Sorry for the forum/blog downtime today. Many things went wrong during davean’s heroic upgrade. (I blame the LHC.)
Feynman used to tell a story about a simple lawn-sprinkler physics problem. The nifty thing about the problem was that the answer was immediately obvious, but to some people it was immediately obvious one way and to some it was immediately obvious the other. (For the record, the answer to Feynman problem, which he never tells you in his book, was that the sprinkler doesn’t move at all. Moreover, he only brought it up to start an argument to act as a diversion while he seduced your mother in the other room.)
The airplane/treadmill problem is similar. It contains a basic ambiguity, and people resolve it one of a couple different ways. The tricky thing is, each group thinks the other is making a very simple physics mistake. So you get two groups each condescendingly explaining basic physics and math to the other. This is why, for example, the airplane/treadmill problem is a banned topic on the xkcd forums (along with argument about whether 0.999… = 1).
The problem is as follows:
Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?
The practical answer is “yes”. A 747’s engines produce a quarter of a million pounds of thrust. That is, each engine is powerful enough to launch a brachiosaurus straight up (see diagram). With that kind of force, no matter what’s happening to the treadmill and wheels, the plane is going to move forward and take off.
But there’s a problem. Let’s take a look at the statement “The conveyor belt is designed to exactly match the speed of the wheels”. What does that mean?
Well, as I see it, there are three possible interpretations. Let’s consider each one based on this diagram:
1. vB=vC: The belt always moves at the same speed as the bottom of the wheel. This is always true if the wheels aren’t sliding, and could simply describe a treadmill with no motor. I haven’t seen many people subscribe to this interpretation.
2. vC=vW: That is, if the axle is moving forward (relative to the ground, not the treadmill) at 5 m/s, the treadmill moves backward at 5 m/s. This is physically plausible. All it means is that the wheels will spin twice as fast as normal, but that won’t stop the plane from taking off. People who subscribe to this interpretation tend to assume the people who disagree with them think airplanes are powered by their wheels.
3. vC=vW+vB: What if we hook up a speedometer to the wheel, and make the treadmill spin backward as fast as the speedometer says the plane is going forward? Then the “speedometer speed” would be vW+vB — the relative speed of the wheel over the treadmill. This is, for example, how a car-on–a-treadmill setup would work. This is the assumption that most of the ‘stationary plane’ people subscribe to. The problem with this is that it’s an ill-defined system. For non-slip tires, vB=vC. So vC=vW+vC. If we make vW positive, there is no value vC can take to make the equation true. (For those stubbornly clinging to vestiges of reality, in a system where the treadmill responds via a PID controller, the result would be the treadmill quickly spinning up to infinity.) So, in this system, the plane cannot have a nonzero speed. (We’ll call this the “JetBlue” scenario.)
But if we push with the engines, what happens? The terms of the problem tell us that the plane cannot have a nonzero speed, but there’s no physical mechanism that would plausibly make this happen. The treadmill could spin the wheels, but the acceleration would destroy them before it stopped the plane. The problem is basically asking “what happens if you take a plane that can’t move and move it?” It might intrigue literary critics, but it’s a poor physics question.
So, people who go with interpretation #3 notice immediately that the plane cannot move and keep trying to condescendingly explain to the #2 crowd that nothing they say changes the basic facts of the problem. The #2 crowd is busy explaining to the #3 crowd that planes aren’t driven by their wheels. Of course, this being the internet, there’s also a #4 crowd loudly arguing that even if the plane was able to move, it couldn’t have been what hit the Pentagon.
All in all, it’s a lovely recipe for an internet argument, and it’s been had too many times. So let’s see if we can avoid that. I suggest posting stories about something that happened to you recently, and post nice things about other peoples’ stories. If you’re desperate to tell me that I’m wrong on the internet, don’t bother. I’ve snuck onto the plane into first class with the #5 crowd and we’re busy finding out how many cocktails they’ll serve while we’re waiting for the treadmill to start. God help us if, after the fourth round of drinks, someone brings up the two envelopes paradox.
xkcd 
Assuming that the plane is stopped at the begining of the belt, then begins moving, it would take a while for the plane to lift off because gravity would keep the plane in contact with the belt, but eventually the thrust created by the engines would be stronger than the gravity enforced friction and the wheels would skid allowing the plane to move forward creating lift sufficiently to take off assuming that it maintains the speed reguired to overpower the friction. So nyeh =P
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Jason has a good approach. It boils down to whether
a 747 can take off with its wheels locked. Even accepting
a mu of 0.2 you are left with about 100,000 lbs of thrust
(depending on exact weight and model of engine). I.e.
it’s like trying to take off with half the engines out.
Is that enough thrust for a 747 to take off? If it is, I
bet it would take a very long runway. Anyone tried
this on a simulator? (We’re assuming that the plane
is fully fuelled. Remember 1/2 the weight is fuel.
Things might be different if the plane was only partially
fuelled.)
Realistically the front tire would shred
and the front landing gear would collapse. This would put
the plane in a nose down attitude which would prevent
take off.
There is a further consideration someone mentioned.
To achieve enough wheel speed to cause tire slippage,
the tread mill would have to be going very fast. (How fast, I
don’t know. Anyone know what the coefficient of dynamic friction is
for wheel bearings?)
The drag of the treadmill surface on the air will cause some wind.
Is it fast enough to cause the air at wing level to reach take
off speed relative to the stationary plane /before/ the plane
starts sliding and the tires blow and the landing gear collapses.
Actually, take off speed is not required, once the air is
moving a bit, that reduces the effective weight of the plane,
and that reduces the maximum rearward force that the tires can
exert. But then that just means that the tires slip and explode
and that the landing gear collapses sooner.
If the plane can take off, I think this is the only effect that will do it.
And that raises an important unknown? How wide is the treadmill.
If it is just wide enough to accommodate the wheels, the generated
wind will be concentrated at the centre and may not reach the
wingtips. This could create vortexes that could prevent flight.
If the treadmill is as wide as the wingspan, then probably the
generated wind would be a significant factor. The tread mill would also
have to be very long, but as already noted, it will take a long runway.
And if the plane does manage to take off, what happens when it
reaches the front of the treadmill and is hit by a giant updraft?
The results won’t be pretty.
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@ Theo, the problem states that the treadmill IS as long and as wide as a regular Runway. Sorry if this is oversimplified, since i dont know much about physics:
Assuming the 747 is thrusting at maximum speed, wouldn’t it be easier if the treadmill just Stopped moving, allowing the 747 to move forward at maximum speed (also assuming that the break is instantaneous). So this would give the pilot time to raise the planes altitude before it gets hit by the updraft.
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I was just wondering…
(By the way, I’m just in ninth grade and taking introductory physics… lol)
Doesn’t the plane need the difference in air pressure that comes from the shape of the wings to basically lift off? Basically wind?
So if there is no flow of air around the wings, then how would the plane take off?
And if there is, where would it come from?
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The whole idea of using the word ‘treadmill’ is just a way of saying the plane is not moving. That’s what the author means when he says treadmill. It’s just another way of saying the rotation of the wheels is always matched by the speed of the treadmill (It goes without saying that obviously physically this would be impossible -and one or the other would soon self destruct- but come on we are talking about a giant hypothetical treadmill). No further explanation is needed as this is the implicit meaning of the word treadmill.
I’ve never seen anyone moving around a gym on a treadmill. treadmills allow you to move but treadmills themselves stay in the same spot.
So no the plane can’t move forward. That means it can’t take off (lift requires an airflow over and under the wings created by moving forward).
Arguing about if the plane could skid forwards or not is missing the point. You guy’s are taking it way to seriously, of course the wheels would break off or the plane might skid forwards but this is not what is meant when we say ‘treadmill’.
A treadmill that allows the plane to move would fall outside the definition of a treadmill.
Now a harrier jump jet could take off on a treadmill because it can angle it’s engine downward to propel itself vertically up. Jumbo jets don’t do this, someone should explain that to xkcd!
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HUH
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Although, obviously putting the engine underneath the brachiosaur would be inhibitive as it would block air intake going into the jet.
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Whilst you’er in first class, waiting for your lemon-soaked paper napkins to arrive…
Wait, that’s another scenario…
Mystic Knight of the Sea
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ooook… here’s my take on this. the wheels upon takeoff are reasonably irrelevant. they produce no energy. (as opposed to a car) so the wheels would techninically be spinning at twice the speed they normally would be. the thrust and movement of the airplane is from the jet engines. and if we wanted to assume that the wheels were not creating friction (i.e. had it’s brakes on), then the reverse treadmill affect would matter nil. the plane would accellerate, take off, and fly just as it always would.
if you don’t agree with me. try this.
find a hot wheels car, and find a treadmill.
turn on treadmill and place hot wheels car on it.
now. push the hotwheels car from behind as if it was the thrust from an air plane engine.
it moves!
all because the wheels are not relevant to the motion of the plane.
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and im gonna have fun bringing this up at the dinner table with my physicist buddies.
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Actually, I’m a pilot. Have flown many types of aircraft including high performance jets. So I’ll tell flying stories here in the spirit of the discussion. It doesn’t matter what the wheels or engines are doing at all only how much lift the wings produce due to the difference in pressure/angle of attack etc. My initial training was in gliders – no engines at all and only a single wheel on the aircraft body and two wing wheels – it flew just fine (no treadmill though thankfully – just a HUGE catapult winch or tow plane). Many a time, due to air density at high altitude or over loading, aircraft have not achieved flight despite fully functioning engines.
Even better! You’re flying along through a winter storm – Ice forms on the leading edge of your wing – changing it’s shape ever so slightly. You are still flying an expensive jet at full military power. How long does it take accident investigators to identify your remains? Yeah, you fall right out of the sky.
Or my favorite! The accelerated stall! So you pull back on your controls into a climb, increasing the angle of the wings compared to the ground until they brake the air instead of generate lift (I’m simplifying a bit here). The wings no longer generate lift and your aircraft noses down into a dive. *Normally* it’s dive restores proper airflow over your wings and you can haul the jet back up to normal level flight. Sometimes people say a stall occurs because airspeed is too low – this is not entirely true. BUT say you are in a turn – flying an F-18 into a high-G bank with the nose pointed downward. You are flying rather fast and everything is peachy. Oops, everything isn’t fine. Your aircraft is suddenly not generating any lift – the angle of attack in your turn – even at high speed is insufficient to maintain lift via the wings and you fall very fast. If you’re lucky you are flying at 35,000 AGL and have plenty of time to correct. If you’re less lucky you are at 400 AGL but punch out in your ejection seat. If you’re very unlucky you’re in the first class section of a 747 in a similar situation and you have a very bad day indeed (mainly because 747’s in high G turns fall out of the sky anyway – but you did enjoy the drinks on the way down right?).
It’s all to do with lift over the wings. The thing is – in high enough winds over your treadmill you *could* lift off. I’ve had perfect engines, wheels, and a nice long runway but a couple tons slung under the wings and zero wind makes it a close thing indeed.
Hell, when you get shot off a carrier via catapult your engines and wheels are fine AND the ship is moving at a good clip into the wind. But if you get a cold-cat (it doesn’t work) you end up going swimming (ahead of a monster of a ship that doesn’t turn or stop easily… Remember that whole “good clip into the wind” thing? Not your friend here). Without the catapult shooting you through the air – your engines, wings and wheels are insufficient to get your Hornet airborne and you hit the drink (major style points go to the pilots who punch out and float onto the deck on a nice gentle silk letdown after a cold-cat for a stiff drink and a change of undies).
Anyway it doesn’t matter because your hypothetical 747 would be incapable of clearing the taxiway to an active runway and everyone would be shot by trigger happy counter-terror operatives convinced the aircraft and treadmill were IEDs. There I’ve run rings round you logically.
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The plane cannot take off as eventually eather the wheels or the surface of the treadmill will shread, causing the plane to fall into the treadmill and ultimatly cause the loss of an expensive plane. This of course cannot be proven, given the fact that no one with the ability to procure such a set up gives a shit, as they have lots of money and therefore need their planes to be in the air and not spinning on a moving treadmill.
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I’m not a physicist, engineer, mathematician, or anything relevant to this conversation. I am however, a semi-intelligent individual. I would say the plane cannot take off because it is not actually moving forward, akin to a person running on a treadmill, there is movement, but no forward momentum (which is why you don’t feel ‘wind’ when you run on a treadmill). Planes use a number of interesting concepts to fly, the primary of which, is lift. Lift cannot occur with out some kind of wind resistance, which would be created by forward motion. Since the airplane is stationary on the ‘treadmill’, there is no wind resistance, thus no lift and no take off capability.
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It seems to me that the wheels, assuming negligible bearing friction, will just spin at ridiculously high rates until they disintegrate, while the plane still goes forward.
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@Rastizak, you forget, the plane has ENGINES, these force AIR (not the ground) backwards, and, according to Isaac Newton’s 2nd law, every action has an equal and opposite reaction, thus moving the plane forwards.
please do not compare this to a person running on a treadmill, it is a completely different scenario, therefore no you are not “a semi-intelligent individual” please grow a brain
I’m gonna say that xkcd has a point, the wording of the problem is so ambiguous that it will NEVER be resolved, I do not disagree with ras’s side of the arguement, just that ras id really bloody stupid
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The funny thing about this comment thread is those who clearly didn’t read the whole article, and simply assert that the plane won’t be moving, and thus can’t take off.
Given the points Randall made, the only rational arguments remaining against the plane taking off are engineering-based arguments asserting that the stresses created would cause the entire contraption to break down in some way (such as the wheels breaking, causing too much friction for the plane to get up to speed, and likely badly damaging the treadmill in the process).
Many prefer to ignore these types of arguments as denying the intent of the thought experiment. After all, who wants to figure out how you can observe a lightbeam bouncing vertically inside a moving spaceship, while observing it from the side, well outside the path of the lightbeam? There goes Einstein’s famous thought experiment for special relativity!
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If all the thrust is coming from the engine (no thrust coming from the wheels), the airplane will move forward and liftoff. The wheels wont move and the treadmill wont move from the plane’s POV, but will move along with the plane from an outsider POV.
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Samot, are you saying that the treadmill itself is going to move forward along with the airplane??? Um…
The “yeah, but” poster above is on the right track. Imagine that the plane is not on a treadmill, but instead were on a perfectly smooth frozen lake that provided ZERO friction to the wheels. Now start up those engines. The plane’s GONNA MOVE FORWARD because of the air going through the engines, even though the wheels remain perfectly still.
The fact is that the wheels effectively negate the effect of the ground’s friction on the plane. So this is what ALWAYS happens when you think about it anyway. Every plane that you’ve ever seen really IS on this hypothetical treadmill. It’s called the WHEELS.
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Wait a sec… nevermind. I’m an idiot. If the plane moves forward, then the wheels are spinning faster than the treadmill, which violates the premise. Then I guess it does depend on whether the treadmill itself generates enough airflow. And that, I have no idea about….
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I see five real possibilities: One; both the plane’s wheels and the treadmill are perfectly frictionless in every way, therefore the treadmill neither generates wind nor force backward on the plane, it just spins to infinity on it’s own as the plane takes off.
Two; the treadmill and the wheels are frictionless on one side (the side where they touch), then the treadmill generates a large gust of wind under the wings, causing the plane to have no lift, the plane doesn’t take off.
Three; same friction as above, except the gust of wind caused by the treadmill is taller than the wings, the plane gets some lift and eventually takes off, then crashes when it reaches the top of the wind or the end of the runway, whichever comes first.
Four; same friction as two, only the gust of wind is short enough to be negligible, the plane takes off at a slightly slower speed because of the wind and the friction on the wheels pushing them back ever so slightly.
Five (my personal favorite); we are woking in a perfect physics environment- no friction, perfect vacuum- the engines stall, no lift is generated, in general nothing happens.
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-The treadmill is preventing the plane from moving: speed of the plane relative to the ground is zero.
-the friction of the treadmill on the air is not enough to create a significant airflow around the wings
– No airflow means no lift. and no air flowing over the control surfaces.
of course you could lift the plane using the engines’ thrust (pointing them downwards) but then the wings are useless
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We’ve been over the fact that the question is asked badly, answering it in a way in which only one answer is the correct one requires assumptions to be made.
So let’s make assumptions that will make this silly internet-argument-creator into an INTERESTING PHYSICS QUESTION (yay!!!)
1. Assume that the wheels can produce any amount of force, dependent on the speed at which they turn, but are also *constrained* by the fact that the treadmill has a certain max speed.
2. Assume that the wheels do not slip on the treadmill
3. Assume that the treadmill is omnipotent and thus can instantly accelerate to the speed required to match the force of the engines through friction, and/or instantly accelerate to its maxspeed. Therefore the plane will never move if the thrust is not great enough to overpower the maxspeed friction of the treadmill.
The friction on the wheels will produce a torque which is in the opposite direction of the spin of the wheel. This torque pushes on the treadmill in the direction of the plane’s front. By Newton’s laws, the treadmill will produce an equal and opposite amount of force, thus pushing the plane backwards.
For simplicity let’s call this frictional force “Ffriction” and say that it’s proportional to the speed at which the wheels turn.
Note that the speed at which the wheels turn is proportional to the treadmill speed plus the plane’s relative ground speed
Ffriction = (constant)*(speed of plane relative to ground + speed of treadmill)
Now, as we know the plane’s engines produce a forward thrust. This can be expressed directly in the form of a force. I’ll call this force “Fplane”
For the plane to accelerate with respect to the ground, Fplane will need to exceed Ffriction
Mass*Acceleration = Ftotal = Fplane – Ffriction (I just treat the forces as scalars since this is 1 dimension and use + or – to denote direction.)
If the plane’s engines cannot produce a force that exceeds the force of friction with the plane’s relative ground speed set to 0, the treadmill will immediately match the force from the engines and the plane will NEVER move.
If the plane’s engines can produce a force that exceeds the force of friction with the plane’s relative ground speed set to 0, the plane will BEGIN to move….. but there’s more.
As the plane moves relative to the ground, the wheels turn even faster than the treadmill alone could spin them, producing more frictional force.
Thus, if the plane reaches a certain speed which is smaller than the takeoff speed, and also is a speed at which the frictional force and thrust force are equal and opposite, the plane will remain at that speed with respect to the ground forever. The plane will no longer be able to accelerate. This is much like terminal velocity when falling through the atmosphere (wheeee!). Of course, the plane will actually only approach that speed asymptotically.
Now, if the thrust is great enough that it exceeds the frictional force, even with the relative ground speed of the plane set to the speed at which it can take off, the plane will be able to reach that speed and leave that blasted giant treadmill. Godzilla really needs to watch where he leaves his things.
One could take this question and put a number in for the constant which relates frictional force to wheel speed, and put a number in for the force which the engines produce, and one would have a nice physics question!
Just for fun, you could also add in a term that takes into account air friction, here’s an example assuming that air friction is proportional to the relative ground speed.
Fairfriction = (constant)*(speed of plane relative to ground)
In this case the equation from before which describes the forces would be…
Mass*Acceleration = Ftotal = Fplane – Ffriction – Fairfriction
But remember to tell whoever you give this problem all of the assumptions that you’re making!!! I’ll list mine again here. The wheels don’t explode. The treadmill can accelerate to the speed of the plane instantly so that it doesn’t accelerate unless it overpowers the maxspeed friction of the treadmill. The wheels will never slip on the treadmill.
All other parts of this problem can be altered to make a more interesting question for whoever you ask. For instance, you can change the equation for Ffriction and Fairfriction to be whatever you like. In mine I assume that they’re directly proportional to spin speed of the wheel and ground speed of the plane, respectively, but that’s not a necessary assumption for this problem.
By the way, if a question seems stupid, blame the person asking, not the one that created the question originally. This has the potential to be a very useful question as long as it is asked correctly. Also, the treadmill is omnipotent. IT CAN SEE INTO YOUR SOUL.
Have fun-
The Argumentatorist
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1. Assume a long treadmill intended for running, that will always match your running speed (relative to ground). This is a small scale version of the treadmill in the problem.
2. Hop on the treadmill. As soon as you start running, the belt will match your speed. Your ground speed will always be zero. This is equivalent to a car on a full scale treadmill.
3. Put on roller skates and get on the belt. Initially, your ground speed is zero, and the belt doesn’t move. This is equivalent to a standing plane on the full scale treadmill. Simulate thrust from jet engines by having a friend (standing next to the treadmill) push you forward. The belt will match the speed of your wheels, but you *will* move forwads. Continuing this thought, the speed of the treadmill doesn’t actually matter at all.
4. Copy and paste this for every idiot who thinks the plane wouldn’t move.
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If the plane is flight-worthy it can take off in several ways. #1 get off the belt. #2 turn around and go the same direction as the belt. Who is the pilot here? Is he licensed? Does he know karate? Where is your preferred destination? Better idea, sell the plane and giant conveyor belt and buy a flame-thrower or something useful. Final answer.
-rock
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I approach the issue from a standpoint of aerodynamics and simple flight physics. Aircraft operate under the influence of 4 forces. Thrust, generated by the engines, moves the aircraft forward. Drag, caused by air friction and wind resistance, negatively impacts thrust. Gravity, which pulls the aircraft towards the ground. Finally, you have lift, which is what enables the aircraft to get off the ground. Engines generate thrust, which move the aircraft forward. Wings generate lift. So regardless of the power put out by the engines, you’re only creating forward thrust (negated by the treadmill, keeping the aircraft in place relative to the ground.) Lift is generated by air movement over the airfoil (wings) and control surfaces (flaps.) If the aircraft’s ground speed is 0, due to the treadmill, and you are in a windless environment, there is no air movement over the airfoil and therefore no lift to enable actual flight, regardless of the massive amounts of thrust the engine may put out, you’re not moving in relation to the air, just the treadmill. So unless it’s a fantastic headwind (around 180-200 knots for a 747,) you’re staying on the ground like a hampster in a wheel.
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I’m going to throw a wrench into the mix and suppose that the treadmill surface is made of teflon, and somebody just squirted oil onto it. :-p
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Just to simplify the two interpretations:
1. The treadmill moves backwards negating the thrust of the engines the plane is stationary, it cannot take off.
2. The treadmill moves ‘forward’ like a conveyor belt, the plane is moving through the air (but the wheels are not moving (assume the brakes are on or something)), so it can take off.
In practice #1 cannot happen, but I don’t really think thats part of the thought experiment…
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“Rastizak says:
March 19, 2009 at 2:39 pm
I’m not a physicist, engineer, mathematician, or anything relevant to this conversation. I am however, a semi-intelligent individual. I would say the plane cannot take off because it is not actually moving forward,”
Emphasis on “semi”? Why would the plane not move forward? Do you have a special kind of plane where the take-off force is conveyed through the wheels, therefore the treadmill would negate the backwards force being conveyed to the ground?
In my scenario, the force is conveyed backwards against the AIR, not the treadmill, so what the treadmill is doing is irrelevant to anything except how fast the wheels are spinning.
Your argument presupposes that a treadmill, running opposite the plane’s airspeed, is somehow conveying a backward force to the plane through free-spinning wheels. How does THAT work, exactly?
If your supposition held true, then if you took an RC plane with free-spinning wheels and put it on a treadmill in your house, and ventured to pull it forward with your hand (to simulate engine thrust) the treadmill would pull the plane (and you with it) completely over top of itself and onto the floor on the other side. Do you think that would really happen? Or do you think you might succeed in pulling the plane towards you fairly easily?
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Forget shredding tires and belts. Forget dinosaurs. Just distractions and red herrings.
I’ll use Vw Vb and Vc from the sketch.
The drawing doesn’t show it well but Vb is rotational. And Vc is backwards. Or rather its value will probably be negative.
Nothing was stated in the problem to inhibit Vw. As nothing was stated then for these puzzles you assume nothing will inhibit Vw. Make no assumptions about things existing that are not stated as existing or you can throw in velociraptors and hot air balloons and become a nimrod.
Airspeed. That is indeed all that is cared about. Airspeed when on the ground is the same as groundspeed. Not wheel speed. Not treadmill speed.
The jet’s engines do not cause the wheels to spin. The jet moving relative to the ground cause the wheels to spin. The jet’s engines cause the jet to move relative to the air. The wheels spin because they roll easier then they skid. With the imaginary treadmill the jet is still moving through the air. No matter how fast the wheels spin or even if they span backwards the jet is moving through the air. The Bernoulli affect of the wings through the air causes lift. Vb and Vc are tied exactly to Va above. and would be based on Vw. Depending upon whether the bearings on the wheels Vb and Vc could approach zero – we posited an impractical implausible treadmill so let’s go all the way and assume it is perfect.
As soon as Vw reaches take-off speed, the plane rises. Maybe using less “treadmill runway” than “regular runway” as the engines do not have to overcome the teeny tiny rolling resistance. The thrust of the engines only has to overcome air resistance in increasing Vw.
Okay that out of the way some more on Vb and Vc
Why did I say Vc is negative? Rolling resistance. As the plane moves it will force the wheel to spin against the ground. If the treadmill is perfect there will be no rotational force on the wheel as the perfect treadmill will actually try to keep the wheel from turn at all so Vb approaches zero and Vc approaches Vw drawn backwards. The treadmill’s surface tries to stay with the airplane. Kewl huh?
Why you throw out the walking comparisons is that with real treadmills and walking the propulsion is about apparent groundspeed and not airspeed. As apparent ground speed increases airspeed is still effectively zero.
I’ve made money off the silly two goats and a car Monty Hall puzzle.
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in my opinion it´s completelty irrelevant that the engines of the plane are running, because even if they were at full speed, they would only cause the wheels to spin and no! moving forward(by definition). the problem with friction lessening because of running turbines is nonsense, because a plane takes off because of aerodynamics (by the airstreamaround the wings) so because there is no lifting, friction is still there, the wheels are hitting the ground at full wheight and no movement kann be made.
qed
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Well I thought, and could be wrong, that air planes only take off because of the air moving under the wings and slighlty moving up causing lift. I mean this is VERY easy to prove by simply putting your hand out of a moving car and slightly tilting it up…
So my problem with this theory is…is there a way to get wind moving around the plane in order for take off to occur o_O? I mean if some how this was achieved it would be the idea of the next few months!
That is just me though, I know I have been wrong on the internet before so…shoot me if I am wrong : /
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My hobby: Allowing comments on controversial issues (controversial only because you can’t grasp the fact that no treadmill can be made that could keep a plane stationary. And so I too fall into his trap, but I installed hidden cameras watching my mom, analyzed by seduction detecting/preventing software) so people can showcase their stupidity.
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It doesn’t seem to me that the terms of the problem imply the plane cannot have a non-zero speed. “plane on a treadmill” doesn’t mean plane that can’t move. It means “plane on a treadmill.” It’s describing what would happen to anything on a treadmill. The effect of a treadmill that can match the forward speed of anything that is ground-friction-propelled (people, cars, bicycles, whatever) is to keep it stationary relative to the ground, because the artificial “ground” of the treadmill is moving against the ground-based thrust mechansim.
It’s just a trick question in that a 747 doesn’t use the wheels to move forward, it uses the jet engines. The treadmill and wheels would simply each move faster as the plane accelerated, and the plane would take off.
If you want to make sure the 747 can’t take off, forget the treadmill. Put it in a perfect vacuum.
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The plane takes off. Mythbusters already did this experiment:
The wheels are turning from the effect of the plane being pushed forward because of the thrust of the engines. The plane is not being pushed forward because the wheels are turning. Some seem to be confusing cause and effect.
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The treadmill part of it makes it too complicated.
There’s a type of model airplane that is basically “tethered”. A rotating fiber wire encased in plastic tubing runs from the control box to the plane, which turns the propeller (the motor is inside the control box). It has no wheels, just some stubs to sit on.
Guess what: no forward momentum, and it can take off. 😛
For that matter, I can walk backwards pulling it on the floor and it still takes off. I can even make it hover stationary at maximum stretch.
Protip: The engines push a lot more air under the wings than you think. Yes, even though jet engines are rear mounted. If they can push a bus over… heh…
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Ok, people, there’s no need for the wheels to be stumps or anything like that. The wheels can keep spinning and spinning, but the plane will still move forward. Essentially, as the plane starts to ‘roll’, the wheels will start to spin. The conveyor will match that speed, but the plane will continue to move forward. The wheels will speed up even more, and with them the conveyor, but the plane still moves forward. On into infinity, the wheels and the conveyor will go faster and faster, but the plane will move forward, because a plane’s takeoff speed isn’t affected by its wheels.
Now, if the wheels blowout from spinning to fast, we have a different scenario.
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You guys are still talking about this?
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as long as the wheels aren’t massless (but idealizing everything else), the plane won’t move forward – the force exerted by the engines will be cancelled out by the force exerted on the wheels by the conveyor belt, and the wheels will spin faster and faster.
i.e., the #3 crowd wins.
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the only rational response to this question is another question. are the engines running?
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or is the treadmill moving (aka powered)
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or is god blowing really fast (wind)
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is the plane level on the x axis or y axis (gravity)
???
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or just think of it this way.
if you had roller blades and wings could you take off a treadmill?
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rob shut up, you just want the 444th post
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444th post!!!1!
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final thought
if the treadmill is going fast enough, can it cause a pressure difference between the top and bottom of the wings by moving the air underneath them?
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It seems to me that the physics problem, from a slightly different angle, is very simple.
The airplane is being acted upon by two forces- the engine pushing forward, and the treadmill pulling backward. But, the treadmill is separated from the airplane by wheel bearings, and the engine is not. So, the treamill has to exert a large multiple of the power of the engines to have even a noticable effect- basically the wheels will need to spin fast enough to boil the grease in the bearings and/or weld the bearings. But in the time needed for that acceleration, the plane would have taken off.
Furthermore, even without the plane achieving forward motion, there would be at least some residual lift generated by the turbulent wind from the engines pulling air over the wings. So, it would likely take even longer for the bearings to melt than an ideal, stationary wheel.
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such physics problems are assumed to be in ideal newtonian settings. this means
– zero air resistance
– no friction due to wheel rotation (and no bearings or whatnot)
– infinite friction between wheel surface and conveyor belt.
etc.
and in this setting, the plane wouldn’t move forward. the wheels would spin like crazy, though.
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The only way the treadmill can keep the plane from taking off is if it can move fast enough that the wheel friction overcomes the engine thrust, or if the wheels break before the treadmill.
We know how to build wheels for a fighter sized aircraft such that the aircraft can achieve supersonic ground speed (some guys ran an F104 starfighter fuselage at 771 mph on the ground).
Good luck building an airplane-size treadmill that can come within take-off speed of that, say 771 mph – 150 mph = 520 mph.
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think of it this way …
if you have a friend riding a bike on a treadmill designed to the specifications in the aforementioned problem, you come up from behind and put your hand on his back, then start walking forward around the treadmill, he’s going to move forward, yes?
the same thing happens for the plane on a treadmill, only your hands have become the plane’s engines and your friend has become the jet.
the wheels don’t power the plane, they’re only a vessel by which the plane is allowed to move forward without requiring massive amounts of force to drag 100+ tons of solid steel across the ground.
you could even look at it with respect to how the engine works, it takes massive amounts of air particles and shoots them out behind it, and with newton’s laws you know that that’s gonna put a force on the airplane in the opposite direction, thus propelling the plane forward.
@Chris – you’re looking at it from an engineer’s point of view. think physics.
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I did not in any way suggest that the wheels powered the airplane.
What I said was that the only way the treadmill could keep the airplane from taking off (from moving) was if it spun fast enough that the wheel (should have said bearing) friction overcomes the engine thrust.
Reaction of air exiting engine at high speed exerts a forward force on the plane. Drag from the wheel system exerts a backwards one. If forwards force exceeds backwards, the plane moves forwards and as long as that remains true accelerates to takeoff speed.
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