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#91
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So...about that plane on the treadmill...
On Tue, 12 Dec 2006 21:23:56 -0800, Darkwing wrote
(in article ): "John T" wrote in message ... "Darkwing" theducksmail"AT"yahoo.com wrote in message This has NOT been adequately explained or there would be no question about it. If the plane is not moving on the treadmill but rather keeping up with the speed that the treadmill is moving (yes planes DO have throttle controls) the thing is going to takeoff with no air moving over the wings? NO WAY. Assuming you're a pilot, I don't understand why you think no air would be moving over the wings, but I'll give this one good "college try"... Yes I am a pilot. First, the question posed in the link by the OP of this thread is an incorrect variation of the original. The original problem asks: "A plane is standing on a giant treadmill. The plane moves in one direction, while the treadmill moves in the opposite direction and at the same speed as the plane. Can the plane take off?" As has been explained, placing a car on the question's treadmill would result in a stationary vehicle relative to the observer standing beside the treadmill. The reason is the car derives its propulsion through the wheels sitting on the treadmill and the speed of the car is measured by how fast the wheels are turning. The faster the wheels turn, the "faster" the car moves. However, this is only relative to the treadmill belt. To the observer standing beside the treadmill, the car is motionless. If the driver placed his hand out the window, he would feel no wind even though his "speed" as indicated by the speedometer may be 100 miles per hour. This is very similar to your example of running on the treadmill. You did not feel a relative wind in your face because you were stationary relative to the observer standing beside the treadmill. The reason you were stationary is you generate your propulsion by moving your feet against the ground (or belt, in this case) and the belt is moving in the opposite direction and same speed of your "travel". Like the car, your speed is measured by how fast your feet move from front to rear and they match the speed of the belt to cancel out each other. Now, replace the car and runner with an airplane. The airplane derives its propulsion from its engine pushing air from front to back. None of this energy is sent to the wheels to propel the airplane. The speed of the airplane is measured by the flow of air past the airplane, not the turning of its wheels. As the airplane's engine spools up to takeoff power, air is forced from front to rear and the plane moves forward regardless how fast its wheels are turning. The observer standing beside the treadmill would notice the treadmill speed up, the airplane's wheels turn twice as fast as normal, and the airplane move forward (not stationary). Speed is relative and the key here is the means of propulsion. The airplane's speed is measured by how fast the air is moving past it, not by how fast its wheels are turning or how fast the ground is flashing by. None of the airplane engine's energy is transmitted to the wheels to generate speed. All of the airplane's propulsion is derived from moving air (otherwise it would never stay in the air after takeoff). Since the treadmill has very little effect on the air (and what little effect it does have actually helps the airplane generate more lift), the airplane will indeed takeoff in the same distance it normally would use without the treadmill. However, the airplane wheels would be turning at twice their normal speed at the time of takeoff. Try this experiment: Take a toy car and attach it to a string. Tie the other end of the string to a small spring scale. Place the car on the treadmill belt and hold the scale in front of the car while you turn on the treadmill. Observe nearly zero (essentially 1G) force being exerted on the string/scale. Speed up the treadmill (for simplicity, let's say you set it to a constant 10mph) and you'll observe no significant difference in force exerted on the string (the only additional force is the friction of the car's axles). Now gently pull the string/scale forward. As long as you maintain a 1G force on the string, the car will continue to accelerate. Now, to the observer standing beside the treadmill, was the car stationary or moving forward? It's speed was certainly not zero as the car most definitely moved from rear to front of the belt. What was the speed of the car relative to the "driver" sitting inside the toy? The wheels would be turning faster than 10mph. If the "driver" were to put his hand out the window, how fast would the air be moving? Much slower than his wheels would say he's moving, but faster than the driver I mentioned at the beginning of this post. Replace the toy with the mythical airplane above, replace your arm with the airplane's engine (and propeller, if appropriate), then replace the string with the airplane engine mounts. You should now be able to visualize why the airplane sitting on that giant treadmill would most definitely takeoff. If not, I wish you good luck and safe flight. You'll need it. -- John T Thank you for your reply. Here is my .02, it would seem that the plane never actually moves in respect to the observer no matter how fast the treadmill moves, the plane will just take off like it is hovering and then slowly accelerate away? I guess I'll have to set this up and try it, I do have a few RC planes laying around and I have a treadmill so I guess I'll know one way or another, unless Mythbusters beats me to the punch. ------------------------------------------------------- DW You assumption is that the plane never moves relative to an observer. In fact, the airplane will accelerate normally and run down the treadmill and take off normally no matter how fast the treadmill is moving. The only thing that would stop it is the wheels coming off. The treadmill cannot keep the airplane from accelerating in this way. An observer standing next to the treadmill will see the airplane moving down the treadmill and taking off, just like it would from a normal runway. Airplane engines cannot feel the wheels. They do not turn the wheels. So the wheels will automatically spin fast enough to keep up with the accelerating aircraft. This is easily demonstrated. All you need is a pair of roller blades, a rope, and a treadmill. You stand on your roller blades on the treadmill with a rope attached to the front. Measure the force needed to pull yourself to the front of the treadmill with the treadmill off. Then try it at different speed settings. It always requires about the same amount of force to pull yourself forward. The only that changes is that your wheels spin faster to compensate. The treadmill could be moving many times faster than the airplane; it does not matter. The airplane will move down the runway and take off normally. The other gotcha in this little puzzle is that it attempts to get you to divide by zero. This is the old Achilles vs. the Tortoise conundrum that so puzzled ancient Greek mathematicians. The puzzle was this: Achilles and a Tortoise agree to have a race. Achilles agrees to let the Tortoise have a head start of getting half way to the finish line. The starting gun sounds and they are off! (Well, the Tortoise is, anyway.) The Tortoise reaches the half-way mark and Achilles starts running. But by the time that Achilles reaches the half-way mark, the Tortoise has moved forward. And by the time that Achilles reaches the point where the Tortoise has moved to, the Tortoise has moved forward again, albeit not as far as before. Again Achilles reaches the third point where the Tortoise was, but the Tortoise has moved forward again. No matter how fast Achilles runs, he can never catch up with the Tortoise. It was this sort of logic that led the Greeks to conclude that everything was imaginary and that motion was impossible. They could not solve the problem because they did not have the number zero. The False Pythagorean theorem is similar; it postulates that the shortest distance between two points is always a right angle, or in other words, the hypotenuse of a right triangle is equal to the sum of the other two sides. It is false on the face of it; we can see that this is obviously not true, but nevertheless you can make a powerful argument that it is. If you have a right triangle ABC where the hypotenuse is AC, you can measure the sum of AB and BC. If you turn the hypotenuse into a series of steps, the rise of the steps will always equal BC and the run of the steps will always equal AB. No matter how large or small you make the steps, the rise will equal BC and the run will equal AB. A straight line hypotenuse and be seen to be simply a series of infinitely small steps; the sum of the rise of the infinite steps must be BC and the sum of the run of the infinite steps must be AB. Therefore AC must equal AB plus BC. Bzzzt. The Greeks could not solve that puzzle, either, until Pythagoras was able to prove that it is the square of the hypotenuse that equals the sum of the squares of the other two sides. But even then a lot of people did not believe him. The airplane-on-a-treadmill is just a restatement of the same problem. It attempts to convince you that the airplane cannot move relative to an outside observer if the treadmill always moves at the same speed as the wheels. If the wheels accelerate, then the treadmill accelerates, so the plane cannot move, right? Wrong. The airplane does move, and it accelerates relative to an outside observer at the same rate as it would if the treadmill remained stationary. The only thing that changes is that the wheels spin faster. None of the thrust of the engines on an airplane is being used to overcome the force of the treadmill because the wheels spin freely. It would be different with an automobile. There the motor has to overcome the force of the treadmill. But the only thing resisting the airplane is air, which remains constant no matter how fast the treadmill is moving. Think of it like this: raise the airplane a few inches off the treadmill, put the engines to full power, and for grins leave the gear down and add a little motor to keep the wheels spinning at the same speed as the treadmill. Have the wheels accelerate at the same speed as they would on a normal takeoff, and have the treadmill match speed with the wheels. Now the airplane is not even touching the treadmill. Do you believe that the airplane will still remain stationary with respect to an outside observer? Yet the treadmill's relevance to the speed of the speed of the wheels is just the same as it was before when the airplane actually sat on the treadmill. And the treadmill is having exactly the same effect on the airplane's forward motion as it did when the airplane was touching the treadmill, which is to say none. |
#92
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So...about that plane on the treadmill...
Surely you jest. Please tell me you're joking.
mike "Darkwing" theducksmailATyahoo.com wrote in message ... Thank you for your reply. Here is my .02, it would seem that the plane never actually moves in respect to the observer no matter how fast the treadmill moves, the plane will just take off like it is hovering and then slowly accelerate away? I guess I'll have to set this up and try it, I do have a few RC planes laying around and I have a treadmill so I guess I'll know one way or another, unless Mythbusters beats me to the punch. ------------------------------------------------------- DW |
#93
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So...about that plane on the treadmill...
Christopher Campbell wrote:
The other gotcha in this little puzzle is that it attempts to get you to divide by zero. Explain to us please where the statement of this problem ever involves division by zero. One can readily see where the statement implies a value of zero for air speed since in the absence of wheel slip: Treadmill speed = wheel speed (stated explicitly in the problem) and Air speed = wheel speed - treadmill speed (assuming calm air) this directly implies that Air speed = 0. But I don't see where division by zero ever comes into play. The stated problem does imply a runaway positive feedback in the treadmill speed control. I.e. the moment the plain starts to roll forward the control system would speed up the treadmill to match the wheel speed. The motion of the treadmill would then speed up the wheel rotation to a higher speed thus forcing the treadmill to move still faster to catch up. The result would be an ever increasing treadmill and wheel speed until something gives - most likely the tires (if we ignore the technical difficulty of building the specified treadmill). This is the old Achilles vs. the Tortoise conundrum that so puzzled ancient Greek mathematicians. The puzzle was this: Achilles and a Tortoise agree to have a race. Achilles agrees to let the Tortoise have a head start of getting half way to the finish line. The starting gun sounds and they are off! (Well, the Tortoise is, anyway.) The Tortoise reaches the half-way mark and Achilles starts running. But by the time that Achilles reaches the half-way mark, the Tortoise has moved forward. And by the time that Achilles reaches the point where the Tortoise has moved to, the Tortoise has moved forward again, albeit not as far as before. Again Achilles reaches the third point where the Tortoise was, but the Tortoise has moved forward again. No matter how fast Achilles runs, he can never catch up with the Tortoise. It was this sort of logic that led the Greeks to conclude that everything was imaginary and that motion was impossible. They could not solve the problem because they did not have the number zero. Zeno's Paradox. But I doubt if you could find any ancient Greeks who actually concluded that motion was impossible. Even while puzzling with Zeno over his problem, they continued to go to the markets to do their shopping and to their respective work places. And there's no need to have the concept of the number zero to solve Zeno's paradox, just the idea of the convergence of some types of infinite sums. I.e. if each successive run of Achilles is half as long as the previous one (say he walks twice as fast as the tortoise) then we have a sum for the total distance 'D' of the form: D = x + x/2 + x/4 + x/8 +... multiplying this by 2 gives: 2D = 2x + x + x/2 + x/4 + x/8 + ... = 2x + D subtract D from both sides and we solve for the total distance Achilles needs to walk: D = 2x; i.e. twice the distance of the headstart he gives the tortoise. The airplane-on-a-treadmill is just a restatement of the same problem. It attempts to convince you that the airplane cannot move relative to an outside observer if the treadmill always moves at the same speed as the wheels. If the wheels accelerate, then the treadmill accelerates, so the plane cannot move, right? Wrong. The airplane does move, and it accelerates relative to an outside observer at the same rate as it would if the treadmill remained stationary. The only thing that changes is that the wheels spin faster. Sure, but airplane wheels have some maximum speed. Once the treadmill gets up to that maximum speed the airplane wheels would fail and the airplane is now sitting on a treadmill with a bunch of failed tires. So the question becomes whether a plane can still take off after you shoot out all the tires when it first begins its takeoff roll. And yes, postulating a frictionless surface for the treadmill gets around the problem and allows a normal takeoff. But the very term treadmill implies a surface with reasonable friction, i.e. the tread. |
#94
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So...about that plane on the treadmill...
"Morgans" wrote in message
... "Travis Marlatte" wrote I guess it's because the forward motion of the carrier negated the forward thrust of the plane. What????????????????????????? You really didn't mean what you said, or say what you believed, did you? That would be a no. I thought it was in keeping with the ridiculous debate over the treadmill "puzzle." If that is what you meant to say, you better get your money back from whoever taught you the ground school portion of your ticket, and then go back and take high school physics again. -- Jim in NC ------------------------------- Travis Lake N3094P PWK |
#95
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So...about that plane on the treadmill...
"Gig 601XL Builder" wrDOTgiaconaATcox.net wrote in message
... "Travis Marlatte" wrote in message et... "Bob Noel" wrote in message ... In article , Jose wrote: The wheels don't have to push on anything for an aircraft to take off...there's no drivetrain feeding power to the wheels! Right. Phrasing it the way I did may get people to realize this, or at least to think about it themselves. If you put an airplane on the roof of a speeding train, would it take off? What if the train were shaped like a runway? What if it were very thin? hmmmm, if you put the airplane on, say, a fast moving ship, could it take off? I wonder.... -- Bob Noel Looking for a sig the lawyers will hate I don't think so. I've seen videos of planes launching from an aircraft carrier (that's a fast moving ship, right) fall right off the end. I guess it's because the forward motion of the carrier negated the forward thrust of the plane. What you saw was an aircraft that failed to achieve and or retain a critical airspeed. Either the catapult failed or the engine failed or, well any number of things. There is a reason carriers turn into the wind to launch aircraft. There is also a reason that carriers can't launch fixed wing aircraft while tied to the dock. Well they might be able to but a lot of things have to be perfect. Thanks. But it was a joke. I do question the word "can't" in your explanation. I would believe "can't launch some fixed wing aircraft but not as a general statement. -- ------------------------------- Travis Lake N3094P PWK |
#96
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So...about that plane on the treadmill...
"Montblack" wrote in message
... ("Darkwing" wrote) Thank you for your reply. Here is my .02, it would seem that the plane never actually moves in respect to the observer no matter how fast the treadmill moves, the plane will just take off like it is hovering and then slowly accelerate away? Not unless the plane's "wheels" are coupled to the shaft of a gyro's rotor. Try this one: You're in a Class B airport terminal. You're on roller-skates, Rollerblades, a skateboard... whatever. You find yourself on an (evil) moving sidewalk - facing the wrong way. The (evil) sidewalk ALWAYS matches your wheels' forward speed. Someone moves a huge Hollywood 'film set' fan, in a few feet behind you. They point the fan at your back and turn it on. You hold open your jacket to make a sail (...like kids at the ice skating rink have done for ages) 1. Will you get blown down to the far end of the moving sidewalk - your destination? 2. Will you remain in the same spot - relative to the wall - no matter how hard the giant fan blows? 3. Forgetting the fan, if you try pulling yourself forward using the stationary handrails, will you in fact move forward? Or will the (evil) moving sidewalk thwart your forward motion by speeding up? Or will your upper body pull itself forward, while your feet remain behind ...(or stationary, relative to the wall and the handrail)? 4. How is this the same as the airplane and the treadmill question? How is it different? Montblack It's basically the same question with the same ambiguities. The crux of most of the hilarious debate is really over what defines the speed of the treadmill. It seems like a more interesting puzzle if the treadmill (or evil moving sidewalk) tries to match the forward speed of the object on the wheels resulting in the wheels simply spinnning at twice the speed of the forward movement of the object. The other interpretation, which leads to an impossible solution, is that the treadmill moves to counteract all forward motion - which results in a treadmill accelerating to infinite speed (or until the wheels explode which ever comes first). -- ------------------------------- Travis Lake N3094P PWK |
#97
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So...about that plane on the treadmill...
"Gig 601XL Builder" wrDOTgiaconaATcox.net wrote in message
... "Rip" wrote in message . net... Ray wrote: Looks like airplane treadmill problem, regularly a spark for flame wars on R.A.P., has made it into the mainstream. http://pogue.blogs.nytimes.com/ Let the arguing begin! - Ray Yes, the airplane will take off. The thrust of the engine is against the AIR. NOT the treadmill. There are two real life situations analogous to this: 1) Will an airplane on an essentially frictionless surface (say, wet ice) take off? Of course it will at airspeed X. And it will do so at a power setting that creates airspeed X. 2) Will a sea plane take off upriver in a current equal to it's take-off speed (this one is a cheat, since it involves drag not involved in the original situation, but should be a good "fire starter" for further discussion). Yes it will and it will do so at a power setting that creates airspeed X x2 Uh. That would not be true. At least not as a general statement. Unless you somehow believe that the extra friction of water moving at twice the takeoff speed requires X power to overcome - which seems unlikely. ------------------------------- Travis Lake N3094P PWK |
#98
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So...about that plane on the treadmill...
wrote in message
ups.com... Rip wrote: Yes, the airplane will take off. The thrust of the engine is against the AIR. NOT the treadmill. The thrust of the engine is not against the air. It generates thrust as a Newtonian reaction to the prop moving air back, not "pushing on other air." A rocket in space has nothing to push against, yet it generates the same thrust as it did in the atmosphere. 1) Will an airplane on an essentially frictionless surface (say, wet ice) take off? Of course, as forward motion creates airflow over the wings. There is no forward motion on the treadmill. Why isn't there forward motion on the treadmill? The pressure differential around the prop or the thrust from a jet will propel the plane forward to takeoff speed on glare ice (wheels don't have to spin at all) or the treadmill (wheels spin at twice the speed). -- ------------------------------- Travis Lake N3094P PWK |
#99
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So...about that plane on the treadmill...
In article ,
"mike regish" wrote: Surely you jest. don't call me... aw heck, it doesn't work closed captioned -- Bob Noel Looking for a sig the lawyers will hate |
#100
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So...about that plane on the treadmill...
On Wed, 13 Dec 2006 14:34:54 -0800, peter wrote
(in article . com): Christopher Campbell wrote: The other gotcha in this little puzzle is that it attempts to get you to divide by zero. Explain to us please where the statement of this problem ever involves division by zero. One can readily see where the statement implies a value of zero for air speed since in the absence of wheel slip: Treadmill speed = wheel speed (stated explicitly in the problem) and Air speed = wheel speed - treadmill speed (assuming calm air) this directly implies that Air speed = 0. But I don't see where division by zero ever comes into play. The stated problem does imply a runaway positive feedback in the treadmill speed control. I.e. the moment the plain starts to roll forward the control system would speed up the treadmill to match the wheel speed. The motion of the treadmill would then speed up the wheel rotation to a higher speed thus forcing the treadmill to move still faster to catch up. The result would be an ever increasing treadmill and wheel speed until something gives - most likely the tires (if we ignore the technical difficulty of building the specified treadmill). This is the old Achilles vs. the Tortoise conundrum that so puzzled ancient Greek mathematicians. The puzzle was this: Achilles and a Tortoise agree to have a race. Achilles agrees to let the Tortoise have a head start of getting half way to the finish line. The starting gun sounds and they are off! (Well, the Tortoise is, anyway.) The Tortoise reaches the half-way mark and Achilles starts running. But by the time that Achilles reaches the half-way mark, the Tortoise has moved forward. And by the time that Achilles reaches the point where the Tortoise has moved to, the Tortoise has moved forward again, albeit not as far as before. Again Achilles reaches the third point where the Tortoise was, but the Tortoise has moved forward again. No matter how fast Achilles runs, he can never catch up with the Tortoise. It was this sort of logic that led the Greeks to conclude that everything was imaginary and that motion was impossible. They could not solve the problem because they did not have the number zero. Zeno's Paradox. But I doubt if you could find any ancient Greeks who actually concluded that motion was impossible. Even while puzzling with Zeno over his problem, they continued to go to the markets to do their shopping and to their respective work places. And there's no need to have the concept of the number zero to solve Zeno's paradox, just the idea of the convergence of some types of infinite sums. I.e. if each successive run of Achilles is half as long as the previous one (say he walks twice as fast as the tortoise) then we have a sum for the total distance 'D' of the form: D = x + x/2 + x/4 + x/8 +... multiplying this by 2 gives: 2D = 2x + x + x/2 + x/4 + x/8 + ... = 2x + D subtract D from both sides and we solve for the total distance Achilles needs to walk: D = 2x; i.e. twice the distance of the headstart he gives the tortoise. The airplane-on-a-treadmill is just a restatement of the same problem. It attempts to convince you that the airplane cannot move relative to an outside observer if the treadmill always moves at the same speed as the wheels. If the wheels accelerate, then the treadmill accelerates, so the plane cannot move, right? Wrong. The airplane does move, and it accelerates relative to an outside observer at the same rate as it would if the treadmill remained stationary. The only thing that changes is that the wheels spin faster. Sure, but airplane wheels have some maximum speed. Once the treadmill gets up to that maximum speed the airplane wheels would fail and the airplane is now sitting on a treadmill with a bunch of failed tires. So the question becomes whether a plane can still take off after you shoot out all the tires when it first begins its takeoff roll. And yes, postulating a frictionless surface for the treadmill gets around the problem and allows a normal takeoff. But the very term treadmill implies a surface with reasonable friction, i.e. the tread. Well, if you understand Zeno's paradox, then you understand enough that the airplane will move forward on the treadmill. If the tires don't blow, it will take off. I will refer you to the book "Godel, Escher, Bach" for a discussion of how the problem is created by an attempt to divide by zero. If your only argument is that airplane tires will not stand the stress, then you are placing a constraint on the problem that is not originally stated. You are basically changing the question. Some airplane tires might stand the stress; others might not. Tires are highly variable in their design and intended purpose. You cannot flat-out declare that all tires would fail. In fact, why would not the treadmill break down before the tires? The motor could overheat and stop the treadmill entirely, or the treadmill surface could disintegrate, or it might be crushed by the airplane. The airplane could be so heavy that the treadmill could not turn at all. We cannot assume that the treadmill is any less immune to stress than anything else stated in the problem. So, lacking any further limitations as stated in the problem, tires must be assumed to be capable of withstanding the stress of the treadmill. Otherwise, why not throw in all other kinds of variables not stated in the problem, like flap settings, wind, temperature, density altitude, fuel on board, payload, visibility, clearance, and whether it would violate FAA rules? No, go with the problem as stated, and let us not make it a trick question by assuming facts not presented to the audience. |
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