You’re standing on the treadmill, but you’re wearing roller skates.
Ahead of you, a rope is attached to the wall.
If you’re holding the rope, the treadmill can be buzzing away below you, but as you’re on skates, you aren’t moving.
Now, if you pull on the rope, you pull yourself forward.
Regardless of how fast the treadmill is going*, you can move yourself forward on your skates by pulling on the rope.
Airplane wheels are like the skates: freely rotating. Airplane engines (propellers, jets, whatever) are like the rope: a means of applying locomotive energy unconnected to the wheels.
Clearer?
Real world speed, not up to some impractical relativistic velocity. That’s the complicated bit that makes the physics geeks object: An arbitrarily fast treadmill is capable of applying lateral force to the wheels via friction, which can conceivably hold the airplane in place. However, this is not where most lay thinkers have difficulty with the scenario, and can disregarded in conventional discussions of the problem.
For those still having trouble visualizing it, imagine a plane with no wheels at all hanging from a giant ceiling by a rope. Fire up the jets (or propeller). What happens? You should be imagining the plane thrusting forward.
Now take the same scenario, but hang a wheel (free spinning) from the bottom of the plane so that it touches the ground. What happens now when you fire up the jets? Same exact thing, yes? The wheel has no bearing on anything.
Now turn the ground into a conveyor belt moving in the opposite direction from the way the plane is facing. All it does is make the wheel spin faster.
brownie your scenario is not analogous to a plane, but rather a car. Instead of imagining yourself running on the treadmill, imagine yourself on rollerskates but with propellers on your arms.
Thanks, now I have a clear picture. Like I said before, it doesn’t even seem worth doing an experiment over --maybe that’s what confused me. Of course it would work. How do people think float planes and artic planes fitted with skis are able to take off?
One more angle. When the propeller starts turning, it pulls the plane forward. The forward motion of the plane thru the air generates lift and it takes off. The propeller’s backwash over the wings is not of consequence.
If the plane couldn’t move forward in otherwise still air, it would not take off. It moves forward because of the propeller (a jet engine or a rope attached to a wall would work, too). It is not hampered by the wheel contact with the ground, because whatever motion is made by the plane OR the treadmill only moves the wheels. Any motion imparted to the wheels has no effect on the plane or the treadmill. The only function of the wheels is to hold the plane off the ground until airborne. How they spin and even in what direction they spin is not a factor.
The treadmill, like any runway, must be long enough to support the plane until airborne.
Thank you, that was the one that pushed me over the edge into full understanding. Xema got me to the brink, but you pushed me over. It’s really all to do with frame of reference and understanding all of the forces in play.
Actually there’s only one thing you need to understand. A car moves by powering the wheels, which push against the ground. A plane does not power its wheels and they do not push against the ground.
If you had never seen a plane or a car, then saw them for the first time, you might not know that just by looking. Now you do. If you understand this, the problem won’t be difficult, either.
There are two debates that occur over this hypothetical problem. One is the debate that we’ve been discussing here with you and others, the answer to which is, as you point out, obvious. For that, mythbusters didn’t need to do squat, as anyone with an ounce of sense (or understanding of basic physics) knows the answer.
Then there is the debate that usually breaks out here on this message board, among other places. THAT debate is tied to interpreting the original problem. For, lo and behold, it turns out that what the plane does depends on how you define the treadmill. IF the treadmill’s speed is defined by the speed of the plane as it rolls forward, then the plane takes off no troubles. BUT, it the speed of the treadmill is defined as being exactly opposite to the speed of the wheels of the plane, THEN eventually the treadmill ends up accellerating to the point that either some mechanical malfunction occurs, or in the thought experiment, the point gets reached where the combination of frictional forces and torque forces end up keeping the plane from moving forward. Or so some assert; there is not universal agreement on this latter point.
If you want some added insight, simply look at the threads I linked earlier in this thread, especially at zut’s excellent summations.
IIRC the wheels are spinning at twice their normal rate.
On a jetliner this scenario may be problematic because at 300 MPH (twice the normal takeoff/landing speed) the wheels may exceed their design limits (that’s without considering the rapidly-accelerating-to-infinity scenario mentioned several times in this thread).
A plane–big, small, propeller, jet, whatever–can move forward in the air without its wheels touching anything at all. (And a seaplane has no wheels. It slides on the surface of water on pontoons.) The wheels are only there to keep the belly of the plane from scraping across the ground. So how could anything a treadmill does prevent a plane from moving forward?
Leave the wheels off altogether. A plane does not need wheels in order to move forward. Take a rocket. Grease it up with KY or something and lay it on a treadmill. Fire rocket. A treadmill spinning backward at the speed of light isn’t gonna stop the rocket from going forward, is it?
I just got back from sushi, and I’ve got a couple Sapporos in me, so pardon me if I’m a bit incoherent, but, I just watched the show before we left (irritating as hell BTW, how many recaps do you need? Seriously, you get five minutes of show and 40 minutes of review) and here’s how I think of it: imagine you’re already in a jet flying at 10,000 feet at 400 miles per hour. Imagine another specially designed plane with a conveyer belt on top of it flies up under your plane, and your plane drops its landing gear down on the other plane’s conveyer belt. The conveyor belt’s going 400 miles per hour one way and your plane’s wheels are spinning 400 miles per hour the other way. Is your plane going to suddenly drop out of the air, or is the speed of your plane’s wheels irrelevant to your flying?
THe plane with the treadmill is flying underneath you at the same speed you are? Nothing much happens other than the wheels spin 400mph. You are still flying 400mph relative to the air.
Yeah, the speed of the plane’s wheels are irrelevant to your flying.
The plane-with-wheels is a different case because its wheels have rotational inertia; that is, they resist changes in the speed of their rotation.
Consider a big drum of solid concrete lying on its side on a deactivated treadmill. When the treadmill is turned on, the drum of concrete doesn’t immediately spin at the final speed of the treadmill; it has a lot of rotational inertia and it has to be gradually ‘spun up’ to its final spin rate. While it is being spun up it will be dragged along with the surface of the treadmill until its spin rate is constant, at which point it will happily roll along, stationary relative to the ground no matter what the treadmill speed is. You get the same effect if you drop a nonspinning wheel onto a treadmill that is already at its final speed; the wheel is dragged along in the direction of the treadmill’s movement until its rotational acceleration has stopped, at which point it can ‘idle’ on the treadmill, experiencing no net forces.
The treadmill CAN impart a net force on the plane through the axle of the wheel, but only when the wheel’s spin rate is changing, because of rotational inertia effects. To impart this kind of force continually, the treadmill must undergo constant, runaway acceleration. Furthermore, the maximum force that can be applied is only as great as that which would cause the wheels to slip; once they start to slip there is no more acceleration and the net force disappears. So, best case scenario- with an infinitely accelerating treadmill and parts that do not fail under the impossible stresses - is the same as if the plane was trying to taxi with its brakes locked. If the plane can throttle up to the point that it can overcome its own brakes, then even a magic treadmill won’t stop it. In the real world, there is no way for a treadmill to accelerate fast enough or for long enough to stop the plane, and a treadmill that doesn’t continually accelerate will have no effect at all.
This has all been discussed before in greater detail.
You will note the phrasing here: “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).” There is nothing about frictionless bearings, insano speed treadmills, etc. The assumption of the problem (reasonably interpreted), is that the treadmill moves backward at the same speed as the plane itself moves forward. The answer here is simple.
Now, the complications arise. You will note that zut is one of the people who Cecil addresses with this second foray into the subject, and this is the same zut who has [post=8878795]very vividly broken the whole thing down for those who don’t understand[/post]. Basically, if you re-word the problem, you end up with a different result. Which result you end up with is rather hilariously stated by zut.
