Interesting physics/logic riddle

[SugrueNSX]

it is not what I am saying at all. if the belt is going at a constant speed, the only resistance applied to the plane is the drag caused by the wheels.. which is not enough to prevent the plane from taking off. however, if the belt is accelerating it will produce greater resistance on the wheels. if the acceleration matches that of the wheels, it will be enough friction to keep the plane stationary.

If the belt is moving at a constant speed and that speed is enough to cause enough drag on the wheels to balance the max thrust of the aircraft then the plane will not move.

We don’t need to concern ourselves with acceleration to demonstrate this.

Regards,

Patrick

 

[nicholas421]

If the belt is moving at a constant speed and that speed is enough to cause enough drag on the wheels to balance the max thrust of the aircraft then the plane will not move.

We don’t need to concern ourselves with acceleration to demonstrate this.

Regards,

Patrick

the constant speed would have to cause enough drag on the wheels to balance the max thrust.. you are correct. my point is that the belt does not have be moving at break neck speeds to keep the plane still. it just needs to match the acceleration of the wheels. if we don't "concern ourselves with acceleration" than one can easily argue that the plane will move forward at low thrust.

 

[FrEsHaZzBuRu]

I thought that the point was made that the thrust of the plane was an independent force in which its only opposite force would be wind resistance. No matter how fast the belt moved, it would only spin the wheels faster, the friction in the wheels/bearings is not enough to have any major effect on the plane's thrust.

If it were a space shuttle in space someone somehow strapped to a belt, would that have any effect on it's thrust? No, it wouldn't, the shuttle will still move forward.

The plane will fly, just as long as the wheels don't explode first.

 

[NSX-Stalker]

Nothing prevents the plane from taking off in the same distance at the same speed.

The force the plane uses is independent of the belt. If you're going to argue about friction then I'll say such a belt could never be built which makes the whole question irrelevant anyway. You have to imagine it could be built and simply focus on how a plane moves forward.

NSX-Stalker

 

[SugrueNSX]

I thought that the point was made that the thrust of the plane was an independent force in which its only opposite force would be wind resistance. No matter how fast the belt moved, it would only spin the wheels faster, the friction in the wheels/bearings is not enough to have any major effect on the plane's thrust.

If it were a space shuttle in space someone somehow strapped to a belt, would that have any effect on it's thrust? No, it wouldn't, the shuttle will still move forward.

The plane will fly, just as long as the wheels don't explode first.

Well, as you say if the wheels explode then the plane does not take off.
But to be fair to the “The plane will take off” camp, we should (for the sake of an interesting argument) deem the wheels to be indestructible.
Now, there is no upper limit to the friction that can be applied to the wheels. The faster the belt speed the more drag on the plane wheels. And I know it’s hard to imagine because we are not subject to these types of speeds or this amount of friction in our daily lives. But at some ridiculously high belt speed. Just for fun let’s say 10,000 mph. The poor old Cessna 182 will not have enough thrust to move against the drag the belt is causing. And at more speed, again just for fun let’s guess 100,000 mph the F4 Tom cat will not move at full afterburner thrust and it might be a million mph or more. (I would guess it’s a lot less but I can’t be bothered to do the math to figure it out) the mighty space shuttle will be stationary under full thrust.
If you still don’t get it. Please go back and read my post # 89 that might help.

Regards,

Patrick

 

[SugrueNSX]

Nothing prevents the plane from taking off in the same distance at the same speed.

The force the plane uses is independent of the belt. If you're going to argue about friction then I'll say such a belt could never be built which makes the whole question irrelevant anyway. You have to imagine it could be built and simply focus on how a plane moves forward.

NSX-Stalker

Just because the thrust of the plane is “independent” of the opposing force due to wheel friction. Does not mean that the two opposing forces can not be in equilibrium.
If you read the puzzle to mean that the belt operator can apply any speed then the plane will not take off.

Regards,

Patrick

 

[nicholas421]

i think for those of us who are geeky enough to still be following this thread agree that the plane will take off if the belt is matching the speed of the plane relative to a fixed object (a tree). what i'm arguing is that the plane will not take off if the belt is matching the speed of the WHEELS. for every full revolution of the wheel, the belt moves the distance of the circumference in the opposite direction. by DEFINITION the plane will not move. i.e.- if you can push a match box car forward on a treadmill then the treadmill can't possibly be matching the wheel speed.

 

[SugrueNSX]

i think for those of us who are geeky enough to still be following this thread agree that the plane will take off if the belt is matching the speed of the plane relative to a fixed object (a tree). what i'm arguing is that the plane will not take off if the belt is matching the speed of the WHEELS. for every full revolution of the wheel, the belt moves the distance of the circumference in the opposite direction. by DEFINITION the plane will not move. i.e.- if you can push a match box car forward on a treadmill then the treadmill can't possibly be matching the wheel speed.

100% all good.

 

[SugrueNSX]

the constant speed would have to cause enough drag on the wheels to balance the max thrust.. you are correct. my point is that the belt does not have be moving at break neck speeds to keep the plane still. it just needs to match the acceleration of the wheels. if we don't "concern ourselves with acceleration" than one can easily argue that the plane will move forward at low thrust.

If the belt operator is told to match the planes “speed” then by definition, as the planes speed changes the operator will have to CHANGE the belt speed to match. That CHANGE in speed IS acceleration because acceleration is just a change in speed. But we don’t have to call out acceleration explicitly because it’s already implicit in the statement.
I don’t understand why you think we need explicitly call out acceleration to cover the low thrust scenario?
Oh and trust me, we are going to be looking at some “break neck” speeds because pretty much all the thrust from that prop is just going to be used to spin them silly little wheels.

Regards,

Patrick

 

[Vega$ NSX]

Here is another visualization for some folks who just aren't getting it. Stand on a skateboard on a treadmill. If you tilt the treadmill forward at a 45 degree angle, so that the front is down and the back end is up, what will happen? You will slide forward off the front of the treadmill, right? Now lets say we turn the treadmill on and do the same thing. Is there a speed in which the treadmill can go that will keep you from sliding forward when you tilt the back end up 45 degrees? Nope. It’s the same thing as the plane. If there is a force pushing on the plane not at the wheels, then treadmill will do nothing (or near nothing) to stop the plane from moving forward.

 

[ZacMan1987]

Well, strange place to make my first post.

As an introduction, I'm an electrical engineering student/co-op doing lots and lots of research, trying to pick out a future car. Who knows what life will be like in 5 years, but it's nice to have something to shoot for. I lurk in OT forums a lot too, because they make great procrastination areas.

Anyway,

This just sort of came to me, and I was surprised that the thought has not been posed yet.

Put a a car on a Dyno. Let's go with a 1980's-ish Civic Hatchback because of the somewhat disasterous consequences of the rest of this experiment.

Begin a Dyno run. Now, we have the speed of the wheels being matched by something approximating this conveyor belt. However, there's still one small piece missing to match the puzzle's description: jet propulsion.

Strap a nice sized jet turbine to the top of said Civic and light it up. Where will the car go?

As has been stated, with jet propulsion and "real world" assumptions, the speed of the wheels relative to the ground has no effect on the plane's ability to move forward.

The plane will move forward.
The plane will take off.

The assumptions I made are:

Wheel bearings will not fail.
Plane has adequate room to take off.

 

[nicholas421]

i appreciate everyone giving the same visualizations over and over again. I "get it"!! In fact, the skateboard analogy was originally made by me with even a little drawing (see page 2). what some of you don't seem to get is that the belt matching the plane's speed relative to a building is NOT the same as the belt matching the wheels' speeds.

several explanations were given previously where the wheels would have to spin twice as fast for the plane to take off. i agree... that's the "belt matching the plane's speed scenario"... not the "belt matching the wheels' speeds".

the belt matching the wheel's speed means for every rotation of the wheel the belt will move in the opposite direction exactly the distance of the circumference. how can any vehicle move forward given this fact? if anyone can make a simple diagram of how this is possible i'd greatly appreciate it

 

[nicholas421]

If the belt operator is told to match the planes “speed” then by definition, as the planes speed changes the operator will have to CHANGE the belt speed to match. That CHANGE in speed IS acceleration because acceleration is just a change in speed.

no, actually it's the rate of change over time. :wink:

But we don’t have to call out acceleration explicitly because it’s already implicit in the statement. I don’t understand why you think we need explicitly call out acceleration to cover the low thrust scenario?
Oh and trust me, we are going to be looking at some “break neck” speeds because pretty much all the thrust from that prop is just going to be used to spin them silly little wheels.

acceleration is key in holding the plane back, NOT speed. remember, force is a product of mass and acceleration... speed is not a factor.

question rephrased: can a car passenger (plane) reach forward and touch the windshield (take off) if the car (conveyor belt) is traveling very fast? of course, even if the car is traveling at 1 million miles per hour. however, with enough acceleration, the passenger can be held back in his seat.

 

[AdnanVCS]

it is possible for the treadmill to accelerate at a rate at which you will not be able to push the car forward.

Yep,

The speed going back is not equal! (just like the sea plane!that's why they have higher take of speeds)

 

[Vega$ NSX]

i appreciate everyone giving the same visualizations over and over again. I "get it"!! In fact, the skateboard analogy was originally made by me with even a little drawing (see page 2). what some of you don't seem to get is that the belt matching the plane's speed relative to a building is NOT the same as the belt matching the wheels' speeds.

several explanations were given previously where the wheels would have to spin twice as fast for the plane to take off. i agree... that's the "belt matching the plane's speed scenario"... not the "belt matching the wheels' speeds".

the belt matching the wheel's speed means for every rotation of the wheel the belt will move in the opposite direction exactly the distance of the circumference. how can any vehicle move forward given this fact? if anyone can make a simple diagram of how this is possible i'd greatly appreciate it

Because you are mistaking that rotational speed of a wheel has anything to do with force. Just because a wheel spins it doesn't mean it applies any force on an object. If the wheel is on a frictionless bearing it will spin and spin but it doesn't apply any forces in the direction of movement on the plane. It is like the wheels "disconnect" the plane from the runway, just as if I put a completely frictionless grease between the plane and belt. If you can agree that if the plane was on a frictionless grease and will still take off, you should be able to see that it is the same thing as a wheel, because a wheel is essentially no different. However, the jet engines do apply forces on the plane. Therefore, if there is thrust to push the plane forward, and the wheels can not apply a force to stop it, the plane will begin to move and will eventually take off.

BTW, I did provide a dynamics "drawing" on this in my other plane post here.

 

[steveny]

So I talked to the local airport and they have agreed to let me use one of their 747's for the purpose of proving or disproving this theory. I also talked with Nordic track and they are in the process of building a treadmill to fit our needs. We will need a 747 pilot and crew in place to get this project off the ground, pun intended. Any takers?

 

[SugrueNSX]

Because you are mistaking that rotational speed of a wheel has anything to do with force. Just because a wheel spins it doesn't mean it applies any force on an object. If the wheel is on a frictionless bearing it will spin and spin but it doesn't apply any forces in the direction of movement on the plane. It is like the wheels "disconnect" the plane from the runway, just as if I put a completely frictionless grease between the plane and belt. If you can agree that if the plane was on a frictionless grease and will still take off, you should be able to see that it is the same thing as a wheel, because a wheel is essentially no different. However, the jet engines do apply forces on the plane. Therefore, if there is thrust to push the plane forward, and the wheels can not apply a force to stop it, the plane will begin to move and will eventually take off.

BTW, I did provide a dynamics "drawing" on this in my other plane post here.

So I think that we all agree that if there is no friction then the plane takes off.

I did go back and read your previous post and I think I understand what our disconnect is.
You stated that “So the end result is that the entire wheel/belt assembly will exert a single force in the direction opposite of the plane’s direction, but will have some cap or limit to it.”

So are you saying that we can calculate friction without factoring in velocity?

Regards,

Patrick

 

[Vega$ NSX]

So I think that we all agree that if there is no friction then the plane takes off.

I did go back and read your previous post and I think I understand what our disconnect is.
You stated that “So the end result is that the entire wheel/belt assembly will exert a single force in the direction opposite of the plane’s direction, but will have some cap or limit to it.”

So are you saying that we can calculate friction without factoring in velocity?

Regards,

Patrick

Yes, if we follow the laws according to classic dynamics, that statement would be correct. Friction is not a function of velocity:

F(r) = Crr * N

F(r) = Rolling Resistance Force
Crr = Coefficient of Rolling Resistance
N = Normal Force (Force = mass * acceleration (aka gravity))

As you can see velocity is does not factor into friction forces. However, what makes that hard to believe or understand is that there are two friction forces: Static friction and dynamic friction. Static friction is the friction force that is required to get a object started moving, afterwhich the friction force is known as the dynamic friction force. As such, static friction is always greater than dynamic friction. Think of it as pushing a heavy box. To get it started takes a lot more force than to keep it moving. That is why if you can run and give it an impulse force and break the static friction force it is often much easier to keep it moving because you are now pushing against a dynamic friction force. So velocity is only a factor in so much that if you are at zero you need to overcome a static friction force. However, once you overcome that static friciton force, you are pushing against a dynamic friction force which is constant and independent of velocity.

Here is another good way to think of it. Think of a merry-go-round or the giant wheel in the Price is Right. To get that wheel moving you need a lot of initial energy to get it spinning. If you apply a single impulse load the wheel will start to spin and then eventually slow down. Those would be the friction forces at work slowing the wheel down until it stops. Now if you keep applying a force to the wheel, i.e. you use your arm to keep it spinning by pushing it down every few seconds, what will happen? If you don't push the wheel hard enough it will still begin to slow down, only slower. If you push too hard, it will begin to speed up. At some pushing pressure the wheel will maintain its speed forever. At that speed, the force you are applying with your arm is exactly the same as the fricional forces trying to slow the wheel down. That is the limit that the fricional forces that the wheel will apply to stop the wheel. All you need to do is apply more forces than that limited frictional force and the wheel will speed up in rotational speed. No matter how fast the wheel spins, the fricional force will not exceed that amount.

 

[sahtt]

Given the amount of information in this post, anyone who still thinks it won't fly based on the QUESTION I FIRST PROPOSED NOT ANOTHER [pointless, usually flawed] VARIANT needs to re-read the thread if they truly want to get a grasp of the concept. It looks like a solid 75-80% 'get it' and are able to look at it from 'outside the box'.

Beyond the immediate answer of 'yes' by understanding the JET ENGINES push the plane and the wheels HAVE NOTHING TO DO WITH IT, if you want to bother dealing with the wheel bearings' friction etc.; all the wheel has to do is spin TWICE THE SPEED OF THE PLANE. The speed of the plane is distance over time, simple as that. You can say fixed against a nearby tree or a fat guy eating a sandwich in the airport; it doesn't matter. Airplane wheel bearings DO NOT produce enough drag to overcome engines producing TONS of force at only twice the speed needed for take-off, roughly 280-300mph for a commercial aircraft, which is on the higher end of required take off speeds for aircraft in general.

Done.

 

[nicholas421]

Given the amount of information in this post, anyone who still thinks it won't fly based on the QUESTION I FIRST PROPOSED NOT ANOTHER [pointless, usually flawed] VARIANT needs to re-read the thread if they truly want to get a grasp of the concept. It looks like a solid 75-80% 'get it' and are able to look at it from 'outside the box'.

Beyond the immediate answer of 'yes' by understanding the JET ENGINES push the plane and the wheels HAVE NOTHING TO DO WITH IT, if you want to bother dealing with the wheel bearings' friction etc.; all the wheel has to do is spin TWICE THE SPEED OF THE PLANE. The speed of the plane is distance over time, simple as that. You can say fixed against a nearby tree or a fat guy eating a sandwich in the airport; it doesn't matter. Airplane wheel bearings DO NOT produce enough drag to overcome engines producing TONS of force at only twice the speed needed for take-off, roughly 280-300mph for a commercial aircraft, which is on the higher end of required take off speeds for aircraft in general.

Done.

no not done. the vagueness of your initial question is what is causing the issues. "speed of the plane" is not very clear. it can be interpreted as the speed at the wheels. don't you see the paradox there? how can the wheel match the belt speed and at the SAME time go twice the speed? last time I checked 2X is not the same as X.

 

[nicholas421]

Because you are mistaking that rotational speed of a wheel has anything to do with force. Just because a wheel spins it doesn't mean it applies any force on an object. If the wheel is on a frictionless bearing it will spin and spin but it doesn't apply any forces in the direction of movement on the plane. It is like the wheels "disconnect" the plane from the runway, just as if I put a completely frictionless grease between the plane and belt. If you can agree that if the plane was on a frictionless grease and will still take off, you should be able to see that it is the same thing as a wheel, because a wheel is essentially no different. However, the jet engines do apply forces on the plane. Therefore, if there is thrust to push the plane forward, and the wheels can not apply a force to stop it, the plane will begin to move and will eventually take off.

BTW, I did provide a dynamics "drawing" on this in my other plane post here.

I will assume I am incorrect in thinking forces of the belt play a role since you do seem to have an academic knowledge on the matter.

I think we are all in agreement that the wheels need to spin faster than the belt in order for the plane to move forward. Are you saying it is possible for the wheels to spin faster than the belt and yet have the belt match the speed of the wheels? i must be missing something.

 

[Vega$ NSX]

I will assume I am incorrect in thinking forces of the belt play a role since you do seem to have an academic knowledge on the matter.

I think we are all in agreement that the wheels need to spin faster than the belt in order for the plane to move forward. Are you saying it is possible for the wheels to spin faster than the belt and yet have the belt match the speed of the wheels? i must be missing something.

Not quite. The wheels are not spinning faster than the plane. The wheels (assuming no slippage) will spin the same speed as the belt always. The part that I think you aren't seeing is that the wheels spinning has nothing to do with the motion of the plane. I think you are thinking like a car, where the wheels spinning is the primary means for the car to move forward. So a car on a Dyno, where a drum moves backwards the same speed as the car moved forward, will remain stationary. However, a plane on a belt is not the same as a car on a belt or dyno. The car uses its wheels to move forward. The forces that it uses to move forward are generated at the wheels and is acted on the belt. It needs the belt to move forward, so if the belt moves backwards the same speed the wheels are trying to move forward, the car goes nowhere. However, a jet turbine on a plane is not the same thing as wheels on a car. A jet engine does not need a belt to "push off" of to move forward. It "pushes" the plane forward because it follows Newton's law of motion (every action has an equal opposite reaction). Basically the "explosion" in the engine pushes forces out in two directions, one out exhaust side of the plane into free air, the other force is pushing on the front of the engine. Since that engine is connected to the plane, that force pushes the plane too. Another way to look at is, imagine a plane and car are floating out in space. If the car floored it, the wheels will spin but the car would go nowhere. That is because it needs a surface to "push off" of to move forward. A plane, could fire it's jet engines and would move forward as it would on earth. That because it doesn't need a surface to push off of and is how the space shuttle moves in space.

So going back to the plane on a the belt. The plane really doesn't care what surface it's on, because the wheels of the plane are free spinning. The belt and wheel could be moving at 1 rpm or 1,000,000 rpms, it doesn't matter because just like the plane in space, it isn't pushing the plane backwards. Put a heavy roller skate on a tablecloth on a table and fill it with sand. If you pull the tablecloth really really really fast, what will happen? The skate will stay still while the cloth moves out from underneath. Even though the cloth moved very fast and the wheels of the skate spun very fast as well, it doesn't move because (other than friction forces) the cloth and wheel doesn't apply any forces in the direction of motion. Now as I showed above, a jet engine does apply forces in the direction of motion. If that is the only force acting on the plane, it will move forward independant of the wheel spinning speed or the belt speed.

 

[Vega$ NSX]

no not done. the vagueness of your initial question is what is causing the issues. "speed of the plane" is not very clear. it can be interpreted as the speed at the wheels. don't you see the paradox there? how can the wheel match the belt speed and at the SAME time go twice the speed? last time I checked 2X is not the same as X.

Note, he's saying the wheels spin twice the speed of the plane, not twice the speed of the belt. The speed of the wheels will match that of the belt. However, it is possible for the plane to move forward at different speed than the wheels or the belt. The plane can move forward at 100 mph, while the wheels are spinning backwards at 200 mph. Remember, these are free spinning wheels, they can spin backwards faster than the plane is moving forwards.

 

[nicholas421]

Not quite. The wheels are not spinning faster than the plane. The wheels (assuming no slippage) will spin the same speed as the belt always. The part that I think you aren't seeing is that the wheels spinning has nothing to do with the motion of the plane. I think you are thinking like a car, where the wheels spinning is the primary means for the car to move forward.

it's getting frustrating because people keep explaining the same thing over and over again without trying to understand what I'm saying. I get that thrust is what puts the plane in motion and not the wheels. i completely understand your reasoning as to why the plane will fly. i realize that you have it in your head that you are absolutely correct but for kicks just pretend that i may possibly have a point and keep an open mind.

The plane can move forward at 100 mph, while the wheels are spinning backwards at 200 mph. Remember, these are free spinning wheels, they can spin backwards faster than the plane is moving forwards.

if the wheels are spinning at 200mph, the belt is spinning at -200mph. if this goes on for half an hour the wheels will have traveld 100miles and the belt will have traveled -100miles. regardless of what the wheels are attached to or what is pushing the vehicle forward, it does not change the fact that the wheels have not moved an inch relative to a fixed object. Please explain to me the flaw in my logic and restrict your response soley to the last paragraph.

 

[SugrueNSX]

Yes, if we follow the laws according to classic dynamics, that statement would be correct. Friction is not a function of velocity:

F(r) = Crr * N

F(r) = Rolling Resistance Force
Crr = Coefficient of Rolling Resistance
N = Normal Force (Force = mass * acceleration (aka gravity))

As you can see velocity is does not factor into friction forces. However, what makes that hard to believe or understand is that there are two friction forces: Static friction and dynamic friction. Static friction is the friction force that is required to get a object started moving, afterwhich the friction force is known as the dynamic friction force. As such, static friction is always greater than dynamic friction. Think of it as pushing a heavy box. To get it started takes a lot more force than to keep it moving. That is why if you can run and give it an impulse force and break the static friction force it is often much easier to keep it moving because you are now pushing against a dynamic friction force. So velocity is only a factor in so much that if you are at zero you need to overcome a static friction force. However, once you overcome that static friciton force, you are pushing against a dynamic friction force which is constant and independent of velocity.

Here is another good way to think of it. Think of a merry-go-round or the giant wheel in the Price is Right. To get that wheel moving you need a lot of initial energy to get it spinning. If you apply a single impulse load the wheel will start to spin and then eventually slow down. Those would be the friction forces at work slowing the wheel down until it stops. Now if you keep applying a force to the wheel, i.e. you use your arm to keep it spinning by pushing it down every few seconds, what will happen? If you don't push the wheel hard enough it will still begin to slow down, only slower. If you push too hard, it will begin to speed up. At some pushing pressure the wheel will maintain its speed forever. At that speed, the force you are applying with your arm is exactly the same as the fricional forces trying to slow the wheel down. That is the limit that the fricional forces that the wheel will apply to stop the wheel. All you need to do is apply more forces than that limited frictional force and the wheel will speed up in rotational speed. No matter how fast the wheel spins, the fricional force will not exceed that amount.

Excellent! I totally understand everything you are saying.
Please indulge me and answer a few more questions to see if what you are stating makes sense.
Remember those old fashioned exercise bikes? The ones with a brake caliper on the flywheel on the front. And you could adjust the brake pressure by cranking down on a spring.
Lets say I had one and it was geared so that for every revolution of the pedals the flywheel went around one tenth of a revolution. And you had an identical bike set at the same brake pressure except yours was geared so that for every revolution of the pedals your flywheel went around ten times.
Our personal trainer requires us to both pedal at a constant sixty pedal revolutions a minute. After we both get out flywheels up to speed, who is doing the most work and why?

Regards,

Patrick