The thing that *really* needs to be clarified is what *speed* is being measured and matched.
I've looked at a few of the other places this basic concept is discussed and they seem to be talking about conveyor speeds similar to the normal take off speed of the aircraft. For example the myth busters used a plane that normally takes off at 25 mph, so they ran the treadmill at 25 mph.
The statement on this thread indicates that wheel encoders are used to measure speed, which implies that aircraft *speed* is measured relative to the conveyor, which sets up the positive feedback resulting in infinite conveyor speed.
So which speed is being matched, the speed of the aircraft relative to the earth, or to the conveyor?
Yes, exactly. Thank you skylight for posting a poorly specified, ambiguous and totally incorrect statement of the original problem. Thus wasting thousands of hours of our lives that are gone forever and could have been used for something productive.
erco,
Too late, a quick google shows 100's of thousands of hits for "jet plane treadmill" or "jet plane conveyor" it even has it's own domain already http://www.airplaneonatreadmill.com/ where the discussion is still going on after four years! This thing could devour the entire internet like some invasive weed.
I suggest we quit this plane an conveyor thread here and now, set fire to the remains, and dowse the place in weed killer. Anyone who wants to continue can do so at the above link.
However. I want to look at one last thing. Phil, skylight and others (although I think Phil has changed his mind) suggest that because the wheels have frictionless bearings the conveyor cannot apply force to, or have an effect on, the plane. Given normal wheels with diameter and mass this is not true. As the conveyor accelerates friction between it and the wheels causes them to rotate and applies a force, in the direction of conveyor movement, on the axles. This is all to do with wheels "moment of inertia".
You can see this for your self, as in my rolling pin experiment previously. Let me reword it a bit for this forum audience:
Place a sheet of A4 paper and lay it flat on a smooth table. (Best move all the beer glasses and such out of the way first).
Take a robot or r/c car wheel stand it on its treads on the paper.
Grab one edge of the paper and pull it horizontally out from under the wheel, in a direction that the wheel might roll in. Accelerating the paper smoothly.
Observe how when the wheel leaves the paper it is not only rotating but moving horizontally in the direction of your paper travel.
In order to check my sanity I have just done this experiment and it was so.
"Ah", you say, "there is no plane here". So what? If we now connect a plane through frictionless bearings to our wheel hub whatever force moves the wheel horizontally as we slide out the paper, as above, will also be trying to move that plane. The wheel will rotate more and the plane+wheel system will travel horizontally less. How much all depends on the mass and diameter of the wheels and the mass of the plane.
This effect is often excluded from the conversation, as it might be small in the case of say a jumbo jet and a slow conveyor, but it is still there. How that effects the given problem I will leave you to consider further.
Dave Hein, has suggested that the only way to satisfy the given conditions in the problem as stated here is for the motors to be off and nothing ever moves. Else we have an impossible run away scenario. I like this reasoning. It occurs to me though that even then the thing is unstable. To meet the problem spec we need high resolution encoders (effectively analog), infinitely fast control and so on. In any real world attempt to build this, even with the jet engine stopped, any noise in the encoders would look like motion of the wheels and the system would immediately destroy itself:)
Here's a video that demonstrates rotational inertia -- http://www.youtube.com/watch?v=7PRZ5IIT5Tg . The disk with the larger moment of inertia accelerates at a slower pace than the other disk. Now if the ramp were an inclined treadmill it would be possible to increase the speed of the treadmill to keep the disks at a fixed location -- at least for a few seconds. The same method could be applied to the jet to keep it in one place as long as the wheels have a nonzero moment of inertia.
Never mind what physics may or may not be taught in school I do wonder if anyone here has ever played with the humble yo-yo. In fact this whole plane problem is much like the yo-yo. Where:
yo-yo = the plane and its wheels.
yo-yo string = conveyor belt.
gravity acting on yo-yo = jet engine thrust.
Hand pulling string = power applied to conveyor belt.
(Yeah, yeah, as above the yo-yo is only wheel and no plane but makes no odds)
So here is a question similar to the jet conveyor problem:
Wind the string around the yo-yo and hold the free end.
Drop the yo-yo
As it drops start pulling the end of the string upwards.
Is it possible to cause the yo-yo to travel upwards against the force of gravity which is pulling it down.(Before reaching the end of the string)
Well, anyone who has played with a yo-yo for five minutes knows it is it is possible. Whilst pulling on the string the yo-yo starts to spin, but because you are pulling against it's rotational inertia it also experiences an up ward force. Pull hard enough an it will rise instead of fall.
What finally convinced me that I was wrong about the moment of inertia thing was the following gedanken experiment, in which two extremes having obvious solutions are observed. In this experiment, a weight is attached to a rope wrapped around a wheel, as shown:
In the leftmost case, the wheel mass D is concentrated on the rim and the weight mass W is attached to the axle. Obviously, the total force exerted on the axle will be W+D.
At the other extreme (the middle setup), the wheel mass is concentrated on the axle, and the weight is attached to the rim. Since the wheel has a zero moment of inertia, the weight is free to strip off as much rope as it wants, spinning the wheel without resistance and exerting no force on the axle. So the net force on the axle is D, the weight of the wheel.
So I had to conclude that if the wheel mass was concentrated at the same radius that the rope was wrapped around, and since nature doesn't make quantum jumps at the macroscopic level, the net force on the axle would be somewhere between the other two extremes.
Other than the "zero moment of inertia" (give me that in a bike wheel) impossibility, this is a fresher and IMHO much more interesting problem.
But I will take my learned opponent PhiPi to task on the far right case. If the wheel is free to spin friction-free and there's zero moment of inertia, then the weight is in free fall and it matters not what the radius is: the weight scale will register D as shown for the middle case.
In the far right-hand case, because the wheel mass (the red circle) is not concentrated at the center, but halfway outward, the moment of inertia is non-zero.
After many hours of calculations, I have determined that the air craft will NOT take off under the following conditions:
1. It is on the moon.
2. It was trying to take off from planet earth before the evolution of photosynthesis.
3. It is on planet Mercury.
4. Its warranty expired one hour ago.
5. The British are shooting frozen chickens at it instead of raw chickens (again).
I get the feeling that some are not taking this seriously enough
After much slapping from members here I have decided to just change one or two things as I don't think it will make the slightest difference to the plane taking off but here goes..
Let's make it more real world:
The wheel bearing having no friction is upsetting some and I really don't want to be a victim of multiple lawsuits to pay for the drugs being prescribed (I've heard of the excessive payouts your legal system hands out!)
So tada the bearings are now normal aircraft wheel bearings which i'm sure are manufactured to the highest standards and so have miniscule friction.
Obviously when stationary the weight of the plane bears down on the bearings to cause a substantial amount of friction that needs to be over come before the plane can move forward and the pilot will take care of that by applying enough throttle to the thrusters to get the plane moving.
as far as the runway goes,it has been mentioned that the encoders mounted on the wheels would cause the runway to spiral out of control in an infinite loop
so therefore lets say that feedback from the aircraft about it's airspeed(presuming it will still read even though the aircraft is still on the runway and trying to take off) is wirelessly transfered to the runway speed controller and to compensate for slow takeup of speed drag etc that the ratio of runway speed to aircraft speed is that the runway is designed to be 1.5 times the aircrafts airspeed. in the opposite direction to the way the plane is moving due to the thrusters.
I believe that even with this frictional real world amendment that the tiny amount of friction in the bearings will cause a very tiny oppositional force on the axle trying to slow down the aircraft and the power of the thrusters will overcome any resistance to take-off.
so therefore lets say that feedback from the aircraft about it's airspeed(presuming it will still read even though the aircraft is still on the runway and trying to take off) is wirelessly transfered to the runway speed controller and to compensate for slow takeup of speed drag etc that the ratio of runway speed to aircraft speed is that the runway is designed to be 1.5 times the aircrafts airspeed. in the opposite direction to the way the plane is moving due to the thrusters.
The aircraft now takes off, it would not have prior to this change.
Haven't you just changed the whole scenario dramatically and in a very wordy way presented a non-problem?
I quite liked the frictionless bearings by the way.
The main energy drain in rotating an aircraft's wheels (real world) is not due to inertia, or the pressure on the bearings but the rolling resistance. When loaded a tire gets deformed. It takes energy to roll the tire, it is like it is always going up hill. If the tire is under-inflated this effect is even greater.
If we reframe the question;
Can a jet take off if it is on a conveyer belt that is pulled rearward at the same speed as the jet would normally take off?
So if the jet needs to go 100 mph to take off and the runway is moving backwards at 100mph, then yes it will still take off - providing that there is enough excess thrust to overcome the extra rolling resistance from spinning the wheels 200 mph (there should be) and providing that the tires do not fail and cause a crash.
Rich, the plane might take off, but it would not remain airborne for more than a second or two. With all that rolling resistance, once it breaks contact with the ground, it will lurch forward. The pilot, with his hands on the yoke, will suddenly be pressed back into his seat, causing him to yank back on the yoke, which will result in an immediate stall.
The wheels don't actually go 100mph (or 200mph) but the plane would need an indicated airspeed of 100mph (typically knots indicated air speed KIA'S) this could be achieved through actual forward motion plus whatever any headwinds contributed......
Depending on the length and width of the treadmill, the stall tendency will be mitigated by ground effects, turbulence and eddy currents generated by the moving treadmill track, thus obviating the need for pilot overcontrol, and the jet will climb swiftly and gracefully into the upper stratosphere.
The wheels don't actually go 100mph (or 200mph) but the plane would need an indicated airspeed of 100mph (typically knots indicated air speed KIA'S) this could be achieved through actual forward motion plus whatever any headwinds contributed.......
First, no headwinds. This experiment is in calm conditions, sea level, standard day. Second, yes the wheels would actually "go" 100 mph since they are attached to the aircraft and it is moving at takeoff speed (100 mph) - which is the same as indicated airspeed since there is no headwind or tailwind. However the wheels would be spinning at the equivalent rpm of 200 mph because the treadmill is moving backwards at 100 mph.
Rich, the plane might take off, but it would not remain airborne for more than a second or two. With all that rolling resistance, once it breaks contact with the ground, it will lurch forward. The pilot, with his hands on the yoke, will suddenly be pressed back into his seat, causing him to yank back on the yoke, which will result in an immediate stall.
-Phil
I don't know about the lurching forward part but there is the effect of the sudden loss of drag parallel to and below the thrust line that would contribute to a pitching up of the aircraft.
This thread has to cease for the sake of the forum members sanity, You dont want them ending up in The Psycho-Neurotic Institute for the Very, Very Nervous do you?
1. propeller starts turning
2. plane starts moving
3. wheel starts turning
4. conveyor starts moving
5. wheel starts turning faster
6. conveyor starts moving faster
7. goto 5 until wheel speed reaches a ridiculously high speed, after which
8. tire explodes under centrifugal force
9. now smaller wheel speeds up even faster
10. metal of wheel explodes under centrifugal force at almost the speed of light
11. metal shards crash into the jet at the speed of light, creating a black hole which destroys the universe
Comments
I've looked at a few of the other places this basic concept is discussed and they seem to be talking about conveyor speeds similar to the normal take off speed of the aircraft. For example the myth busters used a plane that normally takes off at 25 mph, so they ran the treadmill at 25 mph.
The statement on this thread indicates that wheel encoders are used to measure speed, which implies that aircraft *speed* is measured relative to the conveyor, which sets up the positive feedback resulting in infinite conveyor speed.
So which speed is being matched, the speed of the aircraft relative to the earth, or to the conveyor?
C.W.
Yes, exactly. Thank you skylight for posting a poorly specified, ambiguous and totally incorrect statement of the original problem. Thus wasting thousands of hours of our lives that are gone forever and could have been used for something productive.
erco,
Too late, a quick google shows 100's of thousands of hits for "jet plane treadmill" or "jet plane conveyor" it even has it's own domain already http://www.airplaneonatreadmill.com/ where the discussion is still going on after four years! This thing could devour the entire internet like some invasive weed.
I suggest we quit this plane an conveyor thread here and now, set fire to the remains, and dowse the place in weed killer. Anyone who wants to continue can do so at the above link.
However. I want to look at one last thing. Phil, skylight and others (although I think Phil has changed his mind) suggest that because the wheels have frictionless bearings the conveyor cannot apply force to, or have an effect on, the plane. Given normal wheels with diameter and mass this is not true. As the conveyor accelerates friction between it and the wheels causes them to rotate and applies a force, in the direction of conveyor movement, on the axles. This is all to do with wheels "moment of inertia".
You can see this for your self, as in my rolling pin experiment previously. Let me reword it a bit for this forum audience:
Place a sheet of A4 paper and lay it flat on a smooth table. (Best move all the beer glasses and such out of the way first).
Take a robot or r/c car wheel stand it on its treads on the paper.
Grab one edge of the paper and pull it horizontally out from under the wheel, in a direction that the wheel might roll in. Accelerating the paper smoothly.
Observe how when the wheel leaves the paper it is not only rotating but moving horizontally in the direction of your paper travel.
In order to check my sanity I have just done this experiment and it was so.
"Ah", you say, "there is no plane here". So what? If we now connect a plane through frictionless bearings to our wheel hub whatever force moves the wheel horizontally as we slide out the paper, as above, will also be trying to move that plane. The wheel will rotate more and the plane+wheel system will travel horizontally less. How much all depends on the mass and diameter of the wheels and the mass of the plane.
This effect is often excluded from the conversation, as it might be small in the case of say a jumbo jet and a slow conveyor, but it is still there. How that effects the given problem I will leave you to consider further.
Dave Hein, has suggested that the only way to satisfy the given conditions in the problem as stated here is for the motors to be off and nothing ever moves. Else we have an impossible run away scenario. I like this reasoning. It occurs to me though that even then the thing is unstable. To meet the problem spec we need high resolution encoders (effectively analog), infinitely fast control and so on. In any real world attempt to build this, even with the jet engine stopped, any noise in the encoders would look like motion of the wheels and the system would immediately destroy itself:)
Never mind what physics may or may not be taught in school I do wonder if anyone here has ever played with the humble yo-yo. In fact this whole plane problem is much like the yo-yo. Where:
yo-yo = the plane and its wheels.
yo-yo string = conveyor belt.
gravity acting on yo-yo = jet engine thrust.
Hand pulling string = power applied to conveyor belt.
(Yeah, yeah, as above the yo-yo is only wheel and no plane but makes no odds)
So here is a question similar to the jet conveyor problem:
Wind the string around the yo-yo and hold the free end.
Drop the yo-yo
As it drops start pulling the end of the string upwards.
Is it possible to cause the yo-yo to travel upwards against the force of gravity which is pulling it down.(Before reaching the end of the string)
Well, anyone who has played with a yo-yo for five minutes knows it is it is possible. Whilst pulling on the string the yo-yo starts to spin, but because you are pulling against it's rotational inertia it also experiences an up ward force. Pull hard enough an it will rise instead of fall.
In the leftmost case, the wheel mass D is concentrated on the rim and the weight mass W is attached to the axle. Obviously, the total force exerted on the axle will be W+D.
At the other extreme (the middle setup), the wheel mass is concentrated on the axle, and the weight is attached to the rim. Since the wheel has a zero moment of inertia, the weight is free to strip off as much rope as it wants, spinning the wheel without resistance and exerting no force on the axle. So the net force on the axle is D, the weight of the wheel.
So I had to conclude that if the wheel mass was concentrated at the same radius that the rope was wrapped around, and since nature doesn't make quantum jumps at the macroscopic level, the net force on the axle would be somewhere between the other two extremes.
-Phil
But I will take my learned opponent PhiPi to task on the far right case. If the wheel is free to spin friction-free and there's zero moment of inertia, then the weight is in free fall and it matters not what the radius is: the weight scale will register D as shown for the middle case.
In the far right-hand case, because the wheel mass (the red circle) is not concentrated at the center, but halfway outward, the moment of inertia is non-zero.
-Phil
Who are the fiends who spend their days concocting these man-hour wasters?
Let's make it more real world:
The wheel bearing having no friction is upsetting some and I really don't want to be a victim of multiple lawsuits to pay for the drugs being prescribed (I've heard of the excessive payouts your legal system hands out!)
So tada the bearings are now normal aircraft wheel bearings which i'm sure are manufactured to the highest standards and so have miniscule friction.
Obviously when stationary the weight of the plane bears down on the bearings to cause a substantial amount of friction that needs to be over come before the plane can move forward and the pilot will take care of that by applying enough throttle to the thrusters to get the plane moving.
as far as the runway goes,it has been mentioned that the encoders mounted on the wheels would cause the runway to spiral out of control in an infinite loop
so therefore lets say that feedback from the aircraft about it's airspeed(presuming it will still read even though the aircraft is still on the runway and trying to take off) is wirelessly transfered to the runway speed controller and to compensate for slow takeup of speed drag etc that the ratio of runway speed to aircraft speed is that the runway is designed to be 1.5 times the aircrafts airspeed. in the opposite direction to the way the plane is moving due to the thrusters.
I believe that even with this frictional real world amendment that the tiny amount of friction in the bearings will cause a very tiny oppositional force on the axle trying to slow down the aircraft and the power of the thrusters will overcome any resistance to take-off.
Perhaps?
The aircraft now takes off, it would not have prior to this change.
C.W.
Haven't you just changed the whole scenario dramatically and in a very wordy way presented a non-problem?
I quite liked the frictionless bearings by the way.
-Phil
If we reframe the question;
Can a jet take off if it is on a conveyer belt that is pulled rearward at the same speed as the jet would normally take off?
So if the jet needs to go 100 mph to take off and the runway is moving backwards at 100mph, then yes it will still take off - providing that there is enough excess thrust to overcome the extra rolling resistance from spinning the wheels 200 mph (there should be) and providing that the tires do not fail and cause a crash.
You're welcome erco.
Rich: I'd write to say thank you except that it would only bump the thread again.
Oops.
-Phil
Oh, sorry, dead thread.....
CASE CLOSED!
First, no headwinds. This experiment is in calm conditions, sea level, standard day. Second, yes the wheels would actually "go" 100 mph since they are attached to the aircraft and it is moving at takeoff speed (100 mph) - which is the same as indicated airspeed since there is no headwind or tailwind. However the wheels would be spinning at the equivalent rpm of 200 mph because the treadmill is moving backwards at 100 mph.
I don't know about the lurching forward part but there is the effect of the sudden loss of drag parallel to and below the thrust line that would contribute to a pitching up of the aircraft.
http://en.wikipedia.org/wiki/High_Anxiety
1. propeller starts turning
2. plane starts moving
3. wheel starts turning
4. conveyor starts moving
5. wheel starts turning faster
6. conveyor starts moving faster
7. goto 5 until wheel speed reaches a ridiculously high speed, after which
8. tire explodes under centrifugal force
9. now smaller wheel speeds up even faster
10. metal of wheel explodes under centrifugal force at almost the speed of light
11. metal shards crash into the jet at the speed of light, creating a black hole which destroys the universe