# So, you have a plane on a conveyor belt...

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1 hour ago, YNM said:

It ain't magic...

Magic or not, there's an unexplained force in the problem as described.

If the wheels and the treadmill are always moving at the same speed, the plane must be stationary.  If the plane were moving forward, the wheels would be moving faster than the treadmill.  If the plane were moving backward, the wheels would be moving slower than the treadmill.  Therefore, since the problem states they are moving at the same rate, the plane is stationary.

If the plane is stationary, there must be some force counteracting the forward thrust from the engines.  This force is not defined in the problem.  Perhaps someone tied the plane to a tree behind it with a very strong rope?  Perhaps there is a brick wall at the front of the treadmill, preventing the plane from moving forward?  Perhaps there's a wizard in front, shouting "You shall not pass!" at the plane?  Whatever the reason, the plane is not moving, and therefore will not generate sufficient lift to take off.

Once that force is removed, the plane's going to move forward and take off.

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9 minutes ago, razark said:

Magic or not, there's an unexplained force in the problem as described.

If the wheels and the treadmill are always moving at the same speed, the plane must be stationary.  If the plane were moving forward, the wheels would be moving faster than the treadmill.  If the plane were moving backward, the wheels would be moving slower than the treadmill.  Therefore, since the problem states they are moving at the same rate, the plane is stationary.

If the plane is stationary, there must be some force counteracting the forward thrust from the engines.  This force is not defined in the problem.  Perhaps someone tied the plane to a tree behind it with a very strong rope?  Perhaps there is a brick wall at the front of the treadmill, preventing the plane from moving forward?  Perhaps there's a wizard in front, shouting "You shall not pass!" at the plane?  Whatever the reason, the plane is not moving, and therefore will not generate sufficient lift to take off.

Once that force is removed, the plane's going to move forward and take off.

Even so, eventually the plane could lift off. The treadmill, if it goes fast enough, will start to move the air above it, which will cause lift for the plane (increase in airspeed). If this lift gets high enough, the plane takes off.

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1 hour ago, razark said:

there's﻿ an unexplained force in the problem as described.

If the wheels and the treadmill are always moving at the same speed, the plane must be stationary﻿﻿﻿.﻿

Yes.

Briefly, before accelerating and taking off.

Your problem is trying to think the displacement in terms of the wheels. It ain't ! The wheel motion are just implied motion. You can replace it with jello for all that matters.

Edited by YNM

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1 hour ago, razark said:

If the plane is stationary, there must be some force counteracting the forward thrust from the engines.

Gravity. Air resistance. These forces are exactly the same that prevent the plane from moving without the threadmill.

If the propellers are turning and the plane is stationary, then the propellers aren't providing enough force to move the plane, which is exactly the same situation as if you took the threadmill out of the equation.

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12 hours ago, razark said:

Yes, because the thrust from the engines will give the plane positive airspeed, regardless of the speed of the ground.

This, it will be a bit more rolling resistance from the wheels but that is not an serious issue compared to air resistance and momentum.

Note that this can be emulated in KSP, build an large rover with landing gear and jet engines with an flat top, put an small plane on top and match the TWR of platform and plane with the platform going backward.

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1 hour ago, razark said:

If the wheels and the treadmill are always moving at the same speed, the plane must be stationary.  If the plane were moving forward, the wheels would be moving faster than the treadmill.  If the plane were moving backward, the wheels would be moving slower than the treadmill.  Therefore, since the problem states they are moving at the same rate, the plane is stationary.

If the wheels are frictionless the plane won't move, no matter how fast the treadmill is going.

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19 minutes ago, NFUN said:

If﻿ the ﻿wheels are frictionless

Then you have skis.

Edited by YNM

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6 hours ago, Snark said:

Correct, because it can't.  Sliding friction does not increase with speed.﻿

No, it wouldn't "hurl" the aircraft backwards.  It would simply gradually accelerate it backwards.  The amount of acceleration would be μg - a, where μ is the coefficient of friction between wheels and conveyor belt, g is gravity, and a is the acceleration the plane can get from its engines.  Sliding friction of rubber on surfaces will vary based on the surface, but is typically somewhere in the range 0.5 to 1 or thereabouts.  So take that, subtract acceleration from engines, and the backwards acceleration will be significantly less than 1g.  Dramatic, sure, but not fireworks-spectacular.﻿﻿﻿

No, because it would essentially be the same set of forces that the plane experiences when it's landing on a normal runway and turns on the brakes.  Which is why the rear wheels are only slightly behind the CoM, but the front gear is way out in front of the plane.  So that's actually the designed behavior and it's not going to pitch down by any appreciable amount.

This, note that plane wheels are stationary then landing, they are spin up by friction (some uses airspeed to spin up wheels.)

Driving an car on of off an moving car transporter, is not dramatic Car will not jump forward once wheels is on the transporter as the car has lots of mass while the wheels have lite and you are not accelerating hard.

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2 hours ago, razark said:

Magic or not, there's an unexplained force in the problem as described.

If the wheels and the treadmill are always moving at the same speed, the plane must be stationary.  If the plane were moving forward, the wheels would be moving faster than the treadmill.  If the plane were moving backward, the wheels would be moving slower than the treadmill.  Therefore, since the problem states they are moving at the same rate, the plane is stationary.﻿

If the plane is stationary, there must be some force counteracting the forward thrust from the engines.  This force is not defined in the problem.  Perhaps someone tied the plane to a tree behind it with a very strong rope?  Perhaps there is a brick wall at the front of the treadmill, preventing the plane from moving forward?  Perhaps there's a wizard in front, shouting "You shall not pass!" at the plane?  Whatever the reason, the plane is not moving, and therefore will not generate sufficient lift to take off.

Once that force is removed, the plane's going to move forward and take off.

The treadmill will not move as fast as the wheels. Only the rolling resistance move the plane backward, This is pretty constant with speed and way lower than the engine power.
Yes you would destroy the wheels at some speed. this speed will be significantly higher than the take off speed as it must be able to handle high speed rough landings.
Designing an runway size treadmill who can run at far over 300 km/h hold an small plane and accelerate to maximum speed before the plane take of will be an challenge.
While you do that I change the wheel on the plane to solid composite wheels capable to handling far higher speed.

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Me: Oh now i get why its banned on xkcd forum!

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You know... I've seen individual people's brains break from time to time.   Like the time I taught a friend to count in binary, then base 3, base 4, etc.   He had it down pretty good.   Then I had him count in base 11.   I actually got to see a person's brain vapor lock when he tried to say a one digit word for the value of 10 in base 11.

This thread is like that.   But en masse.   You guys are usually the smartest people around.......

And where the heck did bruschetta come from?!?

(Edit: In before the pedants.... value of 10 (in decimal) in base 11)

Edited by Gargamel

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14 minutes ago, Gargamel said:

And where the heck did bruschetta come from?!?

Italy and/or a parallel dimension.

And to stay on topic, if the treadmill is going the same speed as the wheels are turning then the plane won't move. That's logic. However, the treadmill won't be going the same speed as the wheels are turning. That's physics.

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14 hours ago, Gargamel said:

I actually﻿ got to see a person's brain vapor lock when he tried to say a﻿﻿ ﻿﻿one digit word for the value of 10 in base 11.

Got you covered to base 12.

χ and ε.

14 hours ago, 5thHorseman said:

However﻿, the treadmill won't be going the same speed as the wheels are turning.﻿

Unless the plane is stationary wrt the tread. Or the ground.

But those are split-second thing to do. Just like putting in reverse thrust until the plane goes backwards doesn't mean the acceleration gone wonky or anything.

But yeah, hope everyone is fresh again now (I know it's mostly early morning for most of you guys).

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Ok..........    *sigh*

Thank you @Dman979 for the xkcd link.... very apropo.

Ground speed and air speed are completely different beasts in this argument.   (Oh god, I've been sucked in).

With zero wind, the air speed is determined by the amount of thrust the engine can generate, propelling the plane forward.  At some point, the air speed will be enough  to create lift.

The treadmill only determines how fast the wheels will be turning.  There will be minimal friction in the wheel bearings, so the treadmill will have some minimal effect on the planes airspeed, but given we have a smooth treadmill, it would be far less than a very bumpy runway.

You know what.... nevermind....

The only way the plane doesn't take off, given zero wind, is if the air speed plus the treadmill speed exceeds the rated speed of the landing gear.  In that case the gear buckles and everybody dies.

I'll just leave this here:

Edited by Gargamel

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32 minutes ago, Gargamel said:

With zero wind, the air speed is determined by the amount of thrust the engine can generate, propelling the plane forward.  At some point, the air speed will be enough  to create lift.

so, you will not throw gas into the fire by talking about indicated airspeed and true airspeed? :-)

I once saw on the news about an unfortunate (and somewhat dumb) ultralight aeroplane pilot flying "backwards" while trying to come back to land from flying over the seas. At the of the day, the sea is warmer than ground, and then winds blow from land to sea.

If you have a underpowered vessel (and most ultralights do), you can end up without enough power to overcome the wind and being pushed back to the seas. While flying.

IIRC the lucky <piiiiii> had take off with full tanks (what's not much on these aircrafts) and barely managed to land on the shores. If memory serves, he climbed the most he could in circles, then gone for the beach nosediving.

Edited by Lisias

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7 hours ago, YNM said:

Briefly, before accelerating and taking off.

5 hours ago, magnemoe said:

The treadmill will not move as fast as the wheels.

But the problem defines that the wheels and treadmill are moving at the same speed.  If you allow the wheels to spin faster, the plane takes off, but then you have left the hypothetical world defined by the problem, and you are talking about a different question.

Reality: The plane on the treadmill is going to take off.
The problem, as defined: Some phantom force holds the plane stationary, and therefore it cannot take off.

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12 minutes ago, razark said:

But the problem defines that the wheels and treadmill are moving at the same speed.  If you allow the wheels to spin faster, the plane takes off, but then you have left the hypothetical world defined by the problem, and you are talking about a different question.

Reality: The plane on the treadmill is going to take off.
The problem, as defined: Some phantom force holds the plane stationary, and therefore it cannot take off.

Yes so question to kick back is what is the phantom force? its something who hold the plane back, not down but back, tying the tail to something or pressing the nose against an wall will work An wizard doing an force push the the same trust and the engine is the same
however the only thing the treadmill do here is rotating the wheels.

I think this was made up by some who dont understand that planes unlike cars has no power to the wheels. An more stupid version of rockets can not work in space because its nothing to push against.

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Oh my god. This subject.

Let me see if I can manage to hit the high point properly.

There is inferred ambiguity in the way the question is phrased. Without resolving this ambiguity, no conclusion is possible.

So, the question:

Quote

"Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

The problem is in one little phrase: "the conveyor belt is designed to exactly match the speed of the wheels".

What does this mean?

Well, it can mean one of two things:

1. The conveyor belt is designed to measure the tangential speed of the wheels and adjust its speed to match.
2. A series of conditions unspecified in the problem has resulted in the situation where the tangential velocity of the wheels is equal and opposite to the vector of motion of the surface of the conveyor belt.

If the correct meaning is (1), then the conveyor belt will attempt to match the speed of the wheels, but will not be able to do so. The plane takes off. This is the most straightforward interpretation. The question says nothing about what will happen; it only says what the conveyor belt is designed to do. Whenever the conveyor belt detects the wheels moving, it will immediately attempt to match their speed, which will increase their speed, which will cause the conveyor belt to accelerate faster and faster in an attempt to meet its designed performance criteria. Meanwhile, the plane merrily takes off without even noticing.

If the correct meaning is (2), then circumstances are quite different. Nothing the conveyor belt does can exert a rearward force on the plane greater than the mass of the plane multiplied by the coefficient of kinetic friction in the wheel bearings. Therefore, the only circumstance where the tangential velocity of the wheels is equal and opposite to the vector of motion of the surface of the conveyor belt is one where all velocities are zero. The plane is not moving, but neither are the wheels or the conveyor belt, because everything is turned off.

Obviously, I feel (1) is a more accurate interpretation. The question never says anything other than what the conveyor belt is designed to do. It is at this point that many will try to shunt explanation (2) back into (1), saying "But what if the conveyor belt has instantaneous acceleration?" But this is neither specified nor even implied in the original question. The original question only says what the conveyor belt is designed to attempt.

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45 minutes ago, razark said:

But﻿ the problem defines that the wheels and treadmill are moving at the ﻿same speed﻿.﻿﻿

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18 minutes ago, sevenperforce said:

The problem is in one little phrase: "the conveyor belt is designed to exactly match the speed of the wheels".

"Speed of wheels" is problematic to me. Is it the linear speed of the hub with respect to the ground? Or it could be the speed of the outer rim with respect to the hub, or it could be an RPM value, and there could be other interpretations as well.

There are interpretations that result in the plane not moving, interpretations that result in the plane taking off as normal and interpretations where the plane is launched forwards.

This question urines me off because the challenge is most certainly not figuring out what the plane will do, its a challenge of "Can you interpret this really awkward-to-word problem in spite of me wording it deliberately vaguely. Whilst you umm-and-aahh I will laugh in a haughty manner at my own perceived intellectual superiority."

Exactly as you say, if the question is stated clearly, the answer is obvious.

It reminds me of that really annoying "riddle":

"A mugger kills a woman, he steals her phone, her wallet and her keys - what is the first thing the thief takes?"

"Nope, first he takes a breath" the complete urine-taker smugly replies.

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10 hours ago, razark said:

If the plane were moving forward, the wheels would be moving faster than the treadmill.  If the plane were moving backward, the wheels would be moving slower than the treadmill.  Therefore, since the problem states they are moving at the same rate, the plane is stationary.

The problem doesn't state that the wheels are moving at the same rate as the treadmill. It states that the conveyor belt is designed to match the speed of the wheels.

Let us suppose the 747 is stationary on the treadmill, ready for takeoff. The pilot throttles the four engines to 100% and then releases the wheel brakes.

Up to this point, the conveyor belt cannot move. If the conveyor belt is designed to match the speed of the wheels, then the conveyor belt cannot move unless the wheels are moving.

However, we must acknowledge that the conveyor belt can have NO impact on the plane or its wheels unless it moves. So it cannot inhibit the initial motion of the plane. Therefore, the plane is free to move.

If the plane is free to move, then it will begin moving. If it begins moving, it is not stationary. If it is not stationary, then the treadmill will not be able to match the speed of the wheels, even though it will attempt to do so. Thus, the plane will take off.

30 minutes ago, p1t1o said:

"Speed of wheels" is problematic to me. Is it the linear speed of the hub with respect to the ground? Or it could be the speed of the outer rim with respect to the hub, or it could be an RPM value, and there could be other interpretations as well.

The way it is generally understood is that "the speed of the wheels" targeted by the conveyor belt is defined as the revolution rate multiplied by the outer wheel circumference. Not that people sit down and do the math; that's just what the assumed interpretation typically arrives at. This is also the only interpretation that leads to any problems. If you interpret it as "the linear speed of the hub with respect to the ground" then there is no problem; the conveyor is merely accelerating to match the forward speed of the plane which doesn't produce any issues at all.

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Ok, I've been watching this thread with some sort of amusement for the last few days. I am an historian, not a physicist. But I do play KSP and when traveling, I do stay at Holiday Inn Express when I have to travel with my job. So, with that said...

Thrust produces lift. Germany, in World War II, was developing early jet aircraft which didn't have landing gear as we often think of, but had sleds which remained affixed on the ground. It simply served as a means to hold the craft up until enough lift was generated by the wings. The lift was generated by the thrust of the jet engines pushing the craft forward. That thrust also produced forward momentum which is what directly contributed to the production of lift...

• So, no thrust = no forward momentum = no lift when it comes to traditional aircraft, as long as we are using either prop or jet engines.
• An aircraft landing gear are mostly along for the ride... and do not contribute to the take-off speed of the craft (technical note).
• So, a conveyor belt would have to be perfectly matched to negate all forward momentum (which is a technical impossibility) and thus, negating the generation of lift (again, since a conveyor belt has yet to be built that can do this, it cannot be done).

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Ok, I've been watching this thread with some sort of amusement for the last few days. I am an historian, not a physicist. But I do play KSP and when traveling, I do stay at Holiday Inn Express when I have to travel with my job. So, with that said...

Thrust produces lift. Germany, in World War II, was developing early jet aircraft which didn't have landing gear as we often think of, but had sleds which remained affixed on the ground. It simply served as a means to hold the craft up until enough lift was generated by the wings. The lift was generated by the thrust of the jet engines pushing the craft forward. That thrust also produced forward momentum which is what directly contributed to the production of lift...

/pedant, but while I agree with your conclusion, thrust does not produce lift. Thrust moves the plane forward; the motion of the air over the airfoil produces lift. If the plane is somehow held stationary, then all the thrust in the world will do nothing to lift the plane.

Of course, there is no way for the conveyor belt to hold the plane stationary, no matter how fast it goes. So that's that.

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Thrust produces﻿ lift.

Only in jet fighters. A 777 can't do that.

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Spoiler
On 3/25/2015 at 1:29 AM, Randazzo said:

There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Go!

(Sorry mods.)

Yes, by steering sideways onto a stationary piece of tarmac and taxiing to the proper runway. Its only "parked" on the conveyor, and the conveyor is not infinite.

Spoiler
On 3/25/2015 at 1:29 AM, Randazzo said:

There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Go!

(Sorry mods.)

Its never specified that the conveyor matches speed, only that it "runs". Aircraft easily takes off.

Spoiler
On 3/25/2015 at 1:29 AM, Randazzo said:

There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Go!

(Sorry mods.)

The belt has run away in the opposite direction, ergo plane is not on the conveyor any more, takes off normally.

Spoiler
On 3/25/2015 at 1:29 AM, Randazzo said:

There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Go!

(Sorry mods.)

No, because its not at an authorised airfield and has no filed flight plan. Only a high-speed taxi for flightworthiness testing is allowed.

Spoiler
On 3/25/2015 at 1:29 AM, Randazzo said:

There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Go!

(Sorry mods.)

No, because what is being described here is clearly an undercarriage testing rig, the mechanic sitting in the cockpit is fired for starting the engine and attempting to take off.

All of these are allowed via various equally valid interpretations of the question. This is not a science riddle, its a language riddle. Does that sound obnoxious? Thats because its from a class of obnoxious problems.

I mean no disrespect to the OP

Edited by p1t1o

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