i make no other assumptions than the ones given. christ, this isn't a religious debate. there's nothing to debate...there's a wrong and a right answer. the friggin plane will fly dammit!!!
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Interesting physics/logic riddle
- Thread starter sahtt
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i make no other assumptions than the ones given. christ, this isn't a religious debate. there's nothing to debate...there's a wrong and a right answer. the friggin plane will fly dammit!!!
<img src="http://i38.photobucket.com/albums/e131/kevncoll/Emoticons/1f4e507c.gif"> :biggrin:
My plane would "fly" around 120-150...and the wheels/tires were "safe" to about twice that (as I recall)
Apparently I'm one of the few people who thought it was immediately clear that the plane WILL FLY... don't want to offend people or act like I'm a know-it-all, but really it's not that complicated of a problem and I don't see why most people don't get it...?? The only assumption that would prove otherwise was if the rolling resistance was HUGE, but that is a very severe assumption (should be tiny in proportion to aero drag, otherwise when your plane lifts off the ground you would start accelerating much faster all of a sudden) and detracts from the real point of the exercise.
-Derek, a finance major (I'll ask my Boeing engineer roommate tonight, but I'll bet anyone 20:1 that the plane will fly ferchrissakes)
-Derek, a finance major (I'll ask my Boeing engineer roommate tonight, but I'll bet anyone 20:1 that the plane will fly ferchrissakes)
Dang, dude... take a pill. Even if I'm wrong (I'm not conceding until someone can show me a plane that moves forward on the ground without it's wheels moving), why do you have to get so frustrated? I mean, "this isn't a religious debate":biggrin:
Actually, now that I think more about it, I might be able to save a life here. Nicholas, you're right. I was wrong. "the friggin plane will fly, dammit!!!"
There... can you see clearly again now? Heart rate back down? Blood pressure falling? Good. I just saved someone from having a heart attack! :tongue:
Geez, I thought we were all friends here!
J
the vein on my forehead seems to have subsided and the vision in my left eye is slowing returning. that was a close one. thank you.
Can someone explain to me, without jumping down my neck, the flaw in this logic? I'm not being sarcastic... really, just tell me what's flawed so I can think about it some more.
1) engines provide forward thrust to a previously stationary plane on a conveyor belt runway; a conveyor belt that matches the speed of the wheels exactly, only backwards a la a treadmill at your local gym
2) plane starts moving forward, thus the wheels start to turn
3) conveyor belt starts to turn, effectively negating any forward motion of the plane (again, a la a treadmill)
4) more thrust, more speed at the wheels, more treadmill action
The net effect of the above is that the plane remains "stationary" (I keep going back to the treadmill example) and never gets the required airflow over/under the wings to create lift.
J
That's my take on it... can someone enlighten me to my failed logic?
1) engines provide forward thrust to a previously stationary plane on a conveyor belt runway; a conveyor belt that matches the speed of the wheels exactly, only backwards a la a treadmill at your local gym
2) plane starts moving forward, thus the wheels start to turn
3) conveyor belt starts to turn, effectively negating any forward motion of the plane (again, a la a treadmill)
4) more thrust, more speed at the wheels, more treadmill action
The net effect of the above is that the plane remains "stationary" (I keep going back to the treadmill example) and never gets the required airflow over/under the wings to create lift.
J
That's my take on it... can someone enlighten me to my failed logic?
there is your flaw. the movement of the treadmill will not negate the planes forward motion. the plane is not "pushing" against the surface to move forward. it's "pushing" against the air.
As many people are pointing out. The problem with this puzzle is that it’s worded in a somewhat ambiguous way. The crux of the issue is what do we mean by “the plane speed” ? There are two ways to interpret “the plane speed” and IMHO both are valid. So to simplify the discussion, let us assume there is no wind. The first way to interpret “the plane speed” is it’s air speed. Which because there is no wind will be the same as the speed of the plane relative to a tree planted at the end of the conveyer belt ( just to be clear, when the belt moves the tree does not) The second way to interpret “the plane speed” is it’s speed relative to the conveyer belt. The reason that I argue this is also a valid way to interpret “the plane speed” is. If you were running on your tread mill and you had just ran two, six minute miles and your friend said “how far have you run and how fast are you running?” Would you say “I have just run zero miles at zero mph” ? I don’t think so.
So if we are talking airspeed the plane takes off with the wheels going twice as fast as normal, providing the plane has enough power to overcome the extra drag on the wheel bearings and tires. Which most average planes would because they usually have a bit of extra power in reserve.
And if we are talking speed relative to the belt (which is the same as wheel speed) the plane will not take off. And the belt will be going at a crazy speed to create enough drag on the wheels to balance the full force of the engine(s). Under these circumstances in the real world it is most likely that the wheel bearings would melt and or the tires would disintegrate and then the plane would not take off anyway.
Regards,
Patrick
So if we are talking airspeed the plane takes off with the wheels going twice as fast as normal, providing the plane has enough power to overcome the extra drag on the wheel bearings and tires. Which most average planes would because they usually have a bit of extra power in reserve.
And if we are talking speed relative to the belt (which is the same as wheel speed) the plane will not take off. And the belt will be going at a crazy speed to create enough drag on the wheels to balance the full force of the engine(s). Under these circumstances in the real world it is most likely that the wheel bearings would melt and or the tires would disintegrate and then the plane would not take off anyway.
Regards,
Patrick
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so ... regardless of anything else...
if the plane moves in relation to the ground (air is static)... it flys =)
if it for what ever reason stays stationary relative to the ground (air is static too) it doesnt fly =)
i think the real question is, does it have in flight entertainment or not....
if the plane moves in relation to the ground (air is static)... it flys =)
if it for what ever reason stays stationary relative to the ground (air is static too) it doesnt fly =)
i think the real question is, does it have in flight entertainment or not....
Isn't this just the same as someone pushing a box on wheels that's on a treadmill? As soon as you push it forward on the treadmill, it starts to roll forward (on its wheels), doesn't it? But if the treadmill is turned on, the box won't move. I still don't get it. If that frustrates you, then just don't reply and let someone else straighten me out.
J
Yeah, I think the area of disagreement is whether the plane moves in relation to the ground. Oh and if you drink enough, anything is entertaining.
J
Very good! So one of us is wrong. I’m pretty sure it’s you so let me see if I can change your mind and if not then you can try to change mine.
Remember for the sake of this discussion we are defining “plane speed” as the speed relative to the belt.
So first we should agree that the conveyer belt or plane wont fail due to stress. Also please note that the numbers I am using are just arbitrary to demonstrate the concept. Now lets put the plane on the belt and attach a spring balance to the nose of the aircraft and imagine, if you will, that you are standing next to the conveyer belt holding the other end of the spring balance. The engine of the plane is switched off. Now I start to run the conveyer belt at say 5 mph. What do you think the spring balance will show? We know it wont show zero right? It will show a few pounds of pull to overcome the drag on the wheel bearings and tires. And as I increase the speed of the belt you are going to get pulled harder and harder until at some speed say 200 mph or 300 mph or so it’s going to be reading so much that it will pull you off your feet. So we will substitute a steel pole for you and put on a bigger spring balance scale and I will continue to increase the belt speed. When I set the belt speed to something crazy like 3000 mph then the spring balance will read say 1000 lb of pull. Now lets suppose the plane is only capable of producing 1000 lb of static thrust at full throttle. You should now be able to see that we can substitute the engine for the spring balance then everything will be in equilibrium and the plane is not moving relative to somebody standing next to the conveyer belt watching the plane. If the plane does not move it will not take off.
Regards,
Patrick
A good example is the "threadmill" or a car in a dyno machine. You can ran as fast as you can but you're not going anywhere if the threadmill/Dyno matches your speed in the opposite direction. Does that make sense?
You guys made me look this up with all your crazy "the plane won't take off" talk. Turns out...this guy has a great explanation and he's basically made a career out of ALWAYS being right.:biggrin: The plane takes off. End of story.:wink:
http://www.straightdope.com/columns/060203.html
"An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
03-Feb-2006
--------------------------------------------------------------------------------
Dear Cecil:
Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. 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?"
There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail
Cecil replies:
Excuse me--did I hear somebody say Monty Hall?
On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.
First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.
A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.
As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.
--CECIL ADAMS"
http://www.straightdope.com/columns/060203.html
"An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
03-Feb-2006
--------------------------------------------------------------------------------
Dear Cecil:
Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. 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?"
There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail
Cecil replies:
Excuse me--did I hear somebody say Monty Hall?
On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.
First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.
A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.
As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.
--CECIL ADAMS"
You guys made me look this up with all your crazy "the plane won't take off" talk. Turns out...this guy has a great explanation and he's basically made a career out of ALWAYS being right.:biggrin: The plane takes off. End of story.:wink:
http://www.straightdope.com/columns/060203.html
"An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
03-Feb-2006
--------------------------------------------------------------------------------
Dear Cecil:
Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. 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?"
There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail
Cecil replies:
Excuse me--did I hear somebody say Monty Hall?
On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.
First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.
A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.
As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.
--CECIL ADAMS"
As Cecile kind of points out in “The Straight Dope” I think that the crux of this problem is that it’s worded in an ambiguous way. There are two ways to interpret the wording. The whole key here is what do we mean by “The planes speed” ? Speed relative to what?
First scenario is that we are measuring the planes speed relative to a tree at the end of the conveyer belt. Just to be clear, even when the belt is moving the tree is stationary. So let’s say the plane is moving at 5 mph relative to the tree so the robot controlling the belt moves the belt at 5 mph and now the plane is at 0 mph relative to the tree. So we get into an interesting feedback loop here. You could argue that the robot would say to himself “the plane is not moving so I had better set the belt speed back to 0 mph but as he slows the belt speed the plane starts to move forward. So let’s go through the steps. Throughout this process the plane thrust is fixed at what would normally yield 5 mph. Step one Marvin (the robot) slows the belt speed to 4 mph so now the plane is moving forward relative to the tree at 1 mph so Marvin slows the belt down to 2 1/2 mph and now the plane is moving forward relative to the tree at 2 ½ so Marvin is happy. (Marvin is never really happy but that’s a different story). Another way to look at this same scenario is to go back to the point were the stationary plane is thrusting at 5 mph and the belt is running at 5 mph. The pilot is doing his best to take off so he increases the thrust and as he gets to 5 mph relative to the tree by using 10 mph worth of thrust. The robot is happy because he is running the belt at 5 mph so he is in compliance. As others have pointed out this will all result in the plane taking off at say 80 mph with the wheels spinning at 160 mph providing the plane has enough power to overcome the extra drag of spinning the wheels at twice the normal speed which I believe the typical plane would.
OK let’s move on to the Second scenario. I think this one is more in line with the spirit of the puzzle. The robot measures the speed of the plane based on the wheel rotation of the aircraft. In other words he always applies enough belt speed to keep the plane stationary relative to the tree. So the pilot piles on more and more thrust and the robot applies more and more belt speed. Because the planes airspeed is 0 mph and the thrust is not being used to overcome the normal aerodynamic drag it would be subject to. Virtually all the power is being used to spin the wheels. In order for the robot controlling the belt to keep the plane stationary relative to the tree, he is going to have to apply some serious belt speed. I would guess thousands of mph in order for the drag on the tires and wheel bearing to reach equilibrium with the max thrust that the plane is producing. So providing the wheel bearings and tires were indestructible. The plane would just sit there with white hot wheels and never take off. In the real world the tires would blow and the bearings would burn out and consequently the plane would also not take off.
I have great respect for Cecil and the straight dope. I have been going there for years. After I worked on the problem I did go there to read his take. As he points out there is a problem with the wording of the problem. So because it is open to interpretation one can argue that the plane takes off or does not depending on your own interpretation of the wording.
Regards,
Patrick
Exactly! Like I said... space shuttle. The wheels could be spinning, if the space shuttle had wheels on take off, at what ever speed but the thrust is going to get it off the ground always. Might burn up the bearing in the wheels but the plane will take off.
I think he covers both options pretty well.
1) The belt matches plane speed which means the plane takes off no problem.
2) The belt matches wheel speed which means there is a paradox - so the question CANNOT be posed this way.
Meaning, the first way is the only way the question can be logically posed and therefore is the only one that can be logically answered. And the answer is still that it takes off.
Jeeze... where the hell was I!?!! Clearly I need to have read the whole thread.
I was hoping to avoid this and I can’t believe I’m doing this… its like calling the Pope a liar. Cecil is wrong. Oh my God I said it! There is no paradox with the belt going at the same speed as the wheels. That just means that the plane is not moving.
Regards,
Patrick
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It took me a while to grasp this, that was my original thinking too, but the belt moving backwards at the same speed the plane is moving forwards does not keep the plane stationary. It would keep a car stationary, but not a plane.
If you put a boot on a cars wheels to prevent the wheels from turning, a car isn't going to go anywhere because the wheels are what provides momentum to a car, if you put a boot on a planes wheels, the plane is still going to go, it's just going to tear the wheels apart in the process. The wheels have no bearing on a planes movement, they're just there to make it easier for the plane to move forward by rolling.
If a plane is moving forward at 20 mph and you stick it on a treadmill moving backwards at 20mph, the plane is still going to continue moving forward at 20mph, but the wheels will spin at 40mph. The spinning wheels again have no bearing on the motion of the plane since they aren't what's causing the plane to move in the first place.
Apparently you need not... just the first page :wink:
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