Airplane on a Conveyor Belt
December 8, 2005
11:54 am
A riddle was proposed on the Neal Boortz show today:
If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?
Astoundingly, Neal and the rest of his crew took the position that the plane would sit there stationary! Good God… this man is a pilot and has a law degree! I could understand a random high school dropout being fooled by this, but a pilot?
Then I googled the riddle, and found a thread on Airliners.net that has been raging on, with the vast majority of people taking Neal’s position… that the plane would not be able to take off.
Their argument is this, to quote one poster:
Thrust acts accordingly to Newtons Third Law of Motion - every action has an equal and opposite reaction. In the case of an aircraft, the reaction of the engines is that of forward motion, against whatever medium it is stationary. But the ground the aircraft is sitting on in this case is NOT stationary, its providing an exactly CANCELLING force pushing the aircraft back.
The problem here, of course, is that the poster (and Neal) cannot disengage themselves from seeing the airplane as a car. The difference between a car and a grounded airplane is that a car uses its wheels to propel itself forward, and an airplane moves itself forward by moving air. They assume that the runway moving backwards would move the plane backwards. This is what would happen with a car (that is in gear), so why not for an airplane? Well, because an airplane’s wheels are free rolling. There is obviously some friction, so there would be some small backwards force, but it would be infinitely small as compared to the forward thrust of the airplane.
You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control.
So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object. Next, we’ll see what happens when the object is trying to move forward. Attach a string to the matchbox car. Place the car at one end of the paper, and use the string to start pulling the car forward with a steady force. As the car moves forward, start pulling the paper out from under the car, backwards. Do you feel increased resistance as you pull the string? Of course not. The wheels are free rolling! Spinning the wheels does not make the object move!
When an airplane takes off, there is one major forward force… the forward thrust. The main rearward force is air resistance. The turning of the wheels provides a small frictional force, but because the wheels are free-rolling, this friction is very small. Unless the wheels are locked, the friction is always going to be less than the thrust, which means that the overall force is still forward, and the plane will still move.
Gah… people are freakin’ stupid.
Update: There is a variation on this riddle that says that the conveyor belt matches the speed of the plane. It doesn’t matter… the plane still takes off. The conveyor belt could be going 5 times as fast as the plane, and the plane would still take off. You’d get into issues about tires blowing out, but assuming that the wheels can take the strain, the airplane would still take off.
Update: Well here we are more than two years later. The show “Mythbusters” attempted the experiment. And yes, the plane took off. The laws of physics still apply. Back to life as usual.
I’m 100% sure the answer is finite, and the plane won’t move. And I’m not explaining it anymore.
Matt, please tell us what force is acting against that of the engines.
Yes, please tell us, what force is preventing the engines from moving the plane forward?
Is this statement true?
If A can nullify B
and B can nullift C
then A can nullift C
and if C is a force, then B must produce a force to nullify C, and A must produce a force to nullify B.
not necessarily - it doesn’t necessarily take a force to nulliyy something - it could take a LACK of a force to do it too…
Matt, I have no idea what that comment pertains to without further explanation. But, from a logic standpoint, to say that since A nullifies B and B nullifies C then A must nullify C would be a false statement.
The point is, there is NO force capable of cancelling out the force of the engines in this problem. Since there isn’t, there is an imbalance of forces which causes acceleration. The plane will move and thus eventually take off.
sorry- i’m used to answereing a slightly different questoin, let me explain
if the question states the belt matches the speed of the wheels (like other versions say) then the plane won’t go anywhere. If the questions states the belt matches the speed of the plane, then for every foot back the belt goes, the plane will move forward that amount, while the wheels will spin for a covereage of 2 feet. the only difference from no runway being that the wheels speeing at a rate of 2x-y, x being how much it would on a normal runway, and y being the losses due to extra friction. so theoretically the wheels will move just less than twice as fast therefore the acceleration would be slightly less than on a normal runway (depending on the mass of the plane and the inflation of the tires, there is always a possibility (but not a probability) of this hindering take off in a normal distance).
the amount of ground the wheels roll on, increase a force against thrust, therefore if the belt spins fast enough, it can negate the force of the thrust.
from what i said before,
if a belt moves back the same rate as wheels rolling forward (at a set rate) can stop the car relative to earth, and a car that is driving forward can be stopped by someone who put the nitrous (thrust- lets say) on the wrong way relative to earth, and we know thrust is a force, then to stop that force the wheels accelerating must produce a force. then if we know that produces a force, the belt moving back must produce a force. therefore it is possible for the belt to stop the force of a plane. the wheels would move really fast and the belt woudl continue matching that rate until the friction is great enough, the only differene between that and the car is that the car produces a maximum wheel speed. that’s how i see it, anyway
But, please explain how a conveyor belt will stop the acceleration of a plane?
In a car that makes sense since the friction of the tires forces the cars forward. To stop it you simply put it on rollers or a conveyor and the friction is still working, but the car stays in one place.
A jet engine does NOT turn wheels to create friction against the ground. The jet engine uses air to create thrust. Thus the force in question moving the plane forward has NOTHING to do with the ground or the wheels - they are just there for decoration.
If you look at Newton’s 3rd Law (for every action there is an equal and opposite reaction), there is nothing in the conveyor belt that prevents Newton’s 3rd Law from propelling the plane forward. The action is against the AIR the jet engine will create thrust and move the plane relative to the air.
If the plane were dependent on its wheels for acceleration, wouldn’t it stop acclerating immediately after take off?
Using Newton’s 3rd law, there is nothing that will stop the plane except:
- Physically chaining it ot the ground (some plane manufacturers have done this in the past to test engines).
- Operating the engine in a vaccuum. If you take away all the air, the engine has nothing to act on (and there won’t be any combustion in the engine)
But then you’re saying if you turn the engines off, the plane will never slow down, and nothing will ever slow the wheels down. The wheels still need friction to turn, if there were none, the wheels wouldn’t turn whatsoever- from the force of the engines or from the ground. And since there is friction, and friction is a force, there would eventually be enough losses to stop the force of the airplane (even if the treadmill has to move a rate of 5000 m/s or more, it will match the WHEEL SPEED if the question says this and the plane won’t go anywhere). But like I said, if the belt goes the same speed as the plane, then the wheels are moving faster- which this question states.
Why do you think planes can go so much faster than land vehicles. I mean if have a jet that can go mach 5 in the air, and we put its wings on the wrong way to create a downard force instead of lift, to keep it grounded, and we give it as much room as it needs to reach full speed, do you think it can reach mach 5 or anything even close to that with its wheels still making contact with the ground, rolling along? If you say no, then the ground must be creating some force against the jet, and forcing the wheels to cover even more ground (by having a conveyor belt moving back) will only increase this force and continue slowing down the jet. Eventually, theoretically, a speed could be great enough where it will slow it down completely to a stop- and this is where the wheel speed would = belt speed, and the wheel speed would be at it’s maximum possible speed.
Matt, frictional forces do not increase with speed.
Matt - think I will leave you alone now. You obviously aren’t going to grasp the physics here.
In short it doesn’t matter if the wheels turn or not - they mean nothing to a plane. A treadmill will not stop a plane as a plane exerts its force on the air, not on the ground.
But, I will leave you to continue to babble to yourself.
Thanks, can I buy some of your magic wheels, the ones that turn with no losess so they never slow down. dumbasses
no no, I’m sure your mom the chemical engineer and your dad the civil engineer know more than me.
Take your car and step on the gas, just a little, notice you accelerate up to a certain speed then don’t, because the forces are equal therefore no acceleration- yet you have a constant velocity… then you step on the gas a little more and you continue to speed to a certain speed then you get a constant velocity again, because the forces are equal once agian, when under 70 km/h when you aren’t going very fast, aerodynamic forces are fairly small, go learn physics properly, not just the simplified problems they teach you in your first year physics classes where you neglect 3/4 of the small forces, stupid shit.
Now children…
Ive never understood this whole variation of belt speed matching wheel speed for this problem. What does that even mean? I bet people made up the version with wheel speed when they finally figured out that the airplane can indeed fly, and needed to save face..
But either way, wheel speed itself is usually measured in RPMs, therefore to stay consistant, do we measure belt speed in RPMs too? Or is it distance traveled from a point?
There are too many factors involved in this wheel/belt problem variation in order for it to be even a GOOD hypothetical question.
If we replace the belt with another wheel of varying size (crazy missing variable #1), all we have at that point is some kind of fixed ratio gear system. If you had a wheel placed against another wheel of equal size, all you have is a 1 to 1 ratio..
Matt, for all intents and purposes, the losses caused by the wheel bearings will be no different in the case of the plane being on a treadmill compared to it being on a normal runway. If the plane can accelerate and maintain take-off speed on a normal runway it can also do it on a moving treadmill.
One must understand the mechanics of the problem.
The conveyor belt applys a force the the wheels. since the wheels are free spinning, as long as the force of the conveyor belt is greater than the rolling resistance of the wheels then the wheels will spin.
If we assume that the rolling resistance with respect to the applied force of the conveyor belt (as it should be in a real world model) then the plane will remain almost stationary with the wheels spinning. In reality the conveyor belt would exert a small backwards force on the plane due to the rolling resistance (ie rolling friction) of the wheels and tires.
One the plane exerts thrust by moving air (ie pulling or pushing the air) a forward force will be applied to the aircraft and through the aircraft to the wheels. Thefore the speed of the wheels will be a result of the airplane’s exerted thrust plus the applied force of conveyor belt (which are both forcing the wheels to rotate in the same direction) increasing the RPM of the wheels. That is the only affect these forces have on the wheels.
I will therefore be imposible for the converyor to match the speed of the wheels once thrust is applied by the airplane because the wheel RPM is a component of both the aircraft thrust and the conveyorbelt’s applied force. No matter how fast the belt goes the wheels will spin as fast if not faster.
In reality what you have simulated by adding a conveyor belt is a frictionless surface like ice. this model is similar to how a hovercraft works.
The only way for the aircraft to remain on the ground would be if the rolling resistance in the wheels was large enough that (when added to th motion of the conveyor belt) it would prevent the aircraft from reaching takeoff speed in lenth of the runway. This seems unlikely however unless the wheel brakes are on.
sorry meant to say:
“If we assume that the rolling IS NEGLIGABLE (as it should be in a real world model) then the plane will remain almost stationary with the wheels spinning. In reality the conveyor belt would exert a small backwards force on the plane due to the rolling resistance (ie rolling friction) of the wheels and tires.
I’m reposting since I noticed some type-o’s and exclusions in my previous post so her goes
:
One must understand the mechanics of the problem.
The conveyor belt applies a force on the wheels. Since the wheels are free spinning, as long as the force of the conveyor belt is greater than the rolling resistance of the wheels then the wheels will rotate around there axel.
We will first assume that the rolling resistance with respect to the applied force of the conveyor belt is Negligible (as it should be in a real world model). If we were then to turn on just the conveyor belt, it will apply a tangential force to the wheel. As this force is tangentially applied to the wheel it will not be applied to the plane’s axels but strictly to outside of the wheel. The plane will therefore remain almost stationary with the wheels spinning as the force is not transmitted in any way to the aircraft itself.
In reality the conveyor belt would exert a small backwards force on the plane due to the rolling resistance (i.e. rolling friction) of the wheels and tires. (REMEMBER THAT ROLLING RESISTANCE IS SIGNIFICANTLY LESS THAN SLIDING RESISTANCE.). This is why we use wheels on planes in the first place. In summary, once rolling resistance is overcome, all the force applied by the conveyor belt is being used to turn the wheels around their axel and as such is not being applied directly to the plane.
Once the plane exerts thrust by moving air (i.e. pulling or pushing the air) a forward force will be applied to the aircraft and through the aircraft’s axels to the wheels.
If you were to draw a free body diagram of the wheel you would see the conveyor belt apply its force tangentially toward the rear of the plane at the interface point at the bottom of the wheel creating torque. You would also see a smaller rolling resistance countering this force. The rotational force that the plane is applying to the axel will not be opposed by any of the existing forces and will simply add to the rotational velocity of the wheel (through geometry of the landing gear assembly).
This means that the speed of the wheel’s rotation at a given time will be a result of the airplane’s exerted thrust plus the applied force of conveyor belt (which are both forcing the wheels to rotate in the same direction increasing the RPM of the wheels). That is the only affect these forces have on the wheels. This also means it will be impossible for the conveyor to match the speed of the wheels once thrust is applied by the airplane because the wheel RPM is a component of both the aircraft thrust and the conveyor belt’s applied force. No matter how fast the belt goes the wheels will spin as fast if not faster.
In reality the wheels are added to an airplane to simulate a frictionless surface like ice. If each wheel were replaced with a perfectly slippery block of ice with minimal to zero friction you would have the same situation. This model is also similar to how a hovercraft works.
The only way for the aircraft to remain on the ground would be if the rolling resistance in the wheels was large enough that it would prevent the aircraft from reaching takeoff speed in length of the runway. This seems unlikely however unless the wheel brakes are on.
What everyone gets incorrect is that the conveyor will be treading in the same direction of the plane. What was said above is incorrect.
However, the plane will still take off, but the wheels will not move.
-G
ummm…care to explain that?
Every rendition of the riddle states that the conveyor is moving in the opposite direction as the plane.
But none the less as I states the wpeed of the wheels is a component of the Conveyor’s applied force and the aircraft’s applied force. Therefore is the conveyor move in the opposite direction to the aircraft the wheel’s speed of rotation increases (ie wheels get faster) if the conveyor moves in the opposite direction the wheel’s speed of rotation will decrease (wheel’s spin slower).
I would not presume however that the weheels would simply stop as there are other variable to which data has not been provided sufficiently in order to make a precise calculation or wheel speed. (ie rolling resistance coeeficient, appplied force of conveyor, engine power etc.)
ummm…care to explain that?
Every rendition of the riddle states that the conveyor is moving in the opposite direction as the plane.
But none the less as I stated that the speed of the wheels is a component of the Conveyor’s applied force and the aircraft’s applied force. Therefore if the conveyor moves in the opposite direction to the aircraft the wheel’s speed of rotation increases (ie wheels get faster) if the conveyor moves in the same direction as the plane, the wheel’s speed of rotation will decrease (wheel’s spin slower).
I would not presume however that the wheels would simply stop as there are other variables for which data has not been provided sufficiently in order to make a precise calculation of wheel speed. (ie rolling resistance coeeficient, applied force of conveyor, engine power etc.)
Ever heard of co-efficient of friction.
The maximum horizontal force that can be exerted on the plane is not that great.
If the wheels are well lubricated then not much.
A threadmill can not exert enough counter force to keep a plane in one place no matter how “fast” it spins.
—-
Think of the bullet train where it actually levitates off the rails. Stick a rocket on it to propel forward, no matter how fast you move the tracks backwards, you can not keep the train from moving forward.
—-
Technically, with the treadmill moving in the same direction as the wheels at the same speed, you’ve reduced the the force of friction to 0.
Which means the plane will have more forward force.. making it fly quicker, if both start at the exact same time.
That is basically what I said in my previous post:
“In reality the wheels are added to an airplane to simulate a frictionless surface like ice. If each wheel were replaced with a perfectly slippery block of ice with minimal to zero friction you would have the same situation. This model is also similar to how a hovercraft works.”
As I stated the the principle here is rolling resistance vs sliding resistance or simply the Coefficient of Rolling friction vs. Coefficient of sliding friction. Rolling friction is lower than sliding friction so the plane’s wheels will simply spin. See my previous post for a mor detailed explanation.
I have had this argument so many times with people of varying intellect and ego blockage. I am not going to be able to add anything that anybody else hasn’t already mentioned.
There are two versions of this riddle. One relates the speed of the conveyor belt to the speed of the planes wheels. Often times these threads fail to mention that a wheel and a treadmill always move at the same speed. There would be no “programming” required. A relationship exists between the wheel and the conveyer. Say the conveyer belt made a 1000 ft. (or just short of) runway making the belt 2000 ft. lets say your plane wheel travels 1 ft. per rotation. You have a solid unbreakable relation of 2000:1. That means no matter what the rate of the plane speed is in relationship to the ground speed, the wheels will (in this example) spin at a rate of 1 rotation of the conveyor belt to 2000 revelations of the plane wheels. If we are to believe that Newton’s third law is correct, then the conveyor belt will never actually have to move. The wheels will achieve flight 1000 ft down the runway, spinning 1000 times, with the ration remaining at .5 rotations of the conveyor belt to 1000 rotations of the wheel. The plane moved across ½ of the conveyor belt the full length of the runway. This is irrelevant to the speed in which the plane is moving across the ground. Wheels and conveyors move in terms of RPM not MPH.
That said I have heard people try to argue that the questions was worded improperly and that it is sometimes stated that the conveyor belt speed matches the speed of the plane. Then the only required understanding is that once the planes thrust exceeds the friction coefficient (about .002 for normal bearings) then plan will move forward. You and your buds can prove this with a pair of roller blades, a treadmill, a water-ski rope, a fishing scale, and a 4 pack of really good Russian imperial stout. Attach the scale to the wall, the ski rope to the other end of the scale. Have your friend don the roller blades, climb on the treadmill, and power up the treadmill. The beer should be obvious. Note that only a small amount of force will be exerted on the fish weight scale. That will be true no matter what the setting is on the treadmill or even if he pulls himself forward. If a plane requires 65 MPH such as a small sport craft, then the conveyor will be moving backwards at 65 MPH. So? The wheels will turn at an RPM equivilant to 130 MPH realative to the ground below the treadmil. Te point of tangency will be moving at 65 MPH in relation to the wheel and the conveyor. Wheels don’t hold planes back, friction does that task.
In the situation of a car on a conveyor belt the “plane” that the body is pushing off of (the conveyor belt)is moving in the opposite direction. in the case of the airplane on the conveyor belt, the “plane” in which the body is pushing off of (the surrounding air)is not moving.
Folks - the issue for airplanes to fly is airflow over the wings - bernoulli principle, plus a bit of Newton’s 3rd or downwash over the trailing edge. Propulsion (prop, jet etc.) pushes the plane forward thus generating that airflow. No airflow, no lift, no fly. The conveyer would negate airflow and therefore the lift. So no it would not lift. And yep, I’ma pilot.
Some of the comments mention headwinds. Winds introduce complex physics to the equation; however, once airborne, winds are irrelvant to lift with airplanes. The plane doesn’t fel the wind once it’s flying, although ground based observers see the relative motion of the air mass with the plane in it and often assume it does.
I will be happy to provide an advanced ultralight for the the proof test if someone has a suitable conveyor (very low friction - I don’t want my airplane creeping forward and falling off the end).
Mike, I suggest you more fully investigate the question. The conveyor doesn’t prevent the airplane from moving forward and thus doesn’t prevent air from flowing over the wings.
PS - I am assuming the conveyor powered and matching speed with the plane. I should have stated that. If the plane is free to move on the conveyor and the conveyor is not powered, then the plane will accelerate forward, create lift and take off, or drive off the end of a short conveyor! The wheels on a plane are not powered and do not introduce thrust like a car’s drive wheels.
I am starting to second guess myself. I know I am right about needing airflow over the wing to create lift. That much is certain, so the question really boils down to whether or not a plane with freely rotating wheels will be “held” stationary by the backward spinning conveyor, and I need to think about that for a bit.
;))
Bingo.. That is truly what the question is asking.. And to sum up what ive said before, the conveyor cannot keep it from moving, it will accelerate virtually as normal to take off speed and fly away
After thinking through the physics of an unconstrained wheel on a conveyor belt on the drive home last night, I concur with Sooks, given a sufficiently long conveyoer (i.e. one the airplane doesn’t fall off the end of prior to reaching flying speed, it will take off because it will accelerate in much the same fashion as it would on a runway. I believe the only difference is the wheels will be free spinning at about twice their normal speed.
To solve this problem, one must understand that there are two systems at work: (1) dealing with the airplane wing, and (2) dealing with the wheel on a conveyor belt.
I wonder if the authors of the original question reasoned it to be this complex, or were just wondering about the simple act of a plane leaping into the air while at a standstill.
Mike:
The question as posted here is a bastardization of the actual question posed on the Boortz Show (which I heard). The actual gist of the question is a situation where the treadmill counteracts the thrust to where the plane is not moving and, AT THIS POINT will the plane be able to take off. There is no mention of gradually building up speed on an apparently limitless or lengthy runway (here the treadmill). The original question is whether it will (thanks to the props pushing air over the wings etc etc) be able to fly at that instant of zero groundspeed. Which, of course, it can not do.
First off..that isnt the “actual” or “original” question.. but i can understand that it can be something to consider. HOWEVER, the problem with that is there isnt a way that the belt can counteract the thrust of the plane. They are two forces that dont act directly onto one another.
and mike, youre exactly right, it will take off at approx the smae rate with the wheels rotating at twice their original speed.
Sooks - that IS the context of the actual question - whether the plane can lift off any fly at that brief point where the force of the plane’s props counteract the treadmill and the plane is virtually at a standstill with the engine going whole hog. Granted that is a very brief time, but that IS the original question - again, I heard it when it aired. The question isn’t can it, at that place in time, slowly go forward until it can achieve flight. The question was whether it can fly THEN.
Sttork, if that is in fact the question asked, it differs from every other incarnation I’ve ever heard. The belt is said to match the speed of the airplane in the opposite direction, NOT that the belt will keep the plane stationary. That last bit is often simply assumed to be true by those who analyse the problem improperly, but it is not stated explicitly.
I found this thread quite by accident. I was googling for some empirical data on how long it actually takes an aircraft to be come part of the moving airmass it flies in once it leaves the ground. You see numbers like a couple of seconds, and a second or so about aligns with what I feel when I lift off into a strong cross wind in my Cessna 182 or my ultralight, but I was looking for something more “scientific” for a ground school course on taking off into crosswinds or headwinds and overcoming perceptions of student pilots about wind forces on airplanes. (A common leap is that an airplane climbs faster in a headwind. It certainly appears to from the ground of course, but it really makes no difference to the airplane once you’re airborne).
This entire thread is fascinating. I have thought for quite some time that bringing about societal change is much harder in a group of “smarter” change targets as it is much tougher to gain concensus on basic facts, and therefore reach some common ground on why the change is necessary! This thread is good support for my theory as many of the arguments put forth are quite sophisticated, and can seem very convincing, and you really have to have time to think through the problem and a fair bit of solid physics behind you to reason it out. And this in an area where the physics is pretty well understood.
I am wondering just what kind of debates must be ranging on climate change and global warming!
All in all, the original question would be fascinating to work through with high school physics students and a scale model airplane, a variable speed conveyor and some highly sensitive strain guages. A great project for a School Science fair I think with both and RC Car and an Airplane.
nobody accounted for the drag the conveyer belt exert on the tyres? If the plane engine is strong enough (SU-25 foxbat) to overcome this, it will rip of the tyres as the conveyer spins into infinite speed to keep the plane speed to 0. If the plane is weak, ie a fokker, it will stay down there, pulled back by the tyres on the conveyer belt.
am I right?
I agree..the conveyor cannot keep it from moving, it will accelerate virtually as normal to take off speed and fly away.
Is this statement true?
If A can nullify B
and B can nullift C
then A can nullift C
and if C is a force, then B must produce a force to nullify C, and A must produce a force to nullify B.
Corey this is how the puzzle works and confuses.
It gets you to accept something as true that is not true. In this case A can nullify B.
Once you accept that you get the answer of “no”
however A cannot nullify B
The conveyor cannot make the plane stationary.
Engine power alone does cannot lift a plane, otherwise planes could take off of 30ft ramps. It is the lift generated by the turbines PLUS the forward momentum relative to the air, which is why the plane needs to move forward relative to the air to take off. Even with the turbines moving air under the wings, it is not enough to keep it in the air. Think of a school bus going at 100mph, and you are on it and throw a ball straight up, the ball will not hit the back, because it will move relative to the bus REGARDLESS of how little friction. The same thing with the plane. There is not enough forward momentum pushing additional air around the wings to generate liftoff, and being that it will take off relative to the conveyor belt, even though the wheels generate little friction, it can only lift off vertically, and once in the air, it will touch back down immediately due to lack of forward momentum generating the needed additional lift.
Well said. I find it interesting that throughout these posts some people have shown how it can - or can’t - fly when using small models or cars on tracks to prove/disprove the idea. Back in the ’70’s our local airport was converted from a dirt landing strip to concrete. At that time we used a short field take-off (full power, brakes on, brakes released, etc.) to take off. You do, indeed, still need forward momentum to take off. ‘Nuff Said.
It’s not “’nuff said” unless you agree that the plane does move forward. Practically as normal.
The question does not even say that the plane does not move forward.
furthermore it gives no mechanism capable of stopping the plane from going forward.
Now if it has said there was a rope strong enough to stop the plane from moving forward…
How do all the no people not notice the yes people always say the plane moves forward as normal?
The original question asks: “will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?” It further complicates things by adding this info that the plane: “…is trying to take off by exerting the thrust needed to move it forward at 100 knots.” Obviously, if it IS able to exert sufficuent thrust to make it move forward at 100 knots, then of course it WILL have enough airspeed to fly - since it will in this case have plenty of foreard air speed. The way it is worded it answers its own question. The REAL question should be whether is it CAPABLE of exerting enough force to move it forward at 100 knots under this strange circumstance.
As it’s been stated many times previous…a conveyor belt matching the plane’s forward speed cannot impede its motion enough to have much of an effect on it. The plane will take off almost exactly like normal - with no need to invoke some magical circumstance where planes fly with no forward motion. It WILL have forward motion.
And there lies the rub - differences of opinion as to how much the conveyor belt will affect the forward thrust. If the plane derived the force to move forward in the same manner as a car (powered wheels) - then naturally it will not go very far (you ever try running on ball bearings? same idea).
Well of course, but the manner in which an airplane propels itself is very different from that of a car. Wheels on a car provide the vehicle with something to transfer force with, while wheels on an airplane aren’t much more than a friction reducer. Planes with no wheels tend to be inefficient on land :).
This problem is no different to that of a hover craft. The conveyor belt exerts no substantial force I REPEAT NO SUBSTANTIAL force on the plane. The only effect the the conveyor belt will have is to spin the wheels.
Now here is an experiment that I have done with my friends to PROVE this point (even though it was not necessary because the mathematics prove it already and by math I mean real physics not high school intro to physics part 1):
we had
1 treadmill
1 pair of roller blades
1 rope and
1 idiot to put in this situation
1 spring gauge to measure force (borrowed from university civil engineering lab)
Put roller blades on idiot
put idiot on tread mill. tie rope to gauge and anchor the other end of the gauge to the wall
Turned on treadmill had idiot pull himself along treadmill with the rope and measured the force.
Idiot was able to move forward.
Performed same procedure with treadmill turned off.
Idiot pulled himself forward again
Force was almost identical in both cases(discrepencies were very small but present due to rolling resistance)
This means that the force place by the treadmill had very little impact on the idiot’s ability to move forward.
I just wish I was there to see the idiot flapping his arms…heh heh
The ‘equal and opposite reaction’ is not the ground moving backward or the plane moving forward. It’s the wheel’s spinning…that’s the result of the belt moving.
Number one the wheels spinning are not capable of “equal and opposite reaction”. They are made to have as little as possible impact.
Number two propellors are called propellors because they propell the plane forward.
Number three the “equal and opposite reaction” has to act directly on the props.
Number four the question not does not say the plane is stationary, it provides no way the plane can be held stationary. It should have said the plane was held back by a strong rope.
Stephen:
Agreed - the original question is the poster’s variation of the original question and does not fully take into consideration enough details. I heard the question originally stated when it aired and the idea, obviously different from the posted question here, is that a plane on a treadmill, engines full out, is at the point where is it at full power, but not moving forward, and can it fly AT THAT TIME. Not will it eventually get up enough speed to fly. Will it fly AT THAT MOMENT - te answer of which is, naturally, no.
The question HERE adds “by exerting the thrust needed to move it forward at 100 knots” which changes everything and, if it it IS exerting enough move it forward, then sure, it will fly under this condition as the question answers itself by saying that it CAN.
Maybe if people approach this from a different angle; Why does a plane have wheels? The answer is pretty simple. If it didn’t have wheels, then the body would drag against the ground, generating more friction than the engine thrust can counteract. We added tires (and their associated axles and bearings) to help “insulate” the aircraft from friction against the ground. On lower friction surfaces (snow, ice, water) we don’t have to use tires. We can generate enough thrust to counteract ground-friction while using skis, or floats.
Since the plane in this example is for all practical purposes “insulated” from the ground-friction effects of the conveyor belt, the plane moves forward and takes off.
Nothing in any statement of the problem says the conveyor applies some other force vector that the plane is NOT insulated from. If some other vector IS APPLIED that prevents the plane moving forward, then it won’t take off. But without that vector, she rolls forward, eventually leading to flight.
I have read most of the posts here . . . some make valid points others (on both sides) don’t have a clue what they are talking about. Let’s make this VERY simple; I am going to assume most of you have run on a treadmill. When you are done how far have you travelled? If you run faster than the treadmill you would gain ground, but if the treadmill is travelling at the same speed as you do where do you go? When you run on the treadmill do you feel the wind in your hair? NO!!! So . . . even if the plane generates enough thrust for the wheels to roll at 200 knots and the conveyor equals that in the opposite direction, how far can the plane move in relation to the static air? NOWHERE!!! And without air traveling over and under the wings there is NO LIFT, therefore the plane CANNOT get off the ground! It doesn’t matter how much air is passing through the jet engine . . . none is traveling over/under the wings — NO LIFT = NO TAKEOFF!!!!
Im gonna take it, that no you havent read most of the posts otherwise youd see that was brought up many times..
Again, the key difference between you and the plane is where your thrust is derived from…Your feet power you along, however the wheels DO NOT power the plane..they simply spin.. the plane is basically being pushed from behind..
Now, to use your example.. what if your running along… and someone came up and shoved you forward from behind (opposite the direction of the treadmill)… no matter how fast that treadmill is going..your going to jolt forward from that shove… get it now?
To add to that.. what if you had rollerblades on… maybe that would help you.., you had a rope tied around your waist, and I, who is standing off the treadmill, pulled you..that treadmill can be going 1000 mph, but youre still going to move forward…
By the way . . . the question DOES state the following: ” an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots.” SO the question does state equal forces . . .
speed does not equal force
as well to add to that again.. They arent forces acting directly on each other.. The treadmill/treadbelt doesnt directly act upon the plane, only a fraction of its force is transmitted to the plane, and thats through rolling friction which is minimal.
Okay . . . I have tried to open mind up to analyze this (I tend take firm stances). So . . . you are saying with the wheels being free rolling they will begin to spin even if the no thrust is yet applied by the plane (gravity providing the resistance). Now the plane begins thrust and NOT thrusting against the treadmill (as a runner would) but against the static air, thereby creating forward motion . . . Is this your train of thought?
Umm…very close.. The wheels wont spin without any thrust… because there is SOME resistance (force in teh opposite direction) so without any thrust, yes teh plane/rollerblader will begin to move backwards… But with just a lil bit of thrust, the plane/rollerblader overcomes that minimal thrust and moves forward just like you explained from the static air…
Think of it liek the one guy explained..what if the treadbelt was made of ice and instead of wheels the plane was on skis… I think this is easier to visualize for people because with wheels, we tend to link it to a car. The skis on the plane certainlly dont propel it forward.. the prop/jet engine does…
The wheels will roll because the air behind the plane will offer resistance . . . it will still go backwards, but probably not as fast as the conveyor. Then when the engines begin to thrust, as you said, it will easily overcome the conveyor, making forward progress . . . air begins to move over/under the wings and eventually, LIFTOFF!!! You guys won me over . . .
It surprises me how many people claim to be pilots, but don’t seem to understand the difference between ground speed, indicated airspeed and true airspeed. Many seem to forget how to sum ALL the force vectors on the craft.
Anyway, in summary:
- If the conveyor can apply enough force against the forward motion of the plane (i.e. a LOT of drag against tires, bearings, etc.) such that the plane does not move forward, then it cannot generate sufficient lift in order to take off. I don’t think anyone is disputing that — No forward motion, no take off (unless there is suddenly an intense headwind
- If the wheels, bearings, et all, are more like real ones, then the conveyor can’t apply enough force to prevent the plane from moving forward. Even if the conveyor is moving MANY times faster than the speed needed for take off, the plane continues to gather speed and takes off (barring catastrophic failure of the wheels and undercarriage).
I think the whole car/running argument has been adequately debunked.
Frankly, I think both sides are correct in their analysis and that ultimately the puzzle creates a paradox.
If, as stated, the belt and the wheels spin in opposite directions always at the exact same speed (I believe the original problem, as stated, held that the belt matched it’s speed instantly to that of the wheels) then there is no way that the wheels can make any forward progress on the belt. The thrust of the jet (or whatever propulsion method you choose) is what makes the wheels turn, albeit indirectly. The thrust pushes the jet forward and the wheels, designed to reduce friction between the jet and the belt, both turn and move forward as a result of the thrust.
If the belt moves in the opposite direction at the exact opposite speed, instantaneously increasing it’s speed to match the wheels, there is simply no way the wheels can make any forward progress on the belt. Any additional thrust applied to the jet results in increased speed of the wheels which is instantly met with an equal increase in speed of the belt. Without any forward progress on the belt the jet can’t generate any lift under the wings and can’t take off.
However, the other side makes an equally valid point when it discusses the principles of force. The thrust of the engines is a force that acts to move the jet forward. In order for the jet not to move forward there has to be a force to counter the thrust. The only potential force applied to the jet is the resistance between the wheels and the belt (which I think is technically known as “rolling resistance”) and this isn’t enough to counter the thrust of the engines because it doesn’t increase in direct proportion to the increase of the thrust.
So, if you believe the plane can’t fly you have to explain what is countering the thrust of the engines and if you believe it can fly you have to explain how the wheels can make any forward progress when the thrust that causes them to move forward is instantly countered with an increase in belt speed in the opposite direction.
I think what you’re left with is a plane that will take off with wheels that won’t. Since the wheels are attached to the plane this isn’t possible thus the paradox.
Sorry for the length of the post.
Commonsense… glad we could convert you.. dont worry, i originally had the same thoughts as you did, its very hard to visualize at first…
Jeff.. i hear you.
Harry.. Youre actually pretty close to accurate.. What you said at first is correct.. if the conveyor matches the WHEEL SPEED, that will create a paradox where the belt and wheel go to infinity mph almost instantly as the wheel will increase its speed, teh belt will in turn match it, which in turn makes the wheel spin faster, belt matches etc etc..
However, in the original question it states it matches the plane speed, not wheel, speed, but its definately an interesting question to consider.
With your other statement about if the belt went the same direction as the plane, its true the wheels would not spin.. but the plane would in fact be moving forward and would still take off, Remember, it doesnt have to move forward on the belt, it just needs to move forward compared to the earth, or a bystander watching it..
hope that helps.
Skooks,
Thanks for the compliment. I reread the original description of the problem and you are correct that it doesn’t say “wheel speed”, but instead says that the engines are generating enough thrust to move the plane forward at 100 knots.
However, if the plane has a forward speed of 100 knots, don’t the wheels, which are attached to the plane, also have a forward speed of 100 knots?
If so then the conveyor belt must be moving backwards at the same speed as both the plane and the wheels.
If the wheels are moving forward at the same speed as the belt is moving backwards, the wheels cannot make any forward progress on the belt or relative to the ground. Without forward progress, there’s no lift and no take off.
On the other hand, there’s no counter to the thrust, so regardless of whether the belt matches the wheel speed or the plane’s speed (which are always the same anyway), the plane should move forward.
I’m afraid even with the clarification we’re still right back to the paradox conclusion that the plane moves forward and the wheels don’t.
The speed that the wheels are going is a product of the planes forward movement combined with the movement of the belt.. so if the plane is moving forward at 100mph and the belt is going 100 mph in the opposite direction, then the wheels are spinning at 200mph… hence why if it was matching the wheel speed, it wouldnt work and creates a paradox, because the wheel speed is a sum derived from the speed of the belt.
conversely, if the belt was going the same speed as the plane, in the same direction… 100mph (plane) + (-)100mph (belt)= 0 wheel speed
and once again, it doesnt need to make forward progress on the belt..just forward progress to the earth..i.e. airspeed.
Skooks,
I think you’re confusing rotational speed and linear speed. The wheels are actually moving in 2 different directions, they are rotating around a center point (rotational speed) and they are moving forward at the same speed as the plane (linear speed).
I interpreted the puzzle to mean the belt is matching the linear speed of the wheels, not the rotational speed. If you think the speed discussed is rotational, you need to explain how you’re measuring the speed. Is it rotations per minute?
If it is rpm’s, then you have a problem. Since the wheels and the belt/runway are in constant contact and since the wheels are (presumably) much smaller than the belt/runway in terms of circumference, one rotation of the belt will result in many rotations of the wheels. In other words, the wheels and the belt can possibly be turning at the same rpm’s so long as they are in constant contact and different sizes.
But if you’re going to consider the puzzle to be about the rotational speed of the wheels and not the linear speed, and you’re not going to measure the rotational speed in terms of rotations per minute, how are you going to measure it? Remember, however you choose to measure this speed both the larger belt and the smaller wheel have to be travelling at the same speed.
The original puzzle says that the thrust is enough to push the jet forward at 100 knots and the belt moves backwards at 100 knots. Since the wheels are not mentioned, it seems a stretch to interpret the puzzle to be discussing rotational speed of the belt and wheels.
I think it only makes sense if you consider the linear speed of the wheels and then the only answer that makes sense is the paradox previously proposed.