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Old 12-05-2005, 04:14 PM   #1  
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Default Hypothetical Question

A plane is standing on runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not?
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Old 12-05-2005, 04:31 PM   #2  
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Talking Ive got the answer...

The plane will not take off. If maximum thrust is applied(it doesnt even have to be max thrust, whatever thrust you want) it will only counteract the backward motion of the conveyor. No airflow over the wings will occur, no lift. I hope I did not just dork this up and miss the whole joke or something.
 
Old 12-05-2005, 04:34 PM   #3  
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I would have to say no, because if the speed of the conveyor belt is the same then airplane should remain in the same place.
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Old 12-05-2005, 04:43 PM   #4  
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Ok, Ill bite. (Unless this is some sort of trick question) As I recall, two things make an airplane fly. 1. Lots of money, and 2. Bernoulli's Principle. Since all the money has been spent already on the above conveyor contraption, that rules out option one. And since there is no air flow over the airfoil (wind or realitive wind), there is not lift. Don't quote me on this but I think I heard once that you need lift to get an airplane to take off. Hmmmm. Here is another riddle: If a pilot is out in the forest and a tree falls on him (her), will the pilot make a noise?
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Old 12-05-2005, 05:01 PM   #5  
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Ah yes... this one has been around a few boards lately... I was like you guys, until I too was turned. At first glance it seems easy- but once you figure it out and are convinced of the physics, you slap your head.

Here's a "pro's" article on the subject:

The Pilot's Lounge #94: It's The Medium, Manfred

There's a new aviation myth running around the Internet. It involves a conveyer-belt runway and misuse of aerodynamics and ... well, it's better if AVweb's Rick Durden explains it all himself in The Pilot's Lounge.

By Rick Durden
Columnist

The Pilot's Lounge

I heard the commotion as I started down the hall from the flight school to the Pilot's Lounge at the virtual airport. In the few moments it took to get to the door of the Lounge, individual voices became clear, split into two very vocal camps: The vehement "Yes it will!" calls being answered by an equally intense "No it won't!" I thought back to some of the stronger disagreements that had been aired here, such as the use of flaps on landing, but this one seemed a little louder and I wondered whether Old Hack and some of the bigger guys might have to separate combatants.

I stood off to the side and tried to get a handle on the conflict. Old Hack saw me and sidled over with a silly grin on his face. "These guys spend way too much time on the Internet," he said. "Someone has just come up with what looks like a 21st-century version of the old "downwind turn" foolishness and now the engineers and the soft-science folks are having at it."

The "Fatal" Downwind Turn

For those who don't recall the "downwind turn" tale of the last century, it goes like this: People observed that pilots who were flying relatively low on a heading that took them into the wind had a surprisingly high rate of impact with the ground or obstructions if they rolled into a turn and proceeded to a heading that was with the wind direction, or downwind. There were those who insisted that the airplane could not accelerate fast enough in the turn to make the necessary groundspeed change so as to stay above stall speed and thus they crashed.

As an example, we'll take a pilot with a reputation for good stick and rudder skills, a certain Manfred. We'll magically reincarnate him from the Western Front of World War I (where he had perished) and put him in a 65-hp, Piper J-3 Cub. Its cruise speed is pretty close to the Fokker Dr-I that Manfred last flew -- call it 80 mph. (The Fokker Triplane was so maneuverable few enemy pilots ever figured out it was astonishingly slow.)

We'll point Manfred and the J-3 northbound at 500 feet AGL into the teeth of a 40-mph headwind. His groundspeed is, therefore, 40 mph. Now we'll have him roll into a turn and change directions 180 degrees until he is headed south, directly downwind. We'll have him make the turn in 30 seconds, a twice-standard-rate turn. At that airspeed, it's not very steep and certainly not at all unsafe. The next consideration is that in those 30 seconds, Manfred's J-3 has to accelerate from a groundspeed of 40 mph to a groundspeed of 120 mph in order to still be moving through the air at 80 mph. In fact, if he does not accelerate through that needed 80 mph change in groundspeed, the airplane could stall because the airspeed would have dropped off radically.

There were those who were convinced that it was impossible for a 65 hp J-3 to increase its groundspeed by 80 mph in 30 seconds, and therefore the airplane would stall, which was what made downwind turns so dangerous.

Fortunately, back when this was being debated, rationality prevailed. It was pointed out that the airplane was flying through the air, its propeller was acting upon the air and its wings were moving in an airmass. Thus, when it made its turn, its airspeed didn't change. The airplane continued to move through the air at 80 mph. Its groundspeed changed solely because of the fact that the mass of air in which it was operating, the medium upon which it was acting, was moving.

Had the air been calm, Manfred and his J-3 would have had a groundspeed that matched his airspeed.

Interestingly enough, when the famous aviator, Jimmy Doolittle was sent by the Army to M.I.T. to study in the mid-1920s, his dissertation for his Ph.D. included some of this discussion, so the problem's been solved for some time; it just took most of the rest of the century for the understanding to trickle down. (Yeah, that air-racing, aerobatic, military pilot also had one of the first Ph.D.s awarded in aeronautical engineering.) Doolittle also hypothesized that the frequency of crashes during such turns was the visual effect of the rapidly increasing groundspeed causing pilots to believe that the airplane was suddenly going very fast and pulling back on the stick or throttle, leading to a stall or descent into the ground.

For those who still didn't understand that the downwind turn had no effect on the airplane, all it took was a flight on a day with some wind above a solid deck of clouds. Making a few circles made it clear that the airplane and its pilot could not tell anything about the direction of the wind while turning.


Conveyer-Belt Runway

What I learned from Old Hack was that an updated version of a question aimed at confusing folks over relative measurements of airplane motion and the medium in which it operates had shown up on the Internet, and it was causing the fracas in the Lounge.

The question that has been going around is not particularly artfully worded, and I think that has caused some of the disagreements, but I'll repeat it as it is shown: "On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?"

My comment: Notice that the question does not state that the conveyor's movement keeps the airplane over the starting position relative to the ground, just that it moves in the direction opposite to any movement of the airplane.

Initially, about a third of the folks here said that the airplane could not ever takeoff, because the conveyor would overcome the speed of the airplane and it could never get any airspeed. The rest said the airplane would fly.

The "It won't fly, Rocky" group said that the conveyor would hold back the airplane. They asked us to imagine a person running on a treadmill. As he or she sped up, the treadmill would be programmed to speed up, just as the conveyor in the problem, and the person would remain over the same locus on the earth, while running as fast as possible.

The argument was that if the airplane started to move forward, the conveyor program was set up to move the conveyor at exactly that speed, in the opposite direction, thus, the airplane would never move relative to the ground, and, because the air was calm, it could never get any wind over its wings. One of the analogies presented was the person rowing at three mph upstream in a river on a calm day. However, the current was flowing downstream at three mph, so the resultant speed with reference to the stream bank and air was zero, and thus there was no wind on the rowboat.

I watched and listened to the disagreement for a while and was fascinated to see that the argument seemed to split between those who had some engineering or math background, all of whom said the airplane would takeoff and fly without any problem; and those with some other background, who visualized the airplane as having to push against the conveyor in order to gain speed. Because the conveyor equaled the airplane's push against the conveyor, the airplane stayed in one place over the ground and in the calm air could not get any airspeed and fly.

It was an interesting argument, but as things progressed, more rational heads prevailed, pointing out that the airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff. One guy even got one of those rubber band powered wood and plastic airplane that sell for about a buck, put it on the treadmill someone foolishly donated to the Lounge years ago, thinking that pilots might actually exercise. He wound up the rubber band, set the treadmill to be level, and at its highest speed. Then he simultaneously set the airplane on the treadmill and let the prop start to turn. It took off without moving the slightest bit backwards.

Manfred In The 21st Century

OK, let's figure out why the airplane will fly.

We'll use Manfred again. Although we're bringing him forward into the 21st Century, we'll still let him use the 65 hp J-3. It doesn't really matter what airplane he flies, but he got used to the J-3 while he was demonstrating downwind turns and this one happens to have lifting rings on the top of the fuselage. It's also been modified with a starter so no one has to swing the prop.

Manfred's in the airplane. Old Hack has the Army-surplus crane fired up and he's picking up the J-3 and Manfred and carrying them over to Runway 27, which has been transformed into a 3,000-foot conveyor belt. It is a calm day. The conveyor drive is programmed so that if Manfred can start to move in the J-3, if he can generate any airspeed or groundspeed, the conveyor will move toward the east (remember Manfred and the J-3 are facing west) at exactly the speed of the air/groundspeed. Because the wind is calm, if Manfred can generate any indicated airspeed, he will also be generating precisely the same groundspeed. Groundspeed, of course being relative to the ground of the airport surrounding the conveyor belt runway. So, the speed of the conveyor belt eastbound will be the same as Manfred's indicated airspeed, westbound.

(con't)
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Old 12-05-2005, 05:01 PM   #6  
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Part II:

Manfred does his prestart checklist, holds the heel brakes, hits the starter and the little Continental up front clatters to life. Oil pressure comes up and stabilizes and Manfred tries to look busy because the eyes of the world are upon him, but all he can do is make sure the fuel is on and the altimeter and trim are set, then do a quick runup to check the mags and the carb heat. He moves the controls through their full travel and glares at the ailerons, doing his best to look heroic, then holds the stick aft in the slipstream to pin the tail and lets go of the brakes.


Baron of the Belt

So far the J-3 has not moved, nor has the conveyor. At idle power, there's not enough thrust to move the J-3 forward on a level surface, so Manfred starts to bring up the power, intending to take off. The propeller rpm increases and the prop shoves air aft, as it does on every takeoff, causing the airplane to move forward through the air, and as a consequence, forward with regard to the ground. Simultaneously the conveyor creaks to life, moving east, under the tires of the J-3. As the J-3 thrusts its way through the air, driven by its propeller, the airspeed indicator comes off the peg at about 10 mph. At that moment the conveyor is moving at 10 mph to the east and the tires are whirling around at 20 mph because the prop has pulled it to an airspeed, and groundspeed, of 10 mph, westbound. The airplane is moving relative to the still air and the ground at 10 mph, but with regard to the conveyor, which is going the other way at 10 mph, the relative speed is 20 mph.

Manfred relaxes a bit because the conveyor cannot stop him from moving forward. There is nothing on the airplane that pushes against the ground or the conveyor in order for it to accelerate; as Karen -- one of our techies here at the Lounge -- put it, the airplane freewheels. In technical terms, there is some bearing drag on the wheels, but it's under 40 pounds, and the engine has overcome that for years; plus the drag doesn't increase significantly as the wheel speed increases. Unless Manfred applies the brakes, the conveyor cannot affect the rate at which the airplane accelerates.

A few moments later, the roaring Continental, spinning that wooden Sensenich prop, has accelerated the J-3 and Manfred to 25 mph indicated airspeed. He and the airplane are cruising past the cheering spectators at 25 mph, while the conveyor has accelerated to 25 mph eastbound, yet it still has no way of stopping the airplane's movement through the air. The wheels are spinning at 50 mph, so the noise level is a little high, but otherwise, the J-3 is making a normal, calm-wind takeoff.

As the indicated airspeed passes 45 mph, groundspeed -- you know, relative to where all those spectators are standing beside the conveyor belt -- is also 45 mph. (At least that's what it says on Manfred's GPS. Being brought back to life seemed to create an insatiable desire for electronic stuff.) The conveyor is also at 45 mph, and the wheels are whizzing around at 90 -- the groundspeed plus the speed of the conveyor in the opposite direction.

Manfred breaks ground, climbs a few hundred feet, then makes a low pass to see if he can terrify the spectators because they are Americans, descendants of those who defeated his countrymen back in 1918.



It's All About Airspeed



(Don't try this at home!)

While the speed of the conveyor belt in the opposite direction is superficially attractive in saying the airplane cannot accelerate, it truly is irrelevant to what is happening with the airplane, because the medium on which it is acting is the air. The only time it could be a problem is if the wheel speed got so high that the tires blew out.

Put another way, consider the problem with the J-3 mounted on a hovercraft body (yes, similar things were tried about 30 years ago). The hovercraft lifts the airplane a fraction of an inch above the conveyor belt, and so no matter how fast the conveyor spins, it cannot prevent the propeller -- acting on the air -- from accelerating the airplane to takeoff speed. It's the same with wheels rolling on the conveyor belt. Those wheels are not powered and thus do not push against the belt to accelerate the airplane. Were that the case, the vehicle could not reach an airspeed needed to fly, because then the conveyor, the medium acted upon by the propulsive force, would be able to negate the acceleration relative to the air and ground.

I'm reminded of the New York Times editorial when Robert Goddard's rocket experiments were first being publicized. The author of the editorial said that rockets can't work in space because they have nothing to push against. It was laughably wrong, ignoring one of Sir Isaac's laws of physics that for every action there is an equal and opposite reaction. Here the propeller is pushing against the air, as it does every time an airplane takes off. How fast the airplane is moving over the surface on which its wheels rest is irrelevant; the medium is the magic. On a normal takeoff -- no conveyor involved -- if there is a 20 mph headwind, Manfred and the J-3 will lift off at 45 mph indicated airspeed; but relative to the ground, it is only 25 mph. Should the wind increase to 45 mph and if Manfred can get to the runway, he can take off without rolling an inch. His airspeed is 45 and groundspeed is zero. It is not necessary to have any groundspeed to fly, just airspeed. Conversely, if Manfred has a lot of runway and nothing to hit, and takes off downwind in a 25 mph tailwind, the propeller will have to accelerate the airplane to a zero airspeed, which will be a 25 mph groundspeed, and then on to a 45 mph airspeed, which will have him humming across the ground at 70 mph. The speed over the ground, or a conveyor belt, when an airplane takes off is irrelevant; all that matters is its speed through the air, and unless the pilot sets the brakes, a moving conveyor belt -- under the freely turning wheels -- cannot stop the process of acceleration.

Things eventually calmed down as the number of "it won't fly" folks dwindled as they began to understand that the airplane would take off. Old Hack looked at me and suggested we depart as the few holdouts showed no sign of changing their position. So, we headed out into the night to watch the guys take the conveyor out and reinstall the runway.

See you next month.
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Old 12-05-2005, 05:53 PM   #7  
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That is a nice explaination...unfortunately the airplane will not take off. The way the question is posed, the airplane has no relative movment over the ground...ie, it stays in one location, therefore no air flow over the wings. If, however, the airplane had relative wind over the wings, it will lift off the ground, regardless of thrust. A source of thrust and/or any other source of airflow, is needed to overcome the drag, thus keeping the airplane in the air, (along with other factors of course).
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Old 12-05-2005, 06:58 PM   #8  
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Quote:
Originally Posted by clearedtoland
That is a nice explaination...unfortunately the airplane will not take off. The way the question is posed, the airplane has no relative movment over the ground...ie, it stays in one location, therefore no air flow over the wings. If, however, the airplane had relative wind over the wings, it will lift off the ground, regardless of thrust. A source of thrust and/or any other source of airflow, is needed to overcome the drag, thus keeping the airplane in the air, (along with other factors of course).
Unless the aircraft is attached to the belt, there is no way for the belt to be able to keep up with the aircraft's acceleration. It will eventually gain enough speed to lift off of the belt, and depart the ground.
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Old 12-05-2005, 07:05 PM   #9  
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Where in the riddle does it say that? I believe it says the speeds are exactly the same, but in opposite directions. No doubt, with all the assumptions made, the airplane will take off, but with just the information given, physics dictates it will not.
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Old 12-05-2005, 11:40 PM   #10  
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If I want this I'll go to Airliners.net and listen to all the morons on there argue about how thick the belt will need to be since the A380 might need it.


Oh wait, it's already there:
http://www.airliners.net/discussions...d.main/136068/
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