way to look at it....

The airplane is on the stupid belt that's moving backwards at some speed, say 20mph. How much thrust do you imagine it would take to overcome that backwards motion and hold the airplane steady on the belt? Not very much. Just enough to overcome the wheel friction everyone keeps talking about.

Now, we speed the belt up to 70 mph and add just a bit more power to hold the airplane still. It doesn't take much and there's still plenty of throttle remaining. Let's say 70 MPH is the airspeed at which this particular airplane will fly, so the belt is moving at its maximum velocity (it only goes as fast backwards as the airplane can go forward, and anything over 70 means the airplane is flying). So all the excess thrust you have available is there to move the airplane forward on the belt - and there's plenty of thrust available.

Again, the problem doesn't say the belt goes backwards fast enough to hold the airplane in one place. It only goes backwards as fast as the airplane is moving forward. Airplane moving forward at 50 mph, belt going backwards 50 mph. Big deal. So the belt slows the airplane down to 49.9 MPH due to wheel friction. There is plenty of thrust available to overcome the minor impact of the belt.

Next can we talk about conservation of energy and where people go when they die?

 

[drhunt]

Great stuff!

...snip...
Thus: 100lbs thrust applied, 1 lb thrust dissipated through the low friction bearings into the surface. +100-1 = +99lbs excess thrust available to change velocity forward therefore acceleration forward allowing airspeed to build for takeoff.

Agreed but if I can always move the treadmill fast enough, I can offset that. On face value, the problem said the treadmill moves backward to match. I fully agree with Missa that the question leaves out enough so that we could debate this forever

...Side note: Your airboat in a moving river comparison is a good thought process however it does not take into account that in the real world the airboat is partially sunk in the river to displace the weight of the boat itself. That is a lot of frontal surface area for the river to grab onto. It is a very high drag environment. That is the equivalent of holding the brakes in the wheeled airplane.
Think of it this way: Would the airboat accelerate upriver if there was an air cushion between the surface and bottom of the boat like a hovercraft has? Remember that the wheel bearings are friction reduction devices that works similar to lifting the airboat out of the water on a cushion of air plus a bit more drag than a clean air cushion would have..say a water rudder in the river, not the entire bottom of the boat shoved down 6 inches. The correct answer is yes, it would accelerate upriver at the same thrust setting that would just stationkeep if the boat was in the water with all the excess hydrodynamic drag.

But key here is that the friction on the plane will always be there. The only way it gets eliminated is by lift and if we never have forward motion...no airspeed...no lift. Hence, we can't quite get to the hovercraft example. So can't we always dial up more speed on the treadmill or increase the water speed to counter the additional force? A hydroplane probably has relatively less friction from the water than our airboat but if we place a hydroplane going 200 mph in a stream going 200 mph in the opposite direction, it will still be stationary, right? Pick your boat/plane speed, I just set the stream or treadmill to match and we still have a stationary situation.

...snip... I can Q.E.D. hand push my multi thousand pound all steel grand wagoneer jeep all the way across the parking lot with one hand with very little force - rolling friction is relatively very low friction. It takes two hands and a good shove to overcome the stationary static friction then it's a one handed operation because rolling friction is far less than static friction)

How much force would you have to supply to keep the jeep stationary on a treadmill going 10 mph? 50 mph? 100 mph? 200 mph? More and more with each speed increase, right? So whatever you provide, I take away by dialing up more on the treadmill.

...Correct. You forgot the conditional modifier though: rolling friction of the bearings and tire contact is not linear in relation to velocity. I refuse to pull the physics book out right now however to counter takeoff thrust of say 2000lbs at 60mph, you're probably talking 1000+mph of rearward belt velocity at which time you'll probably be into air cushion hydroplaning. As the conditions of the experiment we're discussing here is stated, forward belt velocity is countered by a 1:1 ratio of rearward velocity, not a 1:10 or 1:100 or 1:1000 ratio.

But that is the essence of this debate...I've assumed no limit nor is one specified on the treadmill speed, just that it moves backward emough to offset any forward speed.

Agreed. This is fun.
From this side, we have to justify our logic or you won't come over to our side. Everyone is having to think and make valid connections to the opposing side of the issue.
It's all fun in the name of scientific research theory.


Happy flying...even off the runway conveyor belt from hell.

It has been waaay fun but perhaps hopelessly in a quagmire due to lack of specificity at the onset. So here's to you and all others who jumped in and raised the bar of the discussion. I've got to get off the treadmill

If the plane is not moving in relation to the ground there is no airspeed (calm wind situation) & therfore no flight even if the wheels & belt are both turning 200 kts.

Where is "Relative wind" coming from? There is none!!!!!

Amen Eamon! Couldn't resist that. You still Caravanning around the country?

 

[fgcason]

Agreed but if I can always move the treadmill fast enough, I can offset that.

Yes you can put enough treadmill velocity in to stop the plane with bearing/wheel friction - eventually. However the original condition is:
"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)"

I make two very reasonable assumptions:
(1) That one releases the brakes while attempting to takeoff during the experiment. (This reduces drag from the surface whether it's a conveyor or a normal stationary runway)
(2) That the forward airplane speed and the belt reverse speed is measured relative to the outside world (eg: person standing next to the conveyor belt, not on it) The outside observer with a police radar speed gun would measure airplane +1mph, and the belt would measure -1mph giving a 2mph velocity difference which would be the rotational velocity of the free spinning wheels. (If the person were standing on the belt and measuring from there, the instant the plane started moving forward the belt velocity would jump to infinity within mere seconds which is a bit unrealistic since while the plane would not take off under those conditions, the pieces flying off would likely destroy the Earth and the experiment both)

That said: Since rolling friction is so low, let's say the conveyor needs to reach 500mph to overpower the thrust. The belt will never get going that fast because the plane will lift off far before then. With a 1:1 velocity ratio with a top speed of 60mph at liftoff, (60*2=120 << 500) the free spinning wheels will never apply enough bearing friction to counter the aircraft's forward velocity, thus acceleration and airspeed and eventual liftoff. The friction reducing bearings are too efficient to allow the plane to be pulled back enough to stop forward motion with an outside observer 1:1 velocity increase at the low speeds required here unless one applies the brakes.

But key here is that the friction on the plane will always be there. The only way it gets eliminated is by lift and if we never have forward motion...no airspeed...no lift. Hence, we can't quite get to the hovercraft example. So can't we always dial up more speed on the treadmill or increase the water speed to counter the additional force? A hydroplane probably has relatively less friction from the water than our airboat but if we place a hydroplane going 200 mph in a stream going 200 mph in the opposite direction, it will still be stationary, right? Pick your boat/plane speed, I just set the stream or treadmill to match and we still have a stationary situation.

There is friction however it is an inadequate amount of friction. By releasing the brakes, that is the equivalent of lifting the airboat out of the water onto an air cushion (plus some minor additional drag to equal the rotating bearing drag) which reduces surface friction considerably. There will be forward motion because the plane is not pushing on the belt to propel it forward. It's pushing on the air which is not related or connected to the surface below it. The low friction rotating wheels are reducing the amount of drag that the belt imparts on the airplane adequately to allow forward motion to continue.

How much force would you have to supply to keep the jeep stationary on a treadmill going 10 mph? 50 mph? 100 mph? 200 mph? More and more with each speed increase, right? So whatever you provide, I take away by dialing up more on the treadmill.

Yes the belt could be accelerated adequately to counter the force imparted on the jeep to keep it stationary or even pull it backward, but it's not a 1mph(jeep):1mph(belt) ratio. It's probably more like 1mph(jeep):40mph(belt) ratio.

But that is the essence of this debate...I've assumed no limit nor is one specified on the treadmill speed, just that it moves backward emough to offset any forward speed.

Maybe that's the source of the countering viewpoints. Your viewpoint possibly envisioning unlimited belt velocity to create adequate drag to stop the aircraft. My viewpoint says the belt and aircraft speeds are directly related 1:1 in relation one another from an outside observer relative viewpoint. I'm not sure if that's it, or maybe I'm missing your viewpoint completely, but that's what appears to be going on here. Both viewpoints come up with valid answers within the conditions of the different rules but neither agree with one another either using the other's set of rules.

It has been waaay fun but perhaps hopelessly in a quagmire due to lack of specificity at the onset. So here's to you and all others who jumped in and raised the bar of the discussion. I've got to get off the treadmill

It's waay fun. That's why I keep diving in instead of shutting up like I probably should. I don't have many chances for this type of discussion very often. The last fun one was why frisbees fly and that's been a few years...

 

[jesse]

I don't really think you guys are getting it.

Sure you could increase the belt speed. To say 2000 MPH and be able to cause enough friction to stop this airplane from taking off.
BUT
What is it that would stop the airplane? It's the friction of the tire on the belt. What does friction generate? Heat. You'd be on FIRE before it got to this point.

You cannot overcome the thrust of the engine with the belt BEFORE the wheel bearings and tires fail.

 

[Nav8tor]

Unfortunately, the fan/skateboard video posted by Nav8tor is not a very well controlled experiment (Nav8tor just offered it without comment pro or con).

I don't think it proves anything. I just thought it was funny.

 

[AirBaker]

Arent' there supposed to be 2 trains leaving from Toledo somewhere in this riddle?

 

[Greebo]

Arent' there supposed to be 2 trains leaving from Toledo somewhere in this riddle?

They were, but due to a switching problem they're currently going in circles around each other in Demoines.

 

[Nav8tor]

In this whole debate, the one thing that everyone seems to agree on is that the original question is poorly worded. Beyond that it appears that individual answers depend on the assumptions people make as to the intent of the original question.

Here's my take on it:

If you simply consider the original statement "The plane moves in one direction" that implies that it has relative motion in relation to the ground (From Merriam-Websters Online Dictionary - To Move = to go or pass to another place or in a certain direction with a continuous motion). That being the case then there will be relative wind which increases as the airplane accelerates and once flying speed is reached the airplane will take off. Wheel rpm, conveyor speed and frictional forces are all irrelevant because the fact that the airplane is in motion is given by the problem statement.

If however, the intent was that the conveyor was set up in such a way that it can somehow instantaneously match the rotational velocity of the airplane's wheels, then that is another thing all together, and assuming there is no slippage between the wheels and the conveyor, the aircraft would not move in relation to the ground and as thrust was increased belt speed/wheel speed would increase until either a) thrust was maxed out or b) the tires/wheels/bearings fail in which case the friction would go way up and the thing never gets of the ground anyway.

Lee

 

[Henning]

Runup: Yes. Brakes set = belt stopped = normal stationary runup.

Takeoff: Yes. Wheels are free turning in an airplane. Airspeed is independent from groundspeed. Propulsion is independent from the surface. Liftoff will be the same IAS, wheels will be spinning twice as fast. Very likely additional wheel drag due to the surface movement will result in a slightly longer takeoff run but it'll still lift off in the same general vicinity.

There is one factor being left out here, the carcas strength of the tire. Tires are built to stay together up to a certain speed. If it ends up blowing out a tire overspeeding it your takeoff may get pooched.

 

[Eamon]

EAMON!!! Where ya been?

?

Hey CHip WASSUPPPP??

The first place I moved into here in Wilmington, NC was in the sticks (Leland). The landlord said there was internet service, but the cable company & the phone company said otherwise. So I just moved into the "city" and now I can drink the water (the other place had rotting egg water as well) & I have high speed internet............Life is good.


Now back to the problem...................

The way it is worded says that the bellt will keep up with as much thrust as the plane will provide & keep the plane standing still as far as relative wind. We all know if you put a plane on the belt that it will move foward on the belt faster than the belt can move backward & therefore gain relative wind & take off. But, the question says the belt will move as fast foward as the plane trys to move.

 

[Missa]

Now back to the problem...................

The way it is worded says that the bellt will keep up with as much thrust as the plane will provide & keep the plane standing still as far as relative wind. We all know if you put a plane on the belt that it will move foward on the belt faster than the belt can move backward & therefore gain relative wind & take off. But, the question says the belt will move as fast foward as the plane trys to move.

Eamon, Re read the question, CAREFULLY. I do not think it says what you think it says.

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?

It says the conveyer matches the speed of the plane, not that the conveyer matches the speed of the plane that would be produced by the engine thrust in a non-conveyer system. So you and David Hunt are reading something into the question that was not stated.

"Speed" by definition is relative motion (don't make me quote websters!) and since the plane has speed it is moveing & by the fact that there is no reverse on most airplanes, it's moving forward creating a realitive wind over the wing and producing lift.

In this whole debate, the one thing that everyone seems to agree on is that the original question is poorly worded.

Actually I don't agree, the orignial question was skillfully worded to lead people to assume things that are not stated and therefore spur the debate.

Missa

Oh, and one more thing. Since we have entered the imagnary world where we can make a big coveyer that can produce a speed in the exact oppisite direction of the moving airplane, I would have to say that coveyer would have to have frictonless bareings, a drive unit that can produce as much power as necessary, and be made of industrictable material. You can't put a real airplane in this imagnary world and have a meaningfull debate so it's only logical that this plane has the same chareteristics as the imagnary conveyer so stop the debate on how long till we blow out the tires or bareing of the aiplane because I'm sure we would blow out a real conveyer of that massive side long before we blow out the real airplane tires... it's an ideal airplane on an ideal converyer.

 

[gibbons]

The way it is worded says that the bellt will keep up with as much thrust as the plane will provide & keep the plane standing still as far as relative wind. We all know if you put a plane on the belt that it will move foward on the belt faster than the belt can move backward & therefore gain relative wind & take off. But, the question says the belt will move as fast foward as the plane trys to move.

Ah, read it again my beer swilling friend: "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)."
If the plane is making 30 kts forward speed, the conveyer goes 30 kts the other direction, which has almost no impact on the airplane.

 

[Greebo]

It would be physically impossible for the conveyer belt to match speed of hte plane relative to anything but the non-moving ground. If the conveyer were to try to match speed to the speed of the plane relative to itself, it would create an infinite feedback loop.

EG: The plane moves forward at 1kt relative to the stationary belt and the ground and HOLDS the 1kt speed relative to the ground.
The belt accelerates to 1kt in the opposite direction.
The airplane speed relative to the belt is now 2kts. The belt accelerates to 2kts.
Plane relative speed now 3kts. Belt > 3kts.
Plane 4kts, belt 4kts
And so on, until the belt spins so fast the earth rotation is reversed and we go back in time to before this stupid experiment started...

 

[GaryO]

I think that there are two additional forces that have not been addressed.
The friction between the wheels and the conveyor has been discussed. But everyone seems to be neglecting that there is also friction between the conveyor and the air. This friction will cause an airflow in the direction of the conveyor's travel and thus result in airspeed for the airplane. This will be in addition to the airspeed caused by the airplanes forward movement.
Also, any airspeed at all will allow the wings to generate lift. Even while the lift is insuffecient to allow liftoff any amount of lift generated will reduce the weight carried by the wheels and thus reduce the friction on the wheels. As soon as there is any airspeed at all, lift will be generated, and friction from the wheels will be reduced.

The result is that the airplane will be able to lift off into ground effect with no trouble at all.