Jon MayJan 30, 2008 at 10:36PM

Awesome. Kottke : Mythbusters :: Wonkette : SOTU :: Defamer : Oscars etc.

AMJan 30, 2008 at 10:42PM

Thankyou, from an easily distracted procrastinator in Australia.
(and I was right)

JaredJan 30, 2008 at 10:42PM

Awesome graphic, rendered beforehand right?

I think the episode brought the Mythbuster's official forum down a little while ago, or at least caused it to timeout for me. Looking at the posts though, I don't think people are convinced: http://community.discovery.com/eve/forums/a/tpc/f/9401967776/m/4441931059?r=5311922059#5311922059

JonoJan 30, 2008 at 10:46PM

How does the plane get lift? There is no air friction as there is no forward momentum... If the conveyor can accelerate to the point that the plane can, there wont be any forward momentum...

So im a little lost around the laws of physics... The engines propel the plane forwards, but not up...

greg.orgJan 30, 2008 at 10:46PM

i had to explain to my NASA astrophysicist phd wife why I was interrupting her CSI to tivo this. we ended up watching the last 15 min [what a slow, cheesy show, btw]. Because I set up the situation incorrectly--a conveyor belt counters a plane's thrust and keeps it stationary to the earth/air--we assumed no takeoff because there was no air pressure differential--and so no lift--on the wings.

So the plane engine clearly moving fwd [because thrust > drag and friction] read like a busted experiment, not a busted myth.

DanJan 30, 2008 at 10:51PM

No Greg, the experiment is right, you are wrong. You confuse speed with force. The treadmill can move with an opposing speed to the plane, but it cannot apply an equal and opposing force, because wheel bearings transmit only a very small rolling friction. The question nowhere states that the treadmill counters the plane's thrust or keeps it stationary. It only that it moves in the opposite direction at the same speed.

Troy AllenJan 30, 2008 at 10:53PM

I am completely disappointed at Mythbusters handling of this experiment. The science they used and the “explanations” were both completely flawed. The original myth, and ALL of the discussion, centered around one central conceit: The plane would have NO FORWARD MOTION RELATIVE TO THE GROUND because of the conveyor belt matching the speed of the plane. NOT the “speed of the WHEELS of the plane” or any other contrived version.

Of course the plane is going to take off if it has enough forward motion RELATIVE TO THE GROUND to create the Bernoulli effect required to lift the wing because of the airflow over the wing.

I really expected more “science” from MythBusters. They almost explained it properly with the “model car example”. I guess it was the original Myth that was flawed, or my understanding of the Myth. I guess in their mind the myth is that no plane on a conveyor belt can take off if the “speeds are matching in opposite directions”. That is far too simplistic to make a determination, so it is flawed from the get-go.

Those of us who claimed the plane would not take off without forward motion relative to the ground due to the laws of physics are still correct. The planes both had significant forward motion relative to the ground. I just hope everyone involved in the debate understands these distinctions, otherwise this will just dumb down the TV watching public a bit more. It sure was fun though!

TommyJan 30, 2008 at 10:55PM

I don't know if many here are fans of MythBusters before tonight. I love the show (maybe the concept), but Jason is spot on about how slow the show is. 99 percent of the time I watch it on DVR so I can skip forward. Just as an aside, if others are going to start recording it some of the smaller, side experiments are often the most interesting.

ddJan 30, 2008 at 11:01PM

Once you understand that a plane is not a car, I think the fact of its taking off, every time, becomes more clear. The plane doesn't need the ground. The wheels don't cause anything, they just react to the fact of the plane moving forward.

robJan 30, 2008 at 11:01PM

I see three probabilities. The "plane takes off" camp doesn't understand the question. The "plane stays on the ground" camp doesn't understand the question. Or the Grounders don't understand how airplanes work.

What I saw tonight was a plane overtaking the speed of the pickup, making forward motion and taking off. If they went the same speed he wouldn't have passed any of the traffic cones. What am I not getting?

AjitJan 30, 2008 at 11:01PM

Awesome coverage.

DanJan 30, 2008 at 11:01PM

Troy says that the myth requires that the plane have "NO FORWARD MOTION RELATIVE TO THE GROUND"

Except that is not what the question says. That is what you automatically believe, but you are wrong. I will quote the original question for you and you point out to me where it says that the plane has no forward motion relative to the ground:

"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?"

davidJan 30, 2008 at 11:01PM

Tommy's spot on about why I've never really gotten around to watching the show. It feel like so much plotting and trying things that almost surely won't work before they finally get to a good interesting experiment. That said, your liveblog has made me think harder about watching it.

Matt PoushJan 30, 2008 at 11:02PM

I've been pretty firmly rooted in the 'it will fly' camp, so I didn't particularly need it demonstrated to believe it, but I just happened to catch Mythbusters this evening while flipping channels, so I immediately popped over to kottke.org and was delighted to find the livecast. I think more things should be reported live via blogs. Good job, Jason.

Did you have a different image prepared for the mind-explodingly-impossible possibility that the plane didn't take off?

DanJan 30, 2008 at 11:04PM

If it helps you, I will point out that a plane does not measure it's speed by how fast its wheels are going, but rather by how fast it is moving relative to the Earth. Similarly, a treadmill does not measure it's speed relative to objects on top of it, but on how fast it's surface is moving relative to the Earth.

alex Jan 30, 2008 at 11:04PM

im impressed with that coverage and that is awesome that it works

alex Jan 30, 2008 at 11:04PM

im impressed with that coverage and that is awesome that it works

jhnJan 30, 2008 at 11:09PM

Troy:

If it helps any further, you should realize that no conveyer belt, traveling at any speed, is ever able to stop the forward motion of the plane. The plane ALWAYS moves forward relative to the ground.

JoshuaJan 30, 2008 at 11:11PM

Thanks so much for putting the result in a giant graphic at the top of the page. So glad I didn't want to find out by actually WATCHING it myself.

>:|

TommyJan 30, 2008 at 11:12PM

With the side experiments (Kari, Grant, and Tory) David they usually use one segment to explain the concept, another to do a test on a smaller and/or model scale to test their thinking, then to a full scale production. The problem is they can do two side tests while the main one is made to last for the entire show.

Now it is clear my technical knowledge on this subject is lacking compared to others, so I am not sure I should put forth my two cents .....

But I tend to agree with Rob said:

"What I saw tonight was a plane overtaking the speed of the pickup, making forward motion and taking off. If they went the same speed he wouldn't have passed any of the traffic cones. What am I not getting?"

As I was watching I almost jumped up when I saw this and they also pointed it out and said "WAIT .... that isn't right is it?"

FelipeJan 30, 2008 at 11:14PM

Haha this was a very funny post, Jason!! Specially for the rendered image with the result! You probably had one prepared in case the myth was busted too, right? Please show it to us!! I bet it was something like "oh noez the plane didnt fly!", lolcats-style!

By the way, nice font. Which is it?

Dan BolandJan 30, 2008 at 11:16PM

I guessed wrong but for the wrong reasons -- my thinking was that it wouldn't take off, because if it had, the discovery would have revolutionized the way commercial airports are built, since there would be far less land required to construct runways. What I hadn't counted on was the fact that the conveyor belt wouldn't affect the distance required for the plane to take off.

As far as the show being slow, that's not the half of it -- those three twits really drive me crazy. I don't care about whatever dumb ass shit they're doing, Adam and Jamie are the reason I ever watch the show.

Daniel WorthingtonJan 30, 2008 at 11:17PM

Like many others, I was originally convinced that the plane could not take off. I've since come around, and I think I might have a useful thought experiment to share.

First, I'd like to point out that any reasonable person agrees that if the plane can't move forward relative to the air, then it will not take off. The real question is whether the conveyor belt's matched motion can make this so. The intuitive (and incorrect answer) is that it can. Just like running on a treadmill, or driving a car on one, if the speed of the treadmill is matched in real time to the forward speed of the person or car then surely there will be no movement relative to an observer on the ground. You're just "spinning your wheels."

So here's my thought experiment. You have a treadmill and an object with wheels—let's say a skateboard. Standing on the ground next to the treadmill, you place the skateboard on the treadmill and hold on to it. Imagine the treadmill is moving at any speed you like. Won't you still be able to move the skateboard relative to the ground? Even if the treadmill is moving really fast, you can hold the skateboard where it is, right? And also, you can slide it along the length of the treadmill with no trouble. That seems like it is also intuitive to me. I'm not sure if it will convince any of the skeptics.

If you agree that you can roll a skateboard around on the treadmill pretty much however you like regardless of treadmill speed as long as you have a good grip, then consider this: A plane's engines work pretty much the same way: they "grab" onto the air and pull it forward. In other words, just like with the skateboard the plane has access to something that isn't moving with the treadmill. With the skateboard there is someone holding it, and with the plane there is the air.

In order to keep the plane from moving forward relative to the ground, you would have to make sure not the runway, but the air surrounding the plane, was moving backwards.

DanJan 30, 2008 at 11:19PM

"What I saw tonight was a plane overtaking the speed of the pickup, making forward motion and taking off. If they went the same speed he wouldn't have passed any of the traffic cones. What am I not getting?"

Nobody ever said that the plane was standing still. That was your misconception. The treadmill is moving backwards, the plane is moving forwards at the same speed the treadmill moves backwards. No matter the speed of the treadmill, it can never impart any force to the plane other than a tiny constant rolling friction. The treadmill can go 1000 mph and it still can't stop the plane. It is impossible for a treadmill to hold a plane in one spot because it has no way to apply any force to the plane. I can't believe people still delude themselves that they are right, even when faces with irrefutable proof.

DanJan 30, 2008 at 11:25PM

Hey Dan Boland, You better not be Dan Boland from UBC Mechanical Engineering. You bring shame to all of us if you guessed wrong.

NoelJan 30, 2008 at 11:26PM

Is it possible that the description of the puzzle presents an impossible situation?

So here's an similar experiment:
I put a bike on a treadmill. Instead of riding it, I stand to the side of the treadmill and hold the bike upright with my hands. The treadmill is rigged so that it moves as fast as the bike's wheels move, but in the opposite direction (sound familiar?). Now, from my position off the treadmill, I push the bike forward. Does the bike move forward?

I think the answer is clearly yes. The situation with the plane is the same, the thrust of the plane is based on propulsion that's not related to the wheels. If the bike/plane does move forward, that would mean it's wheels either slide or they revolve faster than the treadmill. So isn't the problem really that the puzzle presents an impossible situation, namely that the treadmill is able to keep up with the wheels?

DanJan 30, 2008 at 11:31PM

you have your frames of reference all mixed up Noel. You should be using the common reference frames for conveyor speed and plane speed, that being the Earth. If the bike is not moving relative to the Earth, the conveyor is not moving relative to the Earth. If the bike is moving 25 mph relative to the Earth, the conveyor is moving backwards 25 mph relative to the Earth.

What you are describing is a physical paradox. Basically that the speed of the conveyor belt = speed of conveyor belt + speed of bicycle. What you have is A=A+B, which is impossible when B>0. And that isn't what the question is talking about. Speed of the plane is obviously the speed of the plane relative to the Earth, nobody measures plane speed by how fast the wheels spin. And speed of the conveyor belt is obviously speed relative to the Earth.

bfos7215Jan 30, 2008 at 11:33PM

Not to be a jerk. But, after all of the explanations about this topic for the time this has been debated, I really feel bad for those who still can't quite understand how the plane, the plane's thrust, and the plane's wheels work together.

DanJan 30, 2008 at 11:41PM

Then for the love of God bfos7215, don't go to the mythbusters message boards. There are about 100 people yelling that the experiment was wrong, get this "because the plane moved forward".

http://community.discovery.com/eve/forums/a/tpc/f/9401967776/m/4441931059/p/8

An analogy someone brought up was this:
Person 1: If I let go of a bowling ball, it will drop to the ground
Person 2: No it won't
Person 1: Okay, let's see (drops the bowling ball)
Person 2: No, the experiment was wrong, the bowling ball didn't float in the air
Person 1 commits suicide.

justinJan 30, 2008 at 11:42PM

Wow, people still think it won't take off? Embarrassing.

MattJan 30, 2008 at 11:45PM

I always read the problem as whatever forward speed the plane gains is matched by the opposite speed of the conveyor belt- meaning if the plane begins to lurch forward on the conveyor belt the experiment is already a failure because if the plane has lurched forward and the conveyor belt is no longer matching the speed of the plane.

Don't misunderstand- the wheels are there to decrease friction on takeoff- but even the tiniest amount of friction (like, say, the amount the White House Press corps gives the President) is enough when you're increasing the speed exponentially, as one would have to do. Don't give me this "you could have it going 1000 mph! It wouldn't matter!" crap- I'm not talking about 1000 mph or a million mph- I'm talking about an exponentially increasing speed to generate enough friction to keep the plane stationary.

If we're talking 25 mph one way and 25 mph in the other of course the plane takes off- that's not even up for debate.

If we're talking 25 mph one way and a speed which increases at the rate that the plane's thrust moves it forward from a fixed point going the other way (again- we're talking exponential speed increases) the plane sits "like a brick" with the wheels spinning faster and faster until a hole is ripped in the space-time continuum and Doc Brown shows up. Time dialation and length contraction ensue.

MythBusters was very specific tonight- they were only testing the easy-to-get-your-head-around version of the problem- the one that can be tested in the real world. They could have at least acknowledged the other reading and not accuse everyone who doesn't think the plane will fly of thinking a plane is a car- that's just silly.

justinJan 30, 2008 at 11:45PM

If the plane didn't move forward, it wouldn't fly.

But the plane does move forward -- regardless of whether or not there's a treadmill moving in the opposite direction below it -- because the forward movement of the plane doesn't rely on the free-spinning wheels. It relies on the propeller, which propels the plane forward no matter how fast the free-spinning wheels are spinning.

Jens AlfkeJan 30, 2008 at 11:45PM

I hadn't heard this one before ... but this was even controversial? People really thought that something going on with the planes silly little vestigial unpowered wheels would somehow stop the its big beefy engines from pushing it forwards against the air?!

Jesus. I'm at a loss for words.

JedJan 30, 2008 at 11:49PM

that was awesome!!!! i knew it would work. i just can't believe how many people (pilots included) thought it wouldn't take off.

sunflowerflyerJan 30, 2008 at 11:49PM

This is really funny... of course the plane will take off. The plane could care less what the ground under is doing (or the earth for that matter), it only cares about the air over it's wings. The engine will still provide the thrust to push the plane forward THROUGH THE AIR, and it will take off regardless of what the wheels are doing. (unless the speed is so great to do damage to tires or bearings).

It's fun to put someone not used to planes in the copilot seat, and start steering the control wheel off the taxiway. They don't realize your actually steering the plane mostly with the rudder (foot pedals), by the air blowing past it. Of course tight turns require differential braking or some planes have the rudder linked to steerable wheels (many just caster freely).

Note also that icy runways don't really cause too much problems for most small planes, as they really don't need there brakes to slow down. It actually smooths out the landing, and any accidental sideways movement is not much of a problem, as it can be on a dry runway.

Why is this so obvious?... I'm a recreational pilot =]

JedJan 30, 2008 at 11:50PM

that was awesome!!!! i knew it would work. i just can't believe how many people (pilots included) thought it wouldn't take off.

brettJan 30, 2008 at 11:51PM

It's not a physics problem - it's a trick question.

Stewart JohnsonJan 31, 2008 at 12:01AM

I've yet to see a good explanation from any of the people who think the plane will stay on the ground to this central question:

How does the conveyor belt stop the plane from moving?

The original questions does NOT say "the conveyor belt pushes backwards on the plane". That's because the conveyor belt CANNOT push on the plane in any direction but UPWARDS. The conveyor belt cannot put any significant sideways force on the airplane.

Therefore the plane will always move forward, and therefore it will always take off.

Bryan WallsJan 31, 2008 at 12:09AM

The upshot is that if the experiment were performed ideally, then the speed the wheels are turning (as measured by the sort of speedometer that cars use) would be exactly twice the speed of the airplane as the wheels left the treadmill (as measured by a radar gun, say).

DavemurfJan 31, 2008 at 12:11AM

In a related matter, an airplane WILL lift off the ground - it will technically "take off" - while standing still on the tarmac, provided there is a fast enough stream of air blowing over the wings.

This can happen in a strong storm, or even when another aircraft generating enough thrust taxis in front of it.

This is why small-plane pilots "tie down" their aircraft, not just chock the wheels. It doesn't matter whatsoever how fast the aircraft is moving relative to the ground. All that matters is how fast the aircraft is moving relative to the air flowing over the wings.

AlexJan 31, 2008 at 12:13AM

The speed of the plane on the conveyor belt is irrelevant. The plane's forward motion is not caused by the movement of the wheels. In fact the wheels move freely. What pulls the plane forward is the propeller. If the air moves fast enough over the wings, the plane flies. The speed of the plane relative to the ground matters not. The crucial thing is the speed of the plane relative to the air. What creates lift is the air moving over the wings.

tomJan 31, 2008 at 12:13AM

everything's a physics problem, literally. And this falls under the category of everything.

MattJan 31, 2008 at 12:18AM

Stewart- friction. The friction of the wheels- while incredibly slight, would, at exponentially increasing speeds, be enough to keep the plane stationary.

I'm not thinking of a plane as a car, by the way- I hope that's clear- I'm talking about steadily increasing the speed of the conveyor belt to keep pace with the speed of the plane- the only drag on the plane would be the wheels- but as stated in the original problem we apparently have a conveyor belt capable of keeping up with the plane- therefore it would need to increase speed rapidly and endlessly. That plane wouldn't move.

That being said, if it's just 25 mph in opposite directions it'll of course take off immediately. Duh.

patmJan 31, 2008 at 12:19AM

Sigh. So much confusion.

As a pilot, a plane with normal (working) easily spinning wheels WILL be able to accerate THROUGH THE AIR MASS pretty normally once take-off (full) engine power is applied and proceed to take off with no problem.. (as shown on the show). Only effect of the belt is that wheels are spinning much faster than normal.

In the theoretical statement of the problem the belt would have had to accerate backwards MUCH MUCH faster than flight normal speeds to try to get rolling wheel friction to match foward propeller thrust. May take a belt speed of 100's mph -- (and would make even a tiny plane need high speed jet tires). But I suspect that even with the belt going and Indy car speeds it's a lost cause because the engine/propeller can still provide MUCH more forward thrust than any reverse drag from wheel friction. (Even a car going 150 mph straight is expending 95% of it's energy pushing air out of the way rather than wheel/road friction. Even more so for a plane.)

The ONLY simple way I can think of to demonstrate the 'failure to fly' situation is to put OVERSIZE ALMOST FLAT tires on the plane so that rolling resistance is VERY LARGE. At that point the tires rolling on the belt could probably be made to keep matching the forward thrust provided by propeller. So THEN maybe you can force a situation where plane won't accelerate forward on this moving belt.

(And the belt acts differently than low/flat tires on a runway. On a normal runway the plane's slowly gathering forward speed would slowly lift weight off the flat tires and allow an actual takeoff to occur (but with a REALLY BAD landing to follow). But with high enough wheel rolling resistance an increasing belt speed could probably keep up with propeller thrust and prevent any lift and lessening of weight on the wheels -- and plane would stay rolling (poorly) on belt even at full engine/propeller thrust.

That's my two cents on this whole thing.

I can't imagine a pilot willing to risk a real plane in such a setup with such mis-behaving wheels. So I suspect this will stay unproven for a long time. ;-)

ReubenJan 31, 2008 at 12:24AM

I'm amazed.

Not because the plane took off, but because I just read the Mythbusters comments and the number of people who misread the question and who are *still* trying to argue that the plane should have remained stationary is truly extraordinary.

RayJan 31, 2008 at 12:26AM

So the basic problem with this problem is that it can't be defined to mean what some people think it seems like it means.

There are really only 2 possible cases, either the "speed of the plane" is measured relative to the ground, or it's measured relative to the conveyor.

I hope everyone sees that if the "speed of the plane" is relative to the surrounding ground that the conveyor can only move if the plane moves relative to the ground. Therefore, the plane has to be moving forward if the conveyor is moving at all. The wheels will spin twice as fast as they would if there was no conveyor, but that's of no import, and is easily accomplished.

The speed being relative to the conveyor is a contradictory definition. If the conveyor starts at 0 speed, then it can only start moving if the plane starts moving relative to the conveyor, but we already decided that the conveyor is stationary relative to the ground, which means that the only way the conveyor could ever start to move *in the infinitesimal boundary case* is if the plane moved *relative to the ground* in the first place. This is a contradiction to the notion that the plane can't move relative to the ground, and, in fact, a contradiction to the notion that the plane can move relative to the conveyor.

If the plane ever *tried* to move forward, the conveyor would have to *instantaneously* come to the speed required to exert an equal and opposite force on the plane through the wheel bearings, which is a physical impossibility. And that's not to mention that the tires would fail *way* before the bearings, causing the plane to crash onto the conveyor, and the conveyor would have to instantaneously stop in order to avoid flinging the plane backwards, another physical impossibility.

The only way this second definition can remain consistent is if the plane never moves relative to the conveyor or the ground. And the only way that could happen, by Newton's Laws, is if you left the brakes on. Which is *technically* consistent, but a trivial statement.

So we're left with 2 possible meanings of the original puzzle, one of which is sane and easily consistent and easily attained, and one that's contradictory, physically impossible, and insane.

Which definition do you think is the "right" one (assuming this problem has any practical application at all)?

Ryan GrayJan 31, 2008 at 12:31AM

Totally disappointing. Of course, the plane would take off for the reasons mentioned. However, I thought I was going to see the myth as I heard it, which was: the conveyor belt was to counter the plane's forward motion so that it could take off with essentially no runway. Given that, of course I would say it wouldn't work since it would require no forward motion of the airplane relative to the air, however, as we know, the conveyor couldn't prevent the forward motion, so for that reason as well, I knew the version of the myth I heard was wrong. Of course, the version the Mythbusters tested was not this version I'd heard. It's quite common for there to be several versions of a myth, and I think this might be the cause of some of the disagreement.

Lewis TateJan 31, 2008 at 12:31AM

Jason: Please please please make some "HELL YEAH THE PLANE TAKES OFF" t-shirts and sell them. I would stand in line to buy one.

MattJan 31, 2008 at 12:34AM

Ray- we're talking about putting planes on conveyor belts and you want to restrict the discussion and keep it realistic?

Really?

ReubenJan 31, 2008 at 12:34AM

I second Lewis on the t-shirt proposition. If you don't make them, I will.

kimax2Jan 31, 2008 at 12:36AM

l-o-v-e the graphic and that roaches won't make it...still trying to catch up on the whole shaving cream/car exploding bit...

it takes offJan 31, 2008 at 12:39AM

Jason, I'll tell you why people watch this show - that female assistant is cute and charming. I've never been able to watch the show longer than the time frame during which she is on.

It's just on now on the west coast.....where is she? It's been 10 minutes since she last made an appearance. sigh.

greg.orgJan 31, 2008 at 12:40AM

as someone who copped right up front to remembering the assumptions wrong from the original question, I'm kind of amused at how pissed off I get to read replies that start with "No, you're wrong..." and "that's your misconception!"

Makes me glad to not have to attend offsites with know-it-all engineers very often.

And about the Mythbuster twits, the phoniness of their TV enthusiasm is surpassed only by those jokers on Pimp My Ride, who sit around a conference table and try to act [sic] like a checklist is somehow dramatic.

How about a nice, old-school-style science show that's as deadpan as a classroom film? It could still be absurd as hell, content-wise, just throw in John Hodgman and a couple of narrating silhouette heads? Maybe call it Science Mystery Theater 3000 or something?

JoelJan 31, 2008 at 12:45AM

The question as asked allows for only one outcome - the plane taking off.

Now, if the question was instead the control system maintains the velocity of the conveyor belt at the same level as the tangential velocity of the wheels but in the opposite direction what do people believe the answer to be?

Ryan GrayJan 31, 2008 at 12:46AM

Addendum:
A variation of the myth as I heard it, which I just made up, would be that rather than a conveyor belt, there is a really fast headwind, which keeps the plane stationary relative to the ground, but is fast enough for take off. The problem then is that the plane is "flying", but it's not getting anywhere relative to the ground. Remember the version of the myth I heard (above) was some system to have essentially zero runway. So, to get the plane to have some ground speed to get anywhere, you'd have to slow down this headwind, or turn a right angle to it.

ToddJan 31, 2008 at 12:48AM

Wow, lots of disappointed people are still making excuses as to why the plane

took off.

"put OVERSIZE ALMOST FLAT tires on the plane", haha thats my favorite!

Why not just strap the plane down to the conveyer belt?

Alex RossJan 31, 2008 at 12:48AM

Could a plane equipped with fixed ice skates instead of wheels take off on a vast sheet of ice? What about a plane in a strong head wind, does it have to move relative to the ground to take off? Or a plane in a strong tail-wind, does it have to move relative to the ground to take off?

The first question is basically the same as the one the mythbusters considered. (Someone will argue with me I'm sure).

But the point is that a plane taking off has absolutely nothing to do with it's motion relative to the ground. It's the plane's motion relative to the AIR that matters. The whole point of the airplanes engine is to push air. It never pushes ground. The airplanes wings also push air, in a somewhat different fashion.

Think about a car equipped with wheels (but no propellor or jet). Can it take off? If it can, how long will it remain airborne? Can the car take off on the giant conveyor belt? What about a car with (fixed) ice skates, can it take off on a vast sheet of ice?

MattJan 31, 2008 at 12:51AM

Ryan- that would be a really neat no-runway takeoff followed by a really spectacular crash... I'd pay to get in to watch that.

MattJan 31, 2008 at 1:01AM

Consider this version of the experiment...

I'm riding a bicycle on a treadmill. The speed of the treadmill matches the speed of my bicycle. In that case, it's pretty clear that I wouldn't move forward. My cycle's tires are propelling me forward against the surface of the treadmill, but the surface of the treadmill is moving backwards at the same speed, negating my progress.

Now, consider this. There's a handrail on either side of the treadmill. I grab hold of those, and allow my bike's wheels to spin freely.

So, the wheels are spinning at the same speed as the treadmill, and I'm at a standstill.

This is a huge point - it takes no effort to hold myself in place. The treadmill exerts no force on me at all - my freespinning wheels allow negate it completely.

Now, I start pulling on the handrail. Clearly, I'm going to start moving forward. Even if the treadmill speeds up, it can't impede my progress at all. My free-spinning wheels will spin faster (in synch with the treadmill), but I can still pull myself forward with the handrails, with minimal effort.

No matter how fast the treadmill moves, my bike's wheels spin to match, and I can still pull myself forward. That's because I'm exerting my force against the handrails, not the treadmill's surface (as was the case in my first example).

The airplane does the same thing - it's not exerting any force against the treadmill. Nor is the treadmill exerting any force against the plane - the plane's freespinning wheels make sure of that.

The plane's propeller, however, IS exerting a force against the air, which is pulling it forward. Eventually, it pulls against the air with sufficient force to propel it towards takeoff speed.

patmJan 31, 2008 at 1:06AM

Todd, I'm not making excuses for why the plane flew. I'm on your side.

I first stated in my earlier post that of course a plane, with properly working wheels, would accerate forward through the air and down the belt and take off -- regardless of belt speed.

But I can say from experience that small planes take MUCH more engine power to roll on severely underinflated wheels, taking up to 40-50% of engine power rather than the normal 10-20% used for taxiing. So severely underinflated tires would be one way to drastically increase wheel/ground friction to force a takeoff failure. Is it a fair test of the problem? No. But it seemed a simple way to describe what level of increase in wheel friction would be needed before the wheel forces would affect forward plane accerlation.

Joseph AbrahamsonJan 31, 2008 at 1:16AM

I'm with Felipe way up above. What font is that?

oscarJan 31, 2008 at 1:31AM

I thought it was hilarious that they insisted this episode would "quell" the debate or somehow "settle it once and for all."

Stephen CaverJan 31, 2008 at 1:33AM

Kottke, your non-enthusiasm for the greatest television show ever conceived disappoints me greatly. There isn't enough shows like Mythbusters on television.

And, predictably, disagreement about what actually happens to the plane can be traced back to a misunderstanding of the question. Seems like every time I debate somebody it gets really heated then when we come back to the original premise and actually try to understand exactly what is being discussed it ends in agreement.

And/or I get a drink in the face.

AndrewJan 31, 2008 at 1:48AM

I'm watching the show in the late-night rerun, and about halfway through I thought, "I wonder if Kottke did anything for this?" Beautiful.

Logical PilotJan 31, 2008 at 1:58AM

(sigh) It's still an invalid test: If the conveyor was matching the FORWARD SPEED of the plane (as stated in the original question), it wouldn't have moved forward; if it hadn't moved forward, there would have been no air flowing over the wings; if there was no air flowing over the wings, it wouldn't have taken off.

So, yes, obviously: If you don't match the forward speed of the plane, and therefore allow it to still move, it's going to still have air over the wings, generating lift. Obvious result.

If this test could be performed to the original specifications (quite likely impossible to achieve), it would be obvious that the plane would NOT take off. But, I'm so sick of hearing about it, I'm happy to have all the "yay, it took off!" idiots amuse themselves that they think they are correct.

RyanJan 31, 2008 at 2:00AM

@kottke please make tshirts

MarkJan 31, 2008 at 2:02AM

How did you make the "HELL YEAH THE PLANE TAKES OFF" graphic in less than 60 seconds?

DanJan 31, 2008 at 2:02AM

Stephen, there is only one correct way to interpret the question. The people who think the plane should stand still and not fly always end up arguing that the plane speed (measured relative to the treadmill) should equal the treadmill speed (relative to the ground) such that the plane speed relative to the ground is always 0. This is physically impossible, because the treadmill can't apply a force to the plane, as soon as the plane starts moving (relative to the ground) the theoretical treadmill speed should shoot up to infinity. This is because the plane speed relative to the treadmill will equal the plane speed relative to the ground + the treadmill speed. And that has to equal the treadmill speed. So you have treadmill speed equals treadmill speed + plane speed. If you want to get silly with it, as the treadmill speed instantly approaches the speed of light it creates a layer of super hot plasma and generates more heat energy than a thousand atom bombs, vaporizing the plane and sending everything in the area high into the air (so the plane does fly).

The much more sensible and correct way to measure speeds is relative to the Earth, the same way we always measure speeds in everyday usage. So the plane speed (relative to the Earth) is equal to the treadmill speed. As we saw, the plane goes 25 mph forward, and the treadmill goes 25 mph backwards... and the plane takes off. The end. It really isn't complicated or anything.

So you have a choice, the physically impossible paradox of measuring plane speed against the treadmill, or the commonly accepted definition of speed (measured relative to the Earth). Neither way results in the plane standing still.

MattJan 31, 2008 at 2:03AM

I third the t-shirt comments-- I'd be up for one of those.

StubbyJan 31, 2008 at 2:06AM

Hey, Logical Pilot. You're wrong. If the conveyor was matching the FORWARD SPEED of the plane, it WOULD have moved forward. The plane would have been pulled through the air by its engines, dragging its tiny little wheels over anything below.

karanJan 31, 2008 at 2:08AM

One more vote for the tshirt! :D submit to Threadless!

RyanJan 31, 2008 at 2:10AM

@Logical Pilot, the conveyor belt does not apply backward force (in any significant measure) to the plane. It doesn't matter how fast it is going. It is no relevant to how a plane takes off. You are wrong. Live with it.

IF the plane wasn't moving forward then it wouldn't take off. IF. Explain how a conveyor belt stops a plane moving forward when the wheels of a plane apply no forward/backward force to a plane (not a measurably significant one anyway).

What is it with people refusing to accept overwhelming evidence and reason?

MattJan 31, 2008 at 2:11AM

Another vote for the shirt!

MichaelJan 31, 2008 at 2:23AM

This has been really interesting and I wish I had the time right now to read through all the comments. That said, maybe this has gone over already:

I think the reason that a lot of us feel that the plane won't fly is that we know that it won't take off if it isn't moving in relation to the air around us. That being that there's no practical use to researching this problem. We won't be able to make shorter runways if we use conveyor belts because they'd just be incredibly expensive runways with unnecessary treadmills on them.

So the real question that's being asked (I believe) is: "If we need to get a plane up to a certain speed to take off, can't we just put them on treadmills and take off in no space at all?" The answer of course is no, it's the airspeed over the wing that's important, not the speed of the wheels. That's something we all agree on.

Now what if we tried some sort of wind tunnel/tread mill combination? Could that be used to create a practical, short runway?

GalenJan 31, 2008 at 2:25AM

I like this myth a lot, and it's obviously a big topic for debate. As the original question asks, if the conveyor matches the plane speed, it will not take off. This is very simplified, first of all, it depends on the plane. The scaled down version used a plane that could take off almost instantaneously, this is a stretch for the myth, because the bernulli effect is the reason the plane cannot take off. Because the force of the model planes engine is so high relative to its mass, it acts as a small rocket. And we all know that a rocket doesn't require air resistance to take off ,( rockets in space... a vacuum)
sooo they used too small of a plane, or the myth cannot cover all types of planes, Adam's jubulent declaration of the plane only requiring "80ft" to take off proves this point. The thrust of the engine is so great, it doesn't require very much air resistance to take off. but your saying, "with the tarp, there was no air resistance?!?!" RONG! the plane is always accelerating, with the reference frame being the plane and tarp, because it moves by the cones. There is no way Jamie's truck accelerates as fast as a plane, and remember, for air resistance to become negligible, (as in no forward motion) the tarp would have to be moving perfectly with the plane. Also this is nothing like a plane on ice, or a friction less surface. Because if it was frictionless a plane would take off even faster, ( bearing are used to reduce friction therefore making forward motion easier) Obviously the plane took off, but it was still moving but it is generally not testing the principle that the wright brothers used to create their wings. I liked this controversial myth, because of it's physics. But they effed it up big time. For the people who understand the physics of flight (like the pilot!!) this seemed pretty straight forward. Oversimplification, and misunderstanding of how a planes wings, and engine thrust work lead to a defeat. This will defiantly be revisited. And for Christ's sake, They have a physicist on the show! (Grant) they shoulda asked him to math it up!

chrisJan 31, 2008 at 2:27AM

im still confused....

if the wheels and the conveyor belt have nothing to do with the plane taking off, then why do planes have wheels in the first place.

if the speed of the wheels has nothing to do with the plane taking of, then why dont they just put some soft rubber pads on the bottom of the plane?

why do planes have to use such a long runway to take off?

StubbyJan 31, 2008 at 2:29AM

I'm want to identify a good way to explain this to non-believer. If you once believed the plane would not fly but now (correctly) see that it will, what changed your mind? Was there a particularly good comment or thought experiment that flipped your switch?

Garrett C.......Jan 31, 2008 at 2:35AM

Lol, this thread is hilarious... but I have a few comments, and I hope people get them. Seriosuly read on though, I actually tried to convey my flawless points in the midst of this.

Ok, i skipped the last... 403538402 posts, because I got sick of seeing the same arguments without my thought being conveyed at all... I cna only assume this hasn't been said.

The "grounders" keep on saying that the plane CANNOT FLY W/O FORWARD MOTION RELATIVE TO THE GROUND.... ok, good for you for yelling that in my face 500 times. But there is one thing you have not considered... in what other situations will a plane take off without forward relative motion?

Ok, Whoa buddy, you've crossed the line here. Thats what you might be thinking, but I don't see where I can be wrong here. If I am not mistaken, the plane takes off, because of the benoulli effect, yadda yadda yadda. More or less, AIR has to move FAST ENOUGH over the wings. Correct? That is pretty much the main requirement here.

Ok, I wish the mythbusters did THIS experiment which would pretty much put this to rest. Put a giant iron stake in the ground. Run a steel cable downwind, attach to front of plane. Stick this setup in wind tunnel, Turn on giant fans.

WOW! The plane flies! and guess what guys(and gals), theres no forward motion relative to the ground. But, because enough wind is moving across the wings, lift is created, and the plane flies.

Ok. Now bear with me. If IN THEORY (actually I don't know if any plane can actually do this) the propeller can provide ENOUGH wind movement(this is what its job is, after all) to PUSH wind OVER the wings, lift is created. Yes? Ok. myth not busted yet.

Now a key component here is the TREADMILL. This myth wants to say that treadmill is the (bear with me) WIND in the WIND TUNNEL, PULLING(or pushing, whatever) the plane backwards. If you chain the front of the plane to a stake ahead, and you pull the tarp(treadmill, whatever) underneath the plane, are not all of the requirements of this myth completed?( note, plane is not running, to prove my point) A- Treadmill moving same "speed" as plane in opposite direction. plane has no relative motion to ground. Plane does not fly. Physics is true, this is obvious.. no air moving over wings. Myth true???????

Alex Ross said it correctly. A big problem with this myth, that everyone kind of takes into consideration, but not really, but is also an argument( its too early to make sense) is that whole argument with the bike that Alex said, how the external force of the propeller(or chain) affects the plane. Everyone keeps on bringing up the retarded argument that "Oh man, you dumbies, the wheels provide no friction cause of the bearings in them, so the planes forward force easily surpasses that reverse friction force, and it moves forward along the tarp and the flies. OK GENIUS! Standing applause for that man.. ok I'm kidding. Did i not state before those people who kept on yelling "W/O FORAWRD MOTION" in our faces? Guess what! The plane has forward motion!!!! SO THAT IS WRONG. You cannot test hte myth when you don't follow it!!!

Essentially, all of this writing was to prove this one point. THE TREADMILL(Tarp, sheet, etc) IS ONE HUNDRED PERCENT POINTLESS. ABSOLUTELY USELESS!!!!!!

I am 99.999% sure that is a right statement unless some professor from MIT proves me wrong, and I humbly accept that. But hear me out.

The treamill is pointless. You know what can replace the treadmill? AN IRON STAKE WITH A CABLE TO THE PLANE in the back!!!!!!! Lets see whats fufilled,shall we?

Plane's ENGINE is running, providing full force of air. CHECK
Plane isn't allowed forward momentum... CHECK

DO THE TEST NOW!!!!

Now, I think that this is testable , however, results will vary with a plane. If you are going with, IS IT POSSIBLE, then yes you will get a plane that can fly, and you will see why in a second. If it is "for every plane", ... well, thats not gonna happen, and i'll say why in a min.

IN THEORY (this is because I have no clue if a plane like this exists), if you stake the plane in the back to the ground, and you have a propeller engine, that is drastically overpowered to the plane, and in even a better situation, two props on the wings.. WHATEVER> the prop in theory, going fast enough(or if it is large enough) will push ENOUGH air over the wings, for them to create lift, and the plane will take off. Yes? I can be flawed, i'm no aeromechanical dynamical thercanical engineer. Guess what ??? MYTH FREAKIN BUSTED!!!! THE plane FLIES.. A- plane is working. B- no forward momentum(replaced treadmill with stake, because as said before they do exactly the same thing)... assuming the original treadmill can provide so much friction on almost frictionless wheels(like 5000mph) that the plane HAS to go full power and provide X much wing like i just said will be enough for lift.

Now, this will not work with pusher props behind the wings, or jets, because they themselves aren't actually pushing air over the wings.

I hope people understand my theory/point/provingness. It doesn't matter is its a treadmill, stake, whatever, for this myth. Because in this myth, all it wants to do is really say " X is preventing the plane from having forward momentum when its under power, can it take off?" I say that you just need a powerful enoguh engine that will blow enough air over the wings.

As a high school student with one year of physics... Yeah, I say it flies under these circumstances. And bring it, I'm prepared to defend this.

Thanks if you've actually read it, and I think you shouldn't type any replies below if you didn't read it and just scrolled to the end to read my conclusion to bash me.

Thanks

StubbyJan 31, 2008 at 2:40AM

Chris @ 2:27am,

On takeoff, planes have wheels to prevent them from dragging their fuselage across the ground. Other than this support, they apply no significant force to body of the plane on takeoff. On landing, they're used for braking.

Rubber pads could work instead of wheels, but they will possibly burn up from being dragged across the ground. Once they burn up, you're back to the plane dragging its fuselage across the ground. I suppose that if you slicked up the runway with a nice coat of lubricant, rubber pads would work just fine. Like a plane on skis taking off from a frozen lake.

On takeoff, planes use runways to obtain the speed necessary to generate lift from their wings. Lighter planes need less runway. Planes with bigger wings need less runway.

Hope this helps.

Garrett C.......Jan 31, 2008 at 2:43AM

And planes have such a long runway to take off because they need to build enough speed to have enough air moving over the wings to create enough lift to counteract the weight of the plane so that it rises. You'd be surprised how little plane needs to take off. That ultralight takes off in 80 feet, i believe the shortest take off for a bushplane is TWENTY FOUR FEET. I know. You're used to giant jumbo jets and C-130 planes in the army.. thats because, as I said, Jet engines dont work in pushing air over wings it pushes the plane into the wind (Or acts as the pulling stake in the windtunnell) and Giant giant prop planes... well i'm sure a powerful enough engine would rip itself out of the plane lol as my point was saying before

MikeJan 31, 2008 at 2:45AM

A plane's wing produces lift because the air above it flows faster than the air below it (due to the wing's shape). Therefore: no air flow, no lift, no takeoff, period.

So what is relevant is the plane's speed relative to the air (i.e. a ground-stationary airplane can take off in a wind tunnel that blows air over the wings). Haven't seen the show, but if the conv. belt is rigged so the plane does not move relative to the air it does not take off. No ifs and buts, thrust, friction, wheels, bearings and tarmac have nothing to do with this, any 'scientist' going that route towards explaining this is really rather laughable.

Think about it: if this would really work would we be building aircraft carriers and runways the way we do?

Garrett C.......Jan 31, 2008 at 2:47AM

Oh, stubby got it, and he used better puncutation than I did..... See two above lol

MattJan 31, 2008 at 2:49AM

If you start with the assumption that the treadmill will keep the plane from moving forward, then no, the plane won't take off. The plane needs air moving past it's wings to generate lift.

But you're missing the point - the treadmill DOES NOT - CAN NOT - keep the plane from moving forward.

A treadmill can keep a jogger, or a car, from moving forward, because joggers and cars generate forward motion by pushing against the ground. If that ground is moving backwards (in the case of a treadmill), then their forward progress is negated.

But a plane doesn't generate forward motion by pushing against the ground - it generates it by using its propellers to move air. So, the treadmill can spin as fast as it wants - the plane's freespinning wheels will just spin faster - but the plane itself will continue to pull itself through the air. Eventually, it pulls fast enough to take off.

All the treadmill has done is make the freespinning wheels spin twice as fast as they otherwise would have.

Garrett C.......Jan 31, 2008 at 2:52AM

Matt, correct, and the point that I was trying to prove was that IF the treadmill somehow got fast enough, and you had crappy bearings in the wheels to provide enough reverse friction, it WOULD hold the plane back. The whole point of this myth is to capture the attention of someone who won't think about it so they can wonder "Oh man, a plane on a treadmill, NEAT-O"... however, again, its easily proven wrong by the fact that a treadmill provides no friction through the wheels!

Thats why I went with the "chain the plan back" style, cause THAT actually tests the theory that the MYTH REALLY WANTS TO TEST>.... the idiot that made up the myth just threw in the treadmill to piss people off.Like me.

John HJan 31, 2008 at 2:55AM

Why is this even newsworthy? The answer is so obvious. Planes are not propelled by their wheels.. I never understood why this became such a debate. It obviously doesn't matter how fast or what direction the wheels are spinning as long as the plane is propelling itself forward via the propeller.

Garrett C.......Jan 31, 2008 at 3:00AM

Yes, John, but thats not What I-Other people who looked more into it are arguing(NOT INSULTING YOU. i just don't know how to say it) WE're arguing that if you actually look INTO the myth, the principles are that can the plane not move and take off.. hence my novel that i wrote.

Alex RossJan 31, 2008 at 3:02AM

chris asks, “if wheels don't affect the planes ability to take off why does a plane need wheels?”

well, chris... the truth is that a plane doesn't need wheels! there are float planes, which land on water and have no wheels. There are planes with ski's too. The thing is that planes have to spend some of their time on the ground. When they're on the ground they need to remain mobile. Actually, a plane with soft rubber pads on the bottom would probably be able to land onto a large sheet of ice. But on concrete, the rubber pads would have a tendency to stick and so landing would become a dangerous proposition.

Runways are very long because it can take a while for an airplane to generate enough airspeed to lift off. Sometimes, a plane might have a problem while it is taking off and might need to have enough room to slow down without running off the end of the runway and into a building or river or what have you. Also, it's important for a plane to have plenty of room to slow down while it's landing.

I'm wondering if any of the “plane stays on the ground” people can explain why a kite will fly? They don't move relative to the ground, at least not very much. But, you need wind to fly a kite right? If the wind isn't blowing, you can make your own by running around. If the wind isn't blowing and you're standing on a conveyor belt that counters your speed exactly, then you won't be able to generate any air flow for the kite. The kite won't fly. But notice, this has nothing do with the ground or the conveyor belt at all. It has to do with the wind! If a breeze kicks up, suddenly your kite will fly. It doesn't matter if you run on the conveyor belt, or stand still. Actually, running and standing still are the same thing from the kite's point of view, because it's anchor to the ground is holding still.

keep it simpleJan 31, 2008 at 3:08AM

Most of you have your minds so stuck in the physical theory's that you can't see the very basic logic of the situation. The wheels being on the ground have absolutely nothing to do with the air speed and friction that the motor and propellers create. Get it the wheel speed has only an infinitesimal amount of friction but it won't impede the air friction at all. and any of you who claim to have Phd's in physics and think that the plane wouldn't be able to get off the ground are morons, cause it happened, your all just upset that you thought you were so smart when it turns out you were really just stupid.

Boeing BobJan 31, 2008 at 3:13AM

As a pilot myself, I'm kind of embarrassed for the ultralight pilot who thought the plane wouldn't take off. I guess that's because ultralight pilots never have to go to ground school, where you learn about the four basic forces acting on an aircraft? :)

As for the rest of the debate - what we continue to have here is again a case of not really understanding the question. If the question is "Does the plane take off?", then the answer is always yes, it doesn't matter the surface, since at full power the plane will be moving forward unless physically attached to the treadmill.

But if you think the question being asked involves a precondition that the plane is stationary somehow, even though it's at full thrust, then you are asking a different question. What needs to be done is to prove that it's possible for a plane at full takeoff power to have it's thrust completely and exactly negated by wheel friction drag. If you can prove that this is possible, more power to you.

But as a pilot and aircraft engineer - I can tell you that won't be able to. Let's be practical, not theoretical. There isn't a plane in the world that can generate enough wheel friction to match that thrust, because the axles will catastrophically fail before reaching that. If you did engineer such a plane, it wouldn't be able to take off under it's own power even without the treadmill, which means it's not a plane in the first place. This, maybe, is what the Mythbusters need to prove for everyone.

But lets be practiacl. I know it's tempting to dive into the theoretical world of "what if" here, but this is kind of like chasing down perpetual motion devices. Good on paper, but they don't work in reality situations, for simple reasons.

So the question the Mythbusters answered tonight is this - If a plane applies takeoff thrust on a moving treadmill, will the plane take off? For every plane ever built, and every plane that will ever be built, the answer is yes.

keep it simple sucks my buttJan 31, 2008 at 3:14AM

Most of us? Cmon, keep it simple. Let's keep it civil.

nexJan 31, 2008 at 3:15AM

Once again, I'll fight against windmills on conveyor belts and try to clear up some misconceptions:

The original myth, and ALL of the discussion, centered around one central conceit: The plane would have NO FORWARD MOTION RELATIVE TO THE GROUND because of the conveyor belt matching the speed of the plane. NOT the “speed of the WHEELS of the plane” or any other contrived version.

Ah, so you're aware that there are bastardised versions of the 'myth' that make crazy/nonsensical/uninteresting assumptions, and that the belt actually has to match the speed of the plane. I'm intrigued, go on.

Of course the plane is going to take off if it has enough forward motion RELATIVE TO THE GROUND to create the Bernoulli effect required to lift the wing because of the airflow over the wing.

Oh well ... it started of so well, but here you reveal that you know jack squat of some critical concepts involved. Firstly, it has been taught in schools for decades that planes fly because of the Bernoulli effect, but that's not true. It's one of those things where every good pupil can recite the 'correct' answer and get points for it, but no one really understands what's going on ... they just assume that the teacher understands it, but they can't yet because it's very complicated, almost like magic. Which seemed plausible back then, because wasn't it also this mysterious effect that caused water circling down a drain go in one direction on the northern hemisphere and in the other direction in the southern hemisphere? Only no one could ever remember which direction was which ... because that's another myth without a basis in reality (and it has also been busted on TV). So all you could do is learn the 'correct' solution by heart, without fully understanding it. There is a component of force here contributed by the Bernoulli effect, but it's way too weak to trump the other parameters; the real-world result is random. In the same vein, pupils were taught that the shape of a wing makes the air on the top side travel faster along the surface than on the bottom side. You can't really see why this would be the case, but you assume the teacher does, so you just believe it. Well, it's wrong. What really happens is that wings deflect air downwards, which results in the equal but opposite force known as lift. Your intuition might not tell you that this is a totally natural, common-place phenomenon unless you've tried standing on a skateboard and throwing a heavy weight away from you, which makes you move in the opposite direction. But it becomes blindingly obvious when you think of helicopter rotors instead of airplane wings. The helicopter throws/pushes air downwards, right? And the craft lifts upwards as a result, right? So there.

Secondly, the conveyor belt does not cause the air above it to move along with it. Well, it does take a tiny sliver of air with it, and above that is a tiny sliver of turbulence, but the wings of the plane are way above that. So, conveyor belt or not, ground speed has no effect on lift, only air speed. I totally agree that it would have been way cool if the Mythbusters would have done another experiment with the belt running in the opposite direction, matching the speed of the plane relative to the earth directly instead of inversely. (I don't think either variation is canonical.) But the truth of the matter is: it doesn't matter anyway!

I guess it was the original Myth that was flawed, or my understanding of the Myth.

Yes. There is a lot of confusion. Most wordings of the 'myth' are ambiguous, but most people don't even begin to consider that it could be ambiguous, because they find their interpretation so obvious. And rightly so, in your case. You seem to be quite clever, and you came up with a very good interpretation. (Stupider people have came up with gems such as "the speed of the wheels matches the thrust", which is just nonsensical gibberish.) The flaw was that other people had different interpretations, but too often they assumed everyone was on the same page, and you were just talking past each other, on different, err, planes.

Those of us who claimed the plane would not take off without forward motion relative to the ground due to the laws of physics are still correct.

Firstly, this is only correct when by 'ground' you mean the earth and not the conveyor belt (potential source of confusion there!), and secondly, even mentioning this in the discussion at hand is a complete non-sequitur. There never was any component mentioned capable of holding the plane in place. The statement above is correct, but it doesn't matter much.

Is it possible that the description of the puzzle presents an impossible situation?

Some descriptions definitely are impossible, yes. The one that was on Boingboing, for example, didn't make any sense at all.

HTH!

What really scares me is that, in that Mythbusters episode, the 'expert' who'd guessed wrong wasn't some anonymous guy posting to the web and claiming to be a pilot, but for the first time (for me) it definitely was an actual, real-world pilot. In my vividly exaggerating imagination, the sort of people who'll fly a plane without really understanding what keeps it up there are also the sort of people who'll put their poddle in the microwave in order to dry it after a walk in the rain.

MICHAELJan 31, 2008 at 3:26AM

after reading all the comments, i think the spirit of the myth has been overlooked. if you hold onto the handrail of a treadmill, and pull yourself "forward", the treadmill is supposed to match the speed of the wheels EXACTLY. no matter how much you pull, the wheels underneath you will compensate....likewise, if you push yourself backward, the treadmill will accelerate to keep the wheels @ a constant speed. THE MYTHBUSTERS basically had a CONSTANT treadmill...(stall speed)...and yes, of course the plane was able to overcome this, and eventually accelerate..AND TAKEOFF!! woo-hoo....if the treadmill was able to keep the wheel speed constant, the plane would not move ANYWHERE...as soon as the treadmill was removed, the plane would accelerate down, and into, the bow of the aircraft carrier that was so bold to experiment with our brave men. LISTEN TO YOUR PILOTS......THEY STUDIED.

nexJan 31, 2008 at 3:26AM

Eek! When I wrote my above comment, I'd thought I could use blockquote tags ... sorry! The quoted parts are the paragraphs with the ALL CAPS WORDS and this: "I guess it was the original Myth that was flawed, or my understanding of the Myth."

> "As a pilot myself, I'm kind of embarrassed for the ultralight pilot who thought the plane wouldn't take off. I guess that's because ultralight pilots never have to go to ground school, where you learn about the four basic forces acting on an aircraft? :)"

You mean the gal/guy who takes me to my holiday destination in a Jumbo is not prone to getting this wrong? Boeing Bob, this is a real relief for me, seriously. I want to hug you!

AirplaneManJan 31, 2008 at 3:28AM

Read the definitive analysis:
http://www.airplaneonatreadmill.com

Alex RossJan 31, 2008 at 3:32AM

nex,

uhm. bernoulli's principle describes why wings generate lift. Because of the wings shape, air passing over the wing must move farther, than air moving under the wing. Since it moves farther, it becomes thinned out and moves faster. This generates lower pressure. The higher pressure air then actually pushes up on the wing. This Bernoulli's effect, and it is why airplanes fly.

If wings had to deflect air to the ground they would generate TONS of drag, and we probably wouldn't have the fancy, efficient airplanes we have today. Also, how would planes at high altitudes remain aloft? They are so high up, they can't possibly be pushing on the ground!

Go purchase a foam airplane wing. Play around with it a little bit. Move it through the air flat, you'll feel it pushing up! Now turn it slightly, and move it again. It won't push away from the ground, it will push perpendicular to whatever plane (sorry!) you're moving the wing through.

nexJan 31, 2008 at 3:35AM

> "if the treadmill was able to keep the wheel speed constant, the plane would not move ANYWHERE..."
Bullshit! (Whoops, wrong TV show.) Now, you don't mean the speed with which the wheels as a whole move around, right? This would be exactly the speed of the plane, of course. So you have to be referring to the speed with which the wheels turn. At the start of the experiment, the wheels are stationary, at rest, no rotational velocity. Now you want to keep it constant. OK: the wheels will therefore never turn. What does this mean? Simple: the surface of the conveyor belt moves along with the plane, tracking its ground (the 'real' ground here, i.e. earth) speed exactly. The wheels have constant speed now, but the plane accelerates and takes off exactly as on a normal runway.

> "if the treadmill was able to keep the wheel speed constant, the plane would not move ANYWHERE"
As I said, bullshit!

HTH!

(My procrastinating ass is sorry for posting three in a row ...)

MICHAELJan 31, 2008 at 3:40AM

are you drunk nex?

mateoJan 31, 2008 at 3:42AM

The problem is poorly worded but brings up many interesting ideas. I have flown planes similar to the one in mythbusters and I am also majoring in physics, so I hope I can provide some insights.

The main point I can see is that the problem is trying to demonstrate Newtons 1st law; objects at rest stay at rest unless acted on by another force. It is trying to show that mass has inertia, and if you have frictionless wheels under any mass, then moving the ground under said mass in any direction will not cause the mass to move.

Of course, to complicate this point, the mass is a plane. The speedometer in a small prop plane measures its speed relative to the air, not the ground (unless you've got a gps system or something measuring speed). A plane like the one shown is perfectly capable of flying into the wind while actually moving backwards relative to earth. In other words, if you are in a plane you could look down and watch yourself move backwards relative to the earth, as long as the wind is moving faster relative to the earth than the plane is relative to the wind.

So, onto the problem. First we use the physics model: You sit in your plane on the treadmill. They start the conveyor belt, and assuming no friction, nothing happens. You start the engine, and the thrust of the prop moves you forward relative to the ground. But wait, the treadmill speeds up to keep you in place -- except it does nothing as Newtons 1st law dictates. So the problem breaks down here. It both demonstrates that the plane will move forward (newtons 2nd law)regardless of the treadmill (1st law), and negates itself by saying the treadmill will keep it in place, when the treadmill has no say in the matter.

A fundamental problem here is this physics model. If you model the wheels and surface as frictionless, the wheels wouldn't even be spinning, so the entire plane is frictionless relative to the ground. In anycase, if you discard the problems requirement at this point that the treadmill keep the plane from moving forward relative to the earth, then the plane will slide without friction forward and eventually takeoff at some point away from your starting point, as if the treadmill never existed.

Now what would happen in the real world? I believe this would be dependent on many variables such as: type of plane, surface of treadmill, coefficents of friction of tires, of wheel axles, wind speed, etc., which could make for very different outcomes. But this is what I would guess before I saw the show: They start the treadmill the moment you start your plane. The coefficent of static friction means you will move backwards at some rate. You start the engine of the plane and it provides some thrust. The wheels overcome the static friction and lurch you forward a bit because kinetic friction is less than static friction. You would begin to move forward, but again we run into the problem of the treadmill trying to hold you in place. It can't. BUT, if you made the surface/wheel axles so full of friction that it effectively held the plane in place, here is what would happen: The plane would not take off unless met with a wind with a speed almost as great as the planes takeoff speed. A prop does not provide that kind of lift, it provides a force to accelerate a plane to a speed at which the speed of the wind relative to the wing is great enough to provide lift. I saw someone mention a rocket. This is not the same problem. The problem involves a wing and lift, while a rocket does not need lift to takeoff. A rocket could fly on the moon, a prop plane could not.

Here is the lift problem simplified: You get in the plane on the runway instead of the treadmill. You put the breaks on the wheels and then power up full throttle. Disregarding a freakish gust of wind, you will NOT take off. You must be moving forward relative to the wind to generate lift. I hope this clarifies some of this.

Sorry for the novel, I didn't intend to write so much, but that's insomnia for ya.

MikeMJan 31, 2008 at 3:46AM

Ray, above, nailed it.

But for your amusement, and for those still pondering, I submit this, which I wrote prior to seeing it all laid out in the open :

OK, I 'm really going to blow your minds here. Not only will the plane take off, but a car-glider, powered only by it's wheels, will do the same thing.

Let's slide into this backwards, looking first at the moment of takeoff. Consider the takeoff moment for a plane:

Plane going forward at 100 mph.
Conveyer belt going the other way at 100mph.
Plane wheels spinning madly.
Plane takes off.


Now imagine a car with large glider wings. Could it be in the above takeoff scenario: going forward at 100mph (relative to earth), with the conveyor going backwards at 100mph (relative to earth)? Sure, and the speedometer will happily read 200mph (pretty beefy engine!). Lucky us, 100mph happens to be the takeoff speed for the car-glider. Whoosh--off it goes, settling down moments later somewhere nearby.

Back to the beginning of the process. Note that if the car is stationary, then per stated conditions, the belt is stationary. Can't have a stationary car and a moving belt. If the car begins moving forward, the belt begins moving backwards at the same speed. Car moving 1mph, belt 1mph, speedometer 2mph. Carry that relationship forward until takeoff speed is reached.

MICHAELJan 31, 2008 at 3:46AM

THE ONLY REAL QUESTION ON THIS MYTHBUSTERS EPISODE IS ..............did the treadmill match the rotation of the wheels on the plane?
correct answer.....NO
we might be able to correctly test this myth in another 500 years, but as for now...if the wheels are turning @ the same velocity as the treadmill, the only way this plane is flying is with a HEAVY HEADWIND

Alex RossJan 31, 2008 at 3:51AM

MikeM,

The only problem with your analysis is that the car's speedometer will read relative not to the earth but to the treadmill, as that's what it's wheels are touching. Presumably, the treadmill's speed will be adjust so that no matter what the cars speedometer is reading, the car will not actually be moving relative the earth.

MICHAELJan 31, 2008 at 3:52AM

BY THE WAY...IF THE TREADMILL IS READING 1 MPH.....THE WHEELS OF THE PLANE ARE MOVING 1 MPH..........not 2

DanJan 31, 2008 at 3:54AM

But Michael, that was not the myth, and it never was. The myth was the speed of the plane. Speed of plane is measured against the Earth, not the treadmill. I will explain... AGAIN:

The Noflys claim that the experiment was performed incorrectly. Their issue is that the speed of the plane should be measured relative to the treadmill, and that the speed of the treadmill should be measured relative to the ground. Thus, the condition that the plane speed equal the treadmill speed implies that the speed of the plane and the speed of the treadmill cancel out and the speed of the plane relative to the ground is 0. So because the speed of the plane relative to the ground was not 0, the experiment was not performed correctly.

This is the incorrect interpretation for many reasons (the correct interpretation is that the speed of the plane is measured relative to Earth, just like everything else): First off, this interpretation uses two separate reference frames, the treadmill and the ground. Nowhere in the question did it implicitly state the reference frames, but if speeds are being compared (and they are) and the reference frame is not stated (and it isn't), it would be a safe bet that both speeds should use the same reference frame. Why would one state that the plane speed equals the treadmill speed if the two weren't measured in relation to the same object?

The second reason that the Nofly interpretation is incorrect, is that the common reference frame that we almost always use for everything is the Earth. If I say that a car is going 50 mph and don't state with relation to what, it is safe to assume that it is going 50 mph relative to the Earth, and not some bird in the sky or the planet Venus. When I am on a moving sidewalk at the airport, I consider myself to be moving faster. This is because I measure my speed relative to the Earth, and the moving sidewalk speeds me up relative to the Earth.

If you measure the speed of the plane relative to the Earth, on takeoff, the plane is going 25mph. The treadmill is also going 25mph in the other direction. The initial conditions are satisfied. The plane flies... it's simple, it's obvious. But apparently it isn't obvious enough.

Now, let's look at it from the Nofly perspective. If the experiment were performed the way they want it. As soon as the plane begins to move (rolling friction is already overcome so the treadmill has no frictional effect), the treadmill must instantly spin up to such a speed that it applies a force which slows down that movement. How might this work? You can't apply a force through an ideal free wheel. For theoretically perfect bearings and no air viscosities it is impossible. The treadmill cannot slow down the airplane, so it accelerates to the speed of light, time comes to a stop and the universe implodes. So in the theoretical world, it is a nonsensical assumption to make.

Now, what about the real world? Well industrial bearings go up to many thousands of rpm. A 2ft diameter plane wheel going 25mph spins at about 350 rpm. So the treadmill would have to go about 10 times faster than that to begin to push the bearing past its working zone and begin to create any frictional forces which can slow down the plane. We'll say at 250 mph the treadmill can start to slow down the plane (just the very light amount of thrust that got the plane to start moving). But wait, in the real world air is a viscous fluid. If this treadmill is very long and very wide, we can assume laminar flow over the surface. And since fluids have a no-stick condition at the surface of the treadmill, the treadmill will pull air along with it. Normally this would be a very thin layer, but it depends on the size of the treadmill. You can use the Navier-Stokes equation to determine the speed at a given height. If the treadmill is large (the size of a runway), the velocity of the air moved by it will indeed by quite high, especially considering that the Cessna's wings are not that high above the treadmill surface. The wind speed will become high enough that it will lift the plane up before the treadmill melts the bearings. The drag from the incoming air is counteracted by additional thrust from the plane's engine. So the plane flies in this case as well.

So no matter which way you cut it, the Noflys are wrong. Their assumption is silly and nonsensical, but it still leads to them being wrong no matter what.

nexJan 31, 2008 at 3:57AM

... make that four posts in a row ... I can't resist trying to educate Alex Ross, above.

> "bernoulli's principle describes why wings generate lift."
That's what you learned in school. It's wrong. If you're as old as me, you were also told as a kid that spinach contains lots of iron. Doesn't mean it's true and still state-of-the-art scientific knowledge.

> "Because of the wings shape, air passing over the wing must move farther, than air moving under the wing. Since it moves farther, it becomes thinned out and moves faster."
No! I assume you're confused because that diagram in your textbook that illustrated the flow of air over the wing made you think the 'upper stream' and 'lower stream' must meet up behind the wing at the same time (counting from when they were parted by the wing's front edge). When in fact, nothing forces them to do that. Yes, the air passing over the wing must move farther, but that doesn't necessarily make it move faster. Also, when you say it is 'thinned out', you're considering only the variable of speed. What about the other variable that compresses the air above because it's moving over that bulge in the wing, causing the lines in the diagram to become smooshed (is that a word?) together? The diagram is actually misleading, it exaggerates the shape of the wing to make it easier to see, but in the real world, the wings are pretty much flat. This is why some planes can fly upside-down.

> "The higher pressure air then actually pushes up on the wing."
That's a myth. Many people learned it in school that way, but it's wrong. Go look it up on Wikipedia.

> "If wings had to deflect air to the ground they would generate TONS of drag"
First of all, they don't deflect air to the ground (sorry if I'd said it that way, I'm not a native English speaker, please have mercy), they deflect air towards the ground. The plane is not actually pushing on the ground! Except for very low altitues, which is the ground effect and results in a much reinforced lift. Again, go look it up. Secondly, now I'm confused, for a change. Are you saying that helicopters don't deflect air towards the ground? Or are you saying that the airfoiles on a helicopter's rotor are working on a completely different principle than the airfoils on a fixed-wing craft?

> "Now turn it slightly, and move it again. It won't push away from the ground, it will push perpendicular to whatever plane (sorry!) you're moving the wing through."
The component of the force that generates LIFT (which, by definition, means away from the ground) still points straight up. When banking, of course there is a second component that makes the plane turn and also drift sideways. That other component is irrelevant here, we're talking about what keeps planes up in the sky, not what makes them go in circles. I totally appreciate the word-play, though :-)

MICHAELJan 31, 2008 at 4:01AM

if you guys cant explain your position in a paragragh.....quit talking

DanJan 31, 2008 at 4:03AM

MICHAEL says: "Ooga booga, too many words, me confused, don't read so good"

mateoJan 31, 2008 at 4:05AM

Dan said:

"If you measure the speed of the plane relative to the Earth, on takeoff, the plane is going 25mph. The treadmill is also going 25mph in the other direction. The initial conditions are satisfied. The plane flies... it's simple, it's obvious. But apparently it isn't obvious enough."

So then the problem boils to this: Can a given planes engine provide enough thrust to reach double its normal takeoff speed?

Is that it?

MICHAELJan 31, 2008 at 4:05AM

not confused, einstien said if u cant explain your position simply, u dont understand the problem........keep talking.

mateoJan 31, 2008 at 4:07AM

damn typo...

So then the problem boils down to this: Can a given plane's engine provide enough thrust to reach double its normal takeoff speed?

Is that it?

MICHAELJan 31, 2008 at 4:08AM

airspeed........how do u accelerate to takeoff velocity, if your wheels are spinning at the same velocity as the ground???????????

Alex RossJan 31, 2008 at 4:08AM

nex,

You took the bait, and I am glad. Wikipedia actually has a pretty great article on Bernoulli's effect, and I think that if YOU read YOU'LL educated. Here is the link, so you don't have to go looking. http://en.wikipedia.org/wiki/Bernoulli's_principle. Scroll down to the part entitled “A common misconception about wings.”

The reason that (some) planes can fly upside down, actually has to do with the shape of their specialized wings. They have a more symmetric, tear-drop shape. The pilot changes the wings angle-of-attack to create the bernoulli effect. Wings like this can fly manage to fly upside down, but not very efficiently.

I hope you don't have too much trouble digging the hook out of your cheek. :)

DanJan 31, 2008 at 4:09AM

Why keep talking if you are content to ignore what I say and wallow in your own ignorance? Sticking your head in the sand does not make you correct, it makes you an ostrich.

MICHAELJan 31, 2008 at 4:10AM

airspeed....how do you reach takeoff velocity, if your wheels are moving at the same speed as the earth?
HURRICANE

mateoJan 31, 2008 at 4:13AM

MICHAEL... the wheels don't matter. Think of a plane on skis and the treadmill as covered in snow.

MICHAELJan 31, 2008 at 4:13AM

I DONT TRUST WIKIPEDIA........quote another source

MICHAELJan 31, 2008 at 4:19AM

thats my POINT mateo...the wheels dont matter......the airspeed is ALL that matters.....the "experiment" the mythbusters conducted is flawed because they could not match the velocity (exactly) of the wheels under the plane to the "earth" .......when/if they do, they will discover that the plane cannot take off because the wings will not function with zero airspeed.

Alex RossJan 31, 2008 at 4:21AM

Micheal,

Perhaps you'll have the patience to read this website then: http://howthingswork.virginia.edu/airplanes.html

The University of Virginia seems like a reputable source.

FibbsJan 31, 2008 at 4:26AM

Dude. It's a state school.

Alex RossJan 31, 2008 at 4:27AM

nex,

A helicopters blades are just wings fixed to a central hub. The wings are spun, generating lift. This lift occurs due to the Bernoulli effect.

MICHAELJan 31, 2008 at 4:27AM

originally, i thought the myth was asking if the the plane could takeoff with a c-belt working FOR the plane.....like a catapult .....i think it absolutely insane to think that if you could match the wheel speed of ANY aircraft (exactly, and opposite) that it would do anything other than be a wonderful flowe pot.

DermoJan 31, 2008 at 4:32AM

Lying. But for what purpose? Anticipating the next post with the dignity of a dog belonging to Pavlov.

MICHAELJan 31, 2008 at 4:33AM

thats a great website , alex.....thank you, how does a 747 takeoff from a runway of ice, with a dumptruck parked at its nosegear?

Alex RossJan 31, 2008 at 4:37AM

It moves the dumptruck.

nexJan 31, 2008 at 4:41AM

Alex Ross, I'm glad you read my lenghty reply, did the research, and came back to inform me! Turns out I've been correct in everything except my stupid, stupid misunderstanding that it isn't Bernoulli's effect at work there, when actually the truth is that Bernoulli's effect is just that nasty thing high-school students (me included) fail to understand fully, which is why it's better to explain the situation differently. And you have been correct in everything except that you believed that airfoils aren't throwing air downwards in order to generate lift. Now we've both learned something and (I hope) are on the same page; this is great! Thanks for your patience with me.

> "A helicopters blades are just wings fixed to a central hub. The wings are spun, generating lift. This lift occurs due to the Bernoulli effect."
Yes. And when you get out of a helicopter while the 'wings' are still spun, you can feel that they're essentially a huge fan that throws air downwards at you.

> "I hope you don't have too much trouble digging the hook out of your cheek. :)"
It hurt a bit, but, as some famous scientist has said, it doesn't matter for how long a researcher strongly believed in a theory and how devastating it may at first be to be proved wrong, the joy of enlightenment outweighs that blow and the true scientist always is happy to embrace the superior teaching. I can't find that quote or its source right now, so this quote by Stephen Jay Gould will have to do:
>> "The story of a theory's failure often strikes readers as sad and unsatisfying. Since science thrives on self-correction, we who practice this most challenging of human arts do not share such a feeling. We may be unhappy if a favored hypothesis loses or chagrined if theories that we proposed prove inadequate. But refutation almost always contains positive lessons that overwhelm disappointment, [...]"

Oh, and please note that Wikipedia still explains that the "equal transit-time theory" is a fallacy. This is the wrong explanation of Bernoulli's effect many of us have been taught in school. In the same section, it also says, "However, it appears some people have incorrectly assumed that the fallacious nature of this equal transit-time theory extends to Bernoulli’s Principle, and that Bernoulli’s Principle is also a fallacy when applied to the lift generated by a wing." So both of us have a crow to swallow ... could you pass the salt?

Obviously my self-esteem has hit an all-time low and I desperately want to justify my position some more; I guess this affords me the level of dignity of a dog belonging to Pavlov :-)

MICHAEL says:
> "are you drunk nex?"
Have you run out of logical arguments and therefore deemed it appropriate to resort to irrelevant ad-hominem attacks, MICHAEL? Are you so resistant to learning something new that you'll keep grapsing for straws when you're already at the bottom of the sea, just so you'll never have to admit to having made a mistake? No? Good! :-)

> "THE ONLY REAL QUESTION ON THIS MYTHBUSTERS EPISODE IS ..............did the treadmill match the rotation of the wheels on the plane?
correct answer.....NO"
So? This proves nothing. It's meaningless and nonsensical to specify that the speed of the conveyor belt's surface relative to the ground has to match the speed of a point on the wheel's outer circumference around the axle. Why? Simple: as the wheels spin more or less freely around their axles, there's absolutely nothing the conveyor belt could do to enforce this constraint, even if it was logically possible to do so. Yes, it is only logically possible as long as the entire plane remains stationary relative to the ground. So? This doesn't mean the belt has the power to hold the plane in place. (A implies B) does not imply (B implies A). An example for those not trained in formal logic: When it rais, the street becomes wet. This does not mean that if the street is wet, it must have been raining. The water could have come from a fire hydrant.

> "if you guys cant explain your position in a paragragh.....quit talking"
Look, we do what we can to explain the situation so even you can understand it, but we can't work magic. If you can't understand a one-paragraph explanation (several have been provided), the 'teacher' may have failed, but that doesn't mean he's wrong.

> "So then the problem boils to this: Can a given plane's engine provide enough thrust to reach double its normal takeoff speed? Is that it?"
No. Take-off speed is air speed, and a plane always takes off at its take-off speed, it doesn't have to accelerate to twice that, even if a hypothetical speedometer connected to the wheels would show the greater number.

> "how do u accelerate to takeoff velocity, if your wheels are spinning at the same velocity as the ground???????????"
Look, 'einstien', the ground isn't 'spinning'. And anyway, you're measuring the velocity of the ground in relation to ... what? If you can't explain your position simply (let alone coherently), you don't understand the problem!

> "how does a 747 takeoff from a runway of ice, with a dumptruck parked at its nosegear?"
The pilot will politely ask someone to get the damn truck out of the fucking way. Now go back under your bridge, troll.

DanJan 31, 2008 at 4:43AM

Don't forget the Coanda effect. You couldn't fly without it

DanJan 31, 2008 at 4:45AM

Michael... if only you understood the question. I explained it to you, but you refused to even read it. I can try again, but you will still refuse to see what you don't want to see:

The Noflys (Michael) claim that the experiment was performed incorrectly. Their issue is that the speed of the plane should be measured relative to the treadmill, and that the speed of the treadmill should be measured relative to the Earth. Thus, the condition that the plane speed equal the treadmill speed implies that the speed of the plane and the speed of the treadmill cancel out and the speed of the plane relative to the Earth is 0. Because the speed of the plane relative to the Earth was not 0 on the show, the experiment was not performed correctly.

This is the incorrect interpretation for many reasons (the correct interpretation is that the speed of the plane is measured relative to Earth, just like everything else): First off, this interpretation uses two separate reference frames, the treadmill and the ground. Nowhere in the question did it implicitly state the reference frames, but if speeds are being compared (and they are) and the reference frame is not stated (and it isn't), it would be a safe bet that both speeds should use the same reference frame. Why would one state that the plane speed equals the treadmill speed if the two weren't measured in relation to the same object?

The second reason that the Nofly interpretation is incorrect, is that the common reference frame that we almost always use for everything is the Earth. It is referred to as "the universal reference frame". If I say that a car is going 50 mph and don't state with relation to what, it is safe to assume that it is going 50 mph relative to the Earth, and not some bird in the sky or the planet Venus. When I am on a moving sidewalk at the airport, I consider myself to be moving faster. This is because I measure my speed relative to the Earth, and the moving sidewalk speeds me up relative to the Earth.

If you measure the speed of the plane relative to the Earth, on takeoff, the plane is going 25mph. The treadmill is also going 25mph in the other direction. The initial conditions are satisfied. The plane flies... it's simple, it's obvious. But apparently it isn't obvious enough.

Now, let's look at it from the Nofly perspective. If the experiment were performed the way they want it, as soon as the plane begins to move (rolling friction is already overcome so the treadmill has no frictional effect), the treadmill must instantly spin up to such a speed that it applies a force which slows down that movement. You can't have the plane moving (relative to the Earth), or else the treadmill is going slower than the plane (treadmill relative to Earth, and plane relative to treadmill). How might this work? You can't apply a force through an ideal free wheel. For theoretically perfect bearings and no air viscosities it is impossible. The treadmill cannot slow down the airplane, so it accelerates to the speed of light, time comes to a stop and the universe implodes. So in the theoretical world, it is a nonsensical assumption to make.

Now, what about the real world? Well industrial bearings go up to many thousands of rpm. A 2ft diameter plane wheel going 25mph spins at about 350 rpm. So the treadmill would have to go about 10 times faster than that to begin to push the bearing past its working zone and begin to create any frictional forces which can slow down the plane. We'll say at 250 mph the treadmill can start to slow down the plane (just the very light amount of thrust that got the plane to start moving). But wait, in the real world air is a viscous fluid. If this treadmill is very long and very wide, we can assume laminar flow over the surface. And since fluids have a no-stick condition at the surface of the treadmill, the treadmill will pull air along with it. Normally this would be a very thin layer, but it depends on the size of the treadmill. You can use the Navier-Stokes equation to determine the speed at a given height. If the treadmill is large (the size of a runway), the velocity of the air moved by it will indeed by quite high, especially considering that the Cessna's wings are not that high above the treadmill surface. That means that as the treadmill picks up speed (remember we are talking about a stupidly fast treadmill now), it begins to slow down the plane not by wheel friction, but by wind, the same wind that gives planes lift. The harder the plane's engines push, the faster the treadmill moves, and if the bearings can hold out, the more lift the plane will get, eventually getting airborne and taking off.

So no matter which way you cut it, the Noflys are wrong. Their assumption is silly and nonsensical, but it still leads to them being wrong no matter what.

TreyJan 31, 2008 at 4:54AM

Here's my question:

If you believe that a treadmill moving in the opposite direction of a plane at a speed equal to the speed of the plane will prevent it from moving forward, I'm assuming you believe that the speed the wheels are spinning at can counteract the force of the plane's propeller.

If that is true, and we're assuming that if a plane's wheels are spinning fast enough that they can prevent the propeller on the plane from moving the plane forward, wouldn't that also mean that if, while in flight, a plane's wheels started spinning fast enough in the opposite direction the plane was traveling, it could feasibly cause the plane to stop moving forward and crash?

Is there a hole in my logic anywhere? And does this scenario seem unlikely to anyone else?

TreyJan 31, 2008 at 4:54AM

Here's my question:

If you believe that a treadmill moving in the opposite direction of a plane at a speed equal to the speed of the plane will prevent it from moving forward, I'm assuming you believe that the speed the wheels are spinning at can counteract the force of the plane's propeller.

If that is true, and we're assuming that if a plane's wheels are spinning fast enough that they can prevent the propeller on the plane from moving the plane forward, wouldn't that also mean that if, while in flight, a plane's wheels started spinning fast enough in the opposite direction the plane was traveling, it could feasibly cause the plane to stop moving forward and crash?

Is there a hole in my logic anywhere? And does this scenario seem unlikely to anyone else?

Alex RossJan 31, 2008 at 4:55AM

nex.

I too saw that bit. So yes, we were both partly right, and both partly wrong. Isn't that the damnedest thing? I learned something today, and I'm glad you did too! Sorry about that dig about the hook, but I just couldn't resist! I had looked the wikipedia article up, before you suggested that I do so. Anyway, I thoroughly enjoyed the discussion and am better for it.

Actually, I was reading some more about wings, and it turns out that even the TOP of a wing manages to throw air downward! WTF?! That's totally bizarre! Actually, if you're willing to do a little more reading this thread is pretty interesting: http://www.pprune.org/forums/archive/index.php/t-6656.html

My self esteem is ok for the most part. I'm used to being wrong (married). (Just kidding honey!) But I am feeling a bit sheepish that it took me so long to realize that Michael is just trolling. Dan! He's a troll, ignore!

MICHAELJan 31, 2008 at 5:00AM

nope, im all fer the "learning derby"........i worded it incorrectly on the 747, which i suspect is the cause of our disagreement on this thing.....wording of the myth....look a@ http://www.airplaneonatreadmill.com.....i still say if the wheels are spinning @ the same velocity as the "enemy" , there is no way it can take off......the mythbusters had a relitavely constant "treadmill" that allowed the plane to accelerate, therefore take-off.....its not physics we are arguing, it is semantics.

MICHAELJan 31, 2008 at 5:06AM

thanks y'all...always like the friendly disagreement...............;)
see ya on the chessboard

nexJan 31, 2008 at 5:24AM

I found a mistake in the post on airplaneonatreadmill.com:
> "and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off? No."
The conclusion would be correct assuming that premise, but the premise is surreal. In order to keep the plane stationary relative to the ground, the pilot wouldn't be allowed to turn on the engines in the first place. Once they're running and generating thrust, the c-belt operator can't do anything to hold the plane in place. (Except in those situations, already mentioned by many posters, in which the belt would accelerate beyond light speed in a microsecond and the universe violently implodes, or something like that. Which obviously neither works in a thought experiment with ideal, friction-less wheels, nor in the real world.) Note that you can 'prove' anything when you start out from a wrong premise. Consider the following statement: "If the circumference of a circle equals its radius, then the pope is a Protestant." Think about it. It's true, literally!

Alex RossJan 31, 2008 at 5:33AM

oh nex. you just opened a big can of worms... i'm outta here!

RyanJan 31, 2008 at 5:48AM

@Michael

As long as the contact between the plane and the ground are practically frictionless then the wheels, sleds or whatever else is on the bottom of the plane is irrelevant.

The wheels of a plane have two purposes:
1. Stop the plane from lying belly down on the ground
2. Provide a frictionless surface for take off

They are free spinning. The impart no significant force to the plane. They simply provide a frictionless surface for the plane to rest on, so the engines can push the plane through the air.

If the plane goes forward at 100mph and the treadmill rotates backward at 100mph, the plane still goes FORWARD at 100mph. The wheels, which are simply free spinning, spin faster to 'compensate' for the backward movement. The plane is getting thrust from the interaction of the engines and the air, NOT the wheels and the ground. The wheels are specifically to remove the friction that the ground would otherwise have with the plane.

bernJan 31, 2008 at 5:55AM

Haven't read all the comments so someone may have said this already. The plane's engines don't push on the tarmac, they push on the air. And it's the plane's relative speed with the air that gives it lift. Make the whole problem easier to understand by thinking of a sea-plane - it don't have wheels.

Not A Believer!Jan 31, 2008 at 7:15AM

It's a lie! It's all a lie!

I cannot accept their findings as they did not follow a method that I approve of, one that will guarantee that I am right that it's dumb to believe that an airplane can take off from a conveyor belt. Their test was stupid and not done correctly, the airplane was MOVING and that is so obviously wrong that I'll stop watching their show , their "treadmill" should have been moving much faster than the plane.

No matter what they say or prove, I cannot be made to believe that an airplane can take off from a conveyor belt. Better luck next time Myth-"busters".

Fred Derf of neowin.netJan 31, 2008 at 7:39AM

The entire point of this question was to root out the people who thought the plane would remain stationary. This exposes the people who think of a plane as a winged car.

JimJan 31, 2008 at 8:15AM

I was thinking this morning that they should have also shown the model plane with no wing on the treadmill. Everyone is hung up on the wind over the wing. But with no wing the plane would have still moved forward. It's all about the prop and the air. Not the wheels, wing and ground.

John SmithJan 31, 2008 at 8:18AM

The airplane will fly.

REWARD - to anyone who can build a conveyor that will actually hold the airplane stationary. You can use a model airplane, or a real one. And you can run the conveyor belt at any speed you like (slower, equal to, or faster than the airplane's forward motion).

I think my money is safe.

I'd also like to buy one of the 'The Airplane Will Fly' t-shirts! :)

cmcaJan 31, 2008 at 8:34AM

Two different situations that help me understand this:

1) Stand on a treadmill wearing rollerskates. Hold on to a chain that is attached to the wall. Treadmill works as above. Pull on the chain. No matter how fast the treadmill moves, if you pull on the chain, and the chain gets shorter, you will move forward. If you had wings and pulled fast enough, you would take off.

2) Bolt an airplane's wheels to the ground. Turn on the jet engine. If the engine is strong enough, the plane will simply (well, no so simply, but whatever) tear off of the bolted wheels and move forward.

Also, sign me up for a "The Airplane Will Fly" t-shirt.

Saint FnordiusJan 31, 2008 at 8:38AM

All in all, if you think about it the only point of this mental experiment (the plane on a treadmill) is to force future engineers (and to a lesser extent pilots) to stop considering the ground in forms of thrust, as even on the ground the plane relies upon airspeed. That's why you require less space to take off or land in a headwind - it's the speed relative to the wind that matters.

The other purpose of the thought experiment is to "cure" the engineer/pilot of thinking the wheels play a role in takeoff thrust. The plane pulls itself through the air, and the wheels merely reduce the friction with the ground.

However, this goes against intuition, that's why we tend to look for reasons why it won't fly. If the plane is flying in relation to the air but not the ground, much like a kite, our intuition screams at us that it is wrong.

So remember, the thought experiment says nothing about cancelling out movement in the air, only cancelling all ground speed. Once contact with the ground is broken by even a millimetre, the conveyer belt no longer matters.

KenJan 31, 2008 at 8:42AM

I cannot believe that people are still arguing about this.

The problem never stated that the conveyor belt would keep the plane stationary. It said that the conveyor belt would match the forward speed of the plane. Any argument that begins with "if the plane isn't moving forward" makes my head explode.

greg.orgJan 31, 2008 at 8:44AM

sign me up for a t-shirt, too. and a Onesie.

and FTR, the reason I won't watch the show again is not the science; it's the beret.

HirodaJan 31, 2008 at 9:17AM

The NO FLY party's main flaw of thinking is that they do not consider a moving object with a NET SPEED of zero (0) as moving at all.

Consider a satellite in geosynchronous orbit. It is not moving relative to a position on the Earth's surface, thus, with a position of reference from the Earth's surface the satellite would not be moving at all. However, the satellite is in fact moving at a very high velocity (speed with direction) that is in effect moving with the Earth's rotation.

Thus this is why a satellite stays in that position exactly. It is rotating around the Earth at a greater speed than the Earth is rotating, in order for it to stay at the same place in reference to a point on the Earth's surface.

In this case, the satellite has a forward speed, a non-existent drag coefficient, no lift (as it is maintaining an orbit above the surface of the earth), and Earth's gravity is affecting it.

If the Earth had no atmosphere (no air friction), and the satellite had a wheel extending to the surface of the Earth, the wheel would only be spinning relative to the Earth.

Replace the satellite with an airplane, put back the atmosphere in the Earth, and put an engine on the plane. Put back in the thrust vector from the plane's engine(s), put back the drag coefficient, and just say that the plane is just above the ground. The wheel would still be only spinning very fast.

Actual air speed and indicated air speed on an aircraft are two very different things. The plane will take off because there is a certain threshold that the plane will reach that will enable it to gain lift and fly, regardless of whether the wheels are still on the ground or not.

On aircraft carriers, they turn to the wind when doing carrier operations. This is to be able to gain an amount of speed on the deck itself for the plane, relative to the carrier. The catapults are similar to the conveyor belt. They present an additional source of airspeed that will enable an aircraft to achieve the necessary speed to produce lift and thus allow the aircraft to fly. The aircraft also goes on full throttle to be able to thrust itself into the air. So: Aircraft Carrier speed + Catapult speed + Aircraft thrust == Thrust necessary for lift. This is actually missing a few other vectors such as the aircraft carrier's speed relative to the sea, and relative to it's position on the Earth's surface, so you get the point.

The reason why aircraft carriers aren't any longer is that it is inefficient for the aircraft to be doing a rolling takeoff instead of a catapulted launch. Also, yes VSTOL aircraft such as the Harrier can do vertical takeoffs, but it would be wasting a lot of fuel doing compared to it doing a rolling launch (if it were loaded with ordance).

The wheels are only there so that the wings don't touch the ground when you take off and land. :D

andrewJan 31, 2008 at 9:38AM

it took me literally 15 minutes of clicking all around the links associated here to get an answer to the only question that matters:

Is there significant airflow over the wings?? (Is the airplane moving forward with respect to the local body of air?)

IF the answer is yes, the airfoil will provide vertical lift, and if the volume (speed) is adequate, then of course the airplane will follow its wings and lift off the ground.

This is why they tie (small) airplanes down at airports. A 70mph gust of wind down the nose of a plane is the same thing as that plane rushing 70mph down a runway on a still day (except that because it's not consistent, as soon as the gust dies the lift will be removed and the craft will remember gravity, catastrophically). This is also why taking off into-the-wind is a good idea, within limits -- more airspeed for the same fuel input, greater lift.

Andrew TanJan 31, 2008 at 9:43AM

So there is no conveyor belt speed that would make the plane move backwards? Seems there must be. If there is such a belt speed, then there must be a belt speed which keeps the plane stationary. If the plane is stationary, it won't fly.

ScottJan 31, 2008 at 9:55AM

Anyone who got this one wrong needs to turn back in or tear up their physics/engineering diploma. This was a VERY simple problem in basic physics.

God knows that with so many AEs getting this wrong, it can only make one wonder about the quality of hardware flying overhead and the teaching of physics 101.

Mark JaquithJan 31, 2008 at 9:56AM

Andrew -- sure there can be such a speed. But it would be much faster than the negative of the speed the plane needs to take off. The conveyor belt doesn't act directly on the plane, it spins the wheels which transfers a very small amount of energy to the plane in the form of friction in the bearings. If you could get a conveyor belt moving backwards at 100,000 mph -- yeah, that might do it. But that's not the question.

nexJan 31, 2008 at 9:58AM

> "So there is no conveyor belt speed that would make the plane move backwards? "
As per the original question, the belt only needs to move as fast as the plane. You're working on a different conundrum here, and my take in that is, if the belt has the power to move arbitrarily fast, it's only fair to grant the plane enough power to move arbitrarily fast (through the air or on a normal runway) as well. Now put this plane on that belt. Since the wheel friction is negligible, it'll still take off.

Dan BolandJan 31, 2008 at 9:59AM

"Hey Dan Boland, You better not be Dan Boland from UBC Mechanical Engineering. You bring shame to all of us if you guessed wrong."

Nope, I'm an entirely different Dan Boland.

TonyJan 31, 2008 at 10:11AM

I'm I right in thinking that if the hypothetical treadmill is turned on before the planes engines are fired, then the essentially friction-free, free-spinning wheels will just turn and the plane will remain static (relative to the earth, and therefore, the air). So if the treadmill was moving forward or backward at 100mph then the plane doesn't move, at 500mph, the plane doesn't move etc etc. [I haven't fired the engines yet, remember]

JoshJan 31, 2008 at 10:16AM

Can I has T-shirtz? Maybe with a little plane taking off of a treadmill on the front, your awesome graphic over the pocket area? lol

TonyJan 31, 2008 at 10:20AM

doh! no edits. I meant to start my post with 'Am I right...' ;)

tcoreybJan 31, 2008 at 10:20AM

All I will say is that it's amazing how many people think of an airplane's wheels without thinking of its engines/propellers.

(I know because.. shudder.. at one point, I was one of those people. When I first ever heard the puzzle a few years ago, I initially fell into the "wheels are making it move, causing the air to pass over the wings" camp... rather than realizing the very simple fact that the engines/props are what moves the damn PLANE THROUGH THE AIR!! It's a sly way to subvert people's simple intuitions. But I am one of the enlightened ones now... :)

And as for the posters above who claim that, for the puzzle to work, the plane has to be motionless relative to the ground: sure, there's a way to do that. just replace the wheels with metal posts driven into the tarmac. And yes, you are correct, the plane will not take off then. The engines, however, may very well rip themselves off of the wings, but that's another subject....)

Mark HurstJan 31, 2008 at 10:25AM

I think much of the confusion has stemmed from the original question being poorly worded. The question really means to ask, if a plane at rest is carried backward at some speed on a conveyor belt, can the plane - using its thrust - eventually push itself into forward motion relative to the ground? The answer is a pretty obvious "yes."

But the way the original question is worded, it almost sounds like it's asking whether a plane can take off, even though its ground speed is zero, when it has a high speed relative to the conveyor belt. The image of a plane taking off with zero ground speed is silly and that's what I think trips people up.

tcoreybJan 31, 2008 at 10:54AM

It's psychologicaly interesting now... more comments have to do with the question, the wording, the opinions, etc., rather than the REAL experiment. :)
I think there are a lot of reasons people don't want to believe the plane will take off... but some people (pilots, physics students, etc.) do a whole lot of OVER thinking the problem. From my point of view, as an "educated layman," it seems a lot of non-physics experts UNDERTHINK it, just as I did.

Like someone said above, there seem to be several levels of misunderstanding. From 'most analytical' to 'least analytical':

1.) OK, imagine a frictionless set of wheels on an infinitely long treadmill... in a sealed chamber filled with 100% pure nitrogen... at absolute zero... the plane is a totally light-absorbent black body...
1.) There aren't enough details specified. Are the flaps down? It's a trick question. etc...
2.) The language is ambiguous... the plane might be moving or not, etc., etc.
3.) The plane is not moving relative to the ground, therefore it can't fly.
4.) The plane needs to move to fly... move, fly... wheels go! Fly! go up, plane! Fly!
5.) What's an airplane?

patmJan 31, 2008 at 11:11AM

To Nex and AlexRoss,

Skip wikipedia and go to the real experts for their position on Bernoulli vs Newton's law with regard to wing lift:

http://www.grc.NASA.gov/WWW/K-12/airplane/bernnew.html

Says NASA: "The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the mass, momentum, and energy in the flow. Newton's laws of motion are statements concerning the conservation of momentum. Bernoulli's equation is derived by considering conservation of energy. So both of these equations are satisfied in the generation of lift; both are correct. " ... "The simultaneous conservation of mass, momentum, and energy of a fluid (while neglecting the effects of air viscosity) are called the Euler Equations." "To truly understand the details of the generation of lift, one has to have a good working knowledge of the Navier-Stokes Equations which extend Euler to include the effects of air viscosity."

FatheadJan 31, 2008 at 11:19AM

I find it amazing that the mouth breathers that actually thought the plane would not take off are still arguing that it won't take off even AFTER IT HAS BEEN PROVEN by both MythBusters and the simple law of physics.

robJan 31, 2008 at 11:38AM

I think actually everyone agrees: if the plane can move forward, it can take off. If it can't move forward, then it can't.

The chief problem here all along has been that the question did not address whether the conveyor was large enough to permit forward motion.

RockkoJan 31, 2008 at 11:46AM

"The airplane does the same thing - it's not exerting any force against the treadmill. Nor is the treadmill exerting any force against the plane - the plane's freespinning wheels make sure of that.

The plane's propeller, however, IS exerting a force against the air, which is pulling it forward. Eventually, it pulls against the air with sufficient force to propel it towards takeoff speed."


EXACTLY, there is no way to prevent the plane from moving forward, no matter how fast the tread mill runs. PERIOD.

The plane is being pulled forward by the Prop cutting through the air, with free-spinning wheels, the treadmill is IRRELEVANT.

D for DopamineJan 31, 2008 at 11:53AM

Slow pace? You're kidding right? I mean, is that a criticism? If so, how "fast" should a TV show be? Do you have any new data on this matter? Relative to the speed of the Earth, the administration of methamphetamines, or....

GregJan 31, 2008 at 11:58AM

To those who still don't believe, the be all and end all should be this...

How does a Seaplane take off from water? It's not like a boat in that in needs a propeller in the water to produce forward motion, it's all engine generated thrust

The plane on a treadmill is the same principal, no momentum is gained from the wheels, they are merely there so it's not scraping on it's belly during take off

Dustin SenosJan 31, 2008 at 12:04PM

Reading this made me realize I was right when I abandoned television a year ago. Lets skip the filler, RSS the information of informative TV shows everywhere. Live RSS anyone?

I just spent 1 minute reading this blog post compared to 1 hour wasted waiting for the end result to slowly trickle to me as they pump my head with commercials.

BobJan 31, 2008 at 12:09PM

"I think actually everyone agrees: if the plane can move forward, it can take off. If it can't move forward, then it can't. "

Relativity, my dear. If it can move relative to the air... not the ground. As everyone else notes - the ground doesn't matter, hence the treadmill doesn't matter. Ground speed only matters in determining how soon you can get a beer, not how fast you are traveling.

Oh, and regarding the complaints about the pace of the show. My son has watched every episode since it first came on when he was about 6 or so. It's designed to appeal to kids as well, so the slower pace. Not sure if it's slow enough for Republicans, though. I keep waiting for them to do a creationism episode.

londenioJan 31, 2008 at 12:12PM

Puzzle: "A man is running on a treadmill. The movement of the treadmill prevents him from using his phone. Can he call his wife?"

Experiment:
1. Put a married man on treadmill.
2. Give him a phone and ask his wife to expect a call.
3. Tell him to call his wife.

Result: The man calls his wife while running on the treadmill.

An Internet debate ensues. Some people claim that the experiment is wrong because the treadmill did not actually prevent the man from using his phone. Other people regard this criticism as stupid, because anyone knows that treadmills hardly affect the use of phones. Yes, the come back, but the puzzle says that the treadmill prevents you from using your phone. Physicists explain why the movement of the treadmill **has nothing to do** with the electromagnetic phenomena that enable mobile telecommunications.

Nobody agrees. Sigh.

GordonJan 31, 2008 at 12:14PM

A plane's engines push against the air, right? What does the ground condition matter, as long as it's level? Could a car drive at 60 mph if the sky were green? It's immaterial.

Also, I'm a little surprised you don't enjoy the show. Adam and Jamie blow stuff up and are total geeks. It's hilarious.

bfos7215Jan 31, 2008 at 12:19PM

I feel so bad for the state of humanity. I am in complete shock that there are this many people who have such a hard time with such a simple concept. Man, this is pathetic.

HawkinsJan 31, 2008 at 12:19PM

Lord, I don't understand why this is so difficult. The wheel motion isn't relative to the speed of the plane because they spin freely like the wheels on a pair of roller skates, so with the conveyor belt pushing against them at the speed of the aircraft the wheels just spin freely twice as fast as the plane gets shoved forward by the engine. Unless they give out from the added strain they're not going to have any effect at all on forward velocity.

Erik J. BarzeskiJan 31, 2008 at 12:42PM

I'm amazed at the incredible depths of stupidity people seem to have regarding physics.

Stand on a treadmill while wearing skates. Strap a jet pack to your back that pushes you 50 MPH. Make the treadmill go 50 MPH and turn the jet pack on. You're gonna roll forward.

Put a plane on a sheet of pure ice. Heck, apply the brakes to the wheels if you want too. The plane takes off normally (and the wheels don't spin).

I honest... I think I'm having a harder time fathoming how stupid people can be than the stupid people are fathoming the simple fact that the plane takes off.

All the "no fly" people are misreading the question, applying their own constraints (which don't exist), or simply don't realize that a propeller or engine pulls against the air, not the thing the wheels sit on.

robJan 31, 2008 at 12:56PM

I just talked to some coworkers about this and have decided it's a misinterpretation of the question by one or the other sides, but each group is correct as to the question they are answering.

If you think the plane can take off you generally think the wheels are absolutely frictionless When the treadmill starts, the plane doesn't move becausethe wheels turn byt themselves, therefore allowing the thrust of the engine to devote all it's power to moving through the air and taking off.

If you think the plane cannot take off, you assume that as soon as the treadmill starts, the plane moves backward (as if the treadmill is a ground surrogate) and thrust must be used to simply keep the plane stationary in relation to the ground. No matter how much more thrust is applied the treadmill is cranked up to match and the plane never gets lift.

Mythbusters' experiment proved nothing, it took off because the plane's speed overcame the pickup's opposite direction speed and moved through air allowing lift. Let's assume a plane requires 100mph to take off, if the pickup was going 50mph north, I guarantee the plane was going 150mph for a net "wing to air" speed of 100mph.

The question should be "What is the question?"

matthewJan 31, 2008 at 1:21PM

this debate and it's random nexus within this site is quite possibly my favorite thing to ever happen on the internet, and brought back my love (and hate) for it once again.

my two cents: the plane takes off. the problem lies in understanding the set-up, i.e. foward motion or not. but in reality, the treadmill would never be able to stop foward motion no matter how fast it ran so that option is moot. therefore the plane takes off.

nexJan 31, 2008 at 1:24PM

Thanks for the link, patm!

> "The chief problem here all along has been that the question did not address whether the conveyor was large enough to permit forward motion."
A chief problem were people who made silly assumptions like that and declared them undoubtably true.

> "each group is correct as to the question they are answering"
You're being too charitable. Most people who got it wrong were answering some question that didn't make any sense. No one can give a correct answer to a nonsensical question; all you can do is point out how it is flawed, and if you fail to recognise the problem, you're simply wrong.

> "No matter how much more thrust is applied the treadmill is cranked up to match and the plane never gets lift."
It was already explained thousands of times that the 'treadmill' cannot keep the plane stationary.

> "Let's assume a plane requires 100mph to take off, if the pickup was going 50mph north, I guarantee the plane was going 150mph for a net "wing to air" speed of 100mph."
Well, yeah, 150mph relative to the conveyor belt. Which is an irrelevant measurement. When a plane has a take-off speed of 100mph, it'll take off at 100mph, period. Air speed of course, that's the measurement that matters.

> "Mythbusters' experiment proved nothing, it took off because the plane's speed overcame the pickup's opposite direction speed and moved through air allowing lift."
Um, it proved nothing except that the plane's speed overcame the pickup's opposite direction speed and took off. That was exactly the question, and it was answered.

jkottkeJan 31, 2008 at 1:27PM

Due to popular demand, the above graphic is available on a t-shirt at CafePress. Prices start at $18 and they're available in men's and women's sizes.

NickJan 31, 2008 at 1:31PM

Most of you are all completely wrong and overthinking the situation. Mythbusters, for the first time, did not hold true to the original conditions. If the intitial conditions that apply state that the belt always maintains the "same speed" as the wheels and nither are ever out of contact with one another than the plane CANNOT MOVE. Friction and airspeed do not matter. if the speed in the forward direction equals the speed in the reverse direction than the total distance traveled is 0. For the plane to move forward the wheels MUST be moving at a greater speed than the belt regardless of how fast the belt is moving. If the engine is supplying the thrust, as the thrust increases the speed of the wheel against the belt (because of the frictional force of gravity pushing the plane to the ground- AKA rolling friction) will increase (think car tire on dyno). At that instance the belt would have to accelerate to keep up with the wheel speed. As the plane continues to move forward the wheels accelerate even more and the belt in turn compensates. While the belt "tries" to match the speed, if the plane is moving forward it is always a step behind the wheel as far a speed goes. Therefore the original conditions of the problem are broken if the plane ever moves forward because forward motion forces the wheels to move faster than the belt as long as both are in contact with one another.

gregJan 31, 2008 at 1:40PM

"The original myth, and ALL of the discussion, centered around one central conceit: The plane would have NO FORWARD MOTION RELATIVE TO THE GROUND because of the conveyor belt matching the speed of the plane. NOT the “speed of the WHEELS of the plane” or any other contrived version."

I have been following this debate since the start and i have NEVER heard the myth stated as the belt matching the speed of the plane. It has ALWAYS been the speed of the wheels

ValectJan 31, 2008 at 1:44PM

The issue isn't a matter of if the plane takes off or not, it's a matter of how the two groups interpret the question.
The "it will not take off group" sees the question as the plane moving forward just enough to stay in place relative to everything else, hence no lift will be created.

The "it will take off group" sees what I feel to be the correct interpretation of "can the conveyor belt stop the plane from generating enough forward thrust to take off"

Ironically, the question itself gives the answer. If the conveyor has any speed to match, then the plane will of course, be moving forward (else all net momentum would be 0, and there would be no debate about it). Because of this, the plane will eventually have enough thrust to take off.

While I have my bias of seeing the "it will not take off" group as being stupid, one must consider how their minds interpret the question instead.

AdamJan 31, 2008 at 2:09PM

I always used to think that everyone in the "airplane doesn't move" camp was stupid, but I'm beginning to understand that there are problems with the question.

I understand it to be a riddle, or a trick question, which is essentially asking, "Can a conveyor belt stop an airplane from moving forward?"

At first you assume that it would, because a conveyor belt can stop a car from moving forward. But then you remember the differences between how cars and airplanes are propelled, and you realize that a conveyor belt would have no effect on an airplane, just as it would have no effect on someone wearing roller skates and a jet pack, or a car in neutral rolling downhill, etc.

I think the detail in the question about speeding up the conveyor belt to match the speed of the wheels is just a distraction to get you associating planes and cars, and was not intended as a rigid requirement of an experiment--one which, of course, could never be realized.

Walter LounsberyJan 31, 2008 at 2:19PM

Congratulations to Mythbusters! This show clearly confused the geeks and brought out all kinds of unsound reasoning. People will eagerly watch the series just for that kind of stimulation.

Understanding the experiment and the results requires: 1. knowing the difference between Lagrangian and Hamiltonian reference points and 2. the ability to draw a Free Body Diagram of forces. OK, maybe add in a rudimentary understanding of aerodynamic lift and ultralight aircraft characteristics. Like an ultralight can easily take off in less than 100 feet with a little headwind.

I'm a Challenger II Light Sport Aircraft pilot and helped design the Gulfstream V business jet. But I guess those PhDs from MIT can figure this out better than some run of the mill Aerospace Engineer with an MS... :-)

tonyJan 31, 2008 at 2:19PM

I love this question. not because it's hard but because even when it's explained to people they still get it wrong. There's a bar trick involving a wine glass that has the same effect. It's just pure entertainment watching people mash their brains and teeth over this problem. pure entertainment.

MadhuJan 31, 2008 at 2:22PM

As others have mentioned, the confusion for some comes from the the phrase "speed of the plane". There are two speeds of interest in a plane: airspeed and ground speed. Planes have airspeed indicators, but rarely do they have ground speed indicators. I took "speed of the plane" to mean what the airspeed indicator in the airplane reads, which is what was tested on Mythbusters.

For those still on the fence, consider the speed of the conveyor belt to be airspeed of plane. In general, pilots are far more interested in airspeed rather than ground speed, for obvious reasons. It's the reason why models are tested in wind tunnels and not on treadmills.

For the record, I am not an airplane pilot. I'm a helicopter pilot. We don't need wheels, but they can be helpful ;-)

Madhu

Mesa MikeJan 31, 2008 at 2:29PM

I think we can assume airspeed = groundspeed, given that wind wasn't specified in the problem.

Why in the world would we consider the speed of the belt to be the airspeed of the plane? That makes no sense.

Mesa MikeJan 31, 2008 at 2:31PM

Oh, never mind about conveyor speed equal to airspeed. That's what's specified in the problem. I misunderstood your statement for a second and was too hasty in hitting the submit button....

gahJan 31, 2008 at 2:37PM

The treadmill has nothing to do with it plane. It's the force of the engine against the air that matters.

Imagine if you had a Saturn V rocket in launch position chained to a giant cart with it's wheels on a standing treadmill. Do you really think it's going to matter? Now start tilting the whole setup until it's laying parallel to the ground. It's still just the thrust of the engine against the air.

EddyJan 31, 2008 at 2:40PM

Imagine a table with a table cloth covering it. Now imagine some stationary plates and silverwares on top of the table cloth. What happens when you pull the table cloth out really fast? If you do it correctly, then the plates and silverwares would stay on the table. So what keeps the plates and silverwares in place? The plates and silverwares stayed in place because when you pull the table cloth out really fast, there is not enough kinetic friction to pull the plates and silverwares along with it.
Now imagine those plates and silverwares as an airplane and the tablecloth as a conveyor belt. If the conveyor belt is going really fast, the airplane would be stationary because only its wheels are spinning and there is not enough translational friction to pull the plane back. The speedometer inside the plane will register no speed because the speedometer measures airflow or the pressure differential, not the speed of the spinning wheels nor the speed relative to the ground. Since this myth says that the plane's speed must match the speed of the conveyor belt, this means the speedometer inside the plane must match the speed of the conveyor belt. So in order for the speedometer to register a speed reading the plane must move forward, and it does so by using the thrust from its propeller. This is why the plane will take off.

aaargh!Jan 31, 2008 at 2:44PM

As admittedly pointless as liveblogging the episode is me posting a comment here. Why? with a 180+ comments, it's unlikely anyone will read this one (I didn't read all the previous ones, after all). What the hell, I'll say it anyway.

The answer is not (a) the plane takes off or (b) the plane doesn't take off. The answer is, in fact, (c) flaming wreckage. It has to do with the way the question is worded: the question stipulates the existence of a magical conveyor belt that can instantly and exactly match the rotational speed of the wheels. The question simply asserts, at the outset, that it is impossible for the plane to move via rotation of its wheels. Forget physics, forces, and free body diagrams. It's a magic conveyor belt. Trying to come up with a meaningful real-life answer when the question involves mixing non-existent devices with real-world devices is, bluntly, stupid. So, we'll try anyway. As soon as you exert a force on the airplane, it is now trying to move forward at velocity of 1 (1 mph, 1mm per hour - doesn't matter). You now have a feedback loop, the conveyor belt is trying to match it's own speed + 1. The belt instantly accelerates to infinity, and the real-world mechanical parts that we've placed on this magical belt either seize, explode, or fly to pieces. Therefore, flaming wreckage.

Do I get a prize?

P.S. I suppose it's unlikely that the wreckage takes off, so technically my answer is (b) the plane doesn't take off, but if I were to just come out and say that, people assume I mean that it's just sitting on the runway/belt with its wheels spinning like crazy and all the thrust from the engines going nowhere.

EddyJan 31, 2008 at 2:48PM

I must also say that the myth only requires the speeds to match. Whether the plane would be stationary or not is a conclusion and is not a criteria of the myth.

MarkJan 31, 2008 at 2:57PM

Hang on a second, didn't Cypher die in the first film? How come Neo didn't recognise him?

omoJan 31, 2008 at 2:59PM

I think people have somewhat covered it already, but the question is so divisive because it is a trick question and plays with people's mind in interpreting the relative speed of the plane in respect to the earth, and layer it on with the "conveyor belt" which, in people's minds, act like an invisible chain of friction and traction that binds the plane horizontally.

But in reality a conveyor belt under a plane's wheel is not the same as a chain locking down a plane, so that's the trick you have to realize.

Big BenJan 31, 2008 at 3:04PM

If the plane takes off, the wrong question was being asked.

Try this instead:
If a plane stands on a conveyer belt that accelerates, such that the plane remains stationary relative to the ground as its jets engage, can the plane take off?

I believe the clear answer here is no. This is because the conveyer belt may move the "ground" more rapidly, but it has a negligible effect on the air around the wings of the plane. If air is not moving rapidly over the top of the wings and creating lower pressure, the Bernoulli effect cannot occur to give the plane lift.

(If you think the plane would still take off, consider this: imagine the plane stationary to the ground, then it leaves the ground and … what? It suddenly rockets forward?)

I would be happy (as, I'm sure, would airport designers) to see this proven wrong. I would very much like to see a true test of this. The Mythbusters workaround was clever, but not analogous, since the plane clearly was not stationary relative to the ground.

PatrikJan 31, 2008 at 3:13PM

I've already been able to experiment in flight simulator the effects of very strong headwinds to make my learjet hover over the tarmac or even fly backwards without any engine power.
But now I'm really hoping the next version will have atleast one airport with a really large treadmill and an option to set it's counteracting speed to either the fusalage or the airplane wheels.
If set to the fuselage, the plane will take off, and if set to the wheels, you'll probably have to pick your type of aircraft very carefully or risk destroying it.

But off to our next question: What if we replace the catapult on an aircraft carrier with a treadmill? A fighterjet then positions itself on one end of the treadmill and stops. The only connection between the aircraft and the treadmill are the wheels of the plane. Brakes are off.
The treadmill is then immidiatly accelerated to a speed that is equal or higher then the take off velocity of the fighterjet. Will the plane take off?

Mike WestfallJan 31, 2008 at 3:15PM

> Try this instead:
> If a plane stands on a conveyer belt that accelerates, such that the plane remains
> stationary relative to the ground as its jets engage, can the plane take off?

Under what circumstances could such a system even be possible?
Remember, the question is "Can the plane take off", which implies that the pilot is TRYING to take off, not just provide only enough thrust to match the negligible friction of the wheels rotating

Shadow RiderJan 31, 2008 at 3:44PM

A plane is flying in a 100MPH headwind. This particular plane can fly stationary relative to the Earth at this speed. The pilot lowers the plane to the ground. He just touches down on the Earth and makes no adjustments to the plane's throttle or bite of the propeller. Does the plane suddenly move forward? No, because the wind didn't suddenly stop. Repeat this experiment, but this time the plane lands on the treadmill. The treadmill is not turning. Does the plane launch forward? Still no. Does the treadmill suddenly start moving? No, why would it? Now, with the plane still flying 100 MPH into the 100 MPH headwind, stationary on the treadmill, start up the treadmill accelerating slowly. At what speed does the plane start moving backwards? The treadmill will continue accelerating until it breaks or the plane's axle breaks. The treadmill could go 1,000 MPH and it would not matter, the plane will not move backwards as the plane's wheels are free to spin and match the treadmill.

Zac EcholaJan 31, 2008 at 3:45PM

HELL YEAH THE PLANE TAKES OFF is the new catch phrase I'm using this week. Thank you Jason. Thank you so much.

AdamJan 31, 2008 at 3:46PM

The way I interpreted the myth was essentially "can the plane takeoff if it had no wheels." I kind of discarded the conveyer belt because that's confusing, and instead pictured the plane with cement shoes. It was essentially: ignoring the weight of the concrete, would the plane be able to generate enough thrust to get the air moving over its wings to spring up into the air?

Big BenJan 31, 2008 at 3:49PM

> Under what circumstances could such a system even be possible?

Under the circumstances outlined. This is a thought experiment. I don't have to provide the mechanics of how such a conveyer belt would match the speed of the wheels. Take this as given: the conveyer belt increases its speed such that the plane does not move forward. The plane cannot move forward if its contact with the ground matches the rotation of the wheels.

> Remember, the question is "Can the plane take off", which implies that the pilot is
> TRYING to take off, not just provide only enough thrust to match the negligible
> friction of the wheels rotating

It doesn't matter what the pilot is "trying" to do. He can apply as much thrust as he likes to the engine. The conveyer belt matches that thrust as manifested in the rotation of the wheels.

I think people are getting hung up on the fact that the wheels don't provide propulsion. That's true. But they're still the contact with the ground and provide the means of movement relative to the ground.

If this magical conveyer belt matches the speed of the wheels' rotation — no matter how fast — the plane remains stationary and grounded.

Mesa MikeJan 31, 2008 at 4:01PM

> the conveyer belt increases its speed such that the plane does not move forward.

But that's not stated in the original problem.
Go back and read it again.

Andrew MundyJan 31, 2008 at 4:06PM

I found reading this (just now) to actually be very enjoyable. I'd already seen the episode last night, but Jason's commentary was amusing and it was almost like... like.... like I have a friend....

But seriously. This is a formal request that this livebloggering by the esteemed Mr. Kottke continue. Maybe do some fashion show or something.

To Infinity and BeyondJan 31, 2008 at 4:07PM

>If this magical conveyer belt matches the speed of the wheels' rotation — no matter how fast — the plane remains stationary and grounded.

How, the plane is accelerating forward and the treadmill isn't exerting any force to stop it? The power of the treadmill will go to infinity trying to match the acceleration of the wheels that are providing no resistance, at least in this idealized magical thought experiment world. You can't have a frictionless treadmill without frictionless wheels on the plane.

Mesa MikeJan 31, 2008 at 4:08PM

> The conveyer belt matches that thrust as manifested in the rotation of the wheels.

This statement shows a complete lack of understanding what of "thrust" is.
Thrust is the force pushing the airplane forward.
There is no "thrust as manifested in the rotation of the wheels."

The wheels have nothing to do with the thrust of the airplane (except for a minimal amount of friction), and the conveyor belt cannot exert any thrust on the airplane (except for the minimal amount to overcome the wheel resistance).

JeremyJan 31, 2008 at 4:08PM

To boldly copy and paste from another forum. He explains it better than I can.

DanRudmin writes:
"
This was the original question:

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

Notice that it doesn't say anywhere that the plane must remain stationary, that is an assumption.

They see the question and they immediately conclude (incorrectly), that the problem is stating that the plane is not allowed to move.

The Noflys claim that the experiment was performed incorrectly. Their issue is that the speed of the plane should be measured relative to the treadmill, and that the speed of the treadmill should be measured relative to the Earth. Thus, the condition that the plane speed equal the treadmill speed implies that the speed of the plane and the speed of the treadmill cancel out and the speed of the plane relative to the Earth is 0. Because the speed of the plane relative to the Earth was not 0 on the show, the experiment was not performed correctly.

This is the incorrect interpretation for many reasons (the correct interpretation is that the speed of the plane is measured relative to Earth, just like everything else): First off, this interpretation uses two separate reference frames, the treadmill and the ground. Nowhere in the question did it implicitly state the reference frames, but if speeds are being compared (and they are) and the reference frame is not stated (and it isn't), it would be a safe bet that both speeds should use the same reference frame. Why would one state that the plane speed equals the treadmill speed if the two weren't measured in relation to the same object?

The second reason that the Nofly interpretation is incorrect, is that the common reference frame that we almost always use for everything is the Earth. It is referred to as "the universal reference frame". If I say that a car is going 50 mph and don't state with relation to what, it is safe to assume that it is going 50 mph relative to the Earth, and not some bird in the sky or the planet Venus. When I am on a moving sidewalk at the airport, I consider myself to be moving faster. This is because I measure my speed relative to the Earth, and the moving sidewalk speeds me up relative to the Earth.

If you measure the speed of the plane relative to the Earth, on takeoff, the plane is going 25mph. The treadmill is also going 25mph in the other direction. The initial conditions are satisfied. The plane flies... it's simple, it's obvious. But apparently it isn't obvious enough.

Now, let's look at it from the Nofly perspective. If the experiment were performed the way they want it, as soon as the plane begins to move (rolling friction is already overcome so the treadmill has no frictional effect), the treadmill must instantly spin up to such a speed that it applies a force which slows down that movement. You can't have the plane moving (relative to the Earth), or else the treadmill is going slower than the plane (treadmill relative to Earth, and plane relative to treadmill). How might this work? You can't apply a force through an ideal free wheel. For theoretically perfect bearings and no air viscosities it is impossible. The treadmill cannot slow down the airplane, so it accelerates to the speed of light, time comes to a stop and the universe implodes. So in the theoretical world, it is a nonsensical assumption to make.

Now, what about the real world? Well industrial bearings go up to many thousands of rpm. A 2ft diameter plane wheel going 25mph spins at about 350 rpm. So the treadmill would have to go about 10 times faster than that to begin to push the bearing past its working zone and begin to create any frictional forces which can slow down the plane. We'll say at 250 mph the treadmill can start to slow down the plane (just the very light amount of thrust that got the plane to start moving). But wait, in the real world air is a viscous fluid. If this treadmill is very long and very wide, we can assume laminar flow over the surface. And since fluids have a no-stick condition at the surface of the treadmill, the treadmill will pull air along with it. Normally this would be a very thin layer, but it depends on the size of the treadmill. You can use the Navier-Stokes equation to determine the speed at a given height. If the treadmill is large (the size of a runway), the velocity of the air moved by it will indeed by quite high, especially considering that the Cessna's wings are not that high above the treadmill surface. That means that as the treadmill picks up speed (remember we are talking about a stupidly fast treadmill now), it begins to slow down the plane not by wheel friction, but by wind, the same wind that gives planes lift. The harder the plane's engines push, the faster the treadmill moves, and if the bearings can hold out, the more lift the plane will get, eventually getting airborne and taking off.

So no matter which way you cut it, the Noflys are wrong. Their assumption is silly and nonsensical, but it still leads to them being wrong no matter what.
"

yourmomJan 31, 2008 at 4:25PM

The stupidity of those who think the plane won't fly is only outdone by the stupidity of those who can't figure out that the first group of stupid people are interpreting the vaguely worded problem differently. I'm talking about the people pissing their pants in excitement because their physics 101 class finally had an application outside of uni.

Sir IsaacJan 31, 2008 at 4:33PM

Hello, my name is Sir Isaac Newton, and I just rolled out of my grave to remind you people that F=ma.

You apply a force, F, to the plane with the prop. Its mass, m, relative to the ground, must accelerate, since F is the only force acting along the horizontal axis (disregarding trivial frictional forces on the wheel bearings). F=ma, so eventually it must reach takeoff speed because it is accelerating relative to ground.

Good day.

EricJan 31, 2008 at 4:43PM

Jason asked, "How does anyone watch this show?"

Not live, that's for sure. Then again, I don't watch anything live. TiVo it, and then watch it later on the elliptical/treadmill/exercise device of your choice.

HughJan 31, 2008 at 5:10PM

Well, thanks for spoilering the episode with the title of the "hell yeah the plane takes off" tshirt thread. Popped up in my RSS feed and knocked the glow off my evening.

Boo.

Karl MarxJan 31, 2008 at 5:33PM

Oh i get it.

the propellor is moving air..no drivetrain scrubbing against the ground.

yeah it'll take off.

nexJan 31, 2008 at 5:35PM

> "Therefore the original conditions of the problem are broken if the plane ever moves forward because forward motion forces the wheels to move faster than the belt as long as both are in contact with one another."
This doesn't mean that the plane can't move forward, but that the experiment you have in mind doesn't make sense. You want the speed of the belt's surface relative to the ground to be the exact opposite of the speed of the plane relative to the belt's surface. Of course this is not the experiment that the Mythbusters carried out, because it's inane! It is based on a requirement that can't possibly be fulfilled. It's utterly wrong to draw the conclusion that the plane won't take off. You could just as well say, "if air is heavier than steel, then the plane won't take off." The statement itself is true, but in the real world it doesn't make any sense and makes no predictions about any planes at all. Mythbusters tested a sane version of the myth in an adequate way and came to a valid conclusion.

> "I have been following this debate since the start and i have NEVER heard the myth stated as the belt matching the speed of the plane. It has ALWAYS been the speed of the wheels"
Yeah, this is the reason why there is such a huge debate in the first place: many people, like you, have read a bastardised version of the 'myth' that ambiguously states some vague, but ultimately nonsensical, requirements regarding wheels, and everyone tried to find a solution to this extremely perplexing conundrum for the sheer geek factor of doing so, interrupted by morons who don't understand the first thing about planes, which triggered even more vigorous discussion. But you must realize: the phrase "the speed of the wheels" by itself doesn't mean anything. Translational or rotational velocity? Relative to the belt's surface or to the ground? And often there were even other ambiguities. You need to do a lot of interpretation to even make sense of that botched wording. One could say that this is in fact feasible, because some possible interpretations can be discarded, since they are self-contradictory (e.g. the interpretation "speed of wheel axle w.r.t. conveyor should be the exact inverse of speed of conveyor w.r.t. ground" is bullshit), and all other interpretations result in the plane taking off.

But if you really want it all to be about "the speed of the wheels", then please specify which speed exactly you're referring to.

> "Understanding the experiment and the results requires: 1. knowing the difference between Lagrangian and Hamiltonian reference points ..."
Bullshit. Just knowing what a frame of reference is and does is enough. Sure, you could do detailed analyses of all parameters involved, do lots of calculus and fluid dynamics and put Euler and Navier-Stokes equations onto your list of requirements, but in fact you're already given a plane that is designed to fly perfectly well and all you need to do is figure out whether it still works when the wheels spin twice as quickly, or maybe not at all. If the question was worded clearly, an 8-year-old could figure that out.
> "... and 2. the ability to draw a Free Body Diagram of forces."
Bullshit again! FBDs are a tool some find very helpful, but you can draw equally sound conclusions via other means.

> "Saturn V rocket [...] thrust of the engine against the air."
Are you sure engines in space craft work by pushing against air?

> "Since this myth says that the plane's speed must match the speed of the conveyor belt, this means the speedometer inside the plane must match the speed of the conveyor belt."
Humpty Dumpty, is that you? I admire you so much. Instead of pointing out ambiguities in poorly worded statements and considering the ramifications of different possible interpretations, you just tell us what each word means! However it appears in your little eggy head, so it must be in the real world ... wow, that's so practical, I envy you.

> "The answer is not (a) the plane takes off or (b) the plane doesn't take off. The answer is, in fact, (c) flaming wreckage."
Oh! So flaming wreckages are the norm in this scenario and the plane taking off unharmed on Mythbusters, that was just a horrible, tragic accident? Well, aaargh!, you do very nicely explain why it's idiotic to assume the plane should under any circumstances remain stationary, but the Mythbusters didn't test the idiotic version of the 'myth'. So, no prize, sorry :-)

> "If the plane takes off, the wrong question was being asked."
Wow, you just discovered a completely new form of Reality Distorsion Field with unprecedented powers! Let's try this technique out on some other examples: "If Hillary Clinton won't become president, the wrong election was being held." "If I don't win the next lottery, the wrong number was drawn." "If shamans are shown to be unable to cure cancer, you must have meant the flu instead."
> "Try this instead:"
Why would anyone substitue the original question with a completely different one supplied by you? That's as if I promised to play Bach's Concerto in D Minor on an organ, utterly failed at the attempt, and then proclaimed that the wrong instrument was supplied and people would hear the music if only they provided me with a player piano with the right notes entered into it. I would strut around and smugly remind people that I would be oh so joyful if they could prove that Bach's Concerto in D Minor won't play upon me pressing the start button. I would admit that, yes, actually playing it live on an organ is a very clever idea, but it wouldn't be a true substitute to the player piano!

It's ironic that in a discussion all about taking off people sink so low ...

Patrik says:
[paraphrasing] "Can a plane be catapulted into the air with a tradmill, if the breaks are off?"

Mike Westfall says:
> "Under what circumstances could such a system even be possible?"

Mike, I guess Patrik didn't seriously want to know the answer to the question, but was just attempting to cleverly llustrate a path to the correct solution for the four or five people who still don't get it ... not counting the trolls :-)

> "It was essentially: ignoring the weight of the concrete, would the plane be able to generate enough thrust to get the air moving over its wings to spring up into the air?"
I hope you've meanwhile found out that planes don't work that way at all. If not, there are some good links further up.

> "The conveyer belt matches that thrust as manifested in the rotation of the wheels."
Sure. Because, as everyone knows, thrust is measured in angular degrees per second.

> "Take this as given: the conveyer belt increases its speed such that the plane does not move forward. The plane cannot move forward if its contact with the ground matches the rotation of the wheels."
Umh, alright, done. Can it be my turn now, please? OK, here, take this as given: The pilot is his own father. You cannot be his brother unless you're also his nephew and his uncle. Look, if you stipulate nonsensical bullshit, it'll result in the darndest conclusions, but they aren't true over here in the real world.

Jason, if I order that t-shirt, will you include a little button that says "proud member of the reality-based community", pretty please?

Erik J. BarzeskiJan 31, 2008 at 5:45PM

Nick said:
If the intitial conditions that apply state that the belt always maintains the "same speed" as the wheels and nither are ever out of contact with one another than the plane CANNOT MOVE.

The original question says nothing about the speed of the wheels - it just says the speed of the plane as a whole. The wheels are spinning 2x as fast as normal at takeoff - nothing more.

On MythBusters, the plane was going 25 MPH to the right, the tarp 25 MPH to the left. Since the wheels were connected to both (to the plane by axles, to the ground via friction) they were spinning at a rate fast enough to be 50 MPH.

I can't believe people are still arguing about this. The "no fly" or "they didn't test it properly" people are out-of-this-world bonkers.


Big Ben said:
If a plane stands on a conveyer belt that accelerates, such that the plane remains stationary relative to the ground as its jets engage, can the plane take off?

No. And the "it will fly" people aren't saying it will. You're the one who seems to think the plane magically remains stationary. It doesn't. It takes off normally.

Big Ben later said:
The plane cannot move forward if its contact with the ground matches the rotation of the wheels.

You seem to have put the "wheels" into the initial question. They're not there. The speed of the plane is matched by the conveyor belt.

Big Ben then says:
The conveyer belt matches that thrust as manifested in the rotation of the wheels.

The manifestation of thrust is not through the wheels. It's through the plane pulling itself forward through the air. The wheels are simply drug along with the plane, and the ball bearings in the wheels are there to reduce friction.

A plane could take off with its brakes locked from a sheet of ice. Same principles.

HELL YEAH THE PLANE TAKES OFF

P.S. Sir Isaac Newton, congrats on perhaps the first "new" approach I've seen taken. The conveyor belt doesn't apply any force that opposes the motion forward of the plane - it can only push upwards.

Erik J. BarzeskiJan 31, 2008 at 5:55PM

I don't want to spend $20 on a shirt, so would it be possible to put the "HELL YEAH" logo on stickers, pins/buttons, coasters, and other CafePress goodies?

Pretty please?

JoshJan 31, 2008 at 6:01PM

I can't believe there's so much arguing about this topic. This is basically a religious argument and there is very little chance that someone's view is going to change no matter how much is written about it, or even if it is shown on TV.

If we're going to kill innocent electrons arguing about something, it should be something towards the common good for all of mankind...like whether Kari should pose for Playboy. I vote yes.

pwbJan 31, 2008 at 6:56PM

If anyone cares, here are two versions of the question:

From Mythbusters: "An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff."

From this thread: "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?"

The NoFlys make two bad assumptions: 1) that the plane remains staitionary and 2) that the conveyor moves at the same speed of the 'wheels'.

Given the two versions of the question above, it's fairly obvious that the plane can take off relatively easy.

Matt WhartonJan 31, 2008 at 7:17PM

I had a feeling that the long awaited Mythbusters episode wouldn't end the debate once and for all because the people who interpret the question as being a situation in which the conveyor belt keeps the plane stationary with respect to the ground and thus the air will always believe that the experiment has been done wrong.

However there is no way in the world given that a airplanes wheels by definition have to have virtually frictionless bearings that the conveyor belt could exert enough force on the plane to prevent the thrust from the engines from moving the plane forward with respect to the ground and the air.

If the wheel bearings were perfectly frictionless at any RPM then the plane may as well be hovering above the conveyor like a hoverboard from Back to the Future 2 and then I believe everyone could understand that the conveyor belt could have no effect on the motion of the plane.

In the less than perfect world the force transferred through the wheels via the bearings to the plane is and will always be tiny in comparison with the thrust generated by the engine so the plane will move forward no matter what the conveyor belt does and as it moves forward it gets lift and thus takes off.

marcusJan 31, 2008 at 7:43PM

After a discussion with a friend, the assumption that the myth-busters used is wrong. The thing is, the conveyer is moving at a speed to *stop forward motion*. Yes the plane doesn't get it's drive through the wheels, but there is some friction, and the belt has to move *damn quickly* but the computer is monitoring the sped of the plane and countering that through the conveyer, so it will have to move fast to create enough friction through he wheels to cause take off.

nexJan 31, 2008 at 8:24PM

> "The thing is, the conveyer is moving at a speed to *stop forward motion*."
Says who?

Mythbusters tested exactly the claim they'd said they would test, therefore there was no wrong assumption.

TracyJan 31, 2008 at 8:40PM

Unfair test and once again, the mythbusters team, substituting equipment and saying that it's the same. No! That plane was on the ground. I want to see it on a real treadmill! This myth is not solved.

Mesa MikeJan 31, 2008 at 8:52PM

Well, I was wondering when I would see that argument, that the weight of the plane was actually felt on the ground through the sheet, so therefore it didn't really test the case of the plane on a treadmill!

RobJan 31, 2008 at 9:07PM

FACT: Rolling resistance doe not increase significantly with speed.

That's why the plane moves forward relitive to all frames of reference in our experiment and takes off. There is nothing else.

JoelJan 31, 2008 at 9:44PM

You know if you did the opposite, moved the air to match the plane's take off speed. the plane would literally be hovering over the earth. It would have no speed and yet be flying.

JohnnieJan 31, 2008 at 9:44PM

Come on people, I will admit I feel into the trap for the first 15 minutes I thought about this problem until I realized the problem in my thinking.

For those still trying to state it won't take off, answer me this.

Imagine the wheels are frictionless and can spin freely (They spin freely on a plane, but of course, aren't totally frictionless, but still for my point).

Now, The airplane is left off, engines are not on. Turn on the conveyor belt AT 200 MPH going in the same direction of the wheels. What happens to the plane? Does it sit though, or does it move back with the conveyor belt?

It sits there. The wheels spin at 200 MPH, the plane just sits there. Under the frictionless model, you won't even need any additional thrust to reach takeoff speed, as the only thing the treadmill affects is the speed the wheels spin at. If the Plane's takeoff speed is 200 Hundred, at that speed, the plane itself will be going 200 MPH in relation to the ground, air, etc, and the wheels would just be going 400. Hell, if the wheels could spin frictionlessly, the Conveyor belt could be travelling at 5000 MPH and it wouldn't have an affect on the planes movement, only on the wheel's spin speed.

All you claiming that the test was wrong, it wasn't. There is no possible way for a conveyor belt to stop a plane from moving forward, and that's the issue people are having a hard time grasping.

DeuceJan 31, 2008 at 9:46PM

I'm a pilot too, and unlike that other guy it's readily apparent that the plane would take off from a treadmill.

Take an Cessna 172. 180hp engine with a takeoff speed of around 60mph. Bolt the plane into position on a treadmill and speed up the treadmill to 60mph. Measure the force applied to the airplane through the wheels. (remember, aircraft wheels are built to spin as freely as possible!)

It's nowhere near 180hp! Now, turn on the engine and release the bolts. The plane has 180hp pushing it forward and MUCH LESS force pushing it back. Physics 101 tell us that the sum of these forces will result in acceleration forward. A plane that can accelerate can take off.

To provide 180hp of "drag" through the spinning wheels, you'd have to spin the treadmill at some ungodly speed.

So yes, the plane will take off, with the wheels spinning at twice their normal speed. (60mph forward movement + 60mph treadmill action) I suppose on some aircraft this would exceed the tire speed limitations and cause a blowout...

Garrett C.......Jan 31, 2008 at 9:58PM

HEY .... wow, did anyone read my post?

Nex and that other guy are the only ones who are supporting it/explaining it further...

Michael? you do not understand the question, you keep on bringing up the fact that "Oh man, the planes moving 1 mph forward, therefore the treadmill is moving 1 mph backward. A- this isn't the problem, because, the myth states speed relative to the ground, and B, its simple math, 1 mph forward, 1 mph backward, equals 2mph on the speedometer, so you are wrong there. But again this is NOTHING TO DO WITH IT.

At 245 am i wrote a flippin long post, and I restated what Alex ross and nex were saying, but some people neglected to read it and throw more crap out there that has already been stated. A- the plane is NOT SUPPOSED TO MOVE RELATIVE TO THE GROUND..... I can see the argument that "the planes movement forward must equal the treadmill speed moving backward."
Now your all putting random numbers, like 250 mph forward and the treadmill, axles melting etc etc etc... well, i believe Alex said it? that if you follow the myth exactly, the plane is actually not moving at all, therefore treadmill is not moving at all. So the treadmills pointless, the myth is a pandora's box condundrum piece of crap that was made to piss you off, leaving us with the original statement that i said, which was "can a plane take off with no forward movement"... I think i proved that we could.... if the plane was powerful enough....

Listen to Alex Ross and Nex, not the people who bring up this treadmill crap over and over, cause its pointless, cause if again, if you follow the myth exactly, the treadmill ain't moving unless we're in a parallel universe

Garrett C.......Jan 31, 2008 at 10:01PM

And Deuce, everything you said was true, and very well put. But again, the plane can have NO FORWARD MOTION RELATIVE TO THE GROUND.. The only thing you said that supports this is when you said "you would have to drag the treadmill at an ungodly speed to negate the force of the engine pulling the plane forward ( aka create 180bhp of drag through the wheels, pretty much impossible)

Again, if we follow the myth EXACTLY...

Garrett C.......Jan 31, 2008 at 10:03PM

Wow, johnnie didn't get it either. THE PLANE CAN HAVE NO FORWARD MOTION RELATIVE TO THE GROUND> RELATIVE TO THE GROUND>RELATIVE TO THE GROUND.....

DouglasJan 31, 2008 at 10:54PM

@Garrett: "its simple math, 1 mph forward, 1 mph backward, equals 2mph on the speedometer, so you are wrong there"

If the plane is moving forwards at 1 mph, the plane's speed is 1 mph. The speed of the plane is the speed at which the plane is moving forwards.

joshJan 31, 2008 at 11:03PM

thanks for ruining the suprise for me, mr. kotke!

mymyselfJan 31, 2008 at 11:46PM

The original question was a riddle meant to test the analytical skills of the person attempting to answer it. After reading it, like all questions/problems, you will lack perfect knowledge about the system being described. Therefore, you will need to make some assumptions based on knowledge of past performance and login/reason.

The question is, are your assumptions about the unknowns as minimalized as possible, or are they huge and wildly out of bounds with how airplanes and conveyor belts work in real world?

Those who think the plane can't take off or that the question/test is wrong are simply exhibiting poor analytical skills because the assumptions they are making are far more complex and divorced from knowledge of past performance than those that say the plane will take off.

The only way to stop the plane from taking off - no matter how fast the conveyer belt goes - is to assume some extra mechanism that translates the backward force of the conveyer belt into the plane. To assume such a mechanism from the text of the question posed violates all sorts of parsimony principles of good analytical and reasoning skills.

To make the matter worse, these same people also are demonstrating the total lack of ability to let go of incorrect, or at best, extremely unjustified assumptions. If this were an interview question, they most definately would not get the job.

ReubenJan 31, 2008 at 11:50PM

Sorry Garrett, can you quote the line in the myth that states "The plane can have no forward motion relative to the ground"?

I don't remember reading or hearing that anywhere. This has been stated above many times already. Here it is again:

"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?"

The speed of the conveyer equalling the speed of the plane does not mean "no forward motion", to create no forward motion would require an unrealistic amount of friction or an infinitely fast conveyer, as explained by many physics experts and pilots above.

The question is a *trick* question, you are tricked into thinking there is no forward motion, but that is not what it postulates at all.

ReubenJan 31, 2008 at 11:57PM

mymyself- you put it much better than me, thankyou...

Pee BeeFeb 01, 2008 at 12:43AM

No. Read the other hundreds of posts here. There is NO stipulation in the original question that states that the conveyor is moving to "stop forward motion". In fact, it can NEVER physically do so.

That is an incorrect assumption forwarded by many people, and is the beginning of where they go wrong.

You might as well say the conveyor is moving to "set the aircraft on fire", or to "dig a huge hole under the aircraft", or to "fill the aircraft with air".

The point is that conveyor has NO possible means to "stop forward motion", or any of the other silly suppositions I presented above.

End of Argument. Lock thread.

paul...a thinking man's manFeb 01, 2008 at 12:54AM

This topic needs everyone to climb back into an Apollo program rocket and journey to and land on the moon. Once there, everyone needs to collect their picnic baskets, moon chairs and assorted eyewear and join me over by the moon buggy. Lets all set out our belongings and get settled into a relaxing posture and gaze back upon our blue planet. Hey, whats the earth doing? Its rotating? Anyone know how fast the earth rotates......about 1000 miles and hour. Guess what the earth reminds me of? Anybody? Anyone? Anyone? Thats right....A big cyclic conveyer "belt". Hey prop aircraft, jet aircraft and even James Bond Cars leave the surface of the 1000 MPH rotating planet.

Andrew TanFeb 01, 2008 at 2:47AM

So if the plane is stationary relative to the belt, and the belt is moving forward (ie. in the same direction the front of the plane is pointing), can the belt ever move forward fast enough that the plane takes off?

nexFeb 01, 2008 at 5:17AM

I second Reuben's comment, the post by mymyself is as close to a hypothetical definite answer as anything I've ever seen! Well, not for physics nerds who want to consider the intricacies of every smallest detail, but that's exactly the point ... you can figure it out with the most basic physics knowledge, but first you must figure out what the 'riddle' actually means. Mymyself put that very eloquently.

> "Guess what the earth reminds me of? Anybody? Anyone? Anyone? Thats right....A big cyclic conveyer 'belt'."
It's completely different. The conveyor isn't supposed to be so massive that it's taking all the air on top of it with it. Also, the earth is not a perfectly flat surface that varies its acceleration according to some measurement taken from the plane. This thought experiment is just completely beside the point. The movement of earth through space is irrelevant for all practical purposes. I'd still fancy a picnic on the moon, though.

> "So if the plane is stationary relative to the belt, and the belt is moving forward (ie. in the same direction the front of the plane is pointing), can the belt ever move forward fast enough that the plane takes off?"
You're implying that the plane has the brakes on and the engines off and is catapulted into the air by the conveyor belt. Well, yes, it's possible, but a more relevant situation would be brakes off, engines on. Then the belt would just have to move along with the plane, so that the plane remains stationary w.r.t. the belt. The belt wouldn't make the plane take off, then, but it would still take off, no problem.

nexFeb 01, 2008 at 5:21AM

Oh, no, wait! I fell into a trap. I took that too literally, "can the belt move fast enough" to catapult the plane into the air ... well, yes, it can, but in that scenario there's another important variable: As soon as the plane begins to lift off, it would lose contact with the belt and therefore its only means of propulsion. So actually it wouldn't really work if the plane wasn't allowed to run the engines. But anyway, it is controlled by a pilot who actually wants to take off, so whatever ;-) Interesting twist, though.

rogFeb 01, 2008 at 5:27AM

yeah, I was gonna say that earth is a conveyor belt analogy is a horrible analogy that will only confuse people trying to see how simple this problem is. Ignore that post at all costs if you are trying to see what is going on in this problem.

ogcFeb 01, 2008 at 5:54AM

hell plane will take off under real conditions obviously.
What if plane is already moving backwards with conveyor belt lets say at 100 miles hour. Will it take of in such situation?

Andrew TanFeb 01, 2008 at 5:55AM

OK, so if the belt can make a stationary (relative to belt) plane take off (yes, the plane will crash right after take off, since it's losing its propulsion, but we only care about the question of take off) - does a forward moving belt reduce the amount of power that a forward moving plane needs to take off?

nexFeb 01, 2008 at 6:57AM

> "yes, the plane will crash right after take off, since it's losing its propulsion"
crash ... let's say land :-)

> "does a forward moving belt reduce the amount of power that a forward moving plane needs to take off?"
Well, you could put on the brakes and use the belt to give the plane a good push to bring it up to speed up to the point when lift causes the grip to diminish. You'd have to accelerate gently in order to prevent slip, so I guess you'd need a ridiculously long belt. Btw. motorless sail planes are often launched into the air with a winch.

> "What if plane is already moving backwards with conveyor belt lets say at 100 miles hour."
Assuming you can do this to the plane without it reacting badly (e.g. flipping over or, if it's a jet, stopping the engines from working) and the belt is long enough so it won't shoot off the back end ...
> "Will it take off in such situation?"
... why not?

ChaseFeb 01, 2008 at 10:33AM

Don't know if its from my submission or not, but I actually suggested that shaving cream myth 2 or 3 years ago. Do you know if/when this episode is going to air again? I couldn't find mention of it on Discovery's website.

Big BenFeb 01, 2008 at 12:39PM

Thanks to everyone belittling the analytical and physical skills of people trying to understand a problem. Jagoffs.

But actually, really thanks to the people taking the time to explain why ultimately the movement of the wheels and, therefore, the conveyer belt is meaningless. Once you understand, it kind of makes the whole question seem pointless.

Here were the two most helpful bits for me finally wrapping my head around why the plane takes off:

Erik J. Barzeski: "A plane could take off with its brakes locked from a sheet of ice. Same principles."

(Although Erik was also pretty much a jerk by calling people "stupid.")

and Johnnie: "If the Plane's takeoff speed is 200 Hundred, at that speed, the plane itself will be going 200 MPH in relation to the ground, air, etc, and the wheels would just be going 400."

Also, still think the Mythbusters experiment sounded flawed.

Finally, it is perfectly reasonable to restate questions to get at different answers. Some of you guys on here got a real bug up your asses.

pwbFeb 01, 2008 at 1:14PM

However there is no way in the world given that a airplanes wheels by definition have to have virtually frictionless bearings that the conveyor belt could exert enough force on the plane to prevent the thrust from the engines from moving the plane forward with respect to the ground and the air.

Actually, it would be rather easy for the conveyor belt to prevent the plane from taking off: the pilot would simply set the engines at a level low enough to merely off-set the frictional force. Mythbusters should have shown this. And then shown that increasing the thrust from this new steady state would cause the aircraft to take off relatively normally.

aaargh!Feb 01, 2008 at 2:24PM

Having finally had a chance to watch the Mythbusters episode, I now understand one big point of confusion. There are multiple versions of this question - I had started out on the one posted on airliners.net, Salon, and David Pogue's column in the NY Times, which states that the conveyor belt matches the rotational speed of the wheels. A completely different proposition from the version Mythbusters tested, which is that the belt matches the speed of the airframe. The former version cannot be tested experientially, for the reasons I stated upthread (and stand by), while the latter version obviously and unequivocally, results in the plane taking off with its wheels spinning twice as fast as normal.

Thanks to nex for their contribution to the art of civil discussion - I would point out that none of my comments were ad hominem, I was simply saying that the question itself, or at least the version I was operating on, was stupid.

ChrisFeb 01, 2008 at 2:33PM

Not sure if this was already commented on, but here goes anyway...

During the full scale test, the pilot was instructed to reach takeoff speed, without taking into account the additional thrust necessary to overcome the force of the treadmill. So that got me to thinking...how much (or little) "drag" does the treadmill place on the aircraft.

Here's a quick, simple experiment to discover the amount of force the treadmill would place on the airplane during takeoff:

1. Measure the exact amount of thrust required to get the plane off the ground. No more. No less. As soon as the wheels separate from the runway is the amount of thrust they should be looking for. Measure the airspeed of the craft at this point.

2. Set the treadmill to the exact speed the plane achieved liftoff.

3. Set the thrust of the aircraft to the exact amount measured in step 1.

4. Measure how much longer the plane would need to travel to gain enough speed to lift off along the treadmill.

Naturally, the measurements and the eventual test would need to be performed during calm winds. Not only would this truly put this myth to bed, it would also explain how little of a difference the treadmill makes.

Just some food for thought.

pwbFeb 01, 2008 at 3:21PM

OK, I see, the NoFlys have a point if the question is phrased (poorly) like this: Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

But they are right for the wrong reason. When the question is phrased like this, stating that the wheels move at the same speed as the belt, that does indeed imply that the plane is stationary. But it's not because the conveyor belt is the actor and is providing substantial force to prevent the plane from moving forward. It's because to achieve this situation, the pilot of the plane would have to provide the minimal amount of thrust to counter-act the very small amount of frictional force conveyed by the belt. If the pilot increases the thrust even slightly, the plan begind to move forward and the wheels start to revolve faster than the belt.

Andrew TanFeb 01, 2008 at 8:22PM

OK, nex, thanks a lot! Let's see if I understand this. Let’s take the puzzle in the more general form of allowing the belt to move backwards or forwards with any speed as a function of time that we wish. I don't think frictionless wheels have anything to do with it. I also don't think the plane or belt accelerate to infinity (which have no consequences anyway in classical classical physics). Also, the belt is not the same as a rotating earth, in that the former does not drag air along with it, but the latter does. So the air is stationary relative to the ground, ie. movement relative to the ground is movement relative to the air. So we are asking if we can make the car accelerate relative to the ground until it reaches a ground speed that will make it take off by Bernoulli’s principle.

Situation 1: For simplicity, the plane has no wheels. It’s just a block with wings and jet engines. The jet engines provide a constant force in the forward direction by pushing on the air. We assume the plane can move forward relative to the belt if the belt is not moving. Thus the constant jet force must be greater than the maximum friction. The maximum friction is given by (coefficient of friction)*(weight of plane). Notably, the maximum friction is neither velocity nor acceleration dependent. If the belt moves backwards, forward or anything, the friction can never increase beyond that. So there is no speed at which the belt can move backwards and make the plane move backwards, because the net force is always in the forward direction, and the net acceleration is always in the forward direction, which means the plane can eventually increase its speed to take-off speed.

The conceptual difficulty comes in 2 alternate cases.
Situation 2: Plane again is a block of wood with wings and jet. If the plane is stationary relative to the belt, but the belt moves forward fast enough, the plane will take off. In this case the plane has accelerated relative to the ground, so the belt is clearly capable of applying sufficient accelerative force to the plane. All’s correct so far, until I ‘generalise’ and think that it can therefore apply a suffcient decelerative force in Situation 1.
Situation 3: Here the plane is a car with wings (which is actually quite a good assumption, since it will take off, glide some distance and then land, so could qualify as a plane in everyday speech). The car generates force by pushing on the belt, and the belt pushes back on it, so the car accelerates forwards, ie. friction provides the forward force. If the belt moves backwards fast enough, the car will not move relative to the ground, and will never take off. We grant the car a maximum finite power, and the belt a maximum finite power, but the belt power is sufficiently greater that there is a finite belt speed so that the car at maximum power will never take off.

The essential difference is that in Situation 1 the jet generates force by pushing on the air (ie something ‘stationary’ relative to the ground), but in Situations 2 & 3 the belt provides the forward force. Let’s consider only Situations 1 and 3 now to see where intuition is failing. The ‘fair’ assumption we make in both cases is that the plane can accelerate when the belt is not moving. The unintuitive thing is that for the assumption to be true, friction points in different directions in each situation! In Situation 1, the forward force generation is independent of the belt, so friction points backwards, so for forward acceleration when the belt is stationary, we require (magnitude of jet force > magnitude of friction force). In Situation 3, friction provides the forward force, so for forward acceleration when the belt is stationary, we require (magnitude of friction > 0). So friction is a very interesting force that ‘self adjusts’ its magnitude and direction.

DraticusFeb 02, 2008 at 4:11AM

"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?"

Ok, I see one assumption that seems to be tripping everyone up. Both sides are right depending on this assumption. Is the conveyor belt moving at a speed equal to the planes air speed or the planes speed relative to the conveyor belt itself? If its moving relative to the planes air speed as many assumed then the plane will indeed take off because when the plane is moving forward at 4mph the belt is moving backwards at 4mph and the wheels simply spin at 8mph and the plane continues moving forward. However, if the belt matches the planes speed relative to itself then the planes forward movement is limited entirely by the delay in which the belt matches its speed. If we assume no limit to the top speed of the belt and an ALMOST instant increase in belt speed then the plane will never take off because an infinite belt speed equals an infinite amount of friction on the axles and eventually the frictions negative force will equal the engines positive force and it will remain motionless. How quickly this happens is limited only by the belts reaction time. Even with a non instant, realistic increase in belt speed the plane will only move forward slightly before the belt reaches an insanely high speed and the plane becomes motionless. (There could be a problem with the plane tipping forward depending on the weight of the plane and how high its engines are off the ground but that still results in no liftoff)

Here it is step by step-
1. The planes starts moving forward and the belt matches its speed.
2. The belt matching the planes speed doesn't stop the plane in its tracks so the planes speed relative to the belt has now increased even more.
3. The belt adjusts to the new speed which causes the planes relative speed to increase and this repeats over and over with the plane moving forward and the fiction on the planes axles increasing infinitely as the speed of the belt increases.
4. At some point the friction on the axles is so much that its stopping the plane with an amount of force equal to the force of the engines pulling the plane forward and the plane comes to a relative stop and just sits there on the belt*which is by now spinning insanely fast)
5. The plane will always be moving faster than the belt until maximum friction is reached and the plane comes to a halt. The belt in this scenario is a fictional belt designed to match the planes speed and stop it from moving forward. There is no reason to assume that it matches the planes speed slowly. Theoretically the belt could accelerate the planes wheels to max friction in seconds which would allow the plane to have moved only inches before it is stopped by the force of gravity pushing down on the axles which are generating too much friction to allow the plane to move forward. No air flow is occuring over the wings so no lift is generated so the plane does not take off.

Think of it this way: The planes wings are meaningless until it reaches a certain forward speed relative to the air. So it might as well be a car until it reaches that speed. If a car were on a conveyor belt that matched the cars speed relative to itself then a fast enough reacting belt would match the cars speed after it has moved a distance limited only by the belts reaction time. Theoretically the belt could match the cars max speed in the amount of time it takes the car to shift gears. Whether the force being exerted is from the wheels pushing against the belt or props pulling the plane forward, either way gravity and friction are the two things stopping it from going faster than the belt. A car with no friction in its engine and no friction on its axle would have no limit to the speed it can reach on the belt because there is also no wind speed. That same friction is present for the plane and would stop the plane from going faster than a certain speed.

I think the question was intended to imply that the belt matches the planes speed relative to itself and therefore prevents significant forward movement. The catch that was supposed to trip people up was that the plane does not take off relative to the speed of the ground below it but rather relative to the speed of the air around it.

If you think the thrust of the plane will move it forward regardless of the amount of friction on the planes axles(which increases with speed without an upper limit other than the axle melting) then imagine an amount of friction equal to a brake. Enough friction at the wheel will prevent forward movement and there is no limit to that friction if there is no limit to the belt speed.

Some people compare it to a rocket but that is completely flawed because a rocket doesn't take off due to lift around the wings but rather creates enough thrust to push off of the air behind it. A rocket doesn't need wings or momentum to leave the ground. If you had infinitely powerful engines then yes, the plane could take off because they could pull the plane into the air even without wing lift but I don't think that was the intention of the original question.

Once again,
If the belt matches the planes speed fast enough the plane will not reach take off speed relative to the air before the tires blow out or the axles create enough friction to counter the engines. You can not achieve lift off unless you have a belt that adjusts speed too slowly, frictionless tires, or engines that achieve enough thrust to pull the plane forward without lift around the wings(like a rocket). Its all about the belts reaction time.

dodserFeb 02, 2008 at 4:56AM

OH FOR CRYING OUT LOUD!!!!
A plane on a conveyor belt will NOT take off.
A flawed experiment proves nothing.
Lift is produced by wind passing over the wings.
If the experiment was carried out correctly, you would have been able to stand stationary alongside the plane touching its wings as its wheels turned on a conveyor belt.
There would have been no wind passing over the wings therefore no lift and no takeoff.

kataFeb 02, 2008 at 12:44PM

dodser:"Lift is produced by wind passing over the wings. "

If this is the only force in play, how does a plane stay in the air once it has left the ground? What is it that ensures that enough wind will continuesly pass over the wings for the duration of flight?

If this experiment was talking about a glider, you're right, it wouldn't take off, but we're talking about an airplane.

MadhuFeb 02, 2008 at 4:19PM

Here are some good videos on YouTube:

Plane/Treadmill 1

Plane/Treadmill 2

Once rolling friction is overcome, the plane will accelerate. The speed of the conveyor is irrelevant.

The plane's propeller produces a force (or thrust). The conveyor adds a negative velocity, but that does not reduce the force from the propeller. Force and velocity are not of the same dimension, they cannot be added or subtracted as some might think. Sure, there's some minor friction from the tires and wheel bearings, but that is (largely) not dependent on wheel speed.

For those who argue Mythbusters did not conduct the test correctly, listen carefully to the announcer:

Mythbusters intro

He clearly states that if a plane is on a conveyor belt and both are going at takeoff speed, but in opposite directions, does the plane take off? This avoids the controversy of which speed is the subject of discussion and the control system etc.

In the RC model example, the Mythbusters clearly showed that a conveyor going at takeoff speed has no effect, as do the videos above.

I think it's safe to say that if a planes maximum speed is 100 MPH and the conveyor belt is going backwards at 200 MPH, the plane still takes off. The force of the propeller causes the plane to accelerate, eventually, it will overcome any negative velocity of the conveyor belt (within reason of course).

Force and velocity are two different quantities. There have been similar misunderstandings on Wikipedia regarding energy and power, they are not the same thing either.

Garrett C.......Feb 02, 2008 at 4:23PM

Lol, I guess we are all in disagreement here.

Whoever had pointed out the 1mph forward and 1mph backward thing = 2mph on me, you're right IDK what was stuck in my head, but I guess I was in car mode at that time, because of course that would now apply to a plane.

And to the other person who called me out on the part of the theory where I kept on stating "Without forward motion.." Well, that's the myth that I got when I researched it online. I was supporting/explaining that myth, or at least that version of it.

I wasn't paying complete attention while watching the show, but I'm guessing that we are all arguing slightly different myths, but the main one in contention is a super basic one stating that the "treadmill matches the forward speed of the plane."

Well, if thats the case, of COURSE the plane will take off.. because it had forward motion.
@Dodsor, it sounds like your arguing against the Postulate of the myth that I was yelling my head off about, with the whole no forward motion and everything. See my obnoxiously long posts way above and i kinda proved something on that if the conditions were right.

Otherwise, this plane is leaving the ground.

Timothy TanFeb 03, 2008 at 12:15AM

Who cares about the speed of the conveyor belt? The wheels act only as ball bearings to reduce friction to the ground. Therefore the speed of the ground is irrelevant. Only the forward force produced by the engines and the speed of the airflow over the wings are relevant.

I knew it would fly!!Feb 03, 2008 at 1:26AM

OMG some people are just such idiots. i can't believe how many people are still trying to argue that the plane shouldn't have taken off.

Andrew TanFeb 03, 2008 at 1:28AM

If we make the assumption that the plane can accelerate from rest relative to the belt when the belt is stationary, then the plane will be able to take off. So let's try not make that assumption. We make the friction so strong that the plane can never move relative to the belt surface even at full thrust. However the plane can still take off when the belt is off, because the belt surface is light, and moves freely relative to its mechanism, ie. the belt accelerates with the plane when the belt mechanism is off, until the belt and plane together reach take off speed, at which point the plane lifts off vertically from the belt. But when the belt is on, the mechanism engages the belt and moves it backwards every time it and the plane move forward. In this scenario, it seems to me that the plane will not take off if the belt mechanism is on.

nexFeb 03, 2008 at 8:21AM

OH FOR CRYING OUT LOUD!!!!
A pot of water on a fire will NOT boil.
A flawed experiment proves nothing.
Boiling is achieved by transfering heat to the water.
If the experiment was carried out correctly, you would have been able to stand next to the pot touching the water as the pot absorbs all the heat from the fire.
There would have been no heat passing into the water, therefore no warming and no boiling.

> "I had started out on the one posted on airliners.net, Salon, and David Pogue's column in the NY Times, which states that the conveyor belt matches the rotational speed of the wheels."
No it doesn't. These sources just say "speed of the wheels". At first glance, it might seem natural to interpret that to mean rotational speed, but it turns out you can't do that when you think everything through. So actually you first have to figure out whether the question is about rotational or translational velocity. The most obvious solution is to go for the latter, which is exactly the speed of the plane itself.

Let's examine what happens if we insist on matching the rotational velocity of the wheels. If the belt moves in the opposite direction as the plane, this cannot possibly work, because this version of the 'conundrum' doesn't make the least bit of sense. When the speed of the belt changes, the rotational velocity of the wheels changes by the same amount, so there is nothing at all the belt can do to compensate for a difference in speeds. (Some people get around this by allowing the belt to match some rotational velocity the wheels had at some point in the past and making the belt turn so fast that it wrecks the plane. If that still wasn't enough to sabotage the experiment, they'd probably crank up the engines until they detach themselves from the aircraft, set the conveyor belt on fire, and shoot the pilot.)

Therefore, when we insist on having the belt match its speed to the rotational velocity of the wheels, the belt must move in the same direction as the plane. There is a solution: The belt moves at half the speed of the plane, which causes the wheels to turn half as fast as on a normal runway. It's the only possible solution, and it won't prevent the plane from taking off.

Now, all of the sources cited above explicitly state that the belt must turn in the opposite direction as the wheels. Therefore, the above solution doesn't apply, thus the assumption that 'speed of the wheels' implies rotational velocity turns the 'conundrum' into paradoxical, nonsensical gibberish. It is a silly assumption to make. You could just as well try to match the speed of the conveyor to the sound of one hand clapping.

(When I say rotational velocity, obviously I'm not measuring the turning rate, as you couldn't match that to the translational velocity of the belt; you'd compare apples to oranges. Instead, we have to measure the speed at which points on the circumference of the wheels move through space.)

The bottom line is: Either the people who posted the wordings cited above were thinking of the translational speed of the wheels, which is the same as the speed of the plane, meaning replacing 'plane' with 'wheels' is just a red herring that confuses people; or they had no clue what they were talking about and were expecting a meaningful answer to a load of bullshit.

RayFeb 03, 2008 at 8:24PM

Ok, I give up on the argument about the plane moving or not relative to the ground.

It *doesn't* matter *even* if the plane doesn't move relative to the ground -- with any reasonable assumptions about the low friction of the wheel bearings, the viscosity of air, the friction of the belt, etc., the plane will take off.

Air isn't motionless relative to the Earth's surface because it's in orbit, it's moving along with the surface of the Earth because all moving surfaces drag along any viscous fluid in contact with them, and air has non-zero viscosity (and if it didn't, the plane probably wouldn't take off even from a *plain concrete* runway).

Any belt speed (likely around 1000+ mph) that is sufficient to apply enough force through the free-wheeling wheel bearings to stop the plane against the engine is *easily* fast enough to drag sufficient air along with it to make the plane take off even if the plane is standing still relative to the ground. Of course, it will level off and hover once it gets high enough that the air is only moving fast enough to do that.

But *at that point*, even if it's only enough to get it a few inches off the ground, the plane isn't not touching the belt at all, so it will start to move forward up to takeoff speed and take off.

It simple doesn't matter which assumption you make. The plane will take off *even if* you make the *ridiculous* assumption that the belt can move fast enough to keep the plane from moving relative to the ground.

Unless you actually go off and research the Navier-Stokes equations and have a cogent argument against this, I'm done.

The only way the plane doesn't take off is if you apply the brakes enough to stop the plane against the engine, and hopefully that's a trivial enough statement that no one cares about it, since it's true even without the conveyor.

Andrew TanFeb 04, 2008 at 6:50AM

The reason the plane does not move relative to the ground is not because the belt is moving very fast. So the argument that the belt is moving so fast to drag air along with it won't hold. The plane does not move because there is a large enough coefficient of friction. This may happen, for example, if the plane has its brakes on (not sure if this is true in real life, but we can imagine toy planes that will do this). We are in this case, but it is not trivial, because the plane is on the belt. When the belt is off, it moves freely relative to its mechanism, so the plane and belt move together until they both achieve take off speed, at which point the plane takes off. When the belt is on, the mechanism detects any forward movement, and moves the belt back quickly, so the plane and belt move forward a bit, then backward. If this mechanism is perfect, then the plane and belt move in opposite directions (relative to each other and the ground) with equal zero speed.

Nathan HarrisonFeb 04, 2008 at 9:03AM

Here's the thought experiment I use when I explain how the plane flies:

You're sitting in a wagon on a long tarp, much like the Mythbusters setup. You hold in your hands a powered winch connected to a long cable, which anchors to a point in the ground far in front of you. It has enough power to pull the wagon forward and overcome friction if the tarp were to remain stationary.

However, at the moment you engage the motor on the winch, a force will engage to attempt to prevent the wagon from moving forward by pulling the tarp backwards, in the opposite direction that the winch is attempting to pull the wagon. Does the wagon move forward?

It will, because it has to. The winch is in no way related to the motion of the tarp, so the wheels will spin faster and faster as the tarp is pulled faster and faster, with no effect on the wagon's forward motion until some piece of equipment breaks (wheel, axle, bearings, tarp, etc.). The wagon will move forward at the same speed relative to a stationary observer as if the tarp weren't being pulled at all.

As different as pulling on cable is from moving air with a propeller, the example is basically the same. Both methods have something to act on on other than the surface of the tarp, so the tarp can never be moving fast enough to prevent forward motion.

Adding the caveat that somehow the tarp or conveyor belt's speed can compensate for this outside force does prevent either vehicle from forward motion... but is impossible to achieve in our universe using any methods myself or anyone else is currently aware of, and therefore makes the question worthless, really.

Mike B.Feb 04, 2008 at 2:43PM

Totally un-repeatable test, and therefore unscientific.

They settled on the minimum speed at which the plane would take off. However, they didn't agree that:

1. The plane must only accelerate its engine to the minimum RPMs required to reach that minimum takeoff speed, AND
2. The truck pulling the "conveyor belt" can only go at the minimum takeoff speed.

They both gunned it and the lightweight plane accelerates faster than the truck. The plane moved horizontally as soon as the test starts. Air passed over the wings. Lift is generated. It takes off.

TreyFeb 04, 2008 at 8:13PM

No, really: If a treadmill can keep a plane from taking off, doesn't that mean that if the wheels on an airplane are spinning fast enough, they can counteract the power of the plane's engines?

And if that's true, wouldn't that also mean that if a plane was in flight and its wheels started spinning quickly enough in the wrong direction, they would be able to slow down and stop the plane?

K.M. EnsignFeb 04, 2008 at 8:48PM

omg. This is pretty sad. THE PLANE IS PULLED THROUGH THE AIR BY THE PROPELLER! How is this so difficult understand? This youtube video shows you why.

Andrew TanFeb 04, 2008 at 10:47PM

What is the logical way to solve the problem? Zeroth assumptions that we don't have to add are stated in the problem, eg. existence of solids. If we are to get the answer that the plane takes off, I used to think we only needed Newton's laws of motion, Newton's gravity plus the additional *first* assumption that the plane can accelerate from rest to take off velocity when the belt is stationary. Now, it seems to me that isn't enough. From the assumption that the plane can accelerate from rest to take off when the belt is stationary, we can deduce that the jet force is greater than the (possibly velocity dependent) maximum friction in this problem. That isn't sufficient to constrain the jet force to be greater than friction for relative speeds of belt and plane greater than take off speed. By measurement on most solids, we know that friction on a solid surface is not strongly velocity dependent, so we have to this amazing fact as a *second* assumption, for the plane not to take off. However, can we prove that there is no material for which friction is velocity dependent? If not, then strictly speaking the conclusion that the plane takes off is not experimentally proven until the test is done on many many surfaces or the assumption of conventional surfaces is added to the problem. For liquids, friction is velocity dependent. Would our answer change if we permitted liquid treadmills, like for sea planes?

Andrew TanFeb 05, 2008 at 8:40PM

In a certain sense, Mythbusters did not do the right experiment. The explanation they gave was that a plane's jet-powered acceleration has nothing to do with its wheels. This can be correct if they also predict that a plane, which has accelerated up to a certain speed, and switches off its jets, will continue to move forward forever if the wheels continue to roll without slipping. Thus the explanation they gave was correct for another experimental condition, not the one they used.

Andrew TanFeb 06, 2008 at 1:16AM

OK, I'm thoroughly confused. If the Mythbusters explanation that the wheels on a plane don't matter is correct, then I don't see why even a car with finite power can't accelerate to an arbitrarily high forward speed over a treadmill moving backwards with any constant speed, no matter how great, provided there's always enough friction to keep the wheels rolling without slipping.

MarkFeb 06, 2008 at 5:20AM

Blatantly they're inside a Matrix even in the 'real' world.

Cliff hartleFeb 06, 2008 at 10:25AM

Only in a frictionless world. The fiction force on the wheel bearings is negligible compared to the force of the propeller on the air.

>In a certain sense, Mythbusters did not do the right experiment. The explanation they gave was that a plane's jet-powered acceleration has nothing to do with its wheels. This can be correct if they also predict that a plane, which has accelerated up to a certain speed, and switches off its jets, will continue to move forward forever if the wheels continue to roll without slipping. Thus the explanation they gave was correct for another experimental condition, not the one they used.

Andrew TanFeb 06, 2008 at 12:06PM

Wow! Rolling friction is quite often speed dependent:
Y. Xu, K. L. Yung, and S. M. Ko. A classroom experiment to measure the speed-dependent coefficient of rolling friction. American Journal of Physics, June 2007, Volume 75, Issue 6, pp. 571-574.

MadhuFeb 06, 2008 at 6:13PM

> This can be correct if they also predict that a plane, which has accelerated up to a certain speed, and switches off its jets, will continue to move forward forever if the wheels continue to roll without slipping.

They don't have to make such a prediction. That was done in 1687 by Sir Isaac Newton. The first law of motion still holds today. Add friction if you like, the first law still works.

Garrett CampbellFeb 06, 2008 at 9:27PM

This is officially dumb. This thread has gotten so long that everyone new is starting to repeat everyone old. Everyone... is... repeating.. everyone... THE PLANE TAKES OFF. WE GOT THE IDEA THAT THE PROP PULLS IT THROUGH THE AIR>... stop restating and read over and you are going to be a new poster

Andrew TanFeb 06, 2008 at 10:15PM

At one place, Mythbusters state the question as plane going forward at take-off speed and treadmill going backwards at take off speed. If these velocities are constant (which is implied by the 'going' in the statement of the problem), and you solve it under the assumption that the plane speed is relative to the ground then the plane takes off. If you assume that plane speed is relative to the treadmill, then, the plane does not take off. No need to consider forces or acceleration here.

The possibilities change (including which assumptions are considered reasonable to make) depending on how the myth is stated, and the fun part is sometimes you get mixed up and answer wrongly one version of the myth using the correct answer for another version. The challenge is not only to get the right answer, but to be very careful in obtaining it the right way (ie. saying what freedom of assumptions are allowed by the particular version of the problem, what assumptions you are putting in etc:)

Andrew TanFeb 07, 2008 at 4:02AM

There's a point I don't understand in the statement that the plane will take off as long as the wheels don't melt. If the wheels are getting hotter when the belt goes faster, that seems to require a velocity dependent friction, at odds with the explanation that the belt speed doesn't matter.

nexFeb 07, 2008 at 5:59AM

> "If the Mythbusters explanation that the wheels on a plane don't matter is correct ..."
Wheels don't matter with regard to what? Surely they didn't say the properties and behaviour of a plane don't change at all when you add or subtract wheels.

> "If the wheels are getting hotter when the belt goes faster, that seems to require a velocity dependent friction, ..."
Yes, but the point at which the wheels become dangerously hot is reached much, much sooner than the point at which any significant force holds the plane back. The former is a valid consideration for the puzzle solved here, whereas the latter only matters for corrupt interpretations that were desperately or playfully constructed in order to keep the plane on the ground.

If I said anything more, I'd repeat explanations that were already made above. The above discussion is full of simplifications, as considering every minute detail is neither possible here, nor in the spirit of the puzzle, but I assure you, if you read it carefully, all bases regarding friction are covered.

RayFeb 08, 2008 at 12:09AM

>The reason the plane does not move relative to the ground is not because the belt is moving very fast. So the argument that the belt is moving so fast to drag air along with it won't hold. The plane does not move because there is a large enough coefficient of friction. This may happen, for example, if the plane has its brakes on (not sure if this is true in real life, but we can imagine toy planes that will do this). We are in this case, but it is not trivial, because the plane is on the belt.

This approaches being a cogent response to my comment, so I'll respond:

Yes, indeed, you're right. If you apply enough brakes on the plane's wheels so that the friction exactly balances the thrust of the engine, the plane will not move forward, *regardless* of the speed of the belt (within the limits of the wheel bearings, of course :-).

The question is: so? If you apply enough brakes on a stationary plane on a stationary piece of concrete so that the friction exactly balances the thrust of the engine, the plane *still* will not move forward relative to the ground, for exactly the same reasons. Bare concrete is equivalent to a belt speed of 0.

Is this supposed to be a surprising result?

If you're allowed to stop the plane with its brakes, why would you ever suspect it would take off? The thing to realize is that the brakes are the *only* reasonable explanation for a coefficient of friction sufficient to do this. The wheel bearings are practically frictionless otherwise and won't apply much force except at *ridiculously* high belt speeds.

If the people arguing the plane won't take off are willing to admit you have to apply the brakes to get this to happen, I'll happily concede that point, trivial though it might be.

UtbildningFeb 08, 2008 at 6:03PM

As we all know, the average guy and girl are obviously used to driving a car and not piloting. Hence, we are so used to vehicles with propulsion coming from the wheels (cars, bicycles, motorcycles etc) that we can hardly think when faced with a different case. The propulsion of an airplane does not originate from the wheels but from the air pressure and air speed produced by either a propeller or a turbine as in a jet engine (as many have stated already). Remember that the airspeed and air pressure produced by the engines that is blown backwards will push the aircraft in the opposite direction, i.e. forward since the surrounding air is standing still. No conveyor belt can stop this. A conveyor belt can only make the wheels spin faster during lift off.

If, on the other hand, there would be a big fan in front of the aircraft blowing air (like in a wind tunnel) at the same speed as the aircraft then the aircraft would not go forward. But it would still lift from the ground since the air passing over and under the wings at a high speed would produce a force lifting the aircraft from the ground. The liftning force is produced due to the profile of the aircraft's wing using Bernoulli's principle.

Utbildning
http://www.stics.se

Andrew TanFeb 09, 2008 at 2:40AM

Anything wrong with this solution?

Quick summary if you don't want to read the equations. I've been bothered by this detail in the proposition that nothing is different except the wheels end up spinning faster. If the wheels end up spinning faster without affecting the translation of the plane, then the angular acceleration must have been greater. Since the only torque on the wheels is due to friction, then friction must be have been greater. Since friction is in the opposite direction of the jet force, then the translational acceleration of the plane must have been less, thus it cannot be true that the translational motion of the plane is unaffected. At the very least, it seems that the plane will need a longer runway to take off.

Consider a plane on a rigid surface with only static friction (Fr) that
increases with applied force up to a maximum (Frmax).

In the case of a plane without wheels, the plane cannot accelerate unless the
jet force (Fj) is greater than Frmax.

But a plane with rigid wheels can accelerate if Fj is less than Frmax.

Assume Fj is applied through the center of mass of the wheel of mass M, radius
R and moment of inertia about its axis I.

Let Ap be the translational acceleration of the wheel relative to the ground.
Let alpha be the rotational acceleration of the wheel about its axis.
Let Ab be the translational acceleration of the belt relative to the ground.

1: Fj-Fr = M*Ap (used 'F=ma')

2: Fr*R=I*alpha (used 'torque=I*alpha')

The plane is moving forwards, the belt is moving backwards, so the translational acceleration of the plane relative to the belt is (Ap+Ab), so for rolling without slipping:

3: (Ap+Ab)=alpha*R

Solving for the friction gives:

Fr=I*(Fj+Ab*M*R^2)/(I+M*R^2)

Thus if Ab=0, then Fr
But for sufficiently great but finite Ab, then Fr=Fj, and the plane cannot accelerate by rolling. It also cannot accelerate by sliding since Fj

Purdue MEFeb 15, 2008 at 10:25AM

I initially predicted that the plane would not take off for lack of forward motion, but then I took about 15 seconds to summarize forces AND THE LOCATION OF FORCES in my head. This is really incredibly simple--it doesn't even require equations, just basic knowledge from the first few days of high school physics. Cars have tires that push on the ground to create forward motion. If a car is moving forward at 60 mph, a 60 mph wind in the opposite direction won't stop the forward motion of the car because the car is applying force TO THE GROUND. Airplanes have engines that push on the air to create forward motion. The speed of the surface the plane is sitting on will have a negligible effect on the speed of the plane. If the plane had to achieve 65 mph to take off, the conveyor could have been moving in the opposite direction at 65, or 95, or 365 mph, or ANY speed for that matter and the plane would still achieve 65 mph in the forward direction in the same amount of time, with no difficulty and take off. THE ONLY TIME THE GROUND MATTERS TO AN AIRPLANE IS WHEN IT CRASHES.

TomFeb 15, 2008 at 6:36PM

An airplane with mass M sits on a conveyor belt. The airplane's jet engine is turned OFF. The conveyor belt starts moving backward at a constant velocity V_conveyor. (note that all velocities will be quoted relative to the ground referential)

Which direction does the plane go? Backward, with velocity V_conveyor.

Intuitively it is reasonable to expect that the plane will have to overcome this backward velocity before taking off.

At time T=0, the jet engine is turned on, generating a thrust, F by pressing against (we all agree) the atmosphere. As a result, the plane experiences a forward acceleration A = F/M. Note that the conveyor belt provides no acceleration, just constant velocity. [As an aside, also note that acceleration is independent of any fixed frame of reference].

We are allowed to decompose the velocity of the plane relative to ground (V_total) into the velocity component due to the conveyor belt (V_conveyor) and the velocity resulting from thrust acceleration (V_plane):

V_total = V_plane - V_conveyor

As velocity is the integral of acceleration, at the instant in time T=0 its (forward) velocity component due to the thrust force is still V_plane = 0: the plane is still moving backward relative to earth with velocity V_conveyor - V_plane = V_conveyor.

Time, T, continues to pass. Thrust F guarantees constant acceleration A=F/M, and the equation for the velocity of the plane due to thrust is V_plane=TA.
Thus V_total = TA - V_conveyor. The plane's ground speed V_total will be zero only when

T_null = V_conveyor/A

Until this time the plane will continue to move backward. As more time passes, the plane's forward velocity component due to thrust will continue to increase linearly with time, whereas the backward velocity component due to the conveyor belt motion will remain constant, and so the plane will progressively pick up forward velocity (V_total = TA - V_conveyor > 0 ), develop lift and take off.

Thus if the conveyor belt has constant velocity the plane will, of course, teventually take off. If the conveyor belt's velocity increases linearly with time at a rate A, then the plane will not develop forward velocity and will not take off.

TomFeb 15, 2008 at 8:06PM

[Sorry- formally speaking the thrust does not come from "pushing against the atmosphere", but simply from conservation of momentum; air with mass m_air is pushed out by the engine at velocity v_air such that momentum P=m_air X v_air, and the thrust F=dP/dt = the mass of air pushed out at velocity v_air per unit time. This does not change anything in the above result. Cheers. ]

Brett ManeyFeb 17, 2008 at 6:36AM

The plane does take off.

The thing that confuses people, including me at first, is that the movement of the conveyor does not keep the plane stationary, it just spins the wheels twice as fast as normal. Because the wheels are spinning faster the wheel mechanism will generate more friction than normal, but this would not be enough to prevent the plane from taking off.

So basically, in order to take off the plane needs its normal take off thrust plus some additional thrust to over come wheel mechanism friction. If you assume the system is frictionless then only normal thrust is needed.