Airplane on a treadmill

[Guest christianholmes]

Thanks :)As you can see though, if the question is intended to mean the treadmill is moving relative to the airport as well, then it is simply unanswerable- not a conundrum, just not physically possible- How can it be moving in two planes of reference at the same time if it is fixed in place? The problem is with that aspect. It's unfortunate, because that clause makes the whole point of the airplane moot- you never even get into a discussion of aerodynamics.But then again, without that aspect, it is very easy- it took me awhile to break it down, and really figure out the true answer.I love brain teasers so I couldn't leave this one alone, even it turned out a bit less than satisfying.

[Guest CowlFlapsOpen]

I agree with those who argue that the problem is framed wrong and the wheels are a Red Herring. The issue is not to get the aircraft to "takeoff" but to "fly". AC fly when Lift equals Weight and they climb (takeoff) when Lift exceeds Weight. (I am ignoring things like potential contributions of drag that acts downward, etc. No consequence here.)The AC does not care one wit about whether it has wheels in this regard and is instead concerned with airflow over the airfoils concerned with lift, the wings primarily. Aircraft "move through the medium of air" and but human sensibilities prefer to think of this as "across the ground". The aircraft doesn't.In usual practice, one cannot generate enough air flow over the wings without moving the aircraft forward across the ground at sufficient speed, but that is just a convenience. There are other ways: Aircraft designers study flight by blowing air past the wing with a sufficient enough speed. Some aircraft are dropped from others in flight. Most importantly, it is not the movement across the ground that is responsible for the sufficient flow of air over the wings, but the action of the propeller on the medium of air around it. AC are pulled by propellers not pushed by their wheels, torque and friction, as autos are, and propellers know nothing of the ground.AC do have a problem tho: For a portion of the range of speeds through the air that thay can display the airflow is not sufficient to equal or exceed its weigh. At speeds less than this critical speed, the ac will sink. This includes no speed at all, on the ground. If you'd like to keep the belly of the fuselage off the ground and have any hope of accelerating to speeds through air sufficient for flight, wheels are a not a bad option. Wheels are not bad to have if you plan to land either!So: Some things that will convince you: An aircraft will not fly if a tail wind were blowing at exactly the same speed at which it were accelerating down the runway, no matter the speed. Corollary: If your airplane rode a conveyor belt forward at the normal speed sufficient for takeoff it would not take off if the tailwind equaled or exceeded this speed.An aircraft will fly if a sufficient headwind (god forbid) is blowing even if you are standing still on the runway.The resistance of water is less that the resistance of tarmac, yet sea planes takeoff at the same airspeed as land craft (as I understand it)Finally, a though experiment: The counteracting conveyor belt idea is not different with regard to the ground than the following: An airplane is rolled on a runway nose-first straight down the face of a sheer cliff. Here the AC's acceleration is governed entirely by gravity, but importantly, the runway surface gives way without resistance exactly in the same manner as the hypothetical conveyor belt. The difference here is that most people can immediately grasp that the plane is still accelerating through the air without any aid from its contact with the ground in this circumstance and have no trouble predicting that at some point it could "pull up" and fly. If not, I would never have survived the years I spent hang gliding in my youth. Bottom line: a conveyor belt would prohibit flight if the plane needed the resistance of the ground to accelerate through the air stream to sufficient speed for flight but the aircraft designer gods have avoided this by giving aircraft propellers that screw their way into the air mass (which is why they used to be called air screws). Burned out conveyor, flying plane.Cheers.

[turner112 52]

"Imagine a plane is sitting on a massive conveyor belt, as wide and as 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 wheel speed while on the ground (assuming no wind) is not responsible for lift but is, in fact, directly related to the speed of the aircraft, which, in turn, is the same as the wind speed created by forward movement.If the aircraft can't gain forward momentum, there is no wind speed, save for the breeze provided by the propeller(s), and therefore no lift.No, a "normal" airplane moving at zero forward velocity cannot take off.Why is this even a puzzle?You're running along a track, and need to jump over a 5-foot gap. You run, you jump, you make it.Now, try the same thing from a treadmill matching your running speed... :)---Andrew

[Guest Gazelle]

Nothing to do with conveyor belts OR wheels and EVERYTHING to do with the distinct lack of airflow over the wings and therefore absolutely NO LIFT from the wing whatsoever. In this case, the conveyor belt could be going at 5000mph or more and assuming the wheels could do the same then there would still be that equilibrium and the aircraft would still be stationary, only the wheels turning, met with equal but opposite speed from the conveyor belt. I've only ever seen one fixed wing aircraft take off vertically without air travelling over the wings to generate lift and that's a Harrier. So that answer is very simple, No it will not take off, not without forward airflow over the wings in order to generate lift. Unless its a Harrier.

[kerosene31 349]

Once again, read the old thread. The plane does NOT sit stationary and does NOT take off vertically.

[turner112 52]

Uh, I did read the "old thread".The plane remains stationary in relation to the ground and its surrounding airmass. Whether it sits on a treadmill, a dynamometer, or a series of super gerbil wheels, it gains no forward momentum. Whatever thrust the aircraft is producing is negated by the treadmill. The treadmill doesn't move, and it only needs to be the length of the wheelbase (a little longer maybe) rather than the length of the runway. Perhaps this is where people are making a mistake?To suggest its wheel speed doesn't relate to its forward movement through the air which would give it lift is nonsense. Some people seem to be saying that the wheel speed isn't the same as the forward thrust or something, and of course, it's not. But it -is- the same as the forward speed.The airspeed indicator will show zero. I can't see a plane taking off with zero airspeed.If the problem is misleading or worded incorrectly based on what someone "meant" to be the actual problem, that's not my problem... the purpose of the treadmill, of many people seem to be asking, is to keep the aircraft stationary in relation to the ground, and, therefore, the airmass around it.Or, maybe I'm wrong ;)Andrew

[kerosene31 349]

>the purpose of the treadmill, of many people seem>to be asking, is to keep the aircraft stationary in relation>to the groundHere is the trap. A treadmill cannot keep a powered aircraft stationary. Go back and look at your assumption about what a treadmill can do. Common sense says a treadmill holds things in place, but an airplane is different. It is crazy because nobody would ever really do it. Your aircraft is tied to the treadmill somehow, and that is not part of the problem. A human running on a treadmill stays in one spot, right? Of course...A car on a treadmill stays in one spot, right? Yep...But what about a powered airplane? What makes any normal powered airplane move forward? A jet engine(s), prop(s), etc. If you tied down an airplane's wings on the ground and put it on a treadmill, it would stay, but without being tied down, it will move forward. Get a huge treadmill, and put a 4 engine 747 on it. Now, fire up those engines with enough thrust to taxi the plane forward at 10 knots. Now, the treadmill spins the opposite direction at 10 knots. What happens? The treadmill spins the wheels of the 747 (so they are moving twice as fast at 20 kts), but the engines of the plane power the aircraft forward. Unless the wheel brakes are on, the plane moves freely with free spinning wheels.

[turner112 52]

Ok, I think I see the point-I think the question as it stands made me visualize the wheels spinning backwards, which, in fact, they don't; they only stand still.. while the plane is catapulted forward at the speed its thrust would create.I believe the treadmill would have to move twice as fast in the opposite direction to keep the aircraft stationary, but I do think that would work.Hm....Andrew

[Guest christianholmes]

Read my post- the question is impossible unless the treadmill is not turned on. It has nothing to do with the friction, or airflow, or anything else. The way the question is phrased, the treadmill can only match the speed of the wheels in it's own plane of reference, not if the plane were moving.If the treadmill is turned on, then the formula for speed becomes the speed of the gears turning against each other, plus the speed of the wheel moving in relation to the airport- where the treadmill is always stationary.Say a=the relationship between treadmill/wheel rotation.Say b=the motion of the wheel forwardSay c=the motion of the treadmill forward (always 0)a + c = a + bThis is false unless b = 0 i.e. treadmill not moving.If the treadmill remains stationary, then it technically is still moving in the opposite direction of the wheels, but only in relation to the wheels.For an example of the above equation, say the wheel is turning at 40 feet per second while stationary. The treadmill would then be turning at 40 feet per second in the opposite direction.So a = aThey match.Now say the airplane accelerates down the runway at 30 feet per second. Well, the treadmill's speed in relation to the airport is always 0, so you've created a self referential equation that can't work.Treadmill + motion = wheel + motiona + 0 = a + 30Remember the treadmill would have to match the speed of the wheel.So you can see easily that it's impossible to create a result that works unless the motion of the wheel is zero.

[michal 44]

>Except that the question postulates that the aircraft wheels'>and the treadmill wheels' rotation have to match. You are>absolutely right with regard to a real world treadmill though.> But you need to read the question a little more carefully. >Kevin,I disagree with you this time. I think you overstated author's intentions. In fact even you get rid of this sentence and state simply that the treadmill moves back say at constant 300 MPH it still poses enormous problems for people - it has been stated in this format on many forums and you can see what sort of problems people have with this 'simplified' formulation. I think it was not the intention of the author of this puzzle to make out of this a word-puzzle-problem with a 'trick' impossible solution but rather to illustrate the actual underlying physics. So I would NOT try very hard to over-interpret the sentence: "The conveyor belt is designed to exactly match the speed of the wheels". Michael J.

[michal 44]

I think we are wasting a great deal of energy on unnecessary arguments. As I stated above (#39) in my reply to Kevin the sentence "The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction" is rather poor choice of words and most likely is against what author envisioned. As a matter of fact I have seen this very problem formulated on different aviation forums in this way: "the treadmill is moving back at constant say 200 KTS." This alone generates thousands of replies and most simply can't believe the aircraft would take off (assuming of course 'idealized' friction and tires). I think this is a much better formulation because it channels people's energy on actual physics rather than making endless arguments about how this treadmill is in fact moving.Michael J.

[Guest Mr Chips]

I agree with above comments that it isn't a word puzzle (as I too wrote earlier). The question, regardless of the wording here, is 'if the treadmill matches the forward ground speed of the aeroplane backwards'. As has been correctly previously stated, in such a case, if the aeroplane was doing 100kts the wheels would be rotating only at exactly 200kts (no more or less). However...If friction is the stumbling block for many people, as Michel suggests, then consider this:The faster the wheels rotate, the lower the friction to a point. There are two types of friction: static and dynamic. Static is the amount of effort needed to intially move a stationary object. Dynamic is the effort needed to keep it going.To visualise, think about pushing a car. It might take two people to get it moving, but once moving just one person can keep it moving and possibly even increase the speed of the push.Therefore, the majority of the friction is getting the wheels moving, as would be the case for an aeroplane starting to taxi at Heathrow. They even have a name for it, the amount of thrust needed to get the aeroplane rolling is called the "cracking thrust". The pilot will know what throttle position is required to get the bird rolling before reducing thrust to maintain a safe taxi speed. One our treadmill aeroplane is rolling, the wheel speed in terms of friction is irrelevant.

[Guest christianholmes]

But answers like your simply make the question arbitrary. It is stated that the treadmill must match the speed of the wheels. So you can't just say the treadmill is moving at a constant speed.This question is simply a play on the car-on-a-treadmill scenerio, but since an aircraft WOULD be capable of moving forward, the question simply becomes impossible-1) Matching the speed of the wheels would not necessarily limit forward movement since the force pulling the wheels is not the same force pushing the wheels!2) Allowing the aircraft to move forward would make "matching the speed of the wheels" impossible because of the physics problem.You can't just state that the treadmill moves forward at 200 knots. That's simply skirting around the inherent problems with the question.It is a word puzzle- if you don't take it literally, you are changing the entire question and scenerio. We all know that if the treadmill moved forward at 200 knots the plane probably wouldn't take off. Say it moved at 5 knots? Then it would... It doesn't make any sense to do that!I FIRMLY believe I have the only correct answer to this question. I have literally googled every version of it I could find and they ALL say the conveyor matches the speed of the wheels. Yet, I found NO ONE who questions the inherent physics involved in "matching" the speed of the wheels.If you are going to change the question, at least post the other version of the question you are referencing.As it stands:1) If the conveyor is not turned on, then it's speed would still match the relative speed of the wheels, and the plane would roll forward and takeoff.2) If the conveyor is turned on, you have a self referential circular equation which cannot be satisfied- Once plane moves forward, the treadmill can never match it's speed since the treadmill is stationary.

[Guest christianholmes]

>I agree with above comments that it isn't a word puzzle (as I>too wrote earlier). The question, regardless of the wording>here, is 'if the treadmill matches the forward ground speed of>the aeroplane backwards'. As has been correctly previously>stated, in such a case, if the aeroplane was doing 100kts the>wheels would be rotating only at exactly 200kts (no more or>less). However...>>If friction is the stumbling block for many people, as Michel>suggests, then consider this:>>The faster the wheels rotate, the lower the friction to a>point. There are two types of friction: static and dynamic.>Static is the amount of effort needed to intially move a>stationary object. Dynamic is the effort needed to keep it>going.>>To visualise, think about pushing a car. It might take two>people to get it moving, but once moving just one person can>keep it moving and possibly even increase the speed of the>push.>>Therefore, the majority of the friction is getting the wheels>moving, as would be the case for an aeroplane starting to taxi>at Heathrow. They even have a name for it, the amount of>thrust needed to get the aeroplane rolling is called the>"cracking thrust". The pilot will know what throttle position>is required to get the bird rolling before reducing thrust to>maintain a safe taxi speed. One our treadmill aeroplane is>rolling, the wheel speed in terms of friction is irrelevant.You're interpreting the question as you want, but that is not, nor is ever, the question. In the same question with a car, the treadmill matching the speed of the wheels will keep the car stationary. It is the exact same prinicipal here, however it becomes ackward because other forces than the wheels influence the aircraft's movement.The question is postulated to make the relationship between the wheels and the treadmill exact- i.e. the treadmill will move at a speed where the wheels can never move forward. However, because the relationship between the treadmill and the wheels is affected by external forces, this criteria is invalid.This is the basis for the question. "Cracking Thrust", friction, etc. are never even brought into play because the question is based on a completely flawed principal.

[turner112 52]

Hang on-"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction."If the aircraft is on a regular old runway, couldn't we say that the runway itself is exactly matching the speed of the wheels, in the opposite direction?[edit]"The question is postulated to make the relationship between the wheels and the treadmill exact- i.e. the treadmill will move at a speed where the wheels can never move forward. However, because the relationship between the treadmill and the wheels is affected by external forces, this criteria is invalid."Not necessarily; we can easily surmise that a system has been specifically set up to do this, as ideal as it may be. The question doesn't require the actual contstruction of a system that can work this way..Andrew