Originally posted by: RapidSnail
Is there something I'm missing here? It's obvious after some logical thought that the plane will take off if the conditions are that the treadmill must match the speed of the airplane's thrusters. Was there another version of the question that has people confused for some reason? The only way the plane couldn't take of is if the treadmill matches the rotational speed of the wheels instead of the thrusters, but other than that there is no argument.
Originally posted by: FrustratedUser
Booooooo!
Nude pics of Kari could still save it.
Originally posted by: smack Down
Originally posted by: randay
Originally posted by: jagec
Originally posted by: randay
You have not addressed the issue that the treadmill can NEVER match the speed of the wheels relative to itself. Which makes the whole infinite-super-treadmill theory bunk.
Also the problem with what you believe is that you assume that the treadmill will stop once net motion is zero, thats not true since the wheels are still spinning and therefore the treadmill is still accelerating and angular momentum is still building. The treadmill will overcome the thrust of the engines(through angular momentum achieved by infinite acceleration and velocity), and then the airplane will accelerate backwards until it takes off anyway. granted, it will not take off very long since there will be no way to control it backwards, however it will gain an infinite amount of speed and eventually and messily, catch air.
Yes I have. Take your initial setup: Plane speed with respect to stationary object = P, treadmill speed with respect to stationary object = T, wheel speed = (P + T). If we try to match the treadmill speed to the wheel speed (T = (P + T)), this looks like a paradox until we realize that as long as the treadmill is accelerating, it can interact with the plane and reduce its speed. So the equation becomes (T = (P-AX) + T), where AX is the acceleration of the treadmill (A) times a term (X) which encapsulates the dimensions of the wheels and converts AX into a velocity. The treadmill has to accelerate at a rate where AX = P. If it accelerates faster, the plane moves backwards on the runway. If it accelerates more slowly, the plane moves forwards on the runway. Once the plane runs out of fuel, the treadmill must stop accelerating and continue at a constant speed.
The bolded portion is untrue. I said that the treadmill will stop ACCELERATING when the plane returns to the control position (its initial position on the runway). It will continue moving at a constant speed, with the wheels turning at a constant speed and angular momentum, with no acceleration and no buildup of further forces.
Explain please, why the treadmill will stop accelerating. The setup is thus: The treadmill will match the speed of the airplane in reverse. speed must be either air speed(same as "speed with respect to a stationary object"), or ground speed(treadmill is the ground). It cant be both, and so the underlined formula seems to be where you went wrong.
If the plane is going backwards then it would mean that the treadmill is no longer matching the wheel speed of the plane. The treadmill would have to be going faster then the wheels. Stop think of the plane as something special just think of it like a car.
Originally posted by: mobobuff
Originally posted by: RapidSnail
Is there something I'm missing here? It's obvious after some logical thought that the plane will take off if the conditions are that the treadmill must match the speed of the airplane's thrusters. Was there another version of the question that has people confused for some reason? The only way the plane couldn't take of is if the treadmill matches the rotational speed of the wheels instead of the thrusters, but other than that there is no argument.
That's pretty much it. The plane takes off in the original sense of the problem, but arguing that has gotten boring. Now the idea is to create a scenario where the plane DOESN'T take off.
Originally posted by: waggy
Originally posted by: smack Down
Originally posted by: randay
Originally posted by: jagec
Originally posted by: randay
You have not addressed the issue that the treadmill can NEVER match the speed of the wheels relative to itself. Which makes the whole infinite-super-treadmill theory bunk.
Also the problem with what you believe is that you assume that the treadmill will stop once net motion is zero, thats not true since the wheels are still spinning and therefore the treadmill is still accelerating and angular momentum is still building. The treadmill will overcome the thrust of the engines(through angular momentum achieved by infinite acceleration and velocity), and then the airplane will accelerate backwards until it takes off anyway. granted, it will not take off very long since there will be no way to control it backwards, however it will gain an infinite amount of speed and eventually and messily, catch air.
Yes I have. Take your initial setup: Plane speed with respect to stationary object = P, treadmill speed with respect to stationary object = T, wheel speed = (P + T). If we try to match the treadmill speed to the wheel speed (T = (P + T)), this looks like a paradox until we realize that as long as the treadmill is accelerating, it can interact with the plane and reduce its speed. So the equation becomes (T = (P-AX) + T), where AX is the acceleration of the treadmill (A) times a term (X) which encapsulates the dimensions of the wheels and converts AX into a velocity. The treadmill has to accelerate at a rate where AX = P. If it accelerates faster, the plane moves backwards on the runway. If it accelerates more slowly, the plane moves forwards on the runway. Once the plane runs out of fuel, the treadmill must stop accelerating and continue at a constant speed.
The bolded portion is untrue. I said that the treadmill will stop ACCELERATING when the plane returns to the control position (its initial position on the runway). It will continue moving at a constant speed, with the wheels turning at a constant speed and angular momentum, with no acceleration and no buildup of further forces.
Explain please, why the treadmill will stop accelerating. The setup is thus: The treadmill will match the speed of the airplane in reverse. speed must be either air speed(same as "speed with respect to a stationary object"), or ground speed(treadmill is the ground). It cant be both, and so the underlined formula seems to be where you went wrong.
If the plane is going backwards then it would mean that the treadmill is no longer matching the wheel speed of the plane. The treadmill would have to be going faster then the wheels. Stop think of the plane as something special just think of it like a car.
thats the problem. THIS IS NOTHING LIKE A CAR.
really its not. a car gets its thrust by the wheels. a plane by the thrust of the engines.
For every action, there is an equal and opposite reaction. the thrust of the engine has to have its opposite action. the wheels/treadmill ARE NOT IT.
Originally posted by: jagec
If it's matching airspeed, that's what I call the "first interpretation", which results in the plane taking off. If it's matching "wheel speed", that's the second interpretation. I believe I have resolved the apparent paradox that this seems to present at first glance.
Airspeed is "P", AKA "plane speed" or "speed with respect to a stationary object".
The treadmill will reduce the speed of the plane via the angular momentum term, albeit at a very small level. In order to do so, it must be accelerating...when the treadmill moves at a constant speed, it has no effect on the plane save through friction, which we are ignoring. When we reduce the speed of the plane to zero by applying an equal and opposite force via the angular momentum term (constantly accelerating the treadmill), the paradox disappears since treadmill speed T = P (plane speed) + W ("wheel" speed), P= 0 so T=W.
I really do prefer to think of it as "hold the aircraft in one spot by twiddling with the treadmill" rather than speed matching...simpler to conceptualize. Either way is the same...no control system is able to keep the error signal at zero at all times, so the treadmill speed will oscillate around the "wheel speed" as the controller changes the rate of acceleration of the treadmill to keep the plane in one spot.
Also, please keep my arguments separate from smack Down's, we're clearly talking about different things.
Originally posted by: FrustratedUser
Booooooo!
Even nude pics of Kari couldn't save it.
Originally posted by: waggy
For every action, there is an equal and opposite reaction.
Originally posted by: randay
Originally posted by: jagec
If it's matching airspeed, that's what I call the "first interpretation", which results in the plane taking off. If it's matching "wheel speed", that's the second interpretation. I believe I have resolved the apparent paradox that this seems to present at first glance.
Airspeed is "P", AKA "plane speed" or "speed with respect to a stationary object".
The treadmill will reduce the speed of the plane via the angular momentum term, albeit at a very small level. In order to do so, it must be accelerating...when the treadmill moves at a constant speed, it has no effect on the plane save through friction, which we are ignoring. When we reduce the speed of the plane to zero by applying an equal and opposite force via the angular momentum term (constantly accelerating the treadmill), the paradox disappears since treadmill speed T = P (plane speed) + W ("wheel" speed), P= 0 so T=W.
I really do prefer to think of it as "hold the aircraft in one spot by twiddling with the treadmill" rather than speed matching...simpler to conceptualize. Either way is the same...no control system is able to keep the error signal at zero at all times, so the treadmill speed will oscillate around the "wheel speed" as the controller changes the rate of acceleration of the treadmill to keep the plane in one spot.
Also, please keep my arguments separate from smack Down's, we're clearly talking about different things.
Once again, T = P + W is not correct since P has nothing to do with T or W. The paradox is still there and speed is still T = T + W. ie: wheel moves 1m/s, treadmill then accelerates to 1m/s to match, wheel is now moving 2m/s.
The plane moves because the friction between the wheels and the plane create a counteracting force and thereby cause the wheels to exert less force (equal and opposite forces) on the treadmill. If there exists no friction between the wheels and the plane BUT exists between the ground and the wheels, then the plane does not move. If there were also no friction between the wheels and the ground then the wheels would not turn.Originally posted by: spidey07
Put a plane on a treadmill with engines off.
The plane will move backwards with wheels spinning.
Originally posted by: NanoStuff
Originally posted by: waggy
For every action, there is an equal and opposite reaction.
Good idea, quote a wise man and suggest that somehow it proves your shat up hypothesis.
Originally posted by: her209
The plane moves because the friction between the wheels and the plane create a counteracting force and thereby cause the wheels to spin at a slower speed than the treadmill. Because of this, not all of the force exerted on the wheel by the treadmill is translated into spinning the wheel and pushes the plane backwards. If there exists no friction between the wheels and the plane BUT exists between the ground and the wheels, then the plane does not move. If there were also no friction between the wheels and the ground then the wheels would not turn.Originally posted by: spidey07
Put a plane on a treadmill with engines off.
The plane will move backwards with wheels spinning.
Originally posted by: mobobuff
Originally posted by: FoBoT
mods, please BAN adam jamie kari and grant and tory
:|
Folks are pissed.
Originally posted by: SsupernovaE
ATOT effect everyone!
Go to the Mythbusters forum and let them have it.
Voice your displeasure!
Originally posted by: sao123
Originally posted by: mobobuff
Originally posted by: FoBoT
mods, please BAN adam jamie kari and grant and tory
:|
Folks are pissed.
HOLYFAIL!!!!
Gravity or more correctly (weight) is a vertical force vector and has no bearing on the horizontal force vector other than keeping the plane in contact with treadmill.Originally posted by: spidey07
Yeah, that whole gravity thing.Originally posted by: her209
The plane moves because the friction between the wheels and the plane create a counteracting force and thereby cause the wheels to spin at a slower speed than the treadmill. Because of this, not all of the force exerted on the wheel by the treadmill is translated into spinning the wheel and pushes the plane backwards. If there exists no friction between the wheels and the plane BUT exists between the ground and the wheels, then the plane does not move. If there were also no friction between the wheels and the ground then the wheels would not turn.Originally posted by: spidey07
Put a plane on a treadmill with engines off.
The plane will move backwards with wheels spinning.
Let's just ignore that. Hell, lets just ignore all the other forces!
Originally posted by: randay
Originally posted by: jagec
If it's matching airspeed, that's what I call the "first interpretation", which results in the plane taking off. If it's matching "wheel speed", that's the second interpretation. I believe I have resolved the apparent paradox that this seems to present at first glance.
Airspeed is "P", AKA "plane speed" or "speed with respect to a stationary object".
The treadmill will reduce the speed of the plane via the angular momentum term, albeit at a very small level. In order to do so, it must be accelerating...when the treadmill moves at a constant speed, it has no effect on the plane save through friction, which we are ignoring. When we reduce the speed of the plane to zero by applying an equal and opposite force via the angular momentum term (constantly accelerating the treadmill), the paradox disappears since treadmill speed T = P (plane speed) + W ("wheel" speed), P= 0 so T=W.
I really do prefer to think of it as "hold the aircraft in one spot by twiddling with the treadmill" rather than speed matching...simpler to conceptualize. Either way is the same...no control system is able to keep the error signal at zero at all times, so the treadmill speed will oscillate around the "wheel speed" as the controller changes the rate of acceleration of the treadmill to keep the plane in one spot.
Also, please keep my arguments separate from smack Down's, we're clearly talking about different things.
Once again, T = P + W is not correct since P has nothing to do with T or W. The paradox is still there and speed is still T = T + W. ie: wheel moves 1m/s, treadmill then accelerates to 1m/s to match, wheel is now moving 2m/s.
Originally posted by: jagec
Take a wheel out in space. Attach a string to the outside of the wheel. Pull the string. You will notice that the wheel spins faster (you added angular momentum), but the wheel also starts to move towards you (you added linear momentum). The relative amount of each depends on the weight distribution and total weight of the wheel, and how far from the center you tied the string. Even with the same force exerted in each case, you can change the relative amount of linear vs. angular momentum by adjusting these parameters. You can even make the angular momentum zero by attaching the string in the middle. You cannot make the linear term zero.
Why is a toy car with a flywheel harder to push across the ground than a Matchbox car? If rotational and linear motion are decoupled, such a thing should be impossible.
Originally posted by: jagec
Once again, P IS connected to T via the angular momentum term! If the treadmill is continuously accelerating in the opposite direction, it can generate a force on the body of the plane via the wheel hubs. If T is accelerated fast enough, it can actually overpower the force of the engines and cause P to become negative. This takes a pretty crazy amount of acceleration, but it is mathematically possible.
"Adam? Jamie? Dan? Someone step up and tell us what happened tonight."
Dear all,
As wbarnhill called out, I thought I should step in to what is rapidly becoming a hornet's nest. I will try to calm things down but I don't hold out much hope!
First up, for those concerned that this story has been cancelled, don't worry, planes on a conveyer belt has been filmed, is spectacular, and will be part of what us Mythbusters refer to as 'episode 97'. Currently that is due to air on January 30th.
Secondly, for those very aggrieved fans feeling "duped" into watching tonight's show, I can only apologise. I'm not sure why the listings / internet advertised that tonight's show contained POCB. I will endeavour to find out an answer but for those conspiracy theorists amongst you, I can assure you that it will have just been an honest mistake. At one point
several months ago, POCB was going to be part of Airplane Hour. Somewhere, someone has mistakenly posted the wrong listing. It will have been a genuine mistake but nonetheless it was a mistake which is unacceptable. As said I will try to find out what went wrong and hope that you will see fit to forgive the team at Discovery.
Thanks in advance,
Dan
Originally posted by: QuantumSlip
It's moved to Jan. 30th
"Adam? Jamie? Dan? Someone step up and tell us what happened tonight."
Dear all,
As wbarnhill called out, I thought I should step in to what is rapidly becoming a hornet's nest. I will try to calm things down but I don't hold out much hope!
First up, for those concerned that this story has been cancelled, don't worry, planes on a conveyer belt has been filmed, is spectacular, and will be part of what us Mythbusters refer to as 'episode 97'. Currently that is due to air on January 30th.
Secondly, for those very aggrieved fans feeling "duped" into watching tonight's show, I can only apologise. I'm not sure why the listings / internet advertised that tonight's show contained POCB. I will endeavour to find out an answer but for those conspiracy theorists amongst you, I can assure you that it will have just been an honest mistake. At one point
several months ago, POCB was going to be part of Airplane Hour. Somewhere, someone has mistakenly posted the wrong listing. It will have been a genuine mistake but nonetheless it was a mistake which is unacceptable. As said I will try to find out what went wrong and hope that you will see fit to forgive the team at Discovery.
Thanks in advance,
Dan