I don't think anyone in the history of this question has ever thought that the wheels are the source of propulsion for the plane. Also, I don't think anyone has ever thought that a plane can take off without air moving over the wings. The question is designed to get groups of people arguing about two completely different scenarios, and these non-points are inherent in the comparison between the two. Based on what you believe the question is stating as the premise (which isn't specified), there are two different outcomes. There is no "right" answer.

yes there is.

dude.

if the plane is going 100 mph, and the track of the treadmill is also going 100mph.....then the plans'e wheels are going 100 mph......but they have no effect on the plane's speed because they rotate

Uh, wheels = 200, Jim.;)
The question was written to lead people into the wrong logic, rather than discarding superfluous information. It is a trick question, but there still is one right answer..... and many wrong answers.

"forward speed" relative to what? Not stated.

Of course, in #3 the plane can slide into forward motion, but that isn't necessary unless in addition to #1. In #2 it just takes off.

rotating 200 mph, yes. moving 100 mph as the plane carries them


relative to the earth, flint, as everything is.

Nor did I say that. I said that if you'd only been in powered-wheel vehicles the situation was counterintuitive.

Oh, by the way:

an airplane that generates some lift in an unorthdox way

This is the internet. It's not over until somebody says something about Hitler and you know it.

Oh, crap. I just blew my nomination for the Hall of Fame. Is a non-productive contribution to the thread still counted as a contribution?

wow, maggie. here's more

why aren't these designs being applied to other aircraft?

George Jr is the observer? No wonder an accurate answer is not possible!

And you mentioned Hitler in the same post! Double whammy.

The speed is obviously defined by this: Again, a reference to the equations F=ma and v=at . Speed does not exist on its own. Speed is a relationship between two references. Force (the "F") defines those two refeneces. Engine creates a force between airplane and air. Therefore speed is also created / measured between airplane and air. "Forward speed" is defined by that phrase Previously posted are the numbers to stick into those equations so that we know how long (t time) that engine (F force) must push the plane (m mass) to obtain minimum takeoff speed (v speed).

how fast would a standard jet have to turn it's engines in order to pull enough wind over its wings to generate lift? assuming it stood still relative to the ground?

They are mounted under the wing, so they couldn't do what you describe. The airflow has to be above the wing.

the air has to go faster above than below, so the engine position below the wing prevents that from ever happening. right on

Well...it looks gooofy, and aviators can be surprisingly conservative. The engineering of it is tricky...I suspect the wing shape has a weight penalty. And once you're airborne there's usually plenty of lift available, as long as you're willing to trade it for induced drag.

It's a rockin' performer on takeoff, but I bet the efficiency blows dead goats in cruise. Nonetheless, Custer apparently sued Fairchild claiming the A-10 Warthog violated his patent.

By the way, The MidAtlantic Air Museum at the Reading Airport has a Channelwing...not currently flyable.

... as it was mistakenly parked on a treadmill.

I'm still trying to envision a treadmill that applies as much force to an aircraft through friction at the wheel bearings as the engines do grabbing at the air.

Without setting fire to the wheelbearings.

Especially interesting in the case of a rocketplane like the Bell X-1, which not many people know was capable of a runway takeoff.

I wonder how fast the treadmill would have to go...:-)

Nah, it was just left out in the weather for like forever.

Heh, thanks.

The right answer is the one that requires no magic treadmill. The plane takes off.

;) :)

I think I'm getting a clearer picture of the car / plane confusion. The wheels on a car rotate, grab the road (with friction), and 'push the road back'. Since the road doesn't move, the car moves forward instead. So, you could change the speed of the car relative to the earth by moving the road like a treadmill.

With a plane, however, the the only purpose of the wheels is to keep the plane above the ground and reduce friction. The plane pushes itself forward by pushing the air back (hence it is easier to take off in a headwind).

Probably the only way to keep the plane from flying would be to immerse it in a tailwind that matched the plane's velocity, or to lash it down and prevent it from rolling.

I also think that people might be confusing velocity and force. Only force can keep the plane from moving, and the treadmill cannot apply enough force.

If you replace the word "force" with "Chuck Norris" you may be on to something.

Oh, gotcha. :redface: Yes, of course.

That channel wing would be very difficult and expensive to build, although with composites it might be feasible. But, like Maggie said, heavy.

As was posted previously: Posting by Torrere is that airplane wheels make that plane 'separate from' (independent of) both runway and treadmill. Treadmill only affects how fast those wheels spin. As MaggieL posted, otherwise those wheels would burn up; function instead like brakes.

Meanwhile, tailwind does not change the problem. Remember the two items that a force - the engine - applies between. Engine force pushes between airplane and air. Tailwind or headwind - still that engine applies same force causing the airplane to have a same velocity relative to air (also called airspeed). Still that same F=ma equation applies. No matter how fast the tailwind is blowing, F=ma makes the plane move a defined speed faster than air because same force (F) is remains between air and the airplane.

Airplane speed relative to runway is speed of airplane created by its engine plus speed of air created by tailwind.

Headwind/tailwind changes the airspeed by the velocity of the wind. A tailwind will make it harder for the plane to reach the airspeed necessary to lift off. And a headwind will make it easier. ;)

It only took us 18 pages, but lookout123 has solved the problem. The giant supernatural treadmill is irrelevant; only Chuck Norris prevent the airplane's movement. Since the problem did not specify that Chuck Norris was holding it back, the airplane flies.

Imagine the treadmill is powered by a jet engine. One thrust cancels out the other one. Nothing flys.

wrong, and misspelled. (flies)

the runway could be powered by chuck norris and clint eastwood and labrat's ass put together. the rotation of the wheels nullifies it's effect. up up and away.

I think they're in danger of burning anyway. Their friction is the only path for the treadmill to transfer energy to the airplane, and they've been specifically designed *not* to do that, whereas the engines are designed specifically to do exactly what they're doing. So the proposed takeoff failure scenario has a power transfer through friction in the wheel bearings equal to the power output of the engines (less engine system losses, of course). So even in a smallish airplane we're talking 100-200 horsepower...which is about 150 kilowatts. How long before the wheel bearings fail from heat?

My auto inspection shop complains about the cost of their treadmill. $20,000+ to test hundreds of horsepower cars (a machine required by the state required and that has not purpose only years later). Same treadmills exist for Indy and F1 racers designed to test 500 and 800 HP engines. I think we can find those bearings.

Maybe we and the Russians could cooperate on buiding one for airports? Anything for world peace. And since we are using labrat's ass, then it would be methane powered. Reduced global warming. No tailwinds. Having tapped chuck norris, the reduction in bullshit story lines means no additional landfills. Clearly there are plenty of spinoffs from this original proposal including 18 pages of deep technical discusion that would make any Congressman proud.

Not quite the same thing. The dynamometers you speak of are purpose built to carry the load of a race car in normal operation. The "no-fly zone" treadmill must run fast enough to dissipate the equivalant of all the power of the aircraft engine[s] through friction at the landing gear bearings alone. (I grant you can postulate treadmills of any desired power handling capability; Heinlein certainly did--convincingly--in "The Roads Must Roll").

The bearings in question are the landing gear wheel bearings, not anything in the treadmill. They weren't built to do anything more than handle relatively short takeoff and landing rolls near the stall speed of the aircraft, and some taxiing around at speeds about as fast as a man can walk.

I will probably be shunned for resurrecting this thread... but I had to bring to everyone's attention that this topic will be covered on "Mythbusters" this week.

Found recently

http://cellar.org/2008/planetreadmill.jpg

Clearly in this case the plane will not take off . . . it won't get past the obstruction at the front of the treadmill.

I think this treadmill was designed for landings only, Sleeve.

They're thinking of installing one at Heathrow.

Help me Obi Wan!!! wow, my brain hurts.

I say no. If the plane is on a tread milbl, there is no forward motion....no Bernoulli effect.

Try this, same question different object...

An armored personnel carrier with full tracks, is driving down the road at 30 MPH. How fast is a track shoe touching the ground, centered on the vehicle moving and in what direction?

Who the fuck cares -just run in the away direction. fast!

don't they wear combat boots anymore?

if you mean the little bits of the tank tracks.....i thought they stayed still?

so ....0mph?

There's no such thing as absolute velocity - all velocity is relative.

Relative to the ground, the part of the track touching the ground is not moving. The upper track is moving forward at twice the velocity of the vehicle (60 mph, in this case).

ohhh HLJ is a smarty pants!

You Sir, get a chocolate cigar!

My crush on SD grows stronger...

I will place my answer and explanation in the context of a few assumptions which follow:
1) We will assume that every piece of equipment will function as intended, regardless of the stresses placed on it. This means that the treadmill and the plane's landing gear will not simply fail by being misused.

We need to assume this because if we don't, the problem is subject to wild speculation on the capability of different elements of the model. One person may think the hypothetical treadmill is only capable of 35mph, another than the engines will overheat and explode if run at higher than taxi speeds without adequate airflow.

2) All other factors that are unstated are assumed not to exist, and will never become important to the conclusion. This means there is no headwind or tailwind, and the action of the treadmill will not create one.

Obviously adding elements not stated can alter the outcome enormously.

3) The airplane's engines are capable of finite thrust, equivalent to any real world example you choose.

4) The hypothetical treadmill is capable of infinite exertion within its role; it will move as quickly as required to keep the plane from moving forward.

We cannot simply say that the hypothetical treadmill is not capable of doing something the model specifically states it will do. That would change the original question itself. (BTW, the particular way the treadmill is stated in the problem is incorrect, but this interpretation attempts to follow the spirit of the question)

5) While equipment is assumed to function as intended, they are still subject to physical limitations. The landing gear are not perfectly frictionless, etc.

So, within this context, the plane can never take off. Lets first look at the plane at rest and the forces acting on it.

At rest, the plane is held in place by inertia and the friction of the landing gear. The landing gear is designed to reduce friction (compared to the belly of the plane), but it is not enough to simply glide across the runway with the slightest push. During use the landing gear will heat up due to this friction, with all the vibration and heat coming from the energy sapped by said friction.

Now if we start up the system the plane must be able to roll forward in order to create the lift required to take off. So, the question becomes "Can the airplane roll forward?" The plane pushes against the air and is held back by the friction of the landing gear, which will scale according to a small percentage of the speed of the wheels against the treadmill. Since the landing gear will always be able to provide a little more resistance if the treadmill's speed increases, the plane cannot roll forward and thus will never take off.


Practical issues with this model include the potential friction absorption capacity of the landing gear itself. The average jet engine can probably output enough thrust to exceed the capacity of the landing gear to shed energy, and they would fail spectacularly at some point. The treadmill will also end up traveling at astounding speed, and might end up creating significant airflow even supposing it could be constructed. But, that isn't the question we were asked.

That's your mistake. The trick in the trick question is that it is phrased in a way that encourages you to interpret its spirit rather than its words. It subtly encourages you to choose the physically impossible interpretation.

If there are two interpretations, and one requires a treadmill that can stop a jet engine using friction in the bearings of the landing gear, pick the other interpretation.

One interpretation requires a treadmill to stop a jet engine using friction in the bearings of the landing gear, which is theoretically possible.

The other interpretation is not internally consistent as it requires the treadmill to be simultaneously stationary and moving. (If the plane rolls forward and the treadmill is matching speed as compared to the ground, to keep it stationary would imply that the treadmill is stationary as well, but also moving at twice the speed the plane is attempting to accelerate) I chose the one that made sense.

Thanks steve. I really appreciate the social responsibility you showed by re-opening this thread.

Also, what is so physically impossible about stopping a jet with landing gear friction? I would wager that the friction of even a single 747's landing gear assembly can stop the thrust of my model rocket's engine, even without a treadmill. If you don't dispute that, the question becomes if the friction scales with speed, which should be clear.

Five!

Just think of it as my own little contribution to our community.

Shawnee seems to be the only one who has given this any serious thought.

Where are you getting the highlighted bit, from the question?

Plane moves forward, relative to the ground, at speed X.
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2 X as plane takes off.

The question tries to trick you into thinking that the "spirit" of the question is that the plane is held stationary relative to the ground, but the words of the question make no such claim.

Plane moves forward, relative to the ground, at speed X.(wheels spin at X, unless you are suggesting chunks of them are departing the plane)
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2X - so the treadmill must be moving at 2X.
Wheels spin at 4X - so the treadmill must be moving at 4X.
Wheels.....

And thus the problem with the statement. Obviously someone was trying to say something else.

Yes...

No.

Or, more accurately, the treadmill is moving at 2X, relative to the plane. It it still, however, only moving at X relative to the ground, matching the plane.

The treadmill matches the plane speed, both speeds relative to the ground. The plane moves at X, the treadmill moves at X in the other direction, and the wheels spin as if the plane were moving at 2X.

I disagree. The wheels don't spin at X. As soon as the plane begins to move forward, the treadmill instantaneously kicks into gear, and the wheels have to move 2X just to keep up with the plane. The plane moves X, but the wheels instantaneously move at 2X.
Yes.
I disagree again. The wheels move at 2X, but the treadmill moves at X. This is why the plane is moving forward relative to the ground.

Treadmills are activated by the force applied to their surface. There is no drive power coming from the wheels. No force
= no treadmill movement. The plane will lift off but won't clear the Universal Gym.








Dirty Damn SteveDallas

But then it's a circular question. For those saying that the plane doesn't move, relative to the ground, X = 0 and 2X = 0, so the treadmill doesn't turn and the plane can't take off. But if the treadmill doesn't turn, the plane can move as normal and will take off as from a normal runway. Which proves that the plane will take off.

DAMN IT!