A jet plane on a large treadmill

**neufox47** · 10-13-2016, 09:14 PM

I have a new perspective on this; if the treadmill could operate at infinite speeds with infinite acceleration, but the plane was limited by normal material / bearing capabilities the wheel bearings or wheels would fail, exploding or melting before the plane ever moved forward an inch. In a perfect treadmill system the wheels would almost instantaneously accelerate to failure speeds, rendering it .

If the wheels materials were made perfect and able to accelerate to infinite speeds it would still sit in place if friction still existed.

Remove friction and the plane takes off.

Im drunk / buzzing on a cigar.

**abraham** · 10-13-2016, 09:51 PM

If you can get a treadmill to infinite speed, or even relativistic speed, you don't need an airplane

doughboyshredder · 10-13-2016, 10:11 PM

Originally Posted by neufox47

I have a new perspective on this; if the treadmill could operate at infinite speeds with infinite acceleration, but the plane was limited by normal material / bearing capabilities the wheel bearings or wheels would fail, exploding or melting before the plane ever moved forward an inch. In a perfect treadmill system the wheels would almost instantaneously accelerate to failure speeds, rendering it .

If the wheels materials were made perfect and able to accelerate to infinite speeds it would still sit in place if friction still existed.

Remove friction and the plane takes off.

Im drunk / buzzing on a cigar.

This was my answer years ago and many pages back

In order for the plane to take off it must be able to achieve forward motion. If the treadmill perfectly opposed the thrust of the plane the wheel bearings melt and the plane does a nose dive

**mcski** · 10-13-2016, 10:54 PM

I only read about 10 pages so far, but did anyone solve the KITT problem? My theory is KITT had a jet engine.

**BmillsSkier** · 10-13-2016, 11:00 PM

Pretty sure KITT had a Hoff.

sb · 10-14-2016, 07:21 AM

KITT was powered by Zima.

**Dantheman** · 10-14-2016, 09:07 AM

Originally Posted by neufox47

I have a new perspective on this; if the treadmill could operate at infinite speeds with infinite acceleration, but the plane was limited by normal material / bearing capabilities the wheel bearings or wheels would fail, exploding or melting before the plane ever moved forward an inch. In a perfect treadmill system the wheels would almost instantaneously accelerate to failure speeds, rendering it .

If the wheels materials were made perfect and able to accelerate to infinite speeds it would still sit in place if friction still existed.

Remove friction and the plane takes off.

Im drunk / buzzing on a cigar.

You should stick to accounting.

Originally Posted by doughboyshredder

This was my answer years ago and many pages back

In order for the plane to take off it must be able to achieve forward motion. If the treadmill perfectly opposed the thrust of the plane the wheel bearings melt and the plane does a nose dive

And you're still wrong.

**DJSapp** · 10-14-2016, 09:33 AM

Originally Posted by grskier

This is going around the book face now Attachment 190120

At least they worded the question better. The wheels and the treadmill reach infinity once the engines spin up and it starts moving, then it's just a question of how long the 747 can keep accelerating on the busted wheels to achieve takeoff airspeed with an assist from the wind induced by the treadmill surface.

Also back to some earlier fun facts: the thrust of four 747 engines can overcome the static friction of having its wheels locked. So if the pilot said "Fuck this stupid problem in it's goddamed ear, I'm taking off with the parking brake on," the plane could take off with a wheelspeed of 0, though the wheels would all be exploded and on fire, but that's a problem for 3 minutes later.

**DJSapp** · 10-14-2016, 09:35 AM

Originally Posted by neufox47

I have a new perspective on this; if the treadmill could operate at infinite speeds with infinite acceleration, but the plane was limited by normal material / bearing capabilities the wheel bearings or wheels would fail, exploding or melting before the plane ever moved forward an inch. In a perfect treadmill system the wheels would almost instantaneously accelerate to failure speeds, rendering it .

If the wheels materials were made perfect and able to accelerate to infinite speeds it would still sit in place if friction still existed.

Remove friction and the plane takes off.

Im drunk / buzzing on a cigar.

We went through this too. If the treadmill could achieve infinite velocity, the air near the treadmill surface would start moving fast enough to lift the plane due to drag on the air induced by the treadmill. Think of the air suction forces when a train or truck passes you closely. It's that, but much, much larger.

And you figured out the paradox of this issue. It is all about how you measure speed. BIG HINT: airplanes don't measure the speed of their wheels, especially at 35,000 feet.

doughboyshredder · 10-14-2016, 09:43 AM

Originally Posted by Dantheman

You should stick to accounting.

And you're still wrong.

No, I'm not.

In order for the plane to have lift it has to have X amount of forward speed.

If the speed of the treadmill is -X and increases at the same rate as the increase of the thrust from the plane, the plane doesn't go anywhere.

The plane has to be able to move forward.

If the plane takes off at 120MPH then the planes wheels have to be moving at 120MPH faster than the treadmill. If the treadmill matches the wheel speed this isn't possible.

**Timberridge** · 10-14-2016, 09:50 AM

If its a gluten free plane loaded with white apologists anything is possible.

**Jong Lafitte** · 10-14-2016, 10:07 AM

I wonder what happened to all the planes that were in the air when Superman clocked the earth back a few rotations? did those people also go back in time or did they just age more slowly (relatively speaking, of course) while he was doing his thing?

**jono** · 10-14-2016, 10:22 AM

Originally Posted by DJSapp

At least they worded the question better. The wheels and the treadmill reach infinity once the engines spin up and it starts moving, then it's just a question of how long the 747 can keep accelerating on the busted wheels to achieve takeoff airspeed with an assist from the wind induced by the treadmill surface.

Also back to some earlier fun facts: the thrust of four 747 engines can overcome the static friction of having its wheels locked. So if the pilot said "Fuck this stupid problem in it's goddamed ear, I'm taking off with the parking brake on," the plane could take off with a wheelspeed of 0, though the wheels would all be exploded and on fire, but that's a problem for 3 minutes later.

New question, new crazy. Since this time the wheels and treadmill must accelerate instantly in order for the plane to move, the force exerted to move the plane will be essentially infinite. So you can't ignore bearing or rolling friction or the wheels' moment of inertia. Until the thrust blows up the wheels (allowing them--and, not incidentally, the treadmill--to stop) the plane's velocity remains literally infinitesimal. The very brief wind offered by the treadmill won't have enough time to lift the plane because the elevators are too high up to get the full force of the blast (the air doesn't accelerate as fast as the wheels) for long enough to lift the nose and give the wings enough angle of attack to overcome the fact that the air below them is moving (briefly) faster than the air above. Or maybe the air takes a while to slow down and the pilot could time it just right as the boundary layer suddenly stops? This seems unlikely.

On the thrust vs. static friction question, it seems like you calculated that the engines could overcome friction up to u=0.83 and then stated that the tires have u=0.85. So the plane would actually not quite move with the parking brake on. That's the kind of thing that really bears looking again to make sure it's right every decade or so.

In this case it might not matter much--the real question is what is the friction coefficient of whatever part of the landing gear the plane rests on after the wheels are burned off?

**Dantheman** · 10-14-2016, 10:25 AM

Man, if Mythbusters were still around they could devote an entire episode to this....

**mcski** · 10-14-2016, 10:27 AM

Even Mythbusters got in on this debacle. Wheels Busted.

http://youtu.be/YORCk1BN7QY

**::: :::** · 10-14-2016, 10:28 AM

i didn't realize how old this thread was

**guroo270** · 10-14-2016, 10:33 AM

Stupidity is timeless.

**Flyoverland Captive** · 10-14-2016, 10:39 AM

Originally Posted by doughboyshredder

No, I'm not.

In order for the plane to have lift it has to have X amount of forward speed.

If the speed of the treadmill is -X and increases at the same rate as the increase of the thrust from the plane, the plane doesn't go anywhere.

The plane has to be able to move forward.

If the plane takes off at 120MPH then the planes wheels have to be moving at 120MPH faster than the treadmill. If the treadmill matches the wheel speed this isn't possible.

...has to have x amount of forward AIR speed. That's the crux.

**east or bust** · 10-14-2016, 10:40 AM

posting in this very important, timeless thread

**east or bust** · 10-14-2016, 10:41 AM

what are the givens yo?

**DJSapp** · 10-14-2016, 10:42 AM

Originally Posted by doughboyshredder

No, I'm not.

In order for the plane to have lift it has to have X amount of forward speed.

If the speed of the treadmill is -X and increases at the same rate as the increase of the thrust from the plane, the plane doesn't go anywhere.

The plane has to be able to move forward.

If the plane takes off at 120MPH then the planes wheels have to be moving at 120MPH faster than the treadmill. If the treadmill matches the wheel speed this isn't possible.

From many pages ago.

There are 3 places to measure speed here

1. Speed of air over the wing
2. Speed of airplane's wheel
3. Speed of treadmill.

Now question 2.0 with the picture explicitly states that the treadmill matches the wheel speed. The original did not. So in the new scenario we know the following:

Per the question:
Wheelspeed + Treadmill speed = 0

Airplanes move by the engines pushing air. This is how they fly without the wheels touching the ground. The wheels are just a low friction platform for the engines and wings to rest upon. Seaplanes and skiplanes don't have wheels, so don't get hung up on these. So while the plane is on the ground, the wheels are just along for the ride based upon the speed that the engines move the wing through the air.

Per physics not on a treadmill:
Airspeed = wheelspeed

Now this is where the paradox begins

Our problem INCORRECTLY assumes the wheels drive the aircraft. They do not. To solve using the above information we agree on:

Airspeed - Wheelspeed = 0 = Wheelspeed + Treadmill speed

Consolidate terms:

Airspeed - 2x Wheelspeed = Treadmill speed.

Further simplification

Airspeed - 2x treadmill speed = Treadmill speed.

This equation is only true for treadmill speeds of zero and infinity. Per physics, the airplane (and therefore the wheels and treadmill) will begin moving as the engines do not act upon the treadmill. This causes the wheels to move. As the equation is only solvable for values of zero and infinity, the treadmill will continue to accelerate to infinity. The friction of the treadmill moving this fast on the air will induce wind (fluid mechanics), which will create lift. The treadmill will also melt the wheels (irrelevant at this point).

Better thought experiment to help you understand this:

Put a 747 on freshly waxed skis. Put this on your treadmill runway moving at infinity. The engines will still push the plane forward creating lift as normal.

Other fun physics fact:

The force of sliding friction is not dependent on velocity. So if the ski is sliding on a flat plane at 1 mph or 1,000 mph, it pushes back with the same force.

**jono** · 10-14-2016, 10:47 AM

You're leaving out the fact that with very high treadmill forces the tires slip, which allows the treadmill to go somewhat slower, since it matches the wheel speed.

Now what are the equations?

Hint: draw the FBD for the Wheels.

**Flyoverland Captive** · 10-14-2016, 10:52 AM

Simplified explanation:

I'm riding my bike on roller trainers, going 20mph, and stationary on the rollers. I pedal faster, the rollers go faster, and I never move.

You enter the room, stand behind me, and push me forward off the rollers. The speed of the rollers can't stop me, because the energy pushing me forward is completely independent of the wheel speed.

You're the jet's engines, pushing the plane forward.