A jet plane on a large treadmill

[MagnificentUnicorn]

The wheels in the OP question have been shown to spin about 2x normal. In 2016 version from page 31 the wheels go the same speed as the belt but in the opposite direction, meaning if the wheels try to roll forward the belt goes just as far in the other direction. In that version the plane never moves but the wheels are free to spin up to any speed and the treadmill will match them. As such, they will go more than 2x the normal speed, assuming they don't fly apart. I'm guessing they would fly apart at 3-4x normal landing speed, but that's entirely a guess.

The "2016" version has been around since at least 2005, see my previous link to The Straight Dope. I think you're wrong about the wheel speed matching version, for starters the wheels on a plane can't roll unless it moves forward or the wheels are powered like a car. I would guess that in the ground speed matching version the tread mill would be going faster than in the wheel speed matching version.

[MagnificentUnicorn]

Same RPM. Huh. I dunno if its what you're getting at but I just realized I've been thinking of the 'speed' matching feature of the treadmill as matching the 'speed' of the plane as it relates to the surface of the belt. Really, it seems that the belt in the question is only set to match the same speed (in the other direction) as the speed of the plane as it is calculated by how fast the wings are moving relative to the ground. The plane gets off even easier.

Yes.

[Mustonen]

Same RPM. Huh. I dunno if its what you're getting at but I just realized I've been thinking of the 'speed' matching feature of the treadmill as matching the 'speed' of the plane as it relates to the surface of the belt. Really, it seems that the belt in the question is only set to match the same speed (in the other direction) as the speed of the plane as it is calculated by how fast the wings are moving relative to the ground. The plane gets off even easier.

In the OP, yes. Not on the new (old) version, though. Which is currently under discussion.

[jono]

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 could answer this way and be mostly right, but putting the plane on blocks and turning the wheels backwards would actually fly. It's just a question of objectives, really.

Similarly, imagine a great wooden badger. Now disassemble it and build a glider. Tie a rope to the glider and hook that to a really fast car. Make sure it's all wheel drive so the front wheels will turn. Drive the car down the treadmill (OP version first, then grskier version from page 31; this is the PR, the dope here is never straight.) How fast is it going when the badger lifts off if the (reconfigured) badger has a stall speed of 2.7 x that of an unladen swallow?

[Mustonen]

The "2016" version has been around since at least 2005, see my previous link to The Straight Dope. I think you're wrong about the wheel speed matching version, for starters the wheels on a plane can't roll unless it moves forward or the wheels are powered like a car. I would guess that in the ground speed matching version the tread mill would be going faster than in the wheel speed matching version.

Yeah, instantaneous response doesn't typically exist (quantum physics?) in the real world, and the illogic of that has me hung up too. That said, If the wheels DO spin, they're going to spin really fast unless they're wicked heavy (in which case they'll still soon be spinning really fast). In either case, it's kind of like inadvertently writing an infinite loop in programming code. It doesn't make sense in a finite world.

In other news, nothing draws a derisive sigh quite like me responding to my wife asking what I'm typing away at on the computer with "I'm posting on TGR about the airplane on the treadmill."

[east or bust]

The funny part about this is you could probably give this problem to a couple upper classmen engineering students and they could have it worked out in a week. It would make a good take home test.

This is really tempting to try and do out. A mechanical background would be more helpful though.

[east or bust]

Engine stats.. this source looks alright? The last engine in the chart listed for 747's.

http://www.geaviation.com/commercial/engines/genx/
http://www.geaviation.com/engines/do...sheet-genx.pdf






747-8 spec sheet
http://www.boeing.com/assets/pdf/com...caps/747_8.pdf
page 95 for tire sizes

[stfu&gbtw]

Somebody FF this for me please... We can't really still be debating the original question, right?


Right?

[Jong Lafitte]

Nomination for treadmill operator, he has experience with tilt-a-whirls:



edit: joke probably already made in this thread somewhere but still...

[jono]

Somebody FF this for me please... We can't really still be debating the original question, right?


Right?

Right. Well, hopefully. Maybe someone is, but...oh, hell, just skim through page 31.

[idahospud]

Somebody FF this for me please... We can't really still be debating the original question, right?


Right?

No shit! Every day I look at Padded Room I'm amazed that this is still here.

Wheel speed has no relation to a plane moving forward, no power is being delivered to the wheels. So long as the engines are producing thrust, the plane will move forward. Problem solved.

Just imagine for a moment, if you will, if this much effort was put into the Plea to Ullr thread.

[jono]

The funny part about this is you could probably give this problem to a couple upper classmen engineering students and they could have it worked out in a week. It would make a good take home test.

This is really tempting to try and do out. A mechanical background would be more helpful though.

You mean actually building the treadmill of seemingly-limitless power? At some small scale?

[billyk]

The funny part about this is you could probably give this problem to a couple upper classmen engineering students and they could have it worked out in a week. It would make a good take home test.

This is really tempting to try and do out. A mechanical background would be more helpful though.

I don't think it would take a week. More like a few seconds of rational thought from anyone who knows basic physics.

[abraham]

Fuckin devil magic!



This thread is awesome

[wyeaster]

https://www.google.com/search?q=plan...obile&ie=UTF-8

[Svengali]

strong work wyeaster!
I liked this one the first time this nonsense "rolled" around

https://blog.xkcd.com/2008/09/09/the...amn-treadmill/

Moreover, he only brought it up to start an argument to act as a diversion while he seduced your mother in the other room.)

[wyeaster]

elegance!

[jono]

From the xkcd blog:

The airplane/treadmill problem...contains a basic ambiguity, and people resolve it one of a couple different ways. The tricky thing is, each group thinks the other is making a very simple physics mistake. So you get two groups each condescendingly explaining basic physics and math to the other.

The "problem" can be stated many different ways, but the versions posted here have each offered a defining assumption in their problem statements, which then turns each into a reading comprehension exercise, for the most part. (The argument that the wheels' speed can be defined at the belt gets tossed before it starts when the problem says "opposite direction.") His versions 2 and 3 are thus illustrated in the OP and by grskier at page 31, respectively.

Version 2 (OP) has been shown to work by Mythbusters' matching the plane's speed (more or less). Unfortunately, matching the wheels' speed would not be possible while pulling with the truck. But even if logic fails you, that version of the problem has been addressed.

The blog post's assertion that a PID controller on the treadmill (in the next version) wouldn't work is overly simplistic since real wheels accelerate in real time, not instantaneously. So the devil is in the details: done right, it works and done wrong the plane either flies or gets shoved backwards as the treadmill out-spins the wheels. I think as a group project the PID system is about a week's work for some engineering students as (I think) east or bust suggested. (It has been shown that the treadmill only needs to compensate for the thrust and accelerate the wheels according to the laws of physics--even with little to no friction. So the challenge is scale and response time, not some logical impossibility.)

Of course, if the PID controlled treadmill "works" it will blow the tires of the plane and what happens next gets less predictable, but is very unlikely to end in the plane flying safely into the sunset.

[old goat]

The plane sits on the treadmill, engines off, brakes off, treadmill accelerates to 500MPH. What happens to the plane? Assuming frictionless wheel bearings, the wheels spin at the speed of the treadmill, the plane doesn't move. In "real" life, the friction of the wheel bearings would be enough to move the plane slowly backwards, but no where near 500mph. Now the engines are started and throttled up. The plane accelerates forward and takes off. The key is that the movement of the treadmill is not coupled to the movement of the plane, because of the freely moving wheels.
What if the brakes are locked--assuming 100% effective brakes and a magic tire compound that doesn't allow the tires to skid on the treadmill? The plane might move forward, backward, or stand still. It wouldn't depend on the speed of the treadmill but on its force. If the treadmill generated force equal to the thrust of plane's engines the treadmill wouldn't move and the plane would standstill. If the treadmill was weaker the plane would move forward, stronger and the plane would move back.

[jono]

The plane sits on the treadmill, engines off, brakes off, treadmill accelerates to 500MPH. What happens to the plane? Assuming frictionless wheel bearings, the wheels spin at the speed of the treadmill, the plane doesn't move. In "real" life, the friction of the wheel bearings would be enough to move the plane slowly backwards, but no where near 500mph. Now the engines are started and throttled up. The plane accelerates forward and takes off. The key is that the movement of the treadmill is not coupled to the movement of the plane, because of the freely moving wheels.
What if the brakes are locked--assuming 100% effective brakes and a magic tire compound that doesn't allow the tires to skid on the treadmill? The plane might move forward, backward, or stand still. It wouldn't depend on the speed of the treadmill but on its force. If the treadmill generated force equal to the thrust of plane's engines the treadmill wouldn't move and the plane would standstill. If the treadmill was weaker the plane would move forward, stronger and the plane would move back.

It depends on how fast you accelerate, because the description ignores the inertia of the wheels.
You can choose to neglect friction and basically get similar answers, but the wheels' mass/inertia/resistance to acceleration is different. If their acceleration is going to be very large you have to factor it in, whereas if they're only going to hit ~2x normal takeoff speed and have time to get there their inertia is negligible. At Very large accelerations the wheels' inertia can absorb all of the engines' thrust, they just wind up going very fast, very quickly.

[Mustonen]

What percentage of the force of the wheels' inertia is transferred to the treadmill?

[jono]

Pretty nearly all of it, since friction starts low and doesn't increase much. 97% maybe?

That's the balance: to keep the plane (even approximately) still, the thrust force has to be balanced by the bearings, which send an equal (but opposite) force into the wheels (pushing them forward and the plane back). Then the wheels see an equal force (back) from the treadmill and since the bearing force is a tire radius distant from the treadmill force that pair of forces torques the wheels up to speed.

In Oldgoat's example, if the treadmill were to apply, say, 500,000 lbs of force while accelerating to 500 mph, the wheels would spin up very fast and the plane would actually go backwards despite its engines' thrust, even without any friction.

It's a shame the Mythbusters guys didn't have a camera pointed at the plane from the side (or didn't show it anyway); the moment the truck started to pull the plane would accelerate back a little and it would be interesting to know if that was visible. Since they didn't keep accelerating it would be very brief anyway.

[Harry]

look at aircraft carrier catapults

Best aircraft carrier video ever:

[sb]

Fkn airdales, they would look silly if we did not let them have a little steam.

[billyk]

This is going around the book face now Attachment 190120

This is a very simple problem if you understand basic physics and answer the problem as it is actually stated rather than make a bunch of assumptions about what is meant.

First of all, what is the "speed of the wheels"? The speed of the wheels is their rate of change in position. Speed is measured in distance/time like miles per hour or meters per second, etc.

If an airplane is rolling down a runway at 10 mph, how fast are the wheels going? They are also going at 10 mph, same as any other part of the plane.

Note that the inertial frame of reference of the plane is the earth, not the runway conveyor belt. If the plane is moving at 10 mph to the west, the conveyor belt is moving at 10 mph to the east. That doesn't mean the plane and its wheels are standing still, though. It is still moving at 10 mph to the west.

F=ma. Newton's some numbered law of physics that is sufficiently correct at sub-light speeds. Force equals mass times acceleration, or using grade school math, a = f/m. If you apply a shit ton of force to a plane by spewing hot gas out of the back of its engines it will begin to accelerate in the opposite direction (due to another of Newton's approximately correct laws). This is regardless of what the wheels and conveyer belt does, as long as there is not sufficient friction in the wheel bearings to cause sufficient force to completely oppose the Massive force of the jet engines. The wheel bearings are in fact designed specifically to be low friction devices, so there is no possible way they would stop the airplane from rolling, forward at an ever faster rate (accelerating forward).

And once the airplane is at takeoff speed, it will rise to the sky and go. It really doesn't matter that there is some huge conveyor belt moving in the opposite direction and the wheel bearings are getting warm. As long as they don't completely fail, seize up, and cause the wheels to drag along the runway with sufficient force to crash the plane, all is well.