Will the plane take off?

[Vega$ NSX]

Second, if the treadmill can accelerate exponentially and infinitely, it is theoretically possible to hold the plane back... preventing it from taking off... assuming that friction exists in this imaginary world.

This is what I keep trying to explain to you people. Assuming the wheels, tires and bearing can handle infinite speed, friction (rolling resistance) reaches a limit. It is not a function of the belt speed or the wheel's rototational velocity. All of the laws of physics, dynamics and engineering state and support this. The equation for friction forces and rolling resistance do not have a "velocity" component to it at all.

If you believe that friction increases as the treadmill speed increases then, yes, your theory is correct. However, that assumption is wrong. Friction does not increase as the treadmill increases; it reaches a limit. If you can understand that concept, then you can understand that if you can overcome this limit, then you can move the plane.

Put a heavy object like a refrigerator in a box on a concrete slab. Ifyou move the box around really slowly by pushing on it, you'll note that it pushes back and it requires some level of force. That's friction pushing back on you. Now start pushing it faster and faster. Does it get harder to push? The faster you move, does it push with an ever increasing force? No, it's the same force as when you were pushing it slowly. In fact you could do an all out sprint and the force would still be the same. That is the limit of the fricitonal force. You could push the box at an infinite speed and it would still push back at the same force. It is independant of velocity.

 

[CL65 Captain]

Slight correction if ya don't mind...
Most general aviation airplanes don't have. Commercial jets do. It is a GPS ground speed. When I taxied the Jumbo Jet you could not tell how fast you were going on the ground by looking out the window. Heavy reliance on GPS ground speed for taxiing.


747-200

I was behind a LUV taxing out the other day in BNA and he was smoking, even hitting all the apexes on the turns! :biggrin: :biggrin: You guys must have the type R chassis braces installed.

 

[flaminio]

Second, if the treadmill can accelerate exponentially and infinitely, it is theoretically possible to hold the plane back... preventing it from taking off... assuming that friction exists in this imaginary world.

But you don't need to reach an "infinite" speed. The wheels only need to spin at twice the necessary takeoff speed. Any plane's wheels can do this; they often spin at more than that speed during landings.

 

[Aero]

Again, rolling resistance in airplane tires does increase some with velocity. Its in the airplane landing gear design handbook I have. Here's an Air Force study to prove it to you. The equations aren't so simple (like I said b4) when you account for tire deflection.

http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=AD746304&Location=U2&doc=GetTRDoc.pdf

However, that assumption is wrong. Friction does not increase as the treadmill increases; it reaches a limit.

 

[skyguy]

I was behind a LUV taxing out the other day in BNA and he was smoking, even hitting all the apexes on the turns! :biggrin: :biggrin: You guys must have the type R chassis braces installed.

Don't taxi faster than V1 or you might get airborne.:biggrin:

Opps-A-Daisy!

Jan 27 2008

SPOKANE, Wash. (AP) - A Southwest Airlines plane with 118 passengers on board skidded off a snow-covered taxiway Sunday afteroon after safely landing at Spokane International Airport, the airline said.

No one was injured.

The pilot of Southwest Flight 485, bound from Portland, Ore., was slowly taxiing to the gate when the front wheels of the plane slid off the taxiway around 1:40 p.m., said Brandy King, a spokeswoman for the Dallas-based carrier.

Heavy snow had been falling on Spokane and the surrounding region since Saturday.

The airport had to shut down operations until crews could move the Boeing 737, which was obstructing a taxiway, King said.

Southwest used three buses to shuttle the plane's passengers and five crew members to the terminal.

The plane will be removed from service for routine inspection to make sure it wasn't damaged and that mechanical failure did not play a role in the incident, King said.

 

[Briank]

Slight correction if ya don't mind...
Most general aviation airplanes don't have. Commercial jets do. It is a GPS ground speed. When I taxied the Jumbo Jet you could not tell how fast you were going on the ground by looking out the window. Heavy reliance on GPS ground speed for taxiing.


747-200

In the Cessna 172's I get to play with the instrumentation is minimal :biggrin:

But as noted the GPS gives ground speed but it is calculated from the change in position and has nothing to do with how fast the wheels are turning.

 

[Vega$ NSX]

Again, rolling resistance in airplane tires does increase some with velocity. Its in the airplane landing gear design handbook I have. Here's an Air Force study to prove it to you. The equations aren't so simple (like I said b4) when you account for tire deflection.

http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=AD746304&Location=U2&doc=GetTRDoc.pdf

Yes, I know what you are getting with on that. But there are three stages of true rolling resistance. Initial, rolling and limit. On initial rolling resistance the friction increases dramatically. Once that stage clears the rolling resistance remains relatively constant; even your reference states that it is nearly constant. (Look at the points before the wheel reaches it's limits, before exponential increase in resistance: it's nearly a horizontal line; slightly linear at best). Then as the wheel reaches the limit of what it can handle, the friction forces again accelerate rapidly. It is that phenomenon that causes the wheel to break apart.

Again, for the example we have to assume the wheel is not in that stage. Otherwise, the wheel/tire assembly will explode far before reaching an infinite speed and the question should be, can the wheel/tire handle the speed or will it explode. So it must be assumed that the tire/wheel assembly is in the stage/phase that it can maintain itself up to infinity. At that stage (stage 2) again, the rolling resistance is essentially flat or constant. It may increase linearly slightly, but when you relate that to infinity, relatively speaking it can be essentially constant. While, yes, in the real world it may rise slightly, it is not enough of a factor to change the outcome of the question.

If I had a car that accelerated 0.00000000000001 mph per year, compared to a car that went infinity mph, any correlations or conclusions I can make between the two would be essentially the same as if I said the car wasn't moving at all.

So if you wanted to be absolutely technical about it, then "yes" in the real world rolling resistance will increase slightly as velocity increases. However, is it essentially constant/zero when compared to an ever increasing velocity? Yes. That is why it does not have enough of an effect on the outcome of the "will the plane fly" question? And the Mythbusters episode proved it. Real world forces were in play, in their real world experiment, but they were insignificant enough to affect the outcome that was predicted by standard Newtonian physics. And remember that is all Newtonian physics is: a rough estimation/model of what we think will happen. However, over hundreds of years, we've found out that we can make these estimations accurate enough that we can undeniably accept their results and build things like buildings and cars using them. So when I demonstrate an equation like a free body diagram, it is not accurate enough to model each and every little atom or molecule and factor them in, but it is an accurate enough model to show those little factors are insignificant enough to generalize or ignore and still come up with the proper outcome.

 

[nicholas421]

So, enlighten us then, Einstein, since we're all so stupid.

sorry you took offense. you mustve felt my comment applied to you... and by reading your car example (again), i can see why.

 

[nicholas421]

But you don't need to reach an "infinite" speed. The wheels only need to spin at twice the necessary takeoff speed. Any plane's wheels can do this; they often spin at more than that speed during landings.

1) infinite speed and accelerating to infinite speed are 2 completely different things.
2) you yourself admite the wheels need to spin twice as fast as the conveyor belt... which is why i state that the issue is in the wording. if the conveyor belt matches the wheel's speed, then by definition the plane is not moving forward.

 

[nicholas421]

If you believe that friction increases as the treadmill speed increases then, yes, your theory is correct. However, that assumption is wrong. Friction does not increase as the treadmill increases; it reaches a limit. If you can understand that concept, then you can understand that if you can overcome this limit, then you can move the plane.

i don't believe velocity increases friction; i believe the rate of change does (acceleration).

 

[flaminio]

if the conveyor belt matches the wheel's speed, then by definition the plane is not moving forward.

No, no, a thousand times no! Planes != cars. If a car's wheels match the conveyor speed, then the car does not move. A plane's wheels provide zero thrust -- they spin free. They can move fast or slow or even backwards and it doesn't affect the plane.

 

[robr]

No, no, a thousand times no! Planes != cars. If a car's wheels match the conveyor speed, then the car does not move. A plane's wheels provide zero thrust -- they spin free. They can move fast or slow or even backwards and it doesn't affect the plane.

I can't believe someone still thinks that somehow spinning the planes wheels has anything what-so-ever to do with the plane's motion. After all the explanations and now MythBusters... people still don't get it. It's so frustrating, isn't it?

 

[Miner]

All the time..
So, if you are "Bucking a headwind" you will see the diff.

BTW: Never say "Bucking a headwind" on the PA.
ie:

Pilot: "Folks, we are going to be Bucking a headwind today."

Old lady passenger: "What are they doing to that headwind? My word!"

That reminds me of a flight one time from Houston's intergallactic to Corpus Christi. I think the headwind we were bucking was greater than our cruise speed for a few minutes. I'd swear we were going backwards. It was an ATR - 72 and we were about 8000 feet. The flight took over 2 hours if I remember, and it is less than 200 miles. Thank goodness for the regional jets now.

Miner

 

[Scruit]

BrianK,

That ultra light did. They had a camcorder aimed on it and used it for determining what the take off speed was. That is why I posted my comment about them not talking about it after the test.

Miner

It was an airspeed indicator, and they only used it to find out how fast the plane takes off at, so they knoew how fast to pul the belt in the other direction.

 

[Miner]

It was an airspeed indicator, and they only used it to find out how fast the plane takes off at, so they knoew how fast to pul the belt in the other direction.

Scruit,

I could have sworn the called it a speedometer, but wasn't paying that close attention. I think it would have helped explain that while the plane was still moving forward at 25, the wheels were spinning at 50.

Miner

 

[nicholas421]

No, no, a thousand times no! Planes != cars. If a car's wheels match the conveyor speed, then the car does not move. A plane's wheels provide zero thrust -- they spin free. They can move fast or slow or even backwards and it doesn't affect the plane.

please understand that I "get" the concept of thrust versus wheels driving a vehicle forward. please think outside of your box for one second and try to understand what i'm saying.

regardless of what the vehicle is, just look at the wording itself. for every revolution of the wheel, the ground underneath has moved the diameter of the wheel. any which way your disect the rest of the problem, the vehicle has not moved forward.

in essense the question can be reworded:
"a plane is stationary, can it take off?"

i agree it would take off if the question was:
"the belt matches the speed of the plane RELATIVE TO THE GROUND, in the opposite direction... can it take off?"
in this case, the wheels would be spinning faster than the belt, allowing it to move forward.

 

[Vega$ NSX]

i don't believe velocity increases friction; i believe the rate of change does (acceleration).

I'm sorry but that is also incorrect. Friction does not increase with acceleration. Sorry, let me rephrase that. In the real world, the increase in friction due to velocity or acceleration is so marginally small that it can be rendered near zero without having an effect as to the questions outcome. When engineers design a car, plane or how to land on the moon, they do not factor any friction due to an increase in velocity or acceleration unless the material/wheel is approaching the limits of structural integrity. There is a band of operation where this marginal increase is so relatively marginal in relation to the overall forces that it is ignored for 99% of real world calculations. Now there is exceptions to every thing so I'm sure in the most critical of critical applications there is a case where it may have to be factored in. But a plane on a treadmill is not one of these cases as it is not as critical (the relatively small increases are not even close to the overall forces such as weight, engine thrust to even remotely impact the outcome of the answer).

Please correct (and forgive) me if I'm wrong but what are you basing these statements on. Gut feelings? Instincts? Observations? You have to keep in mind that there is a dedicated science that is used by millions everyday to explain the motion of objects and their interaction called Engineering Dynamics. It is the foundation of nearly engineered product we rely on. And in the equations and assumptions that they use to model real world examples, significant frictional forces (or rolling resistance) are not a function of acceleration or velocity in the direction of motion. I know that sounds counter intuitive, but it's true. The very concept of a flywheel relies on this concept.

 

[flaminio]

regardless of what the vehicle is, just look at the wording itself. for every revolution of the wheel, the ground underneath has moved the diameter of the wheel. any which way your disect the rest of the problem, the vehicle has not moved forward.

in essense the question can be reworded:
"a plane is stationary, can it take off?"

No, it can't. It might be reworded "if the wheels are stationary, can it take off?" but in no sense is the question saying that the plane must remain stationary. The only thing the wheels do for a plane is to reduce friction. It doesn't even need to be wheels -- snowplanes and seaplanes take off just fine without wheels. Once you have a setup where the friction to the ground is low enough to allow the plane's motor to overcome that friction and propel the plane forward at sufficient speed, flight is inevitable.

The wheels could even be spinning backwards, and it would still not hinder the plane from moving forwards.

 

[Vega$ NSX]

regardless of what the vehicle is, just look at the wording itself. for every revolution of the wheel, the ground underneath has moved the diameter of the wheel. any which way your disect the rest of the problem, the vehicle has not moved forward.

in essense the question can be reworded:
"a plane is stationary, can it take off?"

i agree it would take off if the question was:
"the belt matches the speed of the plane RELATIVE TO THE GROUND, in the opposite direction... can it take off?"
in this case, the wheels would be spinning faster than the belt, allowing it to move forward.

This has been addressed already. In the version that we are talking about the question states that the belt matches the plane's speed. Therefore the wheels can rotate faster than the travel of the belt.

However, I understand that some versions of the question exist that state the belt moves at the speed of the wheel (in other words, travels the same distance as the wheel circumference, not diameter as you state). However, I firmly believe that is a bastardization of the original question as it is a paradoxical statement, which is not the intent of the original question. I discuss this in more detail here, here and here.

Regardless, a treadmill can move and a wheel can spin at infinite speed, it still cannot generate enough forces to keep a plane from taking off.

 

[hofffam]

i don't believe velocity increases friction; i believe the rate of change does (acceleration).

Some devices behave this way - for example shock absorbers. They are designed to resist more with fast motion than slow. Fluids are used to create this behavior. A wheel bearing probably has a liquid-like lubricant (grease) and might have a tiny increase in friction during periods of high acceleration. But it is negligible unless some other factor (like heat or bearing breakdown) occurs.

I think the show illustrated that how fast the landing gear wheels move doesn't prevent a real plane from taking off. The increase in friction isn't enough.

The frame of reference for the thrust (propellor or jet) to cause forward motion is not the "ground" (conveyor belt). The frame of reference is the air surrounding the plane. If the air were moving backwards at a speed that matched the conveyor belt the thrust would be negated and no air flow over the wings would occur. But that isn't what happens. The engine thrust acts against the air, easily overcomes the friction caused by the conveyor+wheels, the wings behave as Bernoulli predicts, and the plane takes off.

 

[Viper Driver]

sorry you took offense. you mustve felt my comment applied to you... and by reading your car example (again), i can see why.

Since the PC police didn't like my last response to this post, I'll apply a little more restraint this time.......Your continuing condescending attitude is noted, though.

I have no need to defend my intelligence, I was right from the beginning in the answer to this question, despite my fifth-grade mindset getting in the way of my thousands of hours of flight time and common sense. I don't need Mythbusters to show me what I already know, and I certainly don't need you to remind me that alternative interpretations exist of the question. The commonly accepted interpretation (and the one I think that the original author of the question intended) is the one that all of us fifth-graders are discussing. Just because you choose to make everyone aware of the the alternative interpretation doesn't make you more intelligent than everyone else......it just means that you took the time to type out what most of us have already considered and dismissed due to it's impossibility. So congratulations......you get a cookie for attempting to remind us all where our place is in this world.

Just because someone chooses not to get into the semantic weeds with you doesn't mean that they lack intelligence. You may consider my own "alternative interpretation" of why we're not doing that.......maybe we've already been down that road before within the confines of our fifth grade minds?

 

[nicholas421]

In the real world, the increase in friction due to velocity or acceleration is so marginally small that it can be rendered near zero without having an effect as to the questions outcome.

i think we can agree that this is a theoretical question.. as in, let the math do the talking.

regardless of how marginally small the friction is caused by acceleration, it is still proporational (linear or otherwise) to the level of acceleration. therefore increasing acceleration infinitely will increase friction infinitely. are you saying this relationship is untrue?

 

[nicholas421]

However, I understand that some versions of the question exist that state the belt moves at the speed of the wheel (in other words, travels the same distance as the wheel circumference, not diameter as you state). However, I firmly believe that is a bastardization of the original question as it is a paradoxical statement, which is not the intent of the original question. I discuss this in more detail here, here and here.

yes i agree. the last version i read (in fchat) is the "paradoxical" version... hence my earlier post.

 

[NCC-1701D]

So, enlighten us then, Einstein, since we're all so stupid.



You're exactly wrong. By definition, the plane IS moving forward if wheel speed is matching the ground speed. Did you mean wheel speed in the opposite direction of ground speed?



You're back into the weeds with the "chicken or the egg" argument. For the treadmill to move, there must be forward movement by the plane. If the plane's just sitting still, the wheels won't be rotating. As has been discussed ad nauseum, the plane is not powering the wheels like a car...the wheels rotate DUE TO the forward motion of the airplane, they do not CAUSE the forward motion of the airplane. So, there can really be no argument made that involves the treadmill "theoretically spinning up to infinity". That would mean that the plane is moving forward at a similar speed, since that is the only thing that causes the wheels to rotate, causing the treadmill to move backwards, and so on, and so on.......

There is no problem to solve in your interpretation of the question, because it requires the wheels to rotate without the plane moving forward. That is impossible.

I have been thinking about since I saw it on mythbusters..

Can we all agree on this...

- the wheels provide no thrust.
- the propellor provides thrust in which the plane moves forward causing the wheels to spin.
- if there is a threadmill that matches the planes speed..The wheels will be spinning because the plane is trying to go forward but the treadmill is spinning in the opposite direction at equal speeds. Therefore the plane has not moved.

since the plane theoretically can't move forward and is at full throttle,
so why not just anchor the plane to a structure to see if it can take lift off the ground...

really it comes down to

can the propellor move enough air to cause lift on the wings or does the propellor create enough movement speed for the air to lift the wings..

if you anchor the plane so there is no forward speed..it should solve this problem...

 

[robr]

I have been thinking about since I saw it on mythbusters..

Can we all agree on this...

- the wheels provide no thrust.
- the propellor provides thrust in which the plane moves forward causing the wheels to spin.
- if there is a threadmill that matches the planes speed..The wheels will be spinning because the plane is trying to go forward but the treadmill is spinning in the opposite direction at equal speeds. Therefore the plane has not moved.

since the plane theoretically can't move forward and is at full throttle,
so why not just anchor the plane to a structure to see if it can take lift off the ground...

really it comes down to

can the propellor move enough air to cause lift on the wings or does the propellor create enough movement speed for the air to lift the wings..

if you anchor the plane so there is no forward speed..it should solve this problem...

We cannot and DO not agree with

"- if there is a threadmill that matches the planes speed..The wheels will be spinning because the plane is trying to go forward but the treadmill is spinning in the opposite direction at equal speeds. Therefore the plane has not moved."

The plane will absolutely continue to move forward no matter how fast the treadmill is moving. The treadmill will not affect the plane speed even one iota. You saw mythbusters and still don't get that?