MythBusters tackles "plane on a conveyor belt problem"

Takuan

and so it continues

Antinous

Why don’t they seal these tombs?

Takuan

guess it’s up to us, got the holy water?

Anonymous

OK, let me solve this once and for all: The plane cannot take off.

Here’s what happens:

Since it is not stated whether the wheel rolls or skids, I assume that it rolls, as that is what wheels are designed to do. Since the wheel is rolling, it can only move forward in space if it can rotate forward faster than the conveyor is moving backwards. The plane cannot move forward if the conveyor exactly matches the rotation speed of the wheels but in reverse.

Now here’s why:

A wheel bearing will have a small non-zero amount of friction. Let’s say that it takes one Newton of force to move the wheel, and that the distance moved in one rotation is one meter. The work required to turn the wheel once is one Joule. The Power required to make that revolution in one second is one Watt. As the conveyor spins backwards faster and faster, the wheel will rotate more each second. 2 Watts, 4 Watts, and so on.

Now think of the propeller. It’s similar to the conveyor in that it is pushing against something. In this case, it is generating forward lift (a propeller is just a rotating wing after all). As the propeller spins, it does work. The faster it spins, the more work it does.

Are you starting to understand?

The propeller has some maximum amount of work per second (power) it can put out. Let’s call this “Pp”. If the plane is to be kept from moving foward, the conveyor will have to move backwards at such a rate that force x distance / time = Pp. Let’s call Power from the conveyor “Pc”.

Or:
Pc = f x d / t.
Pc = Pp
Pc = f x d / t = Pp

Solve for speed:

Pc/Pp = f x d / t
Pc/Pp = 1, so:
1 = f x d / t

d /t is also known as speed, so:
v = d / t
1 = f x v

So we arrive at a magical ratio:
v = 1/f

What this says, is that the less force it takes to turn a wheel, the faster the treadmill will have to move backwards to counteract the power generated by the engine(s). The converse is also true.

Let us check this theory to make sure it sands. Take the case of the plane that has wheels whose bearings are seized up and cannot turn:

v = 1/f. f = infinite (since no amount of force can turn the wheel). v = 1/infinity = 0. Check.

How about a frictionless bearing?
f = 0
v = 1/0
v = infinity

If there is no friction, v would have to spin infinitely fast. I don’t even know what would happen then, since in mathematics we don’t like to actually reach infinity.

Given that if f = 0, v is huge, and if f is huge, v is zero, and that fact that v and f share a simple inverse relationship, what we find is:

At a spicific conveyor speed, the force of the conveyor pulling the plane backwards matches the thrust of engines, and:

The plane cannot take off.

There, so if you still want to flex your liberal arts degree and all that crap you learned about bigfoot, manga, and knitting katamari hats, please, at least know that you are wrong.

kthxbye

dculberson

Enginerd, my experience with riddles or logic puzzles seems to be the opposite of yours. I find that they typically imply an erroneous path that leads you to false assumptions about the situation, and it’s your job as the reasoner to see through that and come to the right conclusion. Thus to me, the airplane-treadmill question is trying to lead you to the conclusion you’ve made, but is able to be worked through to show the answer is the opposite.

I do think it’s outlandish to place a “real-world” airplane on an “ideal” treadmill. That’s a fundamental flaw – a killer flaw. It results in an answer that’s useless and untestable – requiring not science but faith. How would you test your version of the situation? And I don’t see anything in either the original proposition or the incorrectly re-worded version that implies anything of the sort. I guess that’s where our take on the question differs.

jemather

#63 –
FWIW, Jeff, Bernoulli’s Principle does not explain airfoil lift. The Wikipedia article you cited actually explains this rather well:
A common misconception about wings

jere7my

Chainring, your last sentence is entirely correct. However, a treadmill has no good way to stop a plane moving relative to the air.

dculberson

Enginerd, the problem is that you’re placing the treadmill in an “ideal” model and the airplane in a “real-world” model. If you have to factor friction in, you have to factor it in for both components of the equation. So:

Option A: Factor in friction: With friction in play, the treadmill can’t accelerate quickly enough or to a high enough speed to hold the airplane still. It will take time to accelerate, and it will have a maximum speed. The bearings on an airplane wheel would be among the best in the world, thus they will be comparable to the best bearings that could be in the treadmill. The treadmill will not manage to hold the airplane still.

Option B: No friction: No matter how quickly the treadmill spins, it won’t cause any slowdown of the airplane, so obviously the airplane will take off.

Ranting and raving doesn’t help your case, it just makes you sound mean. (and makes for more crow to swallow if you ever do make a mistake..)

Antinous

According to #240, #239 has the liquid supplies.

DrRobert

I never heard this before, but right off I don’t understand why there is even any discussion. I picture the runway as a maglev track (like the trains) and the plane has superconductor magnets instead of wheels. It will float above the runway and take off, when thrust is applied. It doesn’t matter what the ground is doing. Why would the wheels behave any differently?

jere7my

Enginerd, there are two ways around that “contradiction” you point out:

1) The wheels can skid. Imagine, for a moment, that the wheels are locked, but are made of a slippery substance. (This is basically equivalent to a ski-plane landing on ice.) Then, if the plane is moving forward at 80mph, depending on your interpretation, either a) every point on the wheels is moving forward (“speed of the wheels” = 80mph), in which case the belt will move backwards at -80mph (and have no effect), or b) the wheels are not spinning (“speed of the wheels” = 0), so the conveyor is not moving at all. This skidding effect will be present, but less pronounced, in regular wheels, particularly if the conveyor belt is whizzing past at googlysquat mph, so it is indeed possible for the plane to move forward while the belt matches “the speed of the wheels”.

2) (And this is the real answer:) The “speed of the wheels” phrase is a corruption of the original question, which asks what would happen if the conveyor rolled backward at the expected forward speed of the plane. If the engines at throttle setting X usually push the plane up to 80mph, then the belt will roll backwards at 80mph. The “speed of the wheels” is a bad specification of an uninteresting problem â€” as you yourself point out, the wording of the problem, if you ignore skidding, limits the situation to the trivial case. It might as well be, “A plane is nosing up against the White Cliffs of Dover. Can it take off?” That’s not a good puzzle.

I think you’re focusing too closely on the specific words a NYT reporter chose to describe a widespread puzzle, and ignoring the intent of the problem.

Takuan

OK, I’ll rig a conveyor to move the stake forward.

Guysmiley

If you were to put a real aircraft on a real treadmill that really traveled the same speed as an aircraft taking off, only in reverse, the aircraft would take off. Period. The wheels would be rotating at twice the speed of the aircraft, but assuming the wheels/tires don’t explode from the stress, you’ll get airborne.

Frictional losses would not overcome the engine thrust. The MTOW and runway length required may be different, but assuming an aircraft that is not overloaded, it’ll fly.

Saying that their experiment misses the point because it ignores “ideal” treadmills misses the point that magical super treadmills don’t exist.

It’s a good thought experiment and it gets you thinking about what forces are really in play.

nex

The problem states that the conveyor belt matches the speed of the wheels, only in reverse.

No, it doesn’t. The original problem doesn’t say so at all, and the bastardised version doesn’t mean anything, it’s gibberish. (As I’ve conclusively explained before, see above.)

An important part of ‘critical thinking word problems’ is comprehending the meaning of the words. This is tricky when there is no sensible meaning and you’re trying hard to interpret the question in a meaningful way. proper critical thinking gets you there, though.

JakeTheSnake

jere7my said it better than I did.

“wheel speed” is a vague phrasing that transforms this into a semantic problem rather than a physics.

Squashy

This argument seems to make people go crazy. Half the people here are right and half are hopelessly tied up in knots. As soon as the plane starts to move forward at all (which it must do, with nothing actually holding it back), the wheels and the treadmill will both immediately accelerate to infinity. The premise is flawed.

Consider the inverse: if the plane isn’t moving forward, then it follows that the wheels aren’t moving and the treadmill isn’t moving either. Does it make sense to visualise a plane sitting there, blasting its engines on full thrust with nothing happening?

dculberson

Chainring: I want to apologize for my comment last night, and for the tone of my earlier comment to you. I must have been in a bad mood. I’m not usually rude.

arkizzle

Jesus!

I just read all that it one sitting, my mind is fried!

‘Answering the same question’ FTW!!

nzruss

I’m glad we sorted that then.

swestcott

I have to second the smash labs thing I had it on the DVR for one epsode and it was BAD! mythbusters is way better diffrent shows I know but man the hosts on smash labs just seem OFF some how. My whole Fam loves MythBusters its number 1 on the DVR I even watch the comercials some times

the lurch

I can’t help but recall my high-school physics here. Primarily because my physics teacher was a fan of the SIN contest (http://sin.uwaterloo.ca/index.php). Anyhow, he always preached “draw the FBD!” Which is a free-body diagram. Basically, you drew a blob that represented the thing under discussion, and then arrows (or vectors if you prefer) showing the net forces involved. For this one, it’s pretty simple. Gravity vector holds plane to the belt. The belt pushes back equally (normal force). No belt, and the plane takes off, right? So, what forces does the belt apply to impede the plane? Well, none really. Sure, a bit more friction in the wheel bearings. Most of this friction is in the rotation of the bearings. How much of this is normal to the direction of flight? A really small amount. It’s this friction that will drag the plane back. But it is very,very small. (yeah I know, if there was a huge increase in friction there would be no rotation and the wheels would essentially be useless…the plane would have to drag the bloody belt along. But if the belt moved without friction here, the plane would STILL take off) Anyway, most large aircraft have more than enough power to over come this small negative load. Clearly, the force vector moving the plane forward (from the engines) is much greater than the vector moving the plane back (friction from the wheels on the belt) The plane is going to takeoff. It will take a wee bit longer, and the wheels will be spinning a lot faster…but it will fly. Or, think of it this way. Convince yourself the plane WON’T fly. Now, instead of one giant wide belt, set up 3 thin belts…one for each wheel cluster. Same thing right? Ok. Now take one belt away…say the front wheel belt. Front wheel is on the ground, left and right wheels are on belts. Will the plane fly now? Ok. Take another belt away. Will the plane fly now? No? Geez, why not? You know it will fly when you take the third belt away. What magic force is this single belt providing to make the plane stay on the ground? Hmmmm…nothing. The plane will fly.

Daemon

The treadmill thing means the plane isn’t actually moving – just it’s wheels are.

If it’s not moving, then the air isn’t moving accross it’s wings.

No air moving accross the wings means there’s no lift.

No lift = no flying.

I really don’t see why this is so hard for people to understand.

dculberson

I lay $5 on the table that the Mythbuster ultralight will take off. I also lay $20 on the table that some people will still not accept that answer to the problem.

Who gets the money? Umm… how about the EFF? Creative Commons? Derek Zoolander’s School for Kids Who Don’t Read Good and Want to Learn To Do Other Things [Physics] Good, Too.”

ItTookOFF

You could interpret “The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” to mean the linear velocity of the wheels… which would equate to the forward speed of the plane. Just throwing that out there.

You could also interpret it to mean “If purple, then doorknob”. It is vague after all.

Bonzo McGrue

This episode has aired on the East Coast, and Jason Kottke liveblogged it. The outcome is revealed on kottke.org. Good luck!

dculberson

Jeremy, not only that, but like I said, it’s sort of disingenuous (and biased) to give the treadmill ideal bearings and unlimited power but then grant the airplane limited bearings and power. Why would enginerd want it set up that way?

Enginerd, I did great on the SAT’s. You want to compare dick size, too? ‘Cause mine’s pretty good. What’s that got to do with the problem, anyway?

baf

Wait, I’ve got it! Entirely new solution here:

The whole reason there’s any disagreement is that the conditions of the problem don’t make physical sense. We’re told that (a) we’ve got the force of a jet engine pushing the plane forward and only the friction of the wheels on a conveyor belt holding it back, and also that (b) the conveyor belt moves backwards without slipping at the same speed as the wheels, which is only possible if the plane is not moving relative to the belt. Which side of the issue you wind up on depends on which of these conditions you believe.

I’d like to suggest that (a) and (b) are not actually contradictory. It is possible for the engine to thrust the plane forward without the plane moving relative to the belt… if the belt itself is sitting on a frictionless surface! That way, the entire apparatus — plane, converyor belt, and all — moves forward as a unit until the plane has sufficient speed to take off and leave the conveyor behind.

Mithras

Shorter explanation:
It slides, it doesn’t roll.

airship

More Kari Byron!

the lurch

Whatta ya know?
FBD video on YouTube.

http://www.youtube.com/watch?v=siYQU99VaAM

Teresa Nielsen Hayden / Moderator

EngiNerd, if you can’t be civil, you’ll have to leave the conversation.

jere7my

Enginerd, the original question does indeed posit that the treadmill matches the plane’s forward speed â€” or, more precisely, the forward speed that it would have had without the treadmill. The “matching the speed of the wheels” wording is a corruption of the original, inserted to avoid the kind of circumlocution I used in the last sentence.

The original may seem like a trivial question to you, but it was sufficient to generate vast quantities of pointless internet debate, with both engineers and pilots on the wrong side of the issue. People think about cars on treadmills, and try to apply that to planes; the lightbulb moment when they realize that they operate entirely differently is the point of the original question, and for many perfectly intelligent people getting there is worth the price of admission.

The “super-accelerating treadmill” is not as interesting a puzzle, and breaks down upon examination. Yes, if you postulate a magic treadmill that somehow can hold the plane in place, it won’t take off; that’s not the intent of the original question, and as a physics puzzle it has serious flaws. (For one thing, rolling friction does not increase with speed, as you seem to be suggesting. It would only increase once the grease in the bearings began to break down, at which point you’ve got bigger problems.)

dculberson

Jeff, Of course the treadmill has to be as long as a runway for the plane to take off from the treadmill – that’s clear. But no matter how long the treadmill is, it won’t be able to hold the plane still. If it’s too short, the plane will run off the end of the treadmill.

noen

Oh crap, I’m an idiot and a moron. The free-body diagram convinces me. Prop or jet, the plane takes off.

Anonymous

Bardfinn has it. It’s all about bernoulli’s principle. Lift is generated by the difference in pressure between the top and bottom of wings. The curvature of the wings makes a low pressure area over the top, and bam! we have lift. Thus, with respect to the wings, at least, there has to be moving air.

Nevermind the ideal characteristics of the treadmill, or the wheels, or whatever. Does the plane physically move forward with respect to it’s original position? If no, then there has to be some other source of airspeed for the plane to take off.

In the case of a jetplane, where the jets are in the tail of the plane, or are generating thrust behind the plane as in a jumbo jet, there is no airspeed on the lift generating device, the wings. Thus, no takeoff.

The only way these jetplanes that “must” generate takeoff that also “work in space” to work is if they are pointed at the ground, generating lift. However, the question is even dumber then, so let’s say that the engines are pointed parallel to the ground.

If the engines are pointed parallel to the ground, you might as well have a giant team of midgets on each wing, off the conveyor belt, pushing for dear life.

I guess, however, RL engines do generate airflow that cannot be perfectly parallel to the ground, so real engines must generate some push against the ground….

Man On Pink Corner

Oh crap, I’m an idiot and a moron. The free-body diagram convinces me. Prop or jet, the plane takes off.

Hey, you’re smarter than you were 10 minutes ago, which is more than the people who were right to beign with can say.

Chainring

“So it’s their fault you’ve misread and misunderstood the question and therefore were WRONG?

No, it’s a poor problem statement that caused me to misinterpret the problem. This is the part that caused the misunderstanding:

“However, other people are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.”

The implication was that the source of lift would be air pulled/pushed across the wings by the engines/prop. Why would that make any difference if the plane was allowed to move forward? That’s why I concluded (wrongly) that the plane had to stand still.

tanner

damn my lack of cable!

i would be thrilled if you posted their results here on wednesday.

dculberson

Daemon, why would the treadmill keep the plane from moving?

What force is counter acting the thrust from the engines?

franko

so, waitaminnit — when is this “cabin fever” show, and can we really see adam (or jaime?) in longjohns and sleeping cap? i can’t be the only gay man in america who wished i was that piece of tape running across jaime’s mustache in last week’s episode…

dculberson

Noen, you’ve not only learned something but been willing to do so and willing to admit it. That’s admirable.

dculberson

Oh, and while I do like the idea behind Mythbusters, and the people involved, they have a lot of problems with the setup of some of their experiments. Some of them are great, but others are really not testing what they think they are testing.

David

#96 I lay $5 on the table that the Mythbuster ultralight will take off. I also lay $20 on the table that some people will still not accept that answer to the problem.

Spot on baby, spot on.

Jeff

My assumption all along was that the tread moves because its motors are moving it along. I didn’t think this was just a tread on rollers that would only move in response to the motion of the plane’s wheels. And this is why you have catapults on aircraft carriers, not treadmills.

lava

Come on – the plane takes off, of course!

Friction from the wheels? No way. The wheels spin twice as fast as on a stationary runway, no big deal. For a 100mph lift off speed your wheels would be spinning at 200mph. The wheels and bearings would destroy themselves before they would ever overcome the thrust of the plane. Now if you were dragging the stumps of your landing gear, then we’d have something to talk about.

The wheels hinder the plane’s acceleration on take off, yes, but doubling the rpms is not enough to prevent the plane from reaching airspeed.

Bonzo McGrue

Replace the landing gear with casters, and replace the conveyor belt with a moving surface that randomly changes direction (0 – 360 degrees) and speed every second. The plane will take off.

nex

Doug Rogers, you essentially said that the conveyor belt can hold the wheels in place by holding the wheels in place. That’s circular reasoning, not an explanation.

> “So, does Newton’s Law of Motion apply here?”
>> “Newton’s Laws always apply.”
> “Correct. Which one?”
All of them. They are consistent with each other and complement each other. If you examine them one at a time and manage to come to different conclusions each time, you’re doing it wrong.

NE2d

Daemon,

You are mistaken. The plane isn’t propelled by its wheels; it’s propelled by its, well, propeller…or engine. What will happen is that the plane will move forward just like normal (from the perspective of a stationary observer on the ground); the only difference will be that the wheels will be spinning very fast because of the conveyor belt. It

glugenwog

#41 – “As long as the wheels are in contact with the belt, their speed will be /exactly/ that of the belt. You can speed the belt up as much as you like and the negligible friction in the wheel bearings won’t really slow the plane down with respect to the airmass it is moving through.”

Just because the wheels are in contact with the belt doesn’t mean they’re going the same speed. I could take an RC car moving 10mph and put it on a belt going 5mph in the opposite direction, and the car would eventually reach the end of the belt.

ItTookOFF

“Friction, OBVIOUSLY.”

That one made me laugh.

If you want the forces of the plane and the treadmill to be equal, this guy made a model demonstration.

http://youtube.com/watch?v=21U1UVyVvmQ

If you want the treadmill to speed up infinitely but not the plane, you are adding variables to the question. The “treadmill” can already accelerate to infinity, but you want this to be impossible for the plane. You are showing bias against the plane. If one can go to infinity, why not the other? You “engineers” seem to love the world-on-paper point of view, so stop making up limits for the plane but not the conveyor.

‘you can’t add numbers to infinity, it’s not a real number.’ Well… neither is ‘i’, but that doesn’t stop us from using it in algebra.
(infinity + x)<-I shouldn’t be able to do that, but lo and behold, no hole in the time-space-continuum.

“You have to be one of the biggest idiots I’ve ever met in my years of online communication. There, that’s really all I need to say to you at this point. Suck it! Go read the DiVinci code or something.”

*Belly laugh* good counter argument.

Guysmiley

#10, read the problem again, specifically:

The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.

So when the aircraft is moving 10 MPH forwards, the conveyor belt is moving 10 MPH backwards.

Since the wheels on an aircraft are free-wheeling (that is they do not provide propulsion), the wheels will just spin at 20 MPH.

The common misconception is due to people thinking in automotive terms, where the wheels are providing propulsion. In an aircraft that is not the case.

Anonymous

I think this website has the best explanation of what will likely happen:

http://www.modernpolymath.com/journal/2008/1/28/airplane-on-a-conveyer-belt.html

scisco

Okay my 2 cents. If the plane moves with respect to an observer on earth, ie. (plane’s velocity) = -(velocity of the belt) with all w.r.t earth, then the plane will have airspeed and therefore lift off. However if the plane is held stationary w.r.t to earth by increasing the speed of the treadmill (very impractical) it is still possible for the plane to take off because the treadmill will push the air too creating a sort of wind tunnel.

Bonzo McGrue

Put the plane on a treadmill, engines off. Turn the treadmill on. The wheels on the plane spin, but the plane stays still.

ormerodp

Hold up. If the treadmill acts as a frictionless device to hold the plane in place, then perhaps the plane would continually speed up, but why would lift necessarily be generated? When the plane moves forward on the runway, the engines do pull air through the system, but only to accelerate the plane through the giant mass of air on the runway, right? The engines don’t really pull air over the wings (unless perhaps in a prop plane, though i doubt that would be enough to generate sufficient lift). Anyway, it seems that plane weight and wingspan are other important factors to consider. Perhaps a very small plane could get off the ground for a second or two, but a jet?

illflux

Too bad that dude (and Kari Byron) are so annoying. I like that show and would watch it otherwise.

hinten

Yes, I must be living in an alternate universe…

Thought experiment: Someone replaced the conveyor belt with ice and showed that the plane would take off. Same with planes taking off water. Let’s take it one step further, what has even less friction than a conveyor belt (moving at the same speed as the wheels) or ice? How about nothing? How about air? Let’s assume that the plane is in the air and the wheels are not touching anything what would happen then?

Look around you, see many planes falling from the sky?

Teresa Nielsen Hayden / Moderator

DCulberson, I’d have snapped too. Good on you for apologizing, though.

dougrogers

Nex:

” If you examine them one at a time and manage to come to different conclusions each time, you’re doing it wrong.”

Exactly! I say as much in my post at http://www.boingboing.net/2008/01/28/mythbusters-tackles.html#comment-116582

“The planes velocity is zero. It will stay at zero velocity until the engines are turned on. Now, due to the imaginary, hypothetical conveyer belt, any forward motion generated – and that forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated – the external force is balanced.

No forward motion, no lift.

However, if you assume :-) Newton’s Third Law; For every action, there is an equal and opposite reaction – the rocket ship example – then the plane will generate forward thrust despite the hypothetically perfect friction free state.

Forward motion yielding lift.”

ITTOOKOFF:

“I hate to quote myself but it bears repeating:
Me: “The wheels of an airplane are not attached to any driving mechanism. ”

Me, January 31st http://www.boingboing.net/2008/01/28/mythbusters-tackles.html#comment-116134

“Yes, the forward motion is not generated by the wheels. Take the wheels, treadmill out of the question.”

“You … simply are not understanding the problem.

Yes, and you are telling what I know.

“and in this argument you disqualify yourself from having an opinion.”

And you are disqualifying yourself from being able to understand and communicate.

Seriously, I am of the mind that the plane will take off, but intuitively, the first case is/was unresolveable in a way I understood. Newton’s third law holds, just like all the others.

Here’s the answer:

“It will stay at zero velocity until the engines are turned on.”

Newton’s third law

“forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated”

There is already a magic conveyer belt beneath the wheels “moving” in an opposite direction to the wheels forward motion – the ground, the tarmac, the runway.

Hold an image in your mind, frame the plane, it’s engines roaring and generating thrust, centrally, still in the frame, like a camera panning with the forward movement of the plane and see that the wheels are spinning madly and the ground passing beneath the wheels – like the imaginary conveyer belt – is moving at the same speed as the wheels spin.

Yes, so it’s a frame of reference problem.

Do you get it Enginerd?

dculberson

Exactly, guys.. For example, a Boeing 747-200 has 219,000 foot-pounds of thrust in its engines. All that thrust is transferred through the air – it has nothing to do with the wheel rotation speed. No wheel bearings on earth would transfer enough friction to counteract 219,000 lb-ft.

Fnarf

“Airplanes fly because of lift”.

Um, no. They rise up because of lift, but what pulls them forward isn’t lift, it’s thrust. Lift is dependent on air moving across the wing, yes, but thrust is not. Thrust is going to pull the plane forward no matter how fast the wheels are turning, and the forward motion is going to cause lift. The plane takes off.

jccalhoun

If the plane isn’t moving then there’s no lift. No lift means no flight.

Raines Cohen

@33, There’s a book about that.

jere7my

The difference between cars and planes that is illustrated by the original problem is this: cars move forward because they push against the ground, and planes move forward because they push against the air. If the ground moves underneath a car, it will affect its forward movement; if it moves underneath an airplane, it won’t (to any significant degree). That, in a nutshell, is the “Aha!” moment the original puzzle gives people; therein lies its value. It may seem trivial to you, but I’ve participated in quite a few conversations where getting to that revelation was a long uphill battle, and in the end satisfying for that very reason.

I’m not sure I understand your analysis: if a plane and a car are both moving forward at 100mph on the same treadmill, and the treadmill suddenly spins into motion going 100mph in the opposite direction, the plane won’t be significantly affected, but the car, after some transitional skidding, will end up not moving at all relative to the outside world; that seems pretty different to me. If, on the other hand, they’re both moving at 100mph (wrt the outside world) while the treadmill spins beneath them, the car’s speedometer will say 200mph, and the plane’s will say 100mph. The car will be burning fuel at the 200mph rate, while the plane will be burning fuel at the 100mph rate. Again, that seems like a significant difference.

I don’t think the “super-treadmill” interpretation has an “Aha!” moment; nor is it a physically possible system, which makes it inherently less interesting for me. It’s also not the original question, as I’ve said before; a little research should demonstrate that.

NE2d

scisco,

You’re sort of on to something, but the belt wouldn’t move the air like that. The only thing that matters is the plane’s velocity relative to the air around it. So if you had a massive fan in front of the plane creating a wind at air speed velocity, the plane could lift off while remaining motionless relative to the ground. It’s like when you see hawks gliding in place because of a strong wind.

Fnarf

Try this: imagine a plane with no wings at all. It won’t fly, but if you run the engines, it will move forward. It will do this no matter what is happening under the wheels, because the wheels free-wheel.

Your RC car is propelled by its wheels but a plane is not.

Think of it this way: the treadmill is running 100 MPH backward. The plane isn’t going anywhere, because the wheels free-wheel. It just sits there. Then, they start the engines. They trust against the AIR (not the ground), and the plane moves forward. If it has wings, it will eventually be going fast enough to leave the ground.

I’m really having trouble seeing how people are getting this wrong.

ItTookOFF

See post #190, read it carefully.

If you still think the treadmill has anything to do with the airspeed (or ground speed) of the body of the plane, go read a physics book and get back to us.

This might help.
http://en.wikipedia.org/wiki/Ball_bearing

jere7my

A treadmill could be built that would blow out the tires and ground the plane that way, but there’s no way to generate enough rolling friction in airplane wheels to stop an ordinary plane moving forward without damaging it. If you get to specify the plane and the treadmill, though, I agree that it’s possible â€” a tiny model plane on a bumpy treadmill moving at 500mph would not take off, for instance.

However, you run into the chicken-and-egg problem I mentioned above (in which the treadmill can’t start until the plane moves incrementally forward, but any forward motion breaks the problem).

Your approach can lead to an interesting investigation of physics principles, though â€” I don’t think it’s uninteresting, just interesting to a smaller percentage of people. :)

RV9Factory

Guysmiley is correct. Some friends and I have debated this over and over on another (aviation-related) board. The airplane will take off and its wheels will be rotating at slightly less than twice their normal speed. Its groundspeed will also be slightly slower than normal (owing to friction). Bonzo – if you put the plane on a treadmill with engine off, it will move with the treadmill because there is just enough friction for that to happen. You could literally hold the airplane still with one hand though, and in that case its wheels would spin.

jere7my

Enginerd: it should be obvious that the posted question is not the original, since it either makes no sense or is trivial. (As someone on the Straight Dope board said, the question becomes “Consider a wheel and belt such that no forward movement is mathematically possible. Will there ever be forward movement?”) Now, if we’re talking about cars, it makes perfect sense â€” the conveyor matching the speed of the wheels means the car doesn’t move. For airplanes, the question is ambiguous at best, broken at worst.

Even so, the majority of commenters here, in the original Boing Boing post, in the New York Times blog entry, and in the Straight Dope message board it got the puzzle from, managed to puzzle out the intent of the question, rather than focusing on the specific words (which are, after all, ambiguous â€” where on the wheels is the “speed” measured?). “Will a plane on a treadmill take off if the treadmill moves backwards at the speed the plane would ordinarily, without the treadmill, move forwards?” That’s the conversation most of us are having.

I call the BoingBoing version a corruption because it spawns multiple interpretations, and while it’s obvious to me what is meant it splits people into entrenched argument camps over them. Follow the link to the Pogue blog, and follow the link from his blog to the Straight Dope board it came from, and you will see that the wording issue was hashed out, at great length, over two years ago. (I recommend reading that Straight Dope thread, since it recapitulates everything discussed here, often more clearly.)

Haldor

Unlike a car, where the wheels push against the pavement, an airplane engines push against the air. The wheels are irrelevant to an airplane’s forward motion and are present to reduce friction between the plane and the runway.

When running on an exercise treadmill we stay stationary relative to the room because the force generated by our feet pushing against the treadmill belt is not transfered to the floor. If we were to strap on a Buzz Lightyear rocket pack while running on the treadmill and light it off, it wouldn’t matter how fast the treadmill was going because the rocket would be pushing against the air and away we would go.

Simply put, the wheels on an airplane act as a lubricant between the plane and the runway. If the treadmill did counteract the forward motion of an airplane than it would be impossible to take off on an icy runway.

Bonzo McGrue

Lean out of an airborne plane with a wheel on a stick. Touch the wheel to a conveyor belt and hold it there. What happens to the plane?

Now, what if we change the direction and speed of the belt?

Takuan

reminiscent of “what do rockets push against in a vacuum?”

Matthew Miller

It all comes down to: does the treadmill go at a fixed speed inverse to the plane’s normal land speed (resulting the situation described in #18), or do they accelerate to compensate? In the latter case, you get a feedback loop which jumps to infinity and then depending on how theoretical our setup is, maybe the plane catches fire or maybe it takes off.

HP

I don’t know much about physics or aviation, but there’s a third possibility here everyone is ignoring:

When the conveyor belt starts, the ultralight will roll off the back of the conveyor, flip over, and be moderately damaged. The pilot will be unhurt, but the whole deal will be embarrassing and anticlimactic.

If the ultralight doesn’t roll of the back of the conveyor, it will likely veer to the left or right, going off the side of the conveyor, flip, and break a wing. Same outcome.

Stefan Jones

Choose carefully; all proponents of the theory that loses will be condemned to scamper along that runway conveyor belt forever, BWAH-Hah-hah! FLY fools, Fly!

jccalhoun

the real question is, “will being on a treadmill stop a plane from moving forward?”

greebo

I predict that the Mythbusters team will completely fail to demonstrate anything useful about this problem. The problem is that they don’t ask enough basic questions about the meaning of the problem because they are too gung ho about getting out there and building cool stuff.

The original problem (in any of its various forms) is too ambiguous to have a single answer. The Mythbusters team will fail to spot this, and rush ahead with one particular interpretation of the problem. Because that’s what they always do.

It’s a very disappointing show.

Bonzo McGrue

@RV9FACTORY…. “if you put the plane on a treadmill with engine off, it will move with the treadmill because there is just enough friction for that to happen.”

That depends on how quickly the treadmill starts. If it accelerates quickly enough, you’ll be able to do the whole “tablecloth out from under the dishes” trick, yes?

Haldor

Pushing against air is an oversimplification. Propeller driven planes are pushing against the air. Jet engines achieve thrust because the exhaust is pushing against the engine so the presence air is not relevant unless it is required for combustion.

Anonymous

For those that think the plane wouldn’t take off:

Start running on a treadmill.

Then get a friend, not standing on the treadmill, to give you a big shove.

Let us know what happens.

thrustinj

The plane takes off.

The treadmill always moves at the speed the plane is moving forward. The wheels spin at twice the speed the plane is moving, unaffecting the speed of the plane, or the flow of air over the wings.

It’s the same as pushing a matchbox car over a treadmill. You, as a person, use the same amount of force to push the car forward, no matter if the treadmill is on or not. You are the “engine” in that case, completely independent of the treadmill.

dculberson

Enginerd, as Nex says, you’re forcing an ideal constraint on one component of the equation and a real-world constraint on the other. Doing that is a ruse to make the problem fit a specific conclusion. If you put both components into either ideal or real-world categories, the plane will take off.

dculberson

Jccalhoun: Being on a treadmill will not stop a plane from moving forward. As I asked earlier: What force would be counteracting the forward thrust from the engine?

Chainring

As a mechanical engineer, this thread is fantastically amusing. I love it when laypeople try to apply logic where physics is wanted. It reminds me of the episode of ‘This American Life’ where the guy reads a couple of science books and convinces himself that the theory of relativity is wrong.

… btw, the plane won’t fly. In order for a plane to fly, it must move relative to the air, not relative to the ground.

jere7my

Enginerd: Calling people idiots doesn’t help your case.

You can tell that the post is not the original question because there’s a link from BoingBoing to the Times, and a link from the Times to the Straight Dope, and a discussion there that pre-hashes everything we’ve discussed here about the wording of the problem.

The original question is more interesting to me because it illustrates real-world differences between cars and planes, and because it operates on the assumption of a testable, real-world conveyor belt. It leads to interesting conversations, and a very satisfying “Aha!” moment when people catch on. For that reason, I think it makes an excellent brainteaser, and I have observed it doing its job (very well) in the wild.

The “super-treadmill” version, which postulates a treadmill that can somehow hold an airplane in place, falls apart on many levels: the “super-treadmill” is impossible to build (or conceive of building), it’s unnecessary for the puzzle (magic glue would work as well), it leads to endless nit-picking discussions of the precise wording used in the puzzle (which is ambiguous on at least three axes), it creates a chicken-and-egg problem (since the wheels and treadmill can’t start moving until there is forward motion, but the question forbids forward motion), and it reduces the problem to “If a plane can’t move (for some reason), can it take off?” â€” which is trivial. There’s no “Aha!” moment when you figure out that a treadmill and a wheel moving at the same speed, without slipping, result in no forward motion; it’s an “Eh” moment. “So what?” your puzzle-audience says.

I fully agree with you that it is possible to read the problem, as stated, and come to the conclusion that there is some sort of magic treadmill involved that can exactly match itself to the rotation of the wheels, and eat up all of the thrust the airplane’s engines can produce, through bearing friction or something. Once I’ve come to that conclusion, though, I say, “That’s not very interesting â€” what is the question really asking?” and move on to a better way to phrase the puzzle, so I can have what I consider to be the more interesting discussion.

Tom

The lurch @95 & 96: I was reading this thread and getting to the point where I was composing a post in my mind that read “100+ comments and not ONE mention of a free body diagram…” Thanks for proving me wrong.

This is why we have formal tools for analyzing problems. It makes any ambiguities in the problem statement obvious, and inevitably leads to a provably correct solution of a well-posed problem if one can be found.

For those who care, the FBD for this problem looks pretty much like:

<–*—->

where I have neglected gravity and lift. The -> arrow is the thrust from the engine and the * represents the mass of the plane. The wheels are assumed frictionless, and the <- arrow represents aerodynamic drag.

If the wheels are NOT assumed frictionless, then the diagram looks like:

<- <–*—->

where the additional left arrow represents the friction of the wheels, which is assumed to be small. Because friction typically goes as v**2, the wheel friction may eventually rise sufficiently to hold the plane back enough that it doesn’t take off.

So if you want to argue that the plane does not take off, you are arguing about the particular coefficient of friction in a particular aircraft wheel, which is a surprising thing to be so passionate about.

This is a dynamics problem that is presented as a poorly-stated kinematics problem, much like the Monty Hall problem is an issue of conditional probabilities presented as a problem of total probabilities.

dgemmer

Turn this around. You are flying in a plane, jet or prop. Place the wheels down on a conveyor belt. Is there any circumstance, ever (in theory — catastrophic failure of wheels and resulting mess or other practical considerations), in which the movement of the belt in any way would reduce (or increase) the speed of the plane. This assumes the air above the belt is unaffected by the belt, etc. I can think of no way, absent friction or other practicalities, that the mere act of setting a body in flight above a moving surface (assuming no friction from theoretical wheels) will in any way affect the forward speed of the body in flight.

Lift from the wings is irrelevant, it’s just the way the body stays above the belt. Imagine a (perfect, frictionless) pendulum swinging above the belt — no effect. If the pendulum had frictionless wheels that touched the belt, no way the pendulum would change speed or stop.

Imagine the pendulum at rest on the treadmill. Standing off the belt and on the ground beside the pendulum, there is no imaginable way the belt can move which would prevent you from simple shoving the pendulum and starting the pendulum swinging. Shoving the pendulum is the equivalent of cranking up the engine on the plane.

ItTookOFF

*Head explodes in a massive aneurysm*

Holy sweet zombie Je**s isn’t this thread locked yet?

RV9Factory

@Anonymous #88:

>>The problem states that the conveyor belt matches the speed of the wheels, only in reverse. It doesn’t say whether this is practical, it just states it. Since the wheels can’t move forward, and the wheels are attached to the plane, then the plane can’t move forward. If the plane can’t move forward, then it can’t take off. I don’t know of any plane that can take off with zero forward movement. If there is one, then for that specific plane the answer is the “The plane takes off”. For all other planes, which I believe is all of them, the answer is “The plane does not take off”.<<

The wheels /can/ move forward. They are free-wheeling. They move as fast as the difference between the backward motion of the treadmill and the forward motion of the plane.

You are on the wrong side of this argument.

RV9Factory

>>>Turn this around. You are flying in a plane, jet or prop. Place the wheels down on a conveyor belt. Is there any circumstance, ever (in theory — catastrophic failure of wheels and resulting mess or other practical considerations), in which the movement of the belt in any way would reduce (or increase) the speed of the plane. <<<

Say you are landing a plane in still air with an airspeed (and thus groundspeed (still air)) of 100 mph. You touch down on a conveyor belt moving backward at 50 mph. Assuming you don’t hit the breaks, except for a slight slowing due to friction in your wheel bearings, you’ll have a speed relative to the air and ground around the belt of 100 mph until you start decelerating. The instant you touch down, your wheels will start spinning 50% faster than your groundspeed would suggest they should.

Brit

> The conveyor belt is designed to exactly match
> the speed of the wheels, moving in the opposite > direction.
>
> So when the aircraft is moving 10 MPH forwards,
> the conveyor belt is moving 10 MPH backwards.
> Since the wheels on an aircraft are free-wheeling
> (that is they do not provide propulsion), the
> wheels will just spin at 20 MPH.

Right, but read the instructions again: “The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” That means the conveyor belt is moving at 20MPH because the wheels are. But, that means the wheels are now spinning at 30MPH, repeat, repeat, repeat.

> The common misconception is due to people
> thinking in automotive terms, where the wheels
> are providing propulsion. In an aircraft that is
> not the case.

No, you aren’t understanding what’s really going on in this problem. The problem is this: the question is framed ambiguously. We all know that the plane takes off due to the airspeed. The question is this: is the plane moving relative to the world? The question is ambiguous – some people say “yes”, and some people say “no”. If the plane is moving relative to the world, then it has an airspeed, and it will take off. If the plane is not moving relative to the world (and we ignore windspeed and the effects of the propeller pushing air under the wings), then it has no airspeed, and it will NOT take off.

The odd thing is that aircraft use propellers / jets to push themselves forward on the runway, not wheels. So, when the question says, “The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” – the ONLY way that can happen is if the aircraft has zero airspeed. If the aircraft has any airspeed at all, this becomes nonsensical because the spinning of the wheels *cannot* be the same as the movement rate of the conveyor belt. To put it in other terms: the speed of the wheels = airspeed + conveyor belt speed. However, the question says “the speed of the wheels = conveyor belt speed”, so what about the airspeed? Is it zero? If the propeller/jet is pulling the aircraft through the air, then the airspeed will not be zero and so, the speed of the wheels is NOT equal to the conveyor belt speed. People create different answers because the question can be interpreted in two very different ways. However the Mythbusters “test” this, they’re going to take one or the other interpretation – and whichever interpretation they take will be “the winner”.

enginerd94303

ARRRRRGGGG!!!!! You people make me so mad!!!

Can you please stop saying that the treadmill cannot counteract the thrust of the engines?!!! What makes you say that?

If I put a red wagon on a treadmill and start the treadmill at 1 MPH, it’s going to try to pull away from me. If I crank the treadmill up to 5 MPH, it’s going to try to pull away harder. If I crank it up fast enough, it’s going to pull hard enough to equal the thrust of any engine.

All wheels have friction, and the faster they spin, the more force it will take to keep them going! It’s really simple math.

#144 said it really well: The more times the wheels go around per second, the more force is required, since you are doing more work per unit time. More work given constant friction force means more distance. More distance per unit time means faster.

The treadmill just has to go faster as the thrust of a plane increases.

What, do you think that the wheels don’t offer any resistance?

You can’t just say whatever you think ought to be true without demonstrating it.

Sheesh!

putney1968

I think most posters missed the point. The assumption in the experiment is that one can get a treadmill to behave as desired, i.e. keep the plane stationary with respect to the ground. That is a daunting task. Never mind if it requires powered movement by the belt or a freewheeling belt. Airplanes fly because of lift, which is created by relative movement of air past the wings. If no air is moving, there is no lift and no flight. If the treadmill design doesn’t work and the plane moves down the runway, of course it will fly. Rockets do not rquire wings to fly, so don’t include them in the discussion. That’s vertical flight anyway.Bottom line, in the experiment as described, the plane will not fly. Anyone want to place a bet?

dougrogers

Day late and a dollar short.

The wheels and treadmill arrangement are posited so as to instantaneously counteract and eliminate any forward thrust provided by the engine.

If there is no forward motion as a result of thrust, there is no air moving over the airfoil. No moving air, no lift.

Such an ideal frictionless arrangement doesn’t exist in Real Life. There will always be friction which can be overcome, and no system can react instantaneously. In real life there will be forward thrust.

gerta

The airplane treadmill seems to generate a lot of debate b/c the problem is poorly worded and generates confusion. Depending on how you read it, that treadmill is either no problemo or an infinite impossibility.

I originally read it to mean the treadmill was somehow preventing forward motion of the plane relative to the air, so that the plane was essentially taking off vertically. That wouldn’t work, and I think that’s where the confusion comes in — not that people think of planes driving like cars, but that they think air isn’t moving over the wings.

As others point out, there’s really no way a treadmill can pull this off with aircraft wheels. If the problem isn’t constraining the movement of the plane relative to their air and the rest of the earth, the wheels and treadmill are irrelevant — they wheels are only there to minimize the friction between the ground and the plane, and the treadmill has little effect. This seems to be how most people read the problem in the first place.

enginerd94303

#180: Newton’s laws of motion do apply here. Specifically:

Newton’s first law:

“Objects will continue to move in a state of constant velocity unless acted upon by an unbalanced external force.”

The plane on a treadmill question is:

“Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?”

So we don’t really need to invoke any math or anything to prove the plane can’t fly. The problem states that the speed of the wheels is counteracted by the motion of the treadmill. But we can use physics and math to explain WHY that is and HOW the treadmill counteracts the thrust of the engines.

Now if the problem has the treadmill moving at the speed of the PLANE, then the plane could take off. The wheels would just be turning backwards at twice the forward speed. This is probably not fast enough to generate enough drag to keep the plane from moving forward. But that’s not what the problem states, so it’s irrelevant.

ItTookOFF

“forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated”

How is this energy transmitted to the wheels? There are no connecting rods, no universal joints, no drive-shafts. By this argument you are saying ‘in the air the wheels spin at the same speed as the airspeed of the plane.’

“the external force is balanced.” There is no such balance. The logical fallacy “Appeal to authority” in which you say it is so, thusly it is so.

At this point you are no longer answering the question: “Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?”

Nowhere in the question does it state that the airplane remains stationary/motionless. The only variables defined in the question are the plane and the conveyor. What the conveyor does to the wheels has nothing to do with how the plane moves. You can assume variables, but in doing so you are changing the question to suit your answer. Infinite speed of the conveyor will only cause the wheels to spin at Infinite speed + that of the plane; which will cause the conveyor belt to accelerate more. Speed of the conveyor=speed of the wheels (which are = the speed of the plane + the speed of what’s underneath the plane while grounded (which is physically true)). The question doesn’t state the programming involved with the conveyor, only that it is designed to match the speed of the wheels.

Read the question, then formulate an answer based upon it. Don’t make up information that isn’t inherently provided.

WombatSam

#33, that’s an excellent answer.

This problem isn’t just a test of logic. It seems to also test how well you can see things from other people’s point of view.

The winners realise that there’s an ambiguity, because it isn’t specified whether the aircraft is allowed to move relative to the ground and, by extension, the air.

The losers get a coronary from shouting at each other.

jimtealiii

I can see now why this got on Mythbusters.

dculberson

Chainring, what you’re saying is that “since the airplane will take off, thus answering the question, the experiment falls apart.”

The airplane moving does not make the experiment fail. It merely answers the question asked. The question asked does not specify that the plane sit still. It specifies that the treadmill moves. That’s all. You’re adding elements to the equation, then vehemently (and snottily) defending your false conclusion. (“Being a mechanical engineer…”)

dculberson

Oh, and SPOILERS:

The Mythbusters plane-on-the-treadmill.. it took off. Ta-ta.

dculberson

Brit, no matter which interpretation you use, there needs to be a force counteracting engine thrust in order to keep the plane still. What force would that be?

Neither interpretation involves enough force to hold the plane still. The treadmill is not connected in any meaningfully solid way to the aircraft. It has no method of acting with enough force on the airplane to keep it still.

The forces I can see are:
-Thrust
-Drag (Wind Resistance) – same as usual
-Wheel bearing friction – slightly increased

The only change in forces involved is an increase in wheel bearing friction due to the higher speed of the wheels. As long as we’re not jumping into lala land with theoretical instantly accelerating infinite speed capable treadmills that melt the tires, wheel bearings, landing gear, and finally the underbelly of the plane, the plane will move forward just fine. The difference in takeoff speed and travel distance will be minimal.

RV9Factory

>>>If the aircraft has any airspeed at all, this becomes nonsensical because the spinning of the wheels *cannot* be the same as the movement rate of the conveyor belt.<<<

As long as the wheels are in contact with the belt, their speed will be /exactly/ that of the belt. You can speed the belt up as much as you like and the negligible friction in the wheel bearings won’t really slow the plane down with respect to the airmass it is moving through.

dougrogers

Me: But you have an intelligent surface here which detects motion and acts against it, negating any motion of the wheels.
Nex: would it do that? Grab the wheels and glue them in place?

That’s essentially what the conveyer belt does, neutralizes any forward motion applied to the wheels.

Me: So, does Newton’s Law of Motion apply here?
Nex: Newton’s Laws always apply.

Correct. Which one? I’m an artist, not a mathematician or engineer :-)

This problem poses a hypothetical imaginary situation where, the external force is negated. As ENGINERD94303 says:

Newton’s first law: “Objects will continue to move in a state of constant velocity unless acted upon by an unbalanced external force.

The planes velocity is zero. It will stay at zero velocity until the engines are turned on. Now, due to the imaginary, hypothetical conveyer belt, any forward motion generated – and that forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated – the external force is balanced.

No forward motion, no lift.

However, if you assume :-) Newton’s Third Law; For every action, there is an equal and opposite reaction – the rocket ship example – then the plane will generate forward thrust despite the hypothetically perfect friction free state.

Forward motion yielding lift.

Chainring

“The airplane moving does not make the experiment fail. It merely answers the question asked. The question asked does not specify that the plane sit still. It specifies that the treadmill moves.

If you don’t specify that the treadmill must keep the airplane stationary, then the problem is trivial. All that happens is that the wheels spin faster and the plane takes off (as demonstrated). That’s barely even debatable. The whole point of the problem (as I understood it) is to figure out if a plane can produce lift by applying thrust and having its ground motion counteracted by the conveyor. The problem they solved is boring and dumb.

“Chainring: I want to apologize for my comment last night, and for the tone of my earlier comment to you.

Apology accepted.

nex

At first it seems like there is no way a treadmill like this could be built, because the plane could easily roll forward. So most people at first seem to understand that the plane can’t move from a symantic point of view, but don’t understand how this would be possible from a physical point of view.

It only “can’t move” in the sense of “oh no, it can’t move, because as soon as it does, my idiotic interpretation of the question stops making any sense whatsoever and falls apart” — as opposed to “it can’t move because some physical force is holding it in place.” The solution is not that you have to rewrite the laws of physics so that they conform to some moronic, err, sorry, “symantic” point of view. Rather, the solution is that your interpretation of the question is plain wrong. You can prove any statement from false axioms, but it’s an exercise in senselessness.

I imagine you could argue, “oh, no, I’m not talking about the same thing everyone else is talking about, instead I’m thinking of this super treadmill, which is defined to hold everything on it stationary.” But surely that’s not the case; firstly this would be a magic device and wouldn’t have anything to do with the laws of physics, and secondly having trouble with explaining how the plane stays in place when it is defined to do so would be quite embarrassing ;-)

Dangerous

Since the conveyor belt in Pogue’s original thought experiment provides an equal counterforce to the acceleration the plane’s engine would normally create, the plane will remain stationary with respect to the atmosphere.

Because the plane is stationary with respect to the atmosphere, and because lift is a product of the friction of the atmosphere against the lifting surface of the wings caused by the relative motion of the plane through the atmosphere, the plane will not fly.

If you placed the same plane in a windtunnel and locked its wheels then forced air over its wings at the same velocity the plane achieves at takeoff the hypothetical pilot would be able to pull back on the stick and leave the ground. This is how hang gliders work.

LarryPA

The key here is that an airplane moves forward by pushing on the air with the propeller. It doesn’t make any difference if it’s sitting on a treadmill or not. The airplane will accelerate and move forward just as if was on motionless ground and it will take off. The wheels will spin faster than usual to make up for the treadmill motion.

RV9Factory

>>>reminiscent of “what do rockets push against in a vacuum?”<<<

Nothing. But that’s not how rockets work (by pushing against something). It is simple Newtonian physics (mass ejected from the back of the rocket * the mass’ velocity) causes an equal but opposite reaction from the rocket.

But we digress…

Guysmiley

#33: If you read it that way, the plane STILL TAKES OFF. If the conveyor belt keeps the wheels from turning, the aircraft still has a velocity with respect to the Earth, it has “indicated airspeed” and it takes off.

Assuming you could control the treadmill speed perfectly, to an observer on the ground it would look like the aircraft is just moving along the conveyor with the wheels not moving.

There’s nothing magical about it, it’s simple physics.

Takuan

OK, everyone who said it wouldn’t; line up for noogies

dougrogers

ITTOOKOFF, really, you aren’t reading what I wrote very carefully. Who are you arguing with?

Jeff

The important thing is how is the air moving realitve to the wing’s upper surface? There is no air moving over the surface of the wing if the wing is stationary. A plane whose forward momentum is being translated into the treadmill’s surface aquires no lift. The only air that’s moving is caused by the propeller, other than the “hug” air that is dragged along the treadmill surface due to micro vortices caused by the friction of the tread next to stationary air.

Tom

Chainring, you’re a Toronto grad, aren’t you?

dougrogers

More correctly, The thrust provides air moving over the airfoil. If there is no air motion over the airfoil, there is no lift.

dculberson

Dangerous, Pogue wasn’t the originator and completely misunderstood the problem and the forces involved. There is no way for a conveyor belt to provide an “equal counterforce” to the thrust of the airplane’s engines. So it will not be stationary with respect to the atmosphere.

RV9Factory

Dangerous, the original question (as I found it) was posed thusly:

â€œImagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?”

The belt matches the speed of the wheels. This makes sense as long as they are in contact with each other. The real question is: What do the wheels have to do with how fast the plane is moving through the air? The answer is: precisely nothing.

pepik

Ok, my turn.

First, @106:

“the treadmill is running 100 MPH backward. The plane isn’t going anywhere, because the wheels free-wheel. It just sits there.”

You’re kidding — you really think the plane would just sit there on a treadmill going 100 mph? Imagine this with a Hot Wheels car and you might come to a different conclusion.

Now, I do believe the plane will take off. A treadmill going 100 mph one way will not balance 100 mph’s worth of thrust in the other way. A little, but not a lot.

I’ve gone back and forth on this, but I feel I’ve gotten it now. Where I was initially led astray was that I assumed that the force of the treadmill matched that of the thrust. If that were the case, then no forward motion = no lift = no takeoff. But that’s not the situation we have. The speed of the treadmill will make the wheels turn faster, and that’s all. It will not apply an equal magnitude opposing force, but will just add a bit more friction.

Now, if the brakes were on, that’d be different….

Bliss

I think we need to send lots of letters to the FCC asking them to forbid americans and the whole world from discussing airplanes and threadmills in the same environmnet….

I mean, even here, months if not years after the fact, the topic is posted and bang another fight of will take off and will not take offs erupts… this friggin discussion is going to bring around the collapse of civilization, and we need to stop it.

Yes I have my possition on the whole snakes in an airplane floating in an ice cream bowl with infinite cherries on a threadmill discourse, but I’m not going to share it, I’m just fed up. Stop it, just stop it, or else we’ll have to ban all friggin planes from the world…

stewmeat

#5 FTW

The plane will take off.

Guysmiley

#42: No, totally wrong.

What force is counter-acting the thrust from the engine(s)? The wheels free-wheeling below it? Nope, sorry. Unless the brakes are applied, in which case you aren’t taking off anyway.

Either way, the wheels are (nearly) frictionless and unaffected by the motion of the belt.

The. Plane. Takes. Off.

godzillaskid

Hang on.
What colour did they say the seats were?

dougrogers

Aaargh.

The forward thrust provides the motion causing air to move over the airfoil. Without the moving air, there is no lift.

dougrogers

How about this: imagine Magic Masking TapeÂ® holding the plane still so no motion is transmitted; Turn on the conveyer belt going as fast at it can. This transmits motion to the wheels, but not the plane, because it is held still by the Magic Masking TapeÂ® and the bearings and axles are friction free and no energy is transmitted to the plane.

Now turn on the engine.

Teresa Nielsen Hayden / Moderator

Belatedly: ItTookOff, same goes for you.

Umbriel

I’m with Putney on the practical issues. The landing gear are in no way “frictionless”, and there will be sufficient friction between the landing gear and the belt in pretty much any system for the belt’s drag to keep the plane from moving forward under thrust, especially with a mere ultralight engine providing that thrust. There are two ways to get the plane to take off:

1) Reduce the friction between belt and plane. Magical frictionless bearings in the wheels would work, but the only real world option would probably be some sort of air-cushion/”hover” landing gear.

2) Overcome the friction between belt and plane, with sufficiently powerful engines or rockets.

ItTookOFF

Rereading my comments about disqualifying yourself from having an opinion I realize I came off sounding quite arrogant. I would like to apologize to DOUGROGERS for that. Friendly fire ain’t so friendly after all. And you are correct: you have to look at it from the ground or else your head will explode.

On the other hand, ENGINERD94303, NEON, ACE0415, BRIT, JEFF and CHAINRING….. :P

dculberson

I agree that the problem is trivial, but it still provokes endless debate. It’s a “frame of reference” type problem, with enough of a hint of physics for people to think like you did that the plane is supposed to stand still. But no, the question does not state that. It’s worded such that it implies it until you think critically about the forces involved. Once you really do so, without adding in additional variables or specifications, it becomes obvious that the plane will take off.

If the intent is for the plane to stand still, the treadmill is useless. Why have it? It would be just as effective to say the brakes were on and keeping the plane from moving.

Here is the original question:

“A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”

It has nothing beyond an airplane and a conveyor belt, and definitely doesn’t state that the plane stands still. And if you consider the only two components, and how they interact, you realize there’s no way for the conveyor to keep the plane stationary. Thus, the plane takes off. But, people are used to the ground being what you “push off” from to move – thus complicating their thinking. It requires a simple frame of reference shift, which is hard to do – actually seemingly impossible for some people to do.

I hate to say it again (and again …) but: re-read the problem and make sure you’re not inserting elements or conditions that aren’t actually there.

ItTookOFF

DOUGROGERS, “Seriously, I am of the mind that the plane will take off, but intuitively, the first case is/was unresolveable in a way I understood. Newton’s third law holds, just like all the others.”

If you agree the plane will take off, then stop making arguments that state otherwise.

“The planes velocity is zero. It will stay at zero velocity until the engines are turned on. Now, due to the imaginary, hypothetical conveyer belt, any forward motion generated – and that forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated – the external force is balanced.

No forward motion, no lift.”

This leads me to the conclusion you are arguing the “won’t fly” side.

“Engines provide forward motion A, transferred to wheels. A=A
Conveyer moves backward. -A

A-A = 0

Is A the motion of the plane, the same as A the motion of the wheels.

Explain.”

This is a very misleading statement since you are trying to agree that the plane can take off but are providing pseudo-science to indicate otherwise.

Since we are in agreement that the plane can in fact take off, I suppose there is nothing else to debate. *Shakes DOUGROGER’s hand and walks away*

dculberson

Enginerd, Ahh! You’re working from the corrupted version of the question. The original says “plane” and not “wheels.”

Additionally, you adding controls that don’t exist (ideal treadmill, real-world plane) is what has caused the contradiction. There is no such contradiction specified even in the corrupted question: you have added that specification.

You’re answering a question involving a scenario that could never happen. That’s not a physics or logic problem. It’s a non-existent one.

ItTookOFF

Question posed in the link in the original article:
“Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?”

First, let’s examine the question thoroughly. The airplane is sitting on the conveyor belt. The conveyor belt is designed to match the speed of the -WHEELS- in the opposite direction. This means one of two things; 1: the wheels are not spinning or 2: the wheels are spinning at X speed. For the conveyor belt to match the speed of the wheels, the plane is required by the statement to remain stationary. The question is: “Can the plane take off” not “WILL the plane take off”. The answer is yes to the question as written above. The treadmill is designed only to match the speed of the wheels, not to hold the plane in place. The plane will accelerate forward and the treadmill will adjust its speed to match that of the wheels. The question states that the conveyor is -DESIGNED- to match the speed of the wheels of the plane exactly. The conveyor’s design has nothing to do with the plane’s design, which is designed to pull itself forward by pulling air via the propeller. The “infinite loop” paradox comes to thought, but this is also of no consequence. The wheels of an airplane are not attached to any driving mechanism. Furthermore: the wheels are attached to the axle by bearings, which were designed with canceling friction in mind; torsional friction is thereby reduced to near-null. The plane in the question can in fact take off. *Not the answer you expected based on the beginning of this rant eh?*

The question posed in the link in the original article is #1: not the question the Mythbusters tested. #2: The question about wheel speed being equal to the speed of the treadmill is a bastardization of the fundamental question at hand: “Can a conveyor belt act on an airplane in a manner that would prevent the airplane from taking off?” If you say “Yes” you are mistaken. This question has been beaten to death by thousands of people. Every answer is different because everyone looks at the question differently. Submitting the question in the form of a trick-question distracts from the actual problem. Of course a stationary airplane will not take off; it’s not powered by fairy dust. That is beyond the point. Friction coefficients are also a red-herring. The essence of the question is whether or not a treadmill can prevent an airplane from taking off.

A conveyor belt cannot act against an airplane in any manner to prevent it from moving forward and achieving lift. End of story.

benmasterflex

(sarcasm)Based on the Mythbusters’ logic, future airports will be able to build shorter runways, or perhaps just launch pads, and hold the planes back until their engines or propellers are at full speed, then they can take off!(sarcasm)I can’t believe that no one has thought of this before. What are we paying NASA for??(sarcasm)……
It is IMPOSSIBLE for conventional airplanes to take off without great forces of wind pushing on the bottoms of their wings. The force necessary for takeoff cannot be acheived when the plane is stationary as it would be on a treadmill which is moving at the same speed as the airplane. The mythbusters completely warped the point of the “myth” and declared it busted based on their pathetic attempt at experimentation. When their plane on the conveyer belt took off it was passing up the traffic cones beside it and was probably going close to 25mph(its takeoff speed without the conveyor belt). They ignored the actual myth and completely missed the boat on this one. The only myth that was actually busted on this episode was the myth that the cast of this show had any scientific credibility in the first place.

bshort

“What force would be counteracting the forward thrust from the engine?”

Friction in the wheels.

The whole idea here is that the plane is moving very fast with respect to the treadmill, but at zero velocity with respect to the ground and the surrounding air (except for whatever boundary layer is whipped up by the treadmill).

The funny thing is, people seem to think that the plane can have an arbitrarily high propeller velocity, and that at some point the thrust from the propeller will be enough to overcome the friction in the wheels. Friction, though, is a harsh mistress, and increases as lubricants break down and internal temperatures increase.

Jeff

The wheels could be frictionless, and that ideal but not realistic expectation would make it perfectly evident that the forward thrust is being translated by those wheels, right into the tread which moves at equal but opposit speed realitive to the plane. The energy required to lift the plane in now bulding up as heat in the tread and will need to be disapated with air movement and some good liquid coolers as well.

Teresa Nielsen Hayden / Moderator

I love this thread.

Zan

“The wheels and treadmill arrangement are posited so as to instantaneously counteract and eliminate any forward thrust provided by the engine.”

But as the wheels are not coupled to the engine in any meaningful way, the treadmill CAN’T counteract the thrust of the engine.

That’s like saying that you and a buddy are singing, and if your friend starts singing sharp, you instantly counteract it by singing flat. Try as you might, your singing flatter isn’t going to stop your friend from singing sharp.

A giant fan COUNT counteract the thrust from the engines, but it would also provide enough flow over the airfoil to make the plane take off.

dculberson

Chainring, here’s a hint: You’re that guy.

dculberson

Yeah, I feel ashamed for being so involved in this thread. I’m sorry world.

Kevtastic

People need to be reminded here that there are TWo — count ‘em, TWO — questions floating around the Internets.

Treadmill matches WHEEL speed.
Treadmill matches PLANE speed.

Even the original BoingBoing article quoting David Pogue glosses over that the question had changed. Pogue asks about the treadmill matching WHEEL speed. Yet the BoingBoing article was updated with a Straight Dope article with the treadmill matching PLANE speed.

The outcome of the Mythbusters test is going to rely on which question they actually tested, since there are two questions with very important differences.

If the treadmill matches PLANE speed, then the treadmill can go 100 mph backward while the plane goes 100 mph (relative air speed) forward and the wheels spin at 200 mph. The airplane is therefore moving, can get lift, and can take off.

If the treadmill matches WHEEL speed, then the treadmill can go 100 mph backward while the wheels go 100 mph forward and the plane goes 0. The treadmill can go 200 mph backward while the wheels go 200 mph forward and the plane still goes 0. At any point, if the plane starts moving forward and the wheels are still in contact with the treadmill, then the wheels will have to be moving faster than the treadmill. At that point, it’s not about physics anymore, it’s about semantics. You immediately violate the rules of the question and the experiment if, at any time, the wheels move at a different speed than the treadmill, which is the only way the airplane could gain relative air speed and lift.

dculberson

Oh, wait; Teresa likes it!

In that case:

Ace, Jeremy, Jeff, and Ormerodp, you all are making the assumption that the treadmill will hold the airplane in place. It will not. The airplane is free to move forward regardless of the longitudinal motion of the ground beneath it. The treadmill has no reverse action on the thrust generated by the engines.

Mark my words: The plane takes off. I guarantee it.

In fact, it’s been proven experimentally with RC planes. Mythbusters is going to mix it up with the use of a full-scale (if still small) prop plane, but the physics are the same.

In fact, I now know the outcome of the MythBusters experiment, from reading the BoingBoing blurb above and seeing the MythBusters preview.

Guysmiley

#48, 49: Good lord.

You’re saying that if the treadmill either

a. Rotates opposite the motion of the aircraft at equal speed rotating the wheels at twice the speed of the aircraft

or

b. Rotates at the same speed as the aircraft, keeping the wheels from rotating

that will somehow generate as much force as the propulsion from the aircraft engine?

The thought experiment says NOTHING about the motion of the aircraft with respect to the ground. It says the treadmill moves with respect to the WHEELS OF THE PLANE. It also handily can be read two different ways.

Again to be clear: THE TREADMILL SPEED IS NOT RELATED TO THE GROUND SPEED OF THE AIRCRAFT. “speed of the wheels” is NOT “speed of the aircraft“.

Either way you read it, the plane takes off. Either with the wheels spinning at 2x the ground speed or spinning at 0 RPM.

High school physics 101.

mayasthma

Subtle advertising?

dougrogers

So it’s seems to be wrong to try to understand why you are wrong :-) ? I do agree the plane will take off, but I didn’t understand why the plane will take off. I really hope you’re not a teacher.

Rob, Denmark

Here is my 0,02â‚¬:

“The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.”

Assuming we can disregard the friction of the wheels, here is what will happen:

Lets say the thrust of the engine gives the airplane an airspeed of 30 mph (not enough to take off), and holds that speed.

That means the wheels are moving at 30 mph. So the conveyor has to move in the opposite direction, and starts and speeds up to 30 mph.

But since the airspeed still is 30 mph (remember we are holding that speed), what happens is this:

While the conveyor belt accelerates from 0 to 30 mph, the wheels accelerate from 30 to 60 mph (the speed of the conveyor belt + the air speed).

So the conveyor belt accelerates from 30 to 60 mph, while the wheels accelerate from 60 to 90 mph.

So the conveyor belt accelerates from 60 to 90 mph, while the wheels accelerate from 90 to 120 mph.

And so on and so on…

And thats at a fixed speed!

If the airplane accelerates, the numbers ‘accelerate’ as well.

In an ideal world, this is what would happen:

The conveyor belt is able to react to any changes in speed, instantly, and the microsecond the thrust of the engine tries to push the airplane forward with any speed (0,0001 mph), the conveyor belt will accelerate to that speed, the wheels will accelerate (0,0001 + 0,0001 mph), the conveyor belt will accelerate further and so on, towards the speed of light.

In the real world, this will happen:

The conveyor belt is a bit slower to react (i.e. slower than ‘instantly’), and will be a little behind in accelerating to “exactly match the speed of the wheels, moving in the opposite direction.”

Thus the plane will move forward and take off.

But the rule:

“The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.”

is not met, because it is practically impossible for the conveyor belt instantly and all ways exactly match the speed of the wheels.

dculberson

Wheel bearings are made specifically to reduce friction between the vehicle and it’s wheels. They are very good, and very low in friction, especially on something like an aircraft. If there was a lot of friction in the bearing, the aircraft would have trouble overcoming it without the presence of a conveyor belt. They do not have that trouble, and freely take off all the time. Even doubling the friction, which is roughly what the case would be with our hypothetical situation, would not significantly slow the aircraft.

The conveyor belt will “exactly match the speed of the wheels,” which would merely double the speed of the wheels. That would not hold the aircraft still.

dculberson

I’m reminded of the XKCD shirt:

“Science: It works, bitches!”

And I’m still kind of ashamed.

Jeff

Moderator, come on, don’t be shy, tell us if our plane will fly. Or will it simply crash and die?

Takuan

@40
“The term working mass is used primarily in the aerospace field. In more “down to earth” examples the working mass is typically provided by the Earth, which contains so much momentum in comparison to most vehicles that the amount it gains or loses can be ignored. However in the case of an aircraft the working mass is the air, and in the case of a rocket, it is the rocket fuel itself.”

reaction mass = working mass, rockets and planes both

Korpo

The plane’s forward motion is provided by something that doesn’t touch the ground, so being on a treadmill doesn’t make any difference.

Imagine if you were sitting on a skateboard on a sheet of ice, or a treadmill, or whatever. Imagine you had a rope tied to a tree and in your hands. If you pull on the rope you will move forward, no matter what the wheels are doing, no matter what the ground is doing, no matter anything.

polecat

I think it’s pretty obvious that the plane will take off. If we assume that the wheels on which the plane rides are somewhat ideal, i.e. frictionless, then whether or not there is a treadmill or conveyer belt has nothing to do with the problem. This is because a frictionless wheel would have no effect on the motion of the aircraft; whether or not the “ground” is moving, the wheels exert no force opposing motion.
If you think that perhaps the plane will be able to momentarily lift off the ground, but then fall again, consider this. If in fact the plane lifts off, it has clearly generated sufficient lift to overcome gravity, and after losing contact with the ground, the treadmill and wheels will have absolutely no effect on the plane’s flight.
If you are a visual learner, try drawing a free-body diagram of the plane. As stated, there is no force acting on the plane due to friction with the ground. The only force acting on the plane is the thrust from its engines, which will clearly propel the craft forward.
I have to say, it’s kind of sad that mythbusters are wasting their time with something as simple to disprove as this.

BigHead

I’d just like to clarify what I meant by thrust equaling wheel speed. Bad wording I agree, I meant that thrust is coupled to the wheel speed (as in the wheels are driven); so no matter how much you accelerate the wheels they will be countered by the conveyor (since the forces of acceleration are against the conveyor, not the air). As I said, with a plane, the thrust is decoupled from the wheels and acts against the air, not the earth, so the plane will accelerate, gain air speed and fly. It’s been said differently dozens of times. It’s worded like a trick question you’d find in an IQ test. The plane will fly. If the question was worded so that there was a giant fan behind the plane which negated the flow of air over the planes wings, then the plane wouldn’t fly because we’re countering the thrust against the air… :-\ And that’s why planes like to take off and land into the wind since they get more lift with less ground-speed.

ItTookOFF

@BenMasterFlex
Did you actually watch the episode in full? They discussed the science very well, and described WHY the plane can take off. By making the conveyor’s speed equal to the plane’s speed they only doubled the wheels RPM. There are about 30 video’s on youtube on the subject. The “can-nots” only rave on like lunatics and the “cans” usually provide scientific and experimental proof.

If you can demonstrate that a plane on a conveyor can NOT take off, the “Cans” will be stifled for quite a while.

“The force necessary for takeoff cannot be acheived when the plane is stationary as it would be on a treadmill which is moving at the same speed as the airplane.”

http://www.youtube.com/watch?v=21U1UVyVvmQ
If you have any scientific credibility yourself you’ll watch this video. You may want to wear a helmet, because it will blow your mind.

Thank you, and good night.

Jeff

Kevtastic said, “You immediately violate the rules of the question and the experiment if, at any time, the wheels move at a different speed than the treadmill, which is the only way the airplane could gain relative air speed and lift.”

It should be obvious that if the plane moves faster than the tread mill, it will run off the mill and roll onto solid tarmac, probably catastrophically.

Korpo

You can prove this to yourself at your local department store. Buy yourself a Hot Wheels and put it on the rail of the escalator and hold it in place. The wheels are moving the same speed as the treadmill, obviously, since they’re in contact.

Now cause the car to move forward by applying an outside force, i.e. push it. The wheels are still moving at the same speed as the treadmill, and yet the car can move forward because of your external force that isn’t influenced by ground speed.

Now pretend that instead of your hand pushing the car forward, it was a prop on the front of the car that was providing the external force that isn’t influenced by ground speed. The car would still move forward, and if it had wings it would take off.

enginerd94303

DOUROGERS, ITTOOKOFF:

OK, so does the question say the conveyor matches the speed of the plane relative to the earth, or the speed of the wheels relative to the conveyor? Either way, having the thrust provided by the propeller and not the wheels makes no difference.

In the case of the question asked in this thread (matches speed relative to conveyor), any thrust is counteracted by backwards motion of the conveyor.

In the case of the mythbusters (matches speed relative to the earth), a plane or a car with wings could both take off, assuming the car could drive twice as fast as it’s takeoff speed, and the plane could overcome the resistance of its wheels spinning at twice the takeoff speed.

Guysmiley

KEVTASTIC:

That “wheel speed” interpretation is meaningless and collapses to infinity very quickly. If that’s what the statement is intended to be interpreted as you mine as well argue about “what happens when you accelerate when you are traveling at the speed of light?”

theflyingtinman

CHAINRING stated:
That’s why you can only apply a small amount of thrust. Too much thrust and the plane will move forward relative to the earth (air) and the experiment falls apart.

First line of the problem statement:
“Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway.

So why did the problem statement specify a conveyor “as long as a runway.“? It was obviously allowing for the possibility that the plane would move forward no matter how fast speed the conveyor runs.

There was nothing in the problem statement about limiting thrust of the plane.

Takuan

if I shoot an arrow at a tortoise, will it ever hit it?

the lurch

Hey Chainring,

As a engineer, you took statics, kinematics, and thermogoddammics. You doubtless drew a pile of FBD’s

Watch this clip:
http://www.youtube.com/watch?v=siYQU99VaAM

Where do you think the physics is missing? What is going to hold the plane back?

remmelt

@rv9factory: so that’s where the confusion lies. I always understood the problem to mean: the conveyor moves back at a speed that is high enough to keep the plane stationary. No moving of wings through air -> no lift -> no flight.

Jeff

Are there any pilots out there? Air speed over wing surface. You know: http://en.wikipedia.org/wiki/Bernoulli's_principle
You can stand right next to a planes that’s thrusting it’s ass off while on a treadmill. You hold out your hand and feel the air doing what over the wing’s surface? The air isn’t moving, and the plane isn’t flying.

Kevtastic

Arguing the physics of wheel bearings and friction and the like obfuscates all points.

Grab a Hot Wheels car, set it on a treadmill, and prove both questions instantly.

(a) While your finger’s resting atop the Hot Wheels car, the treadmill speed is matching the WHEEL speed and there’s no forward motion of the car. The car is going ZERO. Turn the treadmill on a higher speed. The treadmill and the wheels will both spin faster, but there will still be zero movement by the car, and thus no lift and no flight.

(b) Push the Hot Wheels car forward, the equivalent of thrust. The wheels spin freely, and so long as they’re in contact with the treadmill, they will travel exactly the combined speed of (1) the forward motion of the car, plus (2) the reverse motion of the treadmill. When the treadmill matches/is identical to the speed of the PLANE, the wheel speed is essentially double the individual speed of either the plane or the treadmill. Notably, the car moves forward quite easily, and therefore can generate lift, proving it can take off. Also worth noting is that when the car starting moving forward from “thrust,” the wheel speed no longer matched the treadmill speed (it instead was the treadmill speed plus the plane speed), violating the rules of the version of the question that requires the treadmill matches the WHEEL speed.

Kevtastic

GUYSMILEY:

That, of course, is the problem with the whole scenario.

The original question floating around for years and years and years has always been about whether the treadmill matches the PLANE speed. Aviation magazines I’ve read answered this question and ignored wheel speed questions. Straight Dope did likewise.

It seems to be a relatively recent phenomenon that this turned into a wheel speed question, which IMO is a semantics question, not a physics question.

Chris Schmidt

“Last night I spoke to Adam Savage…”

That’s got to be a great sentence to type.

ItTookOFF

“In the case of the question asked in this thread (matches speed relative to conveyor), any thrust is counteracted by backwards motion of the conveyor.”

How? And don’t say “it just is.”

It’s a MENSA style question that only gives you a couple of variables and tricks you into assuming things that the question never states.

For your convenience:
“Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?”

oafish_brown

reminds me of the feynman/underwater sprinkler problem:
http://everything2.com/index.pl?node_id=1130509

KurtMac

Mythbusters FTW! I was totally going to suggest this myth to them after enduring the miles of discussion on the original post here on BoingBoing. I never got around to registering for the Discovery forums to do so, but I am super stoked that they read my mind through osmosis, now my Wednesday night plans are set! I always thought they would have to resort to a RC airplane, I can’t wait to see them try it with a full size plane!

dougrogers

I’ve read through this thread, through the previous thread and through the kottke thread. There is this guy Nex, who like you above says the same thing over and over again, just like what you say in the last paragraph above, but persists in providing no justification that alas, poor old me can understand.

Engines provide forward motion A, transferred to wheels. A=A
Conveyer moves backward. -A

A-A = 0

Is A the motion of the plane, the same as A the motion of the wheels.

Explain.

Takuan

how do float planes take off?

enginerd94303

DCULBERSON:

The force it takes to push your roller skater along the treadmill increases as the treadmill speed increases. At some speed you reach equilibrium with the force of the propellors. That’s the solution. Yes, that is the solution. That’s it. It’s all. It’s complete. It’s what’s missing when people like ITTOOKOFF who took “physics for poets” on their way to a business administration associate’s degree before becoming Boing Boing regulars try to draw a free body diagram.

ENGINEERNY:

Yes! Someone gets it! I tickles me how we engineers are told repeatedly to read up on physics, LoL.

ITTOOKOFF:

You have to be one of the biggest idiots I’ve ever met in my years of online communication. There, that’s really all I need to say to you at this point. Suck it! Go read the DiVinci code or something.

enginerd94303

Oh, ITTOOKOFF:

Friction, OBVIOUSLY.

This might help:
http://en.wikipedia.org/wiki/Jackass

Jeff

Polecat, the plane can not ride on frictionless wheels. This is a real experiment. The weight of the plane is pushing down on the tread. The speed of the tread is kept at pace with the plane. Forward motion is required for take off (this is not a VTOL). If the forward momentum is transfered to the tread there is never going to be a net gain in airspeed over the wing. Try running on a treadmill with a kite. You run and run, faster all the time and yet that kite isn’t going to catch a breeze and take off. In this case it’s your legs that provide the thrust, but the idea is still the same. Air mass realitive to the movement of the plane or kite.

Takuan

how do helicopters and VTOLs like the Osprey convert to forward flight from a hover?

dougrogers

Yes, the forward motion is not generated by the wheels. Take the wheels, treadmill out of the question.

Imagine the airfoil somehow supported on a frictionless surface so that whatever forward motion is generated by an engine is countered by an opposite motion. Clearly possible in imagination, impossible in real life.

How do you generate the forward motion to create the moving air necessary for lift.

I think that is the circumstance the question intends to generate.

EngineerNY

Guys, come on. This is getting silly. I know this thread is long, but when you read this, I promise you can get some rest. (I suppose I should mention you shouldn’t ACTUALLY do this, but visualize it…don’t want you breaking bones and such)

Put some roller blades on, and step on a treadmill. Turn on the treadmill without holding on to anything.

You move backwards.

The people who assert that “the plane won’t move because the wheels are free-wheeling” are completely missing the point.

Now, hold on to the bars with your arms, as the treadmill moves beneath you.

You don’t go anywhere.

The force in your arms is representative of the airplane’s thrust — a forward force.

If you pull MORE on the bars, you have the potential to move forward, but ONLY if the treadmill does not speed up.

This is where this video is WRONG. http://www.youtube.com/watch?v=siYQU99VaAM

He asserts that there is some other force holding the plane stationary BEFORE any thrust is applied, and that is just not true. Hopefully my above examples will illustrate that.

Thank you, and goodnight.

Chris Tucker

Tanner, BitTorrent and/or NZB+USENET could be your very good friends, when it comes to watching that particular episode of MythBusters, as well as MythBusters in the future.

Indeed, using this link:

http://www.cnet.com/8301-13739_1-9775271-46.html

you can automate the whole downloading procedure and have every new episode of MythBusters delivered to your computer every week.

DO read the comments, the author of the article left out an important step in the process, the needed step is mentioned in the comments.

dculberson

Jeff, you almost made it! The leap of logic that would get you to the answer! Yes, running on a treadmill won’t give you a breeze. But your form of locomotion transfers energy through contact with the ground. An airplane has a completely different method of transferring energy – one that does not act upon the ground.

The friction in the wheel bearings won’t increase enough to slow the plain appreciably.

xzzy

Thrust from the plane is acting against the air, not the pavement. The propeller/jet will move the plane forward whether or not there is a treadmill underneath it.

The speed it achieves will be unrelated to the treadmill, because the wheels are only there to keep the plane from damaging itself while on the ground. I hope Mythbusters have a really really long treadmill, or else the plane will simply pull itself off the end and continue along on solid ground.

The way I envision it is swimming in a fast moving current. You may not be able to swim fast enough to move against the current, but if you had an anchored rope you could pull yourself along. The rope is the air, the water is the treadmill.

dougrogers

Does thrust on a frictionless surface produce motion?

Antinous

On a tangential note.

noen

Here is what will happen. The plane will lift off of the treadmill a few inches and then fall back down. Because it is an ultralight it may even lift off several feet, stall out and fall back to earth because it will have zero air speed.

Imagine a plane resting on a treadmill, both are at rest. The plane does not take off because there is no such thing as magic. You start the engine and the plane begins to accumulate forward momentum but it doesn’t move with respect to the ground because the treadmill applies an equal but opposite force to the plane’s forward momentum. If the equipment is well designed the plane will remain stationary with respect to the ground. As the propeller gathers speed there may by enough air volume flowing over the wings to create some lift but because it has no air speed it can only lift straight up, stall out and then fall back down.

If this was possible we would already be doing it since it would be a great way to launch an airplane or jet from a ship. The fact that we are not doing this is strong circumstantial evidence that it doesn’t work. You’ll notice that we use a catapult, the exact opposite of a treadmill, on aircraft carriers.

Case closed.

jere7my

DCulberson @125:

You might want to re-read my answer â€” I agree with you! The plane will take off, just as someone wearing roller skates on a treadmill will move forward if they pull themselves forward using a rope.

dougrogers

Does thrust on a frictionless surface produce motion?

Imagine a motionless rocket in a vacuum. Ignite the engine it and it will move. Action/Reaction.

Can the airplane engine produce forward momentum on a frictionless surface?

Yes, strictly speaking, because the engine doesn’t act at all against the surface, frictionless or not. It acts against the mass of the plane pulling, or pushing, forward, causing the wheels to move (note the instant assumption of friction due to the coupling, bearings, axles, etc.)

But you have an intelligent surface here which detects motion and acts against it, negating any motion of the wheels.

So, does Newton’s Law of Motion apply here?

ace0415

Ok, I’m sitting at home with the flu (not bird flu, don’t worry), and I have to respond to this, it’s too disturbing not to.

The plane won’t take off. Thrust, relative ground speed, whatever, it needs LIFT to take off. We must overcome the force of gravity holding the plane on the ground. That lift comes from air moving over and under the airfoil wing. THE WING. It doesn’t matter how fast the wheels are moving, if the air is not flowing over the wing (both sides) then it won’t take off. The plane must be moving in relation to the air (or the air in relation to the wing, however you want to look at it) for it to take off. It seems quite clear in the question that the conveyor belt is undoing any of the forward momentum created by the propulsion.

And the tires would not accelerate infinitely, they would only go as fast as the force pushing it, so no burning rubber, no molten treadmill. If you’re getting enough thrust to move the plane 100mph (looks like they’re using an ultralight for the show, they won’t get 100mph out of that) then the wheels will be moving at 100mph. That’s the point of the question; the treadmill and the thrust cancel each other out. To discuss at which point the tires will burn out (which will only send the plane BACKWARD as the treadmill continues on its merry way, taking the plane with it now, which is also what would happen if you put the breaks on, #114) is to miss the point of the question and try to get around the answer on a hypothetical technicality. And it still doesn’t take off in any case, it goes hurtling backward, quite violently.

The argument that the treadmill itself will cause drag on the air, causing wind, causing the plane to take off is partially correct. There will be a breeze, but again especially with the low speed of an ultralight you’re not going to get the movement of a sufficient mass of air by the treadmill to create the airfoil. If the plane did get buffeted into the air (which I don’t see as the same as flying, much like getting under a little plastic balloon and blowing it up in the air doesn’t constitute flight) by the breeze from the treadmill (an ultralight might get buffeted into the air, as it’s, well, ultra light) I would be greatly surprised if it was able to gain enough airspeed to say airborne, since now it’s moving out of the wind from the treadmill and has to power itself through the air, which it can now do as it’s free of the counter effects of the treadmill. It would stall and fall back to the treadmill though, it needs more “runway” to gain speed. That’s not “taking off” in my book, any more than me hopping into the air is me about to take flight.

A quick example of a similar problem; I asked a student of mine (I teach the kids the music) what would happen if while she were ridding along on an airport conveyor belt she jumped into the air. She said she would land behind where she jumped. I tried to explain that she’s wrong, and she would not have any of it. She was a stubborn 13 year old, it was to be expected. She would land exactly where she started, unless she created quite a bit of air drag. The air drag is the only variable in that equation, and unless that conveyor belt is flyin, there’s not going to be enough to worry about.

So, in summary; no airspeed over the wings = no overcoming gravity = no flight. The treadmill will only go as fast as force of the propulsion is pushing it. If it was a rocket on the Moon, on a treadmill, and the vector of the rocket was not directed sufficiently opposed to the pull of the Moon’s gravity (small though it may be), it will not take off. If on Wednesday the little thing takes flight, I will eat crow and be very curious as to why it took off. If it doesn’t take off, I am going to be ashamed that physics professors argued so vehemently that it would.

PS I couldn’t read all the posts, hopefully I didn’t repeat what too many others have said.

ItTookOFF

To elaborate on post #222

“…The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction…”

All this talk about “speed of the wheels” and nobody has actually cared to define what “speed” is.
Websters dictionary defines Speed (in this context) as:

Distance traveled per unit time.
http://www.websters-online-dictionary.org/definition/speed
‘Revolutions per minute’ is only mentioned twice in that article; once in “mining”; and once in Turkish “devir sayÄ±sÄ±” which translates to, you guessed it, RPM.

Looking at the actual definition of “Speed” it can easily be concluded that the treadmill will not match the (Circumference*RPM) of the wheels, but the actual distance of the wheels traveled over time. This would equate to the “speed of the plane” question.

When we think of wheels, we automatically think “rpm”. The question we’re discussing never actually states “rpm” is part of the equation. It is a vague question with only three variables, but the actual definition of the words (not our (mis)understanding of them) lead to the same conclusion as the “plane speed” question.

The two questions “wheel speed” and “plane speed” are actually the same question. The former is only phrased in a manner that provokes the wrong understanding of the question. How many times are we going to hear this answer? Too bad we called that ceasefire, Enginerd and myself. This would pose for some interesting debate (although fruitless still).

jere7my

I find it helps to use Noen’s treadmill and rope example, but with an important difference: picture yourself wearing rollerskates on one of those long airport treadmills. There’s a rope tied to the wall far ahead of you, and your only means of forward motion is to pull yourself along using the rope. Unfortunately, the treadmill exactly matches your speed in the opposite direction. O noes! What will you do?!

Well, obviously, you’ll pull yourself off the treadmill using the rope. If you’re hauling yourself forward at 1 m/s, the treadmill will roll backward at 1 m/s, and your roller skate wheels will be freely spinning at 2 m/s. Your forward motion won’t be significantly impaired by the treadmill, since roller skate wheel bearings are a crappy way to transmit frictional force to your body, and that’s all the treadmill can do. In the same way, the plane engines, pushing against the air, won’t be much bothered by the treadmill â€” that’s the point of the puzzle, to demonstrate that cars and planes are sometimes different in counterintuitive ways.

Alas, the wording on the puzzle has gotten a little munged up, saying that the treadmill matches the wheel speed. That doesn’t make a lot of sense â€” you need to imagine some sort of magic treadmill, since the tiniest forward motion will immediately result in an infinite-speed treadmill and a lot of melted airplane wheels. If the wheel speed exactly matches the treadmill speed at all times, forward motion is thereby defined to be impossible â€” not a very interesting puzzle, and not something that makes a lot of real-world sense re: treadmills.

dculberson

Noen, your “case closed” doesn’t counteract your misunderstanding of the physics involved.

The treadmill has no means with which to “[apply] and equal but opposite force.” It is only contacting the wheels, which are more or less free to spin however fast they wish.

A treadmill does not move the air around it except for a minuscule amount against its surface. Why do you think it would?

Anonymous

As Mr. Miyagi might say:

“Ice… not fight back!”

trieste

“the pilot guessed wrong” – the plane must fly then since pilots are not very smart.

The genius addition in the question is the airplane. If it was a jet engine strapped to a soap-box car and people were asked if it would remain stationary there would be far less debate.

A sad comment on the state of the teaching of science given some of the answers above.

Anonymous

OK my brain hurts after reading all of this.

Am I correct in thinking, a plane can only take off once the lift generated by its wings is greater than the weight of the vehicle itself?

And is lift created by a flow of air over said wings? And is it not correct that as the flow of air is increased over a planes wings its ability to create lift increases? So in this case air flow would be directly related to land speed.

I think this whole thing is being talked about way off point, meaning the argument seems to be the speed of the plane relevant to the speed of the treadmill. But if it were possible to match the power generated by the engine (prop or turbine) by a moving treadmill would there be any air movement over the wings. I still say no. If you run a treadmill is you hair blowing in the breeze.. NO. you are stationary. Now if the plane on the tread mill were to have a strong enough thrust at a certain point it could become air born especially if the trust line of aircraft was pointed up. So IMO it could be possible if the thrust was great enough to overcome the weight of the aircraft.

Example: Wooden rubber band powered airplane. Tighten (wind up) the propeller 25% of its max potential, hold the plane in one hand keeping the prop at 1/4 potential with the other, now let both go. The plane drops.
Wind the prop to 100% of its potential and repeat. If the prop is efficient enough the plane will drop and the thrust in what ever attitude itâ€™s aimed.

Think an aircraft carrier. If air speed were not so important why do they point the ship into the wind (adding air speed) and have the catapults launch the plane for 0-who know what in a matter of a second. If you were to tie a plane to a stake that could not move could the plane create lift with its wings.. Again no it cant. It could possibley profuce a hell of a lot of thrust and my at some point break ground but it wont flyâ€¦ see: Fat Albert Blue Angels C-130

ItTookOFF

@ DOUGROGERS

“Engines provide forward motion A, transferred to wheels. A=A
Conveyer moves backward. -A

A-A = 0″

Clearly you are still under the misconception that an airplane and a car work the same way. The engines of an airplane do not drive (rotate, turn, spin or anything else) the wheels. The inverse is also true: the wheels of a plane do not cause the plane to move forward. The force of the propeller against the air is what draws the plane along the ground, which causes the wheels to rotate.

“Is A the motion of the plane, the same as A the motion of the wheels.”

No, and in this argument you disqualify yourself from having an opinion. You are ignoring the question and the answer and simply are not understanding the problem. In the air, an airplane’s wheels spin freely (and most likely very slowly). On the ground, the wheels rotate because the plane is moving forward, not the other way around.

I too can make the argument “because you say it is so, does not make it so”. If you can prove that the minimal force being transfered to the plane by the interaction of the wheels and the treadmill will be enough to prevent the airplane from taking off, I will have no choice but to concede. This being Earth on the other hand; this friction/force/deceleration/etc. is not enough to do so. I am not a physicist or an aeronautics engineer. This is not a physics question.

“There is this guy Nex, who like you above says the same thing over and over again, just like what you say in the last paragraph above, but persists in providing no justification that alas, poor old me can understand.”

I’ve provided plenty of justification, as anyone else on the “will fly” side of the argument has. If you don’t understand a subject, you cannot have a meaningful opinion on that subject.

I hate to quote myself but it bears repeating:
Me: “The wheels of an airplane are not attached to any driving mechanism. Furthermore: the wheels are attached to the axle by bearings, which were designed with canceling friction in mind; torsional friction is thereby reduced to near-null.”

DOUGROGERS, prove this statement false.

enginerd94303

JEREMY:

OK, you’re answering a different question, and your answer to that question is correct. It’s a trivial question as was mine.

However, the problem does not in fact “illustrate real-world differences between cars and planes”.

If a plane that is traveling 100mph through space is on a treadmill that matches it’s speed but in reverse, then the wheels will spin at 200mph. The same will happen with a car traveling at 100mph through space. It’s wheels will be spinning at 200mpg. Unless you change your frame of reference from absolute speed to speed relative to the treadmill when you switch from plane to car, then the plane and car behave absolutely the same, save for the fact that cars can not actually fly.

In fact, stating that the car and plane behave differently implies the question when applied to the plane is the “ORIGINAL” question, while the question when applied to the car is the “bastardized” question.

TAKUAN:
“yes,but most of them are smart enough to keep it a secret”

Good one. More likely, most of them are not interested in trying to understand what a question is asking in more than one way. If you can supply me with information that makes me look like an idiot, by all means, do so.

enginerd94303

DCOLBERSON:

The question doesn’t ask if the treadmill can keep up with the plane wheels. Of course we can’t build a treadmill that can do that with current technology. If the wheel bearings failed first, the plane could not take off because the wheels would seize up. If the treadmill failed to spin up fast enough, the plane would take off.

But that is missing the point. The question states that the treadmill matches the speed of the wheels. That is the only constraint, and it implies that the treadmill is in fact an “ideal” model of a treadmill. I think the default assumption, and I’m interested to see what your thoughts are on the matter, is that all the pieces involved in the puzzle are assumed to exist in the natural world unless stated otherwise. The question states otherwise in the case of the treadmill, but not in the case of the plane. We don’t need to know how it does that. That’s the whole point of a thought experiment like this. If you like figuring out the answer to riddles like this as I do, then you must realize that many of them have one or more assumptions based on impossible situations.

If in fact the plane did start to roll forward against the treadmill, then we would have a logical paradox because the question states that the treadmill must match the speed of the wheels.

How the treadmill accomplishes this I’ve explained many times over, but really the question contains it’s own answer when you assume that it won’t contradict itself.

ITTOOKOFF:

You are not bringing new information to the table, so hush your belly. You are religious about your science, and that is not acceptable. I am not following links to idiots on youtube, and I will not be reading or answering your posts anymore.

nex

Exactly, some interpretations don’t make any sense; it is not true that with “the Boing Boing question” or “the NY Times blog question” the plane can’t take off. It can always take off as long as it’s possible to give an answer at all.

Mithras

Now I get it!

This at Modern Polymath cleared up my confusion:

“If you still donâ€™t believe me, hold two matchbox cars at the top of a declining platform (Like a propped up book.) Put a piece of paper underneath one of the cars. Let go of the cars and pull out the piece of paper from under the one car in the opposite direction the cars are traveling. Both cars will reach the bottom of the platform at the same time.”

An better example would be to put a glider on a skijump with the conveyer belt under it. Gravity starts to pull the glider down the ramp, but the conveyer belt starts to spin backwards at the rate the wheels are turning. At first, I thought, this would hold the glider in place, but of course it doesn’t. Why not? There is insufficient friction between the turning wheels and the conveyer belt. In essence, the glider starts sliding down the ramp. Same thing with the powered plane on a level surface with the same conveyer. As the physics people have said, there is no countervailing force to offset the thrust of the engines. To us non-physics people, it seems intuitive that the wheels have to turn to allow the plane to move. But that’s not true. The wheels can slide over the conveyer belt without turning faster, so the plane will move forward until it reaches takeoff speed.

nex

Just two days until the mystery will be revealed once and for all, and still another discussion erupts … I’m surprised, but I very much suspect that I shouldn’t have been.

Once again, quite a few people here are confused. Maybe that’s because they’ve never seen the actual airplane-on-a-treadmill brain-teaser, but instead the bastardised nonsense version that was previously featured on bb.

Back then, I said:

[...] Pogue is not just wrong, but so majorly confused that he disqualified himself from having an opinion about this subject. [...] [In the section I'm leaving out here I mentioned that I don't think Pogue is a complete idiot, btw.] if we rule out interpretations that don’t make any sense to begin with, there are only two scenarios: The speed of the conveyor belt’s upper surface, with respect to the ground the belt is sitting on, will match the speed of the plane, with respect to the same ground, in one direction or the other, so the wheels will either turn twice as fast or not at all. In either case, the conveyer belt will have only a minimal impact on the movement of the air above it. No matter in which direction it moves, the plane’s airspeed will hardly change, thus [...]

If you’re interested and don’t mind a spoiler, go to the original bb story and read the full version of my explanation, quoted under the heading “Nex says”. If you want no spoiler at all, you should have stopped reading about 10 lines above :-) If you want just a little hint: I’m quite sure my explanation is correct, because I’ve posted it to several lenghty forum threads chock full with people who enjoy logic puzzles, and no one ever refuted it, though some actual pilots (or so they said) did try. And lo and behold, Mr. Savage says “the pilot guessed wrong.” I think that’s a bit scary, actually.

jere7my

I’ll quote a much wiser man than me, Cecil Adams, on why the “speed of the wheels” formulation is broken:

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane’s forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you’ve got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: “The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.” This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible — simply put, that A = A + 5 — and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

Cecil’s article is linked to from the original BoingBoing post.

Charlie Stross

“zero to thirty degrees below zero”

… Celsius or that weird Fahrenheit-thingy scale? It makes a difference, you know!

EdT.

@72 -Noen:

“Case closed.”? Perhaps you’ll learn why you’re wrong once you realize that you’re not necessarily right…

W. James Au

Mythbusters fucking rocks. They should repackage their shows for a high school physics curriculum, each busted myth demonstrating a specific principle.

nate

What I don’t understand has nothing to do with the question or even the wording of the question.

Why would you ASSUME the airplane is being held stationary? Where in the question does it say that? What is it about the word “treadmill” or “conveyor belt” that automatically means “stationary”? Why would you change the the question to insert your own idea of using a ropes and clamps to hold the airplane from moving forward? I didn’t see those words in the question and neither did you, so why would you change the question with your assumptions?

There’s a conveyor belt, there’s an airplane, and there’s air, nothing more. Don’t add or subtract from what’s given.

BigHead

Okay, I can see this from both sides. One side is that thrust is equal to wheel speed and there is no accelerative force, meaning that there is no flow of air over the wings; the plane is stationary. Obviously if this is the case, the plane will not fly. The other side is thrust is continuously accelerating the object while the conveyor belt reacts to match the wheel speed, but this means that the plane will move through the air. It’s tough to imagine, but and accelerative thrust is independant (decoupled) of the ground. Here’s a thought experiment that explains that decoupling. Imagine this plane is on the conveyorbelt runway and both are stationary with zero speed. Now, imagine there is a teather from this plane to a truck which is not on the converyor belt. The truck takes off. As the truck accelerates the planes wheels begin to move and the conveyor belt reacts by moving backward. Does the backward motion of the conveyor stop the truck from moving? We can see that the truck is independant of the conveyor and will drag the plane forward no matter what the tire speeds are. The truck is the exact same as any form of decoupled thrust. If the thrust came from the tires, the plane would remain stationary (as in a device used to measure horsepower in cars shows), but in this case, thrust is coming from a decoupled source and the plane will fly.

ItTookOFF

What part of the plane being able to take off are you having trouble understanding? That you understand it can is great. Maybe I’m just not ‘in your head’ enough to get to the meat and potatoes…

And no, I’m not a teacher. Only a very frustrated individual with a background in philosophy and logic. Credentials are (excuse the term) also an appeal to authority, as a brain operates independently of any sort of degree or job. I digress.

RugerRedhawk

Fahrenheit.

RV9Factory

@72-Noen:

>>>Case closed<<<

Well geez, that settles it then. Someone with no grasp of the mechanics and physics of what’s going on has declared the debate over. LOL.

Once again, what does the wheels’ interaction with the treadmill have to do with how fast it is moving in relation to the ground and/or the air? The answer is nothing. The wheels spin freely and do not impede the aircraft’s forward motion through the air.

dculberson

Jeremy (138), sorry for lumping you in with the wrong group! I hope they didn’t beat you up too badly. ;-)

tbartels

“This is a real experiment. The weight of the plane is pushing down on the tread. The speed of the tread is kept at pace with the plane.”

This seems to be the general thought behind the theories of all the people that believe the plane would never take off. First of all, the situation you describe here is actually impossible, if the plane isn’t moving how do you adjust the speed of the treadmill to match it? If you measure the speed of the wheels you are only ever matching the speed of the wheels, not the speed of the plane, this would be the same as if you put the plane on the treadmill and held the plane in place with a wall at the end of the treadmill. This would lead to a speed of infinity and you haven’t even started the engine yet.

To better visualize the situation you can ask the question: Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to DOUBLE the speed of the wheels AT TAKE OFF, moving in the opposite direction. Can the plane take off?

If you understand the forces taking place when an airplane takes off you know that even if the treadmill is travelling 10x faster than the wheels or the plane, the plane will still take off.

For a visualization of the forces in place it is best described on The Straight Dope:

“Imagine you’re standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you’ll have to overcome some initial friction tugging you backward, in short order you’ll be able to pull yourself forward easily.”

Basically it doesn’t matter how fast the treadmill is going it is not a factor in the forces necessary to move the airplane.

xadrian

“So you think we could make a lead zeppelin?

Jamie FTW.

My 6 and 3 year old watch this with me, it’s one of their favorite shows. I’m actually a little concerned why Smash Lab is on. It’s like the execs said, “Well, we like Mythbusters, but they don’t always blow stuff up. Can we just make a show where they always blow something up?”

dougrogers

“What part of the plane being able to take off are you having trouble understanding?”

None. No longer a problem after I stepped outside the frame of reference

ItTookOFF

“EngiNerd, if you can’t be civil, you’ll have to leave the conversation.
Belatedly: ItTookOff, same goes for you.”

Duly noted.

Enginerd: “…I will not be reading or answering your posts anymore.”

That’s unfortunate as in my philosophic pondering I have reached the conclusion that our ‘debate’ has in fact run its course. You have your answer and have stated you will never change your mind (if not in those words, then by repeatedly stating the same things) and I have done the same. We’ve both drawn lines in the sand and dared the other to cross.

In other words, we’ve reached a stalemate. Your interpretation of the question is completely different than mine, and further ‘debate’ will not change this fact. *Shakes Enginerd’s hand*

I will now agree to leave your arguments unchallenged as you have agreed to do the same to mine, above.

noen

#73 dculberson

“The treadmill has no means with which to “[apply] and equal but opposite force.” It is only contacting the wheels, which are more or less free to spin however fast they wish.”

The wheels are connected to the plane are they not? They are therefore a part of the equation. If the forward force is 8ft per second and the reverse force is -8ft per second the combined forward force is zero and the plane stays where it is. It is assumed that the treadmill is designed so that it exactly counters any forward momentum. Good wheel bearings should be able to handle anything a prop can throw at them.

“A treadmill does not move the air around it except for a minuscule amount against its surface. Why do you think it would?”

I never said it would. You are misreading me.

#74 trieste
“If it was a jet engine strapped to a soap-box car and people were asked if it would remain stationary there would be far less debate.”

Not the same at all. Some of the thrust from a jet exhaust comes from the force of the exhaust leaving the body of the jet and some comes from the exhaust pushing against the mass of the surrounding air. I think that a jet on this treadmill would take off because it is pushing against everything, the air, the ground and the treadmill. A comparable analogue would be to place a large vacuum directly behind the jet exhaust and designed so that it sucks in the exhaust gases as fast as they are expelled. In that hypothetical, the jet would not move or only move very little.

ItTookOFF

Good. Now who wants nachos?

enginerd94303

JERE7MY:
It’s interesting how you think that the Boing Boing question is easy and trivial, but the NY Times blog question is somehow worthy. Honestly they are both trivial: One can’t take off, and one will take off with the wheels spinning twice as fast as normal. I don’t see either of these questions as being better than one another. It’s interesting though how you have judged the one you were trying to answer better than the one I was trying to answer.

Also, as to it being obvious that the post included on Boing Boing was not original: How? There are a lot of idiots on this Forum.

Hounskull

It’s kind of scary the amount of debate the initial article started. It’s really not very difficult to visualize… but the mind is a terrible thang!

Of course the plane would take off. What matters is the airflow over the wings to generate lift, not the speed at which the ground is traveling. Planes obviously aren’t powered through the wheels like cars. (duh!)

btw, it doesn’t take a “treadmill” to prove this. A take off or landing with a tailwind also has the effect of making the ground move opposite the vector of travel. Also, the wheels (and treadmill) would simply rotate at double the rate of forward speed.

Jeff

@131, I realize that the tread would have to be matching the plane speed, not just through the wheels but with additional assistance from a motor. This experiment is trying to move the earth below the plane, when what has to move is the plane through the air. For that speed to be achived the tread has to be as long as a runway. There is no way to cheat the velocity of air over the wing, except in a wind tunnel.

Chainring

“Chainring, you’re a Toronto grad, aren’t you?

Nope. Bit further south.

“Chainring, here’s a hint: You’re that guy.

… and you’re a jerk. I’m fine with being wrong. Are you okay with being a tool?

“Chainring, your last sentence is entirely correct. However, a treadmill has no good way to stop a plane moving relative to the air.

That’s why you can only apply a small amount of thrust. Too much thrust and the plane will move forward relative to the earth (air) and the experiment falls apart.

“Where do you think the physics is missing? What is going to hold the plane back?

Nothing. That’s my point. Once the plane moves forward relative to the earth, the experiment falls apart. The whole point of the conveyor belt is that it moves at the same speed of the plane. From the problem as stated: “The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” If the plane starts moving relative to the earth (i.e. the wheels turn faster than the belt) then the experiment fails.

What the “it will fly” supporters fail to realize is that the REASON planes require so much thrust to get airborne is the fact that they must fight against air friction to propel the plane forward at high enough speed to get it to take off. Air friction increases as the square of velocity. If the plane has no velocity relative to the surrounding air, the only force the plane has to overcome is the friction of the wheels, so the wheels will turn very fast with only a small amount of thrust. You can see that same principle in practice in bicycle â€œroller racesâ€. (google it) A cyclist who may be able to sprint at a maximum of 35 mph on flat ground may be able to turn his wheels at 80 mph on rollers â€“ because heâ€™s not fighting air friction.

stuiethegod

I just have to get that off my chest…I live in Alaska, and I hate when people refer to the weather in Alaska as if the whole place is exactly the same. It’s twice the size of Texas, and for the record it was a balmy 32 degrees in my hometown last week when I left to go back to school.

Takuan

yes,but most of them are smart enough to keep it a secret

Brian Damage

@#1

If only the summary read “zero to forty degrees below zero” I could have usurped a clever line from Futurama:

Leela: Fry, night lasts two weeks on the moon.
Moon farmer: Yep, drops down to minus-173.
Fry: Celsius or Fahrenheit?
Moon farmer: First one, then the other.

nex

Just hopping in to reply to posts above where I was addressed directly; I’m assuming I’m not adding oil to the fire here as the discussion seems to have petered out with the correct arguments prevailing.

There is this guy Nex, who like you above says the same thing over and over again, just like what you say in the last paragraph above, but persists in providing no justification that alas, poor old me can understand.

Sorry, I hadn’t seen this until now. It’s already been dealt with in the meantime, but I would like to say that I’ve always tried to give meaningful answers to meaningful questions. But here all we have is this:

Engines provide forward motion A, transferred to wheels. A=A
Conveyer moves backward. -A
A-A = 0
Is A the motion of the plane, the same as A the motion of the wheels.
Explain.

What could there possibly be to explain here? You’ve defined that the conveyor moves backwards as fast as the plane moves forward. Backwards is exactly the opposite direction as forwards, so of course the sum of these speeds is 0 and the magnitude of difference is 2A. So? This is just what we’ve been saying all along, what is it supposed to demonstrate? To answer the question: No, A is not the motion of the plane, it is the speed of the plane. No, A is not the motion of the wheels, it is the speed of the wheels. Yes, the speed of the wheels equals the speed of the plane. What in the world is there left to justify?

Besides, I’ve explained and justified every point that was challenged (except for rare occasions where I’d made a mistake, which I’ve always admitted openly and quickly), to the point of repeating what others and myself have said, so if there was a lack of understandable statements, it was certainly not for lack of trying. I certainly can’t give a satisfying answer where I don’t see a coherent question to begin with.

The planes velocity is zero. It will stay at zero velocity until the engines are turned on. Now, due to the imaginary, hypothetical conveyer belt, any forward motion generated – and that forward motion is first applied to the body of the plane, then transmitted to the wheels – is automagically negated

The wording is poorly chosen again (if the plane remains perfectly stationary, then how can forward motion be generated?), and there still is no explanation for how the belt is supposed to do the trick of holding the wheels in place. As long as it isn’t shown that this could possibly work, there’s no evidence that this interpretation even makes sense, hence there’s no reason to pick this interpretation (belt holds plane in place) over others (e.g. belt speed matches plane speed, but in opposite direction) that certainly do make sense.

Please just please just please tell me how the premise of the question (that the wheels and treadmill spin at the same speed) can hold true if the plane takes off.

Wheels and treadmill spinning at the same speed are not the premise of the question. I’d have to say more to completely explain and justify this statement, but you can read all of that above and over on kottke.org, so I’ll avoid being chided again for redundantly repeating stuff that had already been said over and over again and again and just say that natural language often has blanks you must fill in by interpolating intelligently. When you assume that the belt always has to spin just as quickly as the wheels spin, but in the opposite direction, you’ve filled in a blank with random nonsense, which invalidates the assumption.

Anonymous

http://dilldoe.org/blog/?p=119
Comic strip which shows the outcome of a Plane on a Treadmill!

enginerd94303

DCULBERSON:
Enginerd, Ahh! You’re working from the corrupted version of the question. The original says “plane” and not “wheels.”

Dude, guys, look at the parent post. I am not responsible for looking up to ORIGINAL question. I don’t even know if I could prove what the original is! But seriously, the question referenced at the top of THIS page (Click “plane on a conveyor belt problem”) is this:

“Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?”

How can you claim that this is a bastardized version of the original? This IS the original problem referred to in this thread.

DCULBERSON:
Please respond to this post and say something like “You’re right, I wasn’t looking at the right post. You were, but I wasn’t. I’m sorry”.

And although this isn’t the hardest problem to think about, it’s obviously not stupid since so many people have trouble even understanding what is being asked. In my experience, defining the problem is often as tricky as solving the problem.

Maybe what you guys should learn from this is to read the question and don’t assume that because it’s similar as one you’ve heard before that it is identical.

Jeff

I’m quite convinced that this experiment will cause the universe to implode. Hurry Up!

Tom

From two posts above:

“And the tires would not accelerate infinitely, they would only go as fast as the force pushing it…”

and:

“…thrust is equal to wheel speed…”

If either person can explain what they mean by these statements, it might be possible for someone else to explain to them where they are going wrong. But in plain English neither of these statements means anything. They are literally equating apples with oranges (or newtons with metres per second.)

Force is not velocity, and it means nothing to say that you have a situation where a force is equal to a velocity unless you specify the exact size of the frictional forces that are opposing the motion.

I’ve been told that non-physicists all believe the world is governed by Aristotelian physics. Never has this been so apparent. I feel like I’m talking across some Kuhnian paradigm shift, in which one side of the debate is living in a different world from the other.

Others have already given good examples, but here’s one more. I’m a Canadian, and up here we sometimes have planes that take off on skis from icy lakes. Assume our conveyor belt is icy, and the plane has skis. Further assume that the ice/ski contact is perfectly frictionless, and the conveyor can run backwards as fast as the plane’s normal take-off speed.

Now, stand beside the conveyor belt just behind the plane with your finger against the tail as the conveyor belt comes up to speed. Because there is no friction between the skis and the ice, the pressure of your finger is sufficient to hold the plane still relative to the ground, right?

If you disagree with this point, then we really are living in different worlds, or the word “friction” means something different to me than you.

So you have a plane being held still relative the ground by your finger. Now have the pilot fire up the engines. What happens?

Since there is no other force acting on the plane, it moves forward, gains speed relative to the ground (and the air) and takes off.

Now, suppose that instead of having NO friction, consider the other extreme, and assume the plane’s skis are frozen into the ice on the conveyor, and assume the ice is so strong that no amount of force can free it. This is equivalent to having infinite friction.

Now as the conveyor comes up to speed you’d better get your finger out of the way or it’ll be torn off as the plane is carried backwards by the motion of the conveyor relative to the ground.

As before, once the conveyor is up to speed, have the pilot fire up the engines and try to take off. Obviously, the plane will continue hurling backwards, because it is stuck in the damned ice!

So on the one hand we have a situation where the plane winds up travelling backwards at its nominal take-off speed, and on the other it winds up travelling forward at the nominal take-off speed. Which situation we have depends solely on how much friction there is between the plane and the conveyor.

For some particular value of the coefficient of friction, the backward force from the conveyor at the exact take-off speed of the aircraft will exactly match the forward force from the engines, and the plane will not move relative to the ground when the engines are providing enough thrust for it to otherwise take off.

But this is simply one particular value of frictional force. For other values, the plane might move backward or forward while the conveyor happens to be running at that one particular speed.

Ergo, I repeat my earlier point: the people who are arguing so passionately that the plane will not move are making an extremely narrow empirical claim about the particular coefficient of friction that one particular plane’s wheels will have. They are also implicitly ignoring the the most fundamental pinnacle of human scientific knowledge in favour of an intuitively appealing view of the world that was completely discredited over 300 years ago.

This actually gives me a bit more insight into creationists, because this argument is pretty much the physics equivalent of creationism. It is a deeply fascinating sociological and psychological phenomenon.

nex

The plane on a treadmill question is [...] The conveyor belt is designed to exactly match the speed of the wheels

No! It matches the speed of the plane. That’s the actual, original question, which the Mythbusters tackled.

Can you please stop saying that the treadmill cannot counteract the thrust of the engines?

It doesn’t really matter, because it’s wrong to assume the belt is even supposed to counteract the thrust of the engines. Of course the plane won’t take off any longer if you change the experiment around enough. But why specify a real-world plane with realisticly powered engines, but below it an arbitrarily strong super-conveyor from fantasy land? You could just as well require the plane to be fitted with cement shoes.

But you have an intelligent surface here which detects motion and acts against it, negating any motion of the wheels.

How would it do that? Grab the wheels and glue them in place?

So, does Newton’s Law of Motion apply here?

Newton’s Laws always apply.

enginerd94303

No, the “super treadmill” question may not be as interesting to you as it is to me. It’s mainly interesting to me because a lot of people cite “it’s not possible to build that anyway” in their solution, which is a pretty foolish thing to say about pretty much anything that doesn’t outright violate a physics law when taken into historical context. So I think it’s interesting to see what most people think counts as evidence and what they think makes a good argument. Mainly crap it turns out.

I think there is an Aha! moment for the “super treadmill” problem. At first it seems like there is no way a treadmill like this could be built, because the plane could easily roll forward. So most people at first seem to understand that the plane can’t move from a symantic point of view, but don’t understand how this would be possible from a physical point of view. If you look at the thread, you will see people that either learned or remember half of their physics classes, or are just being nerds because it’s fashionable, drawing flawed free body diagrams.

RV9Factory

>>>So why did the problem statement specify a conveyor “as long as a runway.”? It was obviously allowing for the possibility that the plane would move forward no matter how fast speed the conveyor runs.<<<

Methinks you’re reading too much into that. It was specified to be “as wide and long as a runway” to make sure the length of the belt didn’t artificially limit the experiment.

The long and short of it is: Those who said ‘no fly’ were and are wrong, for precisely the reasons the rest of us said they were. Nanner, nanner.

dculberson

Noen, the problem does not specify that the airplane remains stationary. Where do you see that specified?

Also, where do you see it specified that it is a propeller airplane?

nex

PS I couldn’t read all the posts, hopefully I didn’t repeat what too many others have said.

You repeated plenty of points made by those who are utterly wrong. I tend to think there are too many of those.

I love it when laypeople try to apply logic where physics is wanted.

Why would any sane person attempt to think logically when the problem is a matter of physics? How in the world could that possibly be of any help? Seriously, though, you can only get your physics knowledge to work on the solution once you’ve understood the problem, and if you applied some logical thinking to the problem’s wording, you’d discover that it doesn’t have any unambiguous meaning and the breadth of your physics knowledge doesn’t really matter at all.

enginerd94303

DCULBERSON: You’re right. It’s not fair. It’s just plain outlandish and not fair that the question states explicitly that the wheels are matched in speed at all times by the treadmill. I killer flaw that allows you to claim your answer as true while at the same time saying that mine is false.

Point A:
Please just please just please tell me how the premise of the question (that the wheels and treadmill spin at the same speed) can hold true if the plane takes off.

After you drone on about how you think 1) that the wheels can spin freely, and 2) that the power is derived from the propeller and not the wheels, go back to point A, read that sentence again, and then reconcile it with your answer.

You see, if the wheels and treadmill do not spin at the same speed, then we have a contradiction with the premise in Point A.

If you are correct, and let’s be clear: You think the plane can take off. Then the plane must roll faster than the treadmill, and THAT IS A CONTRADICTION.

RV9Factory

>>>So why did the problem statement specify a conveyor “as long as a runway.”? It was obviously allowing for the possibility that the plane would move forward no matter how fast speed the conveyor runs.<<<

Methinks you’re reading too much into that. It was specified to be “as wide and long as a runway” to make sure the length of the belt didn’t artificially limit the experiment.

The long and short of it is: Those who said ‘no fly’ were and are wrong, for precisely the reasons the rest of us said they were. Nanner, nanner.

bardfinn

Airspeed. You either have it or you don’t.

If you don’t, you stall.

Is the prop/engine power/volume able to pull a large volume of _air_over_the_wings_? If so, takeoff occurs.

Questions about whether the treadmill is ideal or practical, whether it accelerates infinitely or can keep up with the wheels, whether the wheels catch fire or not – beside the point.

In short: The entire formulation misses the real point.

Stefan Jones

#28: Phlogiston.

JakeTheSnake

A response to engineerny:

If I’m standing on a treadmill with rollerskates on and let the treadmill accelerate while holding onto the handles to stay in place, will the force required to keep me in place increase with the speed of the treadmill? I say yes, but only because the bearings in the rollerskates aren’t ideal.

At some point the treadmill will be going fast enough that I can’t hold on, assuming I can get the treadmill going fast enough.

So, there are two questions to deal with: can a treadmill overcome the forward thrust of a plane/rocket/whatever? And, does the velocity of the ground matter if you roll it backwards?

If you assume the plane won’t take off, your model assumes that if i had a plane on a treadmill attached to a rope tied to the ground, I could break the rope by running the treadmill fast enough.

This problem mostly is one of semantics, the debate here is more about language than anything.

If my plane were powered by a rocket, would that convince more people that it will take off?

enginerd94303

LOL. Now I get why you think it will take off. You are not reading the question that is stated in the parent to this thread: Go to the top of this page and click the link that says plane on a conveyor belt problem”.

Now that you’ve seen the question we are answering, you should realize that you’ve been answering a different question all along. If you are answering the question that states the treadmill matches the PLANE’S speed, then yes, it will take off, with the wheels turning twice as fast as they normally would.

If you are answering the actual question posed in this thread, not the one mythbusters are answering, and not the one you found somewhere else and claimed was the ORIGINAL (how would you know anyway?) question, then the plane can’t take off.

How absurd is it to think that the treadmill will not pull back on the airplane harder the faster it goes. How absurd also, to post some crap over and over which answers the wrong question? You people must have done really well on the SATs…

Sheesh!

dculberson

EngineerNY, there actually is a sort of force holding the plane still initially: inertia. Now, calm down, I realize inertia isn’t properly a force. But it is a resistance to motion. I guarantee you that if you stand on your treadmill with roller blades on and turn it on, you’re not going to go backwards as quickly as the treadmill is moving. And if you hold onto the treadmill’s bars, you won’t have to grip it with as much strength as your weight would ordinarily require: because the treadmill isn’t applying force directly to you, it’s acting upon the wheels which are light and isolated from you by good bearings.

Now, an airplane is going to have a hell of a lot more mass and thus resist being put into motion more. The bearings will have more friction to mitigate, but they’ll also be a lot higher grade than your rollerblade bearings.

So flick on our hypothetical massive treadmill, and the plane might or might not roll backwards a bit. But if you’ve got a rope tied to it, it won’t take much force at all to hold it still. I bet a guy wearing tennis shoes could hold it still. If not, a few people certainly could. And even a small airplane has many times the power output of a few people.

So your example does not illustrate what you think it does. Try it and let us know.

Enginerd, you said:

“Either way, having the thrust provided by the propeller and not the wheels makes no difference.”

Actually, it does. Really. Think about it some more; having the wheels driven would make all the difference in the world. If you’re “pushing” against the ground, having the ground move can negate all forward movement. If you’re “pushing” against the air, or a wall, or some other non-ground fixed object, the ground moving does not counteract your forward movement. An airplane is “pushing” against the air – thus the movement of the ground has little to no effect on its forward movement. (Only what minuscule amount that can be transmitted through the wheel bearings.)

trieste

#78 Noen: I await in eager anticipation your explanation of how rockets work in space.

Jeff

I want a recount! It is NOT possible that I can be wrong!(I wish!) I want a heavy, real plane to be used, not something made out of tissue paper.

David

I was going to write some uniformed opinion, but I see . . . oh, nevermind . . . I’ll wait until Wednesday evening to find out what Jamie and Adam come up with.

dculberson

But Tom, doesn’t the stone fall to the ground because it’s primarily earth? Doesn’t the smoke rise because it’s primarily air? This “gravity” thing is just a fad.

Like you, I’m just completely disheartened by the vehement “airplane stands still” crowd. It breaks me, a little at a time, and I stand bent and ashamed for having invested anything, however minor, into this “debate.”

Okay, not really, it’s kind of fun.

jere7my

Enginerd, you seem to be missing a pretty fundamental flaw in your analysis: rolling friction does not increase with velocity. It depends only on the weight of the plane (or wagon) and the material of the tires and treadmill. Whether the treadmill is crawling at 5mph or zipping along at 50mph, the force required to hold your red wagon in place is the same. The force will only increase 1) if the oil in the bearings heats up and begins to break down, or 2) if irregularities in the treadmill actually strike the wheels at high speed, causing them to jerk about and apply a momentary impulse to the wagon, or 3) if the tires blow out. Rolling friction is not a reasonable way to hold an airplane in place, even if we postulate a magic treadmill.

There is another flaw: in your interpretation of the problem, the moment the plane’s engines overcome the static friction of the wheels, the treadmill will instantly accelerate to whatever ungodly speed is necessary to create enough rolling friction to stop the plane (or, realistically, to blow out the tires). All of the force to rotate the wheels, all of their angular momentum, comes from the treadmill. There’s a chicken and egg problem here â€” what it causing the treadmill to accelerate? The wheels rolling. But what is causing the wheels to roll? The acceleration of the treadmill. Since (as you posit) the plane isn’t moving in the slightest, the wheels are only spinning because the treadmill is, and vice versa.

In your comment above, you say, “a plane or a car with wings could both take off” in the Mythbusters version of the experiment, which leads me to believe you haven’t quite gotten the question here. If you stick wings on a car and set it to rolling on a treadmill at 80mph, the treadmill will roll backwards at -80mph, and the car will be stationary at 0mph: it won’t take off. If you set a plane on the treadmill and push the throttle to 80mph (or whatever throttle setting would ordinarily translate to 80mph), the treadmill will roll backwards at -80mph, and the plane will zip forward normally at 80mph, with the wheels spinning as if it were moving at 160mph. That’s the difference, and that’s what the question is examining: the fact that planes don’t push against the ground, so treadmills don’t affect them.

The “super-accelerating treadmill” question, which somehow uses rolling friction (which is constant) to hold a plane in place against the power of the engines, is broken: as soon as the plane moves forward the merest fraction of a micron, the conditions of the question (as you interpret them) fall apart. It also has nothing to do with our real-world understanding of planes or treadmills; it posits a treadmill going crazy, like a belt sander, trying to hold a plane stationary by rubbing madly against the bottoms of its free-spinning wheels. That’s a ludicrous image. It’s not an interesting question, and it’s overspecified â€” you could do the same with glue, or by setting the plane’s brakes. The treadmill, in that interpretation, is a red herring. Isn’t it more likely that the super-treadmill interpretation is a corruption of the original, which is more interesting, and makes sense in the real world?

Also, you’re being very rude. I understand you’re frustrated, but I wish you wouldn’t.

noen

#76= EdT.

“”Case closed.”? Perhaps you’ll learn why you’re wrong once you realize that you’re not necessarily right…”

Oh come on, I said that mainly to get people’s goat. This is not that big of a deal. Chill.

For this MythBusters example the plane is a prop plane and it will not move forward because a prop generates forward momentum by the screw action of the propeller. Imagine that you are on a treadmill and you try to move forward by pulling on an infinite rope. You will not move forward because for every step and pull on the rope the treadmill moves back. It would be a different matter if the rope were attached to the treadmill. In that case you could pull yourself forward. In this example it isn’t connected to the treadmill and you stay put.

dculberson

Enginerd, I assumed you had read all the comments in this thread – which do address the “original” question – and perhaps even researched the history of the question. I was mistaken there, but not mistaken in any other way.

enginerd94303

Nex: You’re a douche.

Anonymous

This reminds me of a critical thinking word problem like we had in grade school. The purpose of those problems is to let people condense out the important information and discard the rest.

Since a plane must move forward through the air to generate lift in order to take off, The question can be reduced as follows:

“Can a plane that is on a treadmill that keeps it from moving forward move forward?”

The answer becomes obvious: “No”.

The problem states that the conveyor belt matches the speed of the wheels, only in reverse. It doesn’t say whether this is practical, it just states it. Since the wheels can’t move forward, and the wheels are attached to the plane, then the plane can’t move forward. If the plane can’t move forward, then it can’t take off. I don’t know of any plane that can take off with zero forward movement. If there is one, then for that specific plane the answer is the “The plane takes off”. For all other planes, which I believe is all of them, the answer is “The plane does not take off”.

Done.

Guysmiley

If you don’t specify that the treadmill must keep the airplane stationary, then the problem is trivial. All that happens is that the wheels spin faster and the plane takes off (as demonstrated). That’s barely even debatable. The whole point of the problem (as I understood it) is to figure out if a plane can produce lift by applying thrust and having its ground motion counteracted by the conveyor. The problem they solved is boring and dumb.

So it’s their fault you’ve misread and misunderstood the question and therefore were WRONG?

And Jeff: Told ya so.

Takuan

plane takes off

MythBusters tackles "plane on a conveyor belt problem"

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