StroppyChops wrote:There would be no uplift until the plane is moving forward - however the question is academic (cannot be positively answered).

You guys are taking the piss, right? This is a troll, to catch up presumptuous assholes who might assume anyone could dumb enough to not know the answer, right? Well, I'll bite.

Of course the question can be positively answered. The treadmill is not moving air and it's air thrust, provided by jet engines or propellers, against a relatively stationary atmosphere that moves the plane forward. As forward thrust is applied, the plane moves forward through the (relatively) stationary atmosphere and lift is created as the air velocity increases, via Bernoulli's principle, over the top of the air foil, creating lift in a direction perpendicular to the direction of motion. Once again: If thrust is provided, the plane will move forward. The wheels would spin faster to compensate for the moving treadmill, but forward motion would not be affected, as the wheels are turning freely and independently. Forward motion creates lift and the plane will take flight.

Now if the pilot slammed on the brakes...

Garry.Crabtree wrote:Didn't Mythbusters confirm that a plane cannot take off it moving at the same speed?

Just the opposite:

The thrust would drive it forward, just as it does in the air. I don't think the wheels on a treadmill would stop it going forward.
I disagee with those that think lift would be produced. Planes have to reach a certain speed before takeoff, to ensure enough lift.

terrifiedanimal wrote:

StroppyChops wrote:There would be no uplift until the plane is moving forward - however the question is academic (cannot be positively answered).

Of course the question can be positively answered.

You might want to check your understanding of how "it's academic" and "cannot be positively answered" are related. Note also that I used the word 'until'.

I just learned that a 747 under full engines has enough power for vertical takeoff with power to spare - didn't know that.

The question is basically “Can a plane accelerate if the wheels have 0 traction.” This happens all the time, since the wheels on an airplane have no traction while the airplane is in flight, and airplanes accelerate in flight all the time. Slightly more scientifically, the engines (whether it’s a prop or a jet doesn’t matter) use the air around the airplane to create thrust and lift; the runway serves no purpose except to reduce friction from grass and weeds and rocks and small mammals. For a similar real world example, look at sea planes. In fact, the water creates more drag on the pontoons than a runway or a treadmill at any speed could produce on the airplane, and yet sea planes can still take off.

Airplane engines create thrust, either by creating forward lift using a prop, or by creating a Newtonian action-reaction by the combustion of a fuel. In either case, whatever the plane is resting on has no affect on the plane’s ability to move forward, except where it creates drag (friction) against the plane’s wheels.

The forward thrust of the engines causes the plane to move forward. The movement of the (relatively) motionless air passing over the lifting surface of the wings creates lift. This works using Bernoulli’s principal. Again, whatever the plane is resting on has no affect on the plane’s ability to create lift.

An airplane’s wheels are free-spinning, except in some very expensive airplanes that have motors built in to spin the wheels up prior to landing – this reduces wear on the tires. Except for during landing (or braking), these expensive wheels are still free-spinning.

Now to answer the question about the treadmill.
1.1: The treadmill is free-moving. Friction between the wheels and the treadmill will cause them both to move forward in tandem as the plane’s engine pulls the plane forward. The plane would take off normally, except there would be no tire wear from rolling down a runway. If we assume that the treadmill runs on a frictionless track, the plane would actually take off faster, since friction between an ordinary plane’s wheels and the runway slows the plane’s acceleration.
1.2: Vb = Vc. As the plane’s engine pulls it forward, the treadmill starts moving forward (as in 1.1), which causes the plane’s wheels to turn forwards (by some phantasmic unnatural force, or just a motor linked to a speedometer attached to the treadmill). The forward motion of the wheels against the treadmill increases the plane’s rate of acceleration and the plane hopefully takes off, leaving the treadmill behind, before this feedback loop causes it to accelerate to Warp Factor 10.

2. Vc= Vw. The answer given is correct, the wheels will spin freely, twice as fast as the plane’s ground speed (Vb = 2*Vw), but the plane would take off the same as if it was on a normal runway. There would be a negligible amount of friction in the wheel’s bearings that might slow the plane’s acceleration slightly.

3. The equation doesn’t match the premise.
3.1: “What if we hook up a speedometer to the *wheel*, and make the treadmill spin backward as fast as the speedometer says the plane is going forward?” The speedometer is linked to the wheel, and not the plane’s air or ground speed indicators, and therefore it’s the same as 1.2: Vb = Vc.

3.2: Vc = Vb + Vw. In this scenario, as the plane’s engine generates thrust and pulls the plane forward, Vw > 0, the treadmill would start moving backward at Vw. In this first infinitesimally small moment, Vb is still 0. In the very next infinitesimally small moment, the treadmill motion forces the wheels to start turning and Vb = Vw = Vc. Once we move past the infinitesimal, the stated answer is correct that the treadmill would very quickly ramp up to infinite speed. Your wheels would burn off and, if the plane didn’t manage to get airborne before then, the whole plane would crash on an infinitely speedy treadmill. But, depending on how long it took that treadmill to increase in speed, it’s possible the airplane would be able to take off, since, as the wheels are free spinning, the motion of the treadmill has a negligible affect on the plane’s forward motion.

i love watching people fight over this question. When I asked it on facebook it topped 400 replies...

OrangeDragon wrote:i love watching people fight.

I fixed that for you.

terrifiedanimal wrote:Plane takes off like it normally would. It's not like the plane uses a drive to the wheels to obtain forward speed, so however fast the wheels are turning is irrelevant.

This is the right answer. Imagine holding a toy car with spinny wheels in your hand while it's on a treadmill... your hand is the force that drives it forward and the treadmill can only make the wheels spin faster, not push it backwards. Rotational friction is a constant, making the slight bit of backwards force it could apply to the wheels irrelevant in the face of any significant forward thrust. This means the air pressure the engines exert would drive it forward as normal and it would take right off.