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Wirehead Studios > General Discussion > Off-Topic > Plane on a treadmill (Will it take off?)
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Author Topic: Plane on a treadmill (Will it take off?)  (Read 5267 times)
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LeeMon
 
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« on: 2006-02-28, 22:02 »
The question:
Quote
A plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane's speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

Will the plane be able to take off?

I think it's actually a challenging question that requires a good degree of thought, and the answer is not as obvious as it appears.

What do you think?
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scalliano
 

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« Reply #1 on: 2006-02-28, 23:39 »
Given that this effectively makes the plane stationery, thus resulting in a total lack of airflow under the wings and fuseilage (I hope I've spelt that right) required for the plane to actually fly, I would say no.
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Lopson
 

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« Reply #2 on: 2006-03-01, 00:24 »
A NO, since there would be no velocity for takeoff due to the velocities of both objects nullifying themselves when one velocity is deducted by other velocity:

v1 - velocity 1
v2 - velocity 2

v1-v2=0
« Last Edit: 2006-03-01, 00:24 by [KruzadeR] » Logged
Phoenix
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« Reply #3 on: 2006-03-01, 00:46 »
No.  The plane must have air flowing over the wings in order to generate lift.  The propulsive force of the jet engines only acts to move the plane's mass forward.  It is the forward motion of the plane through a (relatively) stationary air volume that generates lift.  On a treadmill the air volume and plane's body are both static, well, except for what the engines suck through and blow out the back.  Still, it would no more take off than if you strapped horizontal rocket engines to a giant brick with wheels.

Kruzader:  Lift is a bit more complex than that since you're dealing with a fluid volume.  For example, the plane could be stationary on the ground but encounter a 300 MPH headwind and it would generate enough lift to throw the plane into the air.  A helicopter can hover with no lateral or vertical velocity because its wing (the rotor) is always moving through an air volume to constantly generate lift.  Lift is, in essence, a reaction force of a solid working against a fluid, in this case a gas we call air.  The solid pushes against the fluid, and the fluid pushes back.  It doesn't seem like the fluid can push back because the fluid is moved out of the way, but it does.  Try sticking your hand out the window of a car while on the highway sometime, you'll encounter a great deal of pushing.  Pay attention to how hard you have to push against it to keep your arm stiff.  You just have to either be very close to the density of the fluid, or else push on a lot of it very rapidly (moving a lot of it out of the way in the process) in order to overcome gravity's acceleration.

Edit:  There is one exception to this scenario, if this is one of those "trick question" deals, and that is if the runway is capable of creating enough fluidic friction to accelerate the air between the plane and the runway to a high enough velocity to create a "ground effect" pressure zone under the plane.  This could lift the plane a very slight distance, but the plane still could not fly in the traditional sense.  Once it left the length of the runway - if it left at all - its airspeed would be too low and it would stall, which would not be too good at full throttle over the grass.  If you're not familiar with the concept of fluidic friction, a simple example would be to try sucking water through a very tiny straw and noting the difficulty involved.  I doubt this is part of the mental excercise, but fluidic friction is something often overlooked.
« Last Edit: 2006-03-01, 00:52 by Phoenix » Logged

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LeeMon
 
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« Reply #4 on: 2006-03-01, 22:31 »
The place where I saw this question listed had mostly "yes" answers.  Of course, it had a lot of bickering, chiding, and flames, so that doesn't make them better people. ;^)

Here's my thinking.  It'd drawn-out, so bear with me.


The idea behind the technology of the wheel (that is, any wheel not used for drive or propulsion) is that it reduces or eliminates the effect ground friction has on the vehicle's movement.  In a perfect scenario (with a wheel with perfect bearings, and where the wheel's surface had perfect grip but zero friction), you need only exert the force to push the wheeled object where you want it to go.  You would not need to exert any force to overcome ground friction.  The wheels still have grip (they don't peel out), but it's like pushing around a wet bar of soap.

Subsequently, in a perfect no-friction scenario, pretend that you stand on a level treadmill wearing a pair of perfect-ball-bearing rollerblades.  As the treadmill starts, you'll remain in place.  The wheels have grip (they turn with the treadmill), but they don't have friction; there's no resistance preventing them from turning as fast as they need to.  As such, you stay in place while the wheels turn.  In this perfect scenario, it doesn't matter how fast the treadmill goes or how quickly it accelerates; you won't move.

In the real world, however, your rollerblades do have friction.  So, when the treadmill starts, you'd roll back a bit.  Now, if the treadmill goes at an absolute crawl, the friction might be high enough that the wheels don't even rotate; you just move backward to match the treadmill.  However, the faster the treadmill goes, the less friction matters.  When the friction is less than the force of inertia (your inherent tendency to stay still), you won't keep up with the treadmill anymore.

This is the problem with the plane example; you can't visualize it like a car.  The plane isn't pushing by the wheels, it's pushing against the air.  If there were no friction in the wheels (even if the wheels maintained perfect grip), they wouldn't be part of the equation; it'd be the same as if the plane wasn't touching the ground.

Thus, the treadmill cannot "match the speed of the plane" because no matter how fast it goes, it can't push the plan back any faster than the friction of the wheels.  If it's attempting to speed up such that the plane stays in place (a reasonable assumption), it's going to keep accelerating, but it's not going to hold the plane back much.

As such, my expectation is that, barring the wheels melting, the plane will simply push off the air with a much greater force than the treadmill can achieve with wheel friction (at any speed), and the plane with take off amidst the smoldering remains of an overworked treadmill.  ;^)
« Last Edit: 2006-03-01, 22:31 by LeeMon » Logged
Phoenix
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« Reply #5 on: 2006-03-01, 23:40 »
You know it's bad form to throw extra variables in after the function is defined.  You generate compiler errors that way. Slipgate - Exhausted

The first problem with this new example is that the wheels DO have friction with the surface they are on.  They have to have friction or you would have no traction.  That's why roads are made from concrete and tires from rubber - rubber and concrete, against each other, have one of the highest frictional coefficients known (remember your basic physics here!)  Also, wheels are not a perfect cylinder with a 1-dimensional point of contact (a horizontal line tangent to the cylinder at exactly one point of contact with zero thickness).  Rubber tires squish and flatten against the ground under weight.  You also have mechanical friction that exists within the landing gear itself.  Bearings are not perfect, and you can't just throw friction out the window with this kind of scenario because it exists in the real world.  Your initial example did not exclude friction, so you have to assume it's going to be considered in any responses.

The second problem is saying the plane's engines "push on air".  Werver Von Braun would be displeased.  A jet engine does NOT push against air by nature - it is a reaction engine like a rocket.  The exhaust pushes against the engine.  If it pushed against air a rocket would not work in vacuum.  A rocket and a jet work the same except for the fact that a jet pulls air into it and compresses it to oxidize the fuel.  A rocket is just a jet engine without an intake that uses a liquid or solid oxidizer.  A turbofan engine is a bit more complex than a straight turbojet in that it uses a fan to drive air in addition to raw jet exhaust, but the effect is still pushing the plane's mass forward.  A propeller-driven airplane does push solely against the air, but it's still irrelevent for the next reason, as well as the "rollerblader" example.

The third problem is you stated the treadmill could automatically and instantaneously adjust to match the plane's speed.  With inherent surface and mechanical friction considered, so long as the treadmill can match the speed of the plane's wheels, the plane will remain relatively stationary.  If the plane's speed were to decrease relative to the treadmill, the treadmill would push it backward, and if the plane's speed were to increase above that of the treadmill's, it would begin to drift forward.  This is the same principle that differential gearing is based on.  If you take two plates and sandwich a roller inbetween them, the roller will remain relatively stationary so long as the two plates move at equal speeds in opposite directions.  If one plate's speed exceeds the other, the roller will spin at a speed 1/2 of the difference of the plates' speed and begin to drift around in the direction of the faster plate.  Replace this setup with a flat belt, and attach a framework to the roller that has a jet engine on it, and there's your airplane example.  It's no different than a rocket-powered car sitting on the treadmill.  The physics are absolutely no different.

Lastly, the fact that the plane has wings may make someone think it can take off, but a wing is useless without one factor - AIRSPEED.  Airspeed == LAW when it comes to flight.  Nothing - absolutely NOTHING else generates lift except moving air over a wing at the proper speed.  Unless you can either move the air over the wing, or move the wing through the air, your plane is stuck on the ground.  Period.  The plane MUST move forward to lift off.  The only way your mental exercise can allow the plane to lift off is if the plane's wheels are allowed to spin faster than the treadmill can adjust, allowing the plane to move forward, or if the wheels are allowed to skid along the surface.  No forward wing motion, no flight.  End of line.

Now if, as you suggest, you throw ground friction completely out as well as mechanical friction inherent in the landing gear, then yes, the force acting upon the plane's wheels by the treadmill would be zero.  It would essentially slide across the surface and the jet engines could act fully on the plane's mass, accelerating it forward, and allowing the plane to lift off because it's airspeed is increasing relative to the air volume it is within.  Remember too, either the relative rotational speed of the wheels is going to exceed your conditions of the treadmill keeping up, or else the wheels have to skid as the plane goes forward.  Realistically, yes, the plane would take off if you do not limit the wheel speed by the conditions of the test and the plane can then accelerate forward.  It would EASILY take off in that scenario.  However, so long as this experiment is conducted in a "realworld" set of conditions, gravity is pulling the plane down, and friction is going to play a roll.  So long as friction plays a roll, the treadmill is going to exert a force against the plane.  So long as the treadmill exerts a force and is programmed to exactly match the plane's speed, and the wheels are not allowed to exceed the treadmill's speed, nor allowed to skid, the plane will maintain a relative position of zero, have zero airspeed, will never, ever lift off.
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LeeMon
 
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« Reply #6 on: 2006-03-02, 09:57 »
See, it isn't a clear answer at all.  That's part of why it's fun.  ;^)  It's such an absurd theoretical example that it's hard to put all the pieces together.

By the way, I'm cheating by way of things other people already looked up in the discussion, so I claim no credit or victory.

Too much of this boils down to the treadmill's goal.  "Matching the speed of the plane" is silly when the plane's force is applied to itself, not the ground.  It's not pushing off the air, but it's not pushing off the ground, either.  To simplify trying to define things that happen in response to each other simultaneously, I'm operating under the assumption that the treadmill follows a program similar to the following:

10 TV = CURRENT_TREADMILL_VELOCITY()
20 WV = CURRENT_WHEEL_VELOCITY()
30 IF (TV > WV) THEN TV++
40 GOTO 10

Of course, the treadmill makes the measurements and necessary speed adjustments thousands of times per second or more.  It's going to need to.

This link helps a bit to visualize the "rollerblade" theory:
http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

Like I said, if the treadmill our rollerblader is on goes very slowly, the wheels won't move at all.  But once you hit a certain threshold, you not only slow down, you virtually stop moving.

The plane is generating its own force forward, and the treadmill intends to counter it.  The problem is once you've reached the threshold of motion, and the wheels start turning, the amount of force the treadmill can provide backwards remains near-constant, regardless of how fast it moves.  This constant level of frictional force is only true up to a point, but that means that during those critical first few seconds, once the tires start moving, it's all about the thrust of the plane vs. the kinetic friction of the wheels (which the treadmill cannot increase by speeding up, at least not until reaching several orders of magnitude of speed).

Someone posted that a 1937 study of airplane tire friction.  The worst result they received was a coefficient of 0.035.  Making the assumption that current tires have as much friction or less, that would provide a rolling resistance against an 850,000 pound plane approximately 30,000 pounds of friction.  The four engines, on the other hand, each produce about 58,000 pounds of thrust (for a total of 232,000).

So, putting this in snapshots of tiny fractions of a second:
The treadmill does nothing until the plane moves, as it has no wheel velocity to match.
When the wheels start moving and have a velocity, the treadmill can only counteract with kinetic friction, which is a near-constant.  As such, no matter what speed it goes (up to a point), it can only generate 30,000 pounds of friction to slow the plane down, which is no match for the plane's 232,000 pounds of thrust.
Thus, the plane continues to accelerate, the wheels gain velocity, the treadmill tries to counteract with additional velocity, but does not generate enough friction to overcome the engine thrust.  Effectively, the treadmill goes much faster, and the wheels go much faster, but the wheels are still going slightly faster than the treadmill (because the engine is overcoming the kinetic friction of the wheels).

=====

Hopefully this does a much better job of putting it all together.

The one theory that is central to how I understand the scenario presented, is that once an object starts moving, kinetic friction is near-constant.  That is, you can't generate additional friction by going faster.  It's the same reason a box is easier to push while it's moving than if you let it stop, and it just gets easier the harder you push (because your force gets greater and the kinetic friction remains the same).

If kinetic friction is near-constant, the treadmill will fail in its goal of making wheel speed equal treadmill speed, no matter how fast it goes.  As I explained, it'll make both wheel and treadmill go really fast, but since virtually no additional friction is being generated (and the engines are still wining by about 232,000 to 30,000), the wheel will continue to travel faster than the treadmill.  As such, the plane moves forward, because it's having virtually no more trouble overcoming wheel friction than it does any other day of the week.

At the point where this breaks down, we're certainly no longer talking about standard operating procedure for any of the equipment involved.  I'm not going to begin to decide, or even guess, where the wheels fail, or lock up, or simply start slipping off the treadmill... or what the limits of the treadmill's acceleration are.  Besides, when we go an order or two of magnitude above the speed a plane normally goes, doesn't the air above the treadmill catch a significant degree of friction itself, and start moving backward itself?  In Ludicrous Speed mode, this might be enough to generate lift (though again, we're talking silliness again).

So, my guess remains: Within boundaries of speed, thrust, and acceleration that have any degree of feasibility for the equipment involved, the treadmill cannot overcome thrust (since kinetic friction is near-constant, and the engines overwhelm that friction), and the plane will successfully move forward relative to the air, generating lift and taking off despite the treadmill's best efforts to go really really fast.  The first point of failure I expect (after choosing to ignore how a plane got on a giant treadmill and how it can accelerate so much mass to such a velocity in such a short time) will be the physical integrity of the wheels.

But I could still be wrong.  That's why I posted.
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Phoenix
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« Reply #7 on: 2006-03-03, 00:16 »
You are somewhat correct about sliding friction (which you refer to as kinetic friction) as opposed to static friction.  This is why constant pressure on a brake will produce a constant deceleration until the rotational energy of a wheel is insufficient to overcome the static friction coefficient of the braking surface.  Now static friction is always maintained between a wheel on a surface, which is why traction works, but does not affect a vehicle's velocity much when rolling since it only works against sliding movements, which is why wheels are used in the first place.  Sliding friciton exists within the bearings of the landing gear, but is lessened by the use of roller and ball bearings, though it cannot be eliminated completely.  Static friction won't be as much of a concern on the tire surfaces as opposed to a box sliding on the floor since rolling wheels do in fact roll, but the deformation of the tires does a bit more to increase it to a slight degree.  Wheels have to maintain a 2-dimensional contact area on the ground or your vehicle skids like it's on ice.  Remember too that rubber tires squish and deform a LOT more under the weight of an airliner than hard plastic wheels do under the weight of a rollerblading skater girl (or boy). Slipgate - Smile

The main flaw from all of this is the original constraint of the experiment.  Like I said, I was playing by the rules, assuming that the treadmill can always match the wheel velocity, which you stated as an initial condition.  If that is the case, then the wheels will never be able to roll fast enough for the plane to run off the end of the treadmill, making lift-off impossible simply because the experiment does not allow for it.  Remove that constraint and allow the plane to do what it could do normally and the plane could easily outpace the treadmill once you threw the engines to full throttle.  Like I said, if that constraint is removed and the wheels are allowed to turn faster than the treadmill can keep pace, the plane will move forward and take off as easily as if the runway were stationary, for the reasons you expressed, provided that the wheels don't fly apart from exceeding their maximum rotational velocity and cause the plane to cartwheel forward onto one very fast moving belt sander! Slipgate - Laugh

In essence, the entire experiment is based on a flawed premise - that the treadmill can keep pace with the airplane.  Physically that is impossible.  However, since it was dictated as a predefined condition, then it is a "given" that the plane's wheel velocity can never exceed the treadmill's speed.  The conditions of the test are dictating the result, as opposed to the laws of physics that would provide a much different result if it was an open experiment.  Like tic-tac-toe on the computer, the only winning move for this mental exercise is not to play. Slipgate - Wink
« Last Edit: 2006-03-03, 00:16 by Phoenix » Logged

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Hedhunta
 
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« Reply #8 on: 2006-03-07, 16:25 »
that treadmill would need to be both really huge and spinning really fast..   sides, simply put, its not "wheel" speed that makes an aircraft fly, because youre NOT powering the wheels, they are simply there so you dont slide all over the ground and can make a safe takeoff and landing.

what were talking about here is basically the same as a huge aircraft dyno like they use to determine cars HP, etc. the cars wheels spin(because they are powered, unlike an aircraft) and the duno only needs the powered wheels to make contact, the drum spins, and the car goes nowhere(theoretically anyhow they still bolt and strap them down anyways)

like pho said, airspeed + airflow over wings is what makes them fly, doesnt matter how fast you spin the wheels, it wont just "take off" see the same principle of the doolittle raid here: they wanted slow bombers to take off from a carrier.. they could come close, but not quite.. so they turned the carrier INTO the wind(extra airflow! + more lift) and went full speed ahead.

lift makes flight. not speed. i mean, look at hang gliders? they go probably less than 3mph and they still fly. if you were running on a treadmill holding a hang glider, you arent going anywhere are you?
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