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Imagine a plane is sitting on a treadmill

A physics and engineering riddle

Toytown Germany > Discussion forum > Themes > Miscellaneous
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eurovol
Aren't the Mutant Ninja Turtles green?
Dafydd
eurovol
Unless that is Dumbo, it ain't gonna fly.
Wheel
QUOTE (Sin @ Dec 20 2006, 11:02 pm) *
Post ONE THOUSAND on this thread!

And it's still only at no. 6 in the hot topics chart.
Silly Point
@Dafydd - Be serious, I ain't never seen an elephant fly.
Dafydd
But you been done seen 'bout everything, right?
eurovol
I have seen a peanut stand and heard a rubber band.
Silly Point
and I've seen a pub crawl
bluedave
But how does a tooth pick ? huh.gif
Dafydd
Who says the car can't fly...

Old Chestnut from the Darwin Awards.

The Arizona Highway Patrol were mystified when they came upon a pile of smoldering wreckage embedded in the side of a cliff rising above the road at the apex of a curve. The metal debris resembled the site of an airplane crash, but it turned out to be the vaporized remains of an automobile. The make of the vehicle was unidentifiable at the scene.

The folks in the lab finally figured out what it was, and pieced together the events that led up to its demise.

It seems that a former Air Force sergeant had somehow got hold of a JATO (Jet Assisted Take-Off) unit. JATO units are solid fuel rockets used to give heavy military transport airplanes an extra push for take-off from short airfields.

Dried desert lakebeds are the location of choice for breaking the world ground vehicle speed record. The sergeant took the JATO unit into the Arizona desert and found a long, straight stretch of road. He attached the JATO unit to his car, jumped in, accelerated to a high speed, and fired off the rocket.

The facts, as best as could be determined, are as follows:

The operator was driving a 1967 Chevy Impala. He ignited the JATO unit approximately 3.9 miles from the crash site. This was established by the location of a prominently scorched and melted strip of asphalt. The vehicle quickly reached a speed of between 250 and 300 mph and continued at that speed, under full power, for an additional 20-25 seconds. The soon-to-be pilot experienced G-forces usually reserved for dog-fighting F-14 jocks under full afterburners.

The Chevy remained on the straight highway for approximately 2.6 miles (15-20 seconds) before the driver applied the brakes, completely melting them, blowing the tires, and leaving thick rubber marks on the road surface. The vehicle then became airborne for an additional 1.3 miles, impacted the cliff face at a height of 125 feet, and left a blackened crater 3 feet deep in the rock.

Most of the driver's remains were not recovered; however, small fragments of bone, teeth, and hair were extracted from the crater, and fingernail and bone shards were removed from a piece of debris believed to be a portion of the steering wheel.

Ironically a still-legible bumper sticker was found, reading
"How do you like my driving? Dial 1-800-EAT-SHIT."

bluedave
Fix the attachment mate.
DrivinWest
The plane will fly. It was answered correctly in post #2 and correctly explained within the first two pages.

The whole key to the problem is getting your head around the fact that the treadmill/conveyor belt is completely irrelevant as the wheels aren't driven and are allowed to freewheel under the plane. As such, the means of propulsion is completely relevant; by very definition, the drive wheels of a car do not freewheel!

If you wanna get geeky.

The linked picture is not necessary to solve the problem. It is useful for understanding the deeper issues at work like friction with wheels moving twice the normal speed. Tom17 said it and I'll repeat it; the force of friction is not a function of speed. Yes, the wheels have to spin twice as fast and they might not be able to do that but harping on that point is getting away from the spirit of the question; it isn’t meant to test your knowledge of tire integrity at high speed.

And those of you who claimed to be trolling all along... I call shenanigans.

I'm off to the US in the morning so that's it for me the year. 1000+ posts = AWESOME!
bluedave
Strange that your diagram has a lawn dart on it though DW laugh.gif
eurovol
QUOTE (DrivinWest @ Dec 20 2006, 11:16 pm) *
As such, the means of propulsion is completely relevant.

No it ain't. Think about it and you will come to understand the force. Unless of course you are trolling here and trying to get to number "1" on the Hit Parade.

PS: I like the fact that your link suggests that you have to assume the threadmill length has to be adequate. tongue.gif

QUOTE (Dafydd @ Dec 20 2006, 11:17 pm) *
Who says the car can't fly...

Old Chestnut from the Darwin Awards.

MythBusters proved that was just a tale. I watched the program and them trying to get ahold of a rocket was more fun than watching nothing happen to the pick'em-up truck.
Wheel
A lot of fun and a lot of frustration. Cheers DW, have a happy Christmas.
Dafydd
Love the Algebra but where's Frank Muir when you need him?

eurovol
QUOTE (Wheel @ Dec 20 2006, 8:18 pm) *
Do you have to do this? It's fucking childish.

Just trying to help out the Germans.
wink.gif
DrivinWest
QUOTE (eurovol @ Dec 20 2006, 11:29 pm) *
No it ain't.

Like I said:

QUOTE (DrivinWest @ Dec 19 2006, 12:19 pm) *
I'm not going to bother stating my answer because it doesn't matter. The debate will continue regardless of the explanation given or who gives it. If you google this question, as I'm sure many of you have, you'll inevitably find people who've answered the question correctly and umpteen people who emphatically disagree with the correct answer.

If you think the means of propulsion is relevant then I think the question you are answering isn't the one asked.

Google: physics forum airplane treadmill

Just about everybody gets there in the end (usually with a smack on the forehead).

The Straight Dope #1
The Straight Dope #2

Note: I've seen this question phrased as the "the conveyor belt matches the speed of the wheels" not the "speed of the plane." This is a different question (see The Straight Dope #1).
DrivinWest
That should have read: If you think the means of propulsion is irrelevant then I think the question you are answering isn't the one asked.
BadDoggie
QUOTE (Dafydd @ Dec 20 2006, 11:17 pm) *
Who says the car can't fly...

That's an Urban Legend. Go read the origins from the author (who used to have this as a single page on an AOL site and has spent a lot of time over the years adding more information).

QUOTE (DrivinWest @ Dec 20 2006, 11:25 pm) *
And those of you who claimed to be trolling all along... I call shenanigans.

Call it all you want. Look at my posts again; I kept steering shit back to the wheels. I just did my BFR dude! Granted that wasn't a physics 203 exam but still...

woof.
Grinner
When at Cranfield Uni this was discussed to the Nth degree..

Althoughmy first post says NO. 100% not, that was refering to the Wood plane picture that was removed.. ( thanks Mods)

However, it is thought that sa soon as the plane lifts off, it will crash straight back down!

G
Scogs
over a thousand posts on this thread...people have way too much time on their hands at max and eads
eurovol
Imagine a car is on a massive conveyor belt, as long as forever. The conveyor belt is designed to match the speed of the car (not the wheels) exactly but moves in the opposite direction. The engines are running, the brakes are off, etc. Everything is normal save for the fact the car is on a really long treadmill.

How fast can the car move forward from a fixed point given its top speed is 200mph under normal conditions?

Can that car pull a plane (a small light jobby-DW's question said nothing about it being a jet anyway) fast enough so that the plane achieves lift?

rolleyes.gif

It matters only what the conveyor belt is matching.

QUOTE
Here’s another telling of the plane question. Someone in the comments on boing boing claims that this is the correct version.

Here’s the original problem essentially as it was posed to us: “A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. 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). Can the plane take off?�

Alas. The ‘real’ question turns out to be so boring that you could only get the wrong answer if you misunderstood the question. And that would be the questioner’s fault for not being more clear.

Boing Boing was talking about an airplane on a treadmill problem this morning (See also David Pogue’s NYTimes blog and a thread at The Straight Dope). The problem is as follows:

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Can the plane take off?
Yeti
Do the hamsters know how to drive a stick-shift or is it an automatic ?
sGb27
QUOTE (eurovol @ Dec 21 2006, 8:48 am) *
Imagine a car is on a massive conveyor belt, as long as forever. The conveyor belt is designed to match the speed of the car (not the wheels) exactly but moves in the opposite direction. The engines are running, the brakes are off, etc. Everything is normal save for the fact the car is on a really long treadmill.

How fast can the car move forward from a fixed point given its top speed is 200mph under normal conditions?

A bit over 100mph (given that most cars aren't actually at maximum RPM in the highest gear at Vmax)
Yeti
QUOTE (eurovol @ Dec 21 2006, 8:48 am) *
The engines are running,

Is this car a hybrid ?
eurovol
Give that may a cigar. He has just lifted off an airplane with a car on a conveyor belt. wink.gif
Sin
QUOTE (DrivinWest @ Dec 20 2006, 11:25 pm) *
And those of you who claimed to be trolling all along... I call shenanigans.

If you call that pub in Kilarney, the plane will never fly.
Yeti
But at least you can refuel easily.

(@Sin, you are missing an 'l' in the spelling Bassman, but I'm impressed at your powers of memory.)
Tom17
On the u-bahn this moring, I got what eurovol was trying to say. I was previously making the same assumption about the cars measured speed (at the wheels rather than absolute) as the no-fly people were making about the planes measured speed.

But eurovol was using the same (un-intuitive for a car) scenario of measuring the absolute speed rather than wheel speed so...

If the cars specified max speed is defined as a function of max engine rpm then the absolute max speed on the conveyor matching its absolute speed, would be half of its top speed.

However, if the cars specified max speed is a function of wind resistance and power/torque, then the speed on the conveyor would not be so easily defined. As the wind speed for the car is about half, I would assume that the engine would easily overcome this and rev out in top gear so the max speed would be half of that which is higher than half of the cars top rated speed. - Not clear, I know but it's early.

Certainly is another interesting thought experiment though. it goes to show that what is intuitive for one type of vehicle is not necessarily so intuitive for another smile.gif

All of that aside, it had nothign to do with the original question smile.gif And a thrust-based propulsuion system will still be able to achieve its max needed speed on the treadmil.
Sin
QUOTE (Yeti @ Dec 21 2006, 9:08 am) *
But at least you can refuel easily.
(@Sin, you are missing an 'l' in the spelling Bassman, but I'm impressed at your powers of memory.)

Thank you, Oh great potato man from the earth. I have a memory of 3.7kb. May your fermentatious orbs bring robust mystical rhythmic joy to chromosomes of the XX variety, and remain a mystery to the XY.

What was the question again? unsure.gif
Yeti
If you had chips in a chippan all facing north while the handle of the chippan is facing due south south east how much batter will you need to cover a 200 gram piece of plaice, all other factors being equal ?
sGb27
If you are allowed to change the gearing of a car, one on a converyor belt will reach about 80% of the speed it would reach without the conveyor. There's only two equations you need to know, tractive force = BHP / (speed of wheels), and drag force is (roughly) proportional to air speed squared. A little algebra and you get the result.
Yeti
What about the elbow out the window factor ? If the driver has hairy arms how much extra drag will this cause ?
eurovol
QUOTE (sGb27 @ Dec 20 2006, 2:45 pm) *
Interpretation 2: Conveyor speed = planes wheel speed, this means the conveyor does whatever is necessary to keep the plane stationary relative to the ground. Result: A conveyor with ever increasing speed and a stationary plane. As a further discussion, the conveyor could generate enough wind to lift the plane eventually (as the conveyor speed is ever increasing). But before that happens the wheels will probably break off and the plane will be catapulted backwards by the conveyor, so not really worth discussing.

Hum, isn't the only time that can possibly happen at a speed of 0 (wheels not moving)? Otherwise, the plane would take off in violation of the "Interpretation 2" question's premise unless it had ballistic flight capability.
Silly Point
Fucking hell, why do I keep checking this thread? It's like I'm running on a treadmill and no matter how hard I try I can't get off. Now, who was it that posted the hamster in a wheel analogy?
Yeti
What about if it gets complicated, like this ?
sGb27
QUOTE (eurovol @ Dec 21 2006, 10:10 am) *
Hum, isn't the only time that can possibly happen at a speed of 0 (wheels not moving)? Otherwise, the plane would take off in violation of the "Interpretation 2" question's premise unless it had ballistic flight capability.

One relationship handles everything: air speed = wheel speed - belt speed. I1 is that belt speed = air speed (hence wheel speed = 2x air speed), I2 is that belt speed = wheel speed (hence air speed = 0)

I don't understand what you mean by 'would take off in violation of the "Interpretation 2" question's premise'.
Tom17
QUOTE (eurovol @ Dec 21 2006, 11:10 am) *
Hum, isn't the only time that can possibly happen at a speed of 0 (wheels not moving)? Otherwise, the plane would take off in violation of the "Interpretation 2" question's premise unless it had ballistic flight capability.

I'm not sure what you are saying is violating anything, but lets put that "interpretation2" scenario into something that we can relate to.

Get yourself a string-powered Gyroscope, we all had one of these as a kid.

Load up the string and hold the frame of the gyroscope in your left hand. This is the plane (the frame) the thrust(your arm) and one of the planes wheels (the gyroscope wheel).

Now hold the string in your right hand. the string is analogous to the treadmill and where it is wrapped around the gyroscope shaft is analogous to the contact patch between the treadmill and planes wheel.

Now, imagine you want to apply some "thrust" with your left hand (the plane & engines) and you want to counteract this thrust with the string (treadmill) so that the gyroscope frame (plane) effectively does not move and stays stationary.

What happens? The exerted force gets transferred into angular momentum in the gyroscope (the planes wheels). As you do this, your right hand and the string(treadmill) is accelerating away from the gyroscope (plane).

So his scenario does not violate "interpretation 2". Its just very impossible to achieve on that kind of scale.
coolerking
all of this reminds of the film chicken run
Sin
QUOTE (Tom17 @ Dec 21 2006, 10:30 am) *
Get yourself a string-powered Gyroscope, we all had one of these as a kid.

I didn't. sad.gif

You've ruined my day. sad.gif

I feel like I've missed out on a normal part of everybody else's childhood. sad.gif
Yeti
We didn't even have string.
Tom17
We weren't even allowed to know what string WAS!

AND!! We weren't allowed a childhood. Sin were lucky!
Yeti
We were allowed to know what it was but it was a sin so you were not allowed to enjoy it.

Besides we were too busy eating unwashed gravel.
Tom17
We used to DREEEEAM about gravel!
Sanwald
We dreamed of having unwashed gravel!
Sin
Nothin'!

In my day we were only allowed to suck the shit off the gravel for the rich people.
Yeti
At least you had shit, we used to want to dream about shit but it wasn't allowed.
Tom17
DREAMS? Why, if we were caught dreaming we'd be killed to within an inch of our lives... And THEN be grateful for it!

p.s. Anyone see the Vic Reeves, Eddie Izzard, Harry Enfield and Alan Rickman one? Piss funny.
Yeti
My dad used to wake us up every 5 minutes with a burning torch under our nostrils to check we weren't dreaming but we had to get up before we went to bed anyway to get our morning beating before going to work a 27 hour shift in the coal mine using blunt spoons.

And we had to walk there barefoot, uphill, dragging the rocks that we had scraped clean with our fingernails.
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