Airplane on a treadmill
- Thread starter Scn64
- Start date
BeardofPants
New Member
*sigh* There are two different questions. This is the straight dope question: "Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
Can the plane take off?"
The answer to that question is YES, the plane will take off as per the straight dope column that was posted up by the thread starter. HOWEVER, according to the parameters set up by THIS thread in which the treadmill will match what the plane does in terms of speed, the plane will never gain acceleration to take off.
Can the plane take off?"
The answer to that question is YES, the plane will take off as per the straight dope column that was posted up by the thread starter. HOWEVER, according to the parameters set up by THIS thread in which the treadmill will match what the plane does in terms of speed, the plane will never gain acceleration to take off.
Scn64
New Member
Answer: No
If you want to keep redefining the problem you can make it so the plane takes off but as originally stated the answer is still no.
That the treadmill keeps the plane from moving forward is implicit in that statement.
Also the wheels do have friction, they will keep a plane from moving against the thrust of the engines (as in a takeoff from an aircraft carrier again). If you want to make it a semantics problem that's your business, but as a physics problem and as originally stated, the plane won't fly.
Now, given that the treadmill only matches the speed of the wheels, I still say no (but in this case I am uncertain). In the case of our imaginary 747 it needs 360 kph through the air to take off. this can be any combination of ground speed and air speed but it takes that much, no less. In other words, given this redefinition of the thought experiment, you'd have to thrust the plane up to 360 kph faster than the wheel speed. Possible? I have no idea. Thrust is not unlimited though, so I still doubt that it would. If you'd like to add unlimited thrust to the equation then yes, you'll be able to take off.
By the way Scn64, go back to physics class. Jet engines don't push against the air. Propellers do but jets don't. If they did, then rockets wouldn't work in space. They don't push against anything, they just create thrust (every action has an equal and opposite reaction).
People with much more physics knowledge than myself have agreed with me. In fact, they were the ones who convinced me I was wrong when I originally thought the plane would NOT take off. The wheels do have some amount of friction but it's not enough to stop the plane from moving forward. Plus, if the treadmill is moving at all, it means the plane is also moving. The treadmill matches the speed of the plane, not the wheels, not the thrust of the engines. If the plane is not physically moving forward, the treadmill isn't moving either. If the treadmill is moving at ANY speed, the plane must also be moving FORWARD at that speed.
Scn64
New Member
If the treadmill was matching the speed of the wheels then the treadmill would have to gain speed infinitely if the plane ever moved. If the plane is moving, the wheels MUST be spinning at the combined speed of the plane and treadmill and then the treadmill is NOT matching the speed of the wheels. In my question, the treadmill would be moving slower than the wheels. You're saying that if the treadmill is moving slower than the wheels, the plane can't move forward, but if it's moving as fast as the wheels, it CAN move forward? What sense does that make?
When the treadmill pushes against the wheels, it only adds more speed to the wheels.
A.B.Normal
New Member
Your the one that keeps redefining
If I were to really get pedantic I'd note that airplanes measure "air" speed (flow over their surface) not ground speed .
I could see this as a question posed to a physics class ,where an instructor could lead the questioning as to what speed was,but as it stands now its too vague a question .
chcr
Too cute for words
Exactly right, AB. Ground speed doesn't mean anything to an airplane. I assumed that the treadmill was magically keeping the airplane stationary because that's what it says:
It doesn't say air speed or ground speed but since we're talking avionics, convention says it means air speed.
It's not moving through the air according to the problem. You're arguing semantics now, not physics.Scn64, I know a lot more physics than you do and I say it won't take off. Where does that leave you?
A.B.Normal
New Member
so then the airplane has "0mph " Speed, so that argument is busted .
You all seem to be answering this as a physics question which without a proper posing of the question is left to iterpretation,if you see it more of a logic question ,i.e. "If a rooster lays an egg which side of the roof will it fall",or "where do you bury the survivors" then the fact the plane has speed (defined as distance X time) and must be moving .A stationary airplane has NO speed.
Scn64
New Member
There's no magic in the question. Don't even think about the treadmill matching the speed of the plane, that just adds more confusion. Just imagine that the treadmill is moving at 500mph. The plane is sitting on the treadmill and, at this time, is not even attempting to move forward. At this point in time, yes the treadmill is, of course, moving the plane backwards.
However, when the planes engines are started and attempt to move the plane forward, there is now a force being applied on the plane in the opposite direction that the treadmill is moving. This new force is not affected by the moving treadmill. Think of it like a brick wall that has appeared behind the plane that moves forward and pushes the plane along with it. Let's say the engines are applying the thrust required to move a plane forward at 50mph. Even though the plane is only being pushed at 50mph and the treadmill is moving at 500mph, the plane would still move forward.
It tells me you should think about the question a little more. Since you have more physics knowledge than me, you should certainly be able to figure out why the plane will still fly.
A.B.Normal
New Member
Alright lets stick with the wheels then,if the plane has no forward movement the wheels remain stationary,but a turning wheel on an aircraft means it has forward momentum,so even that remains a paradox .
unclehobart
New Member
The whole bs of bricks and strings and whatnot is whats throwing everyone off. I will try to expand a little in the way I thought of a solution.
Hypothetical setup: 150,000 lb plane with four engines that can deliver a combined level of 200,000lb of thrust. The vector for gravity at rest is straight down. In normal thrust/driving the vector starts to go forward to reflect acceleration and the change of that vector. In the case of a reactive treadmill, the correction of the treadmill always makes this vector stay straight down as if at rest.
In the case of a car, the added momentum is added through the wheels and is always matchable by the treadmill. The treadmill can always keep up. It is different for a plane.
In a plane the thrust is through the props/jets/turbofans .. whatever. The imporant thing is that the thrust is through the body of the craft itself and independent of the wheels. The wheels just spin freely.
When the plane is undergoing greater and greater thrust it is slowly reducing the effect of the treadmill by making the backward rolling drag of the plane slowly become weightless.
It is at the magic point that the planes thrust output overtakes the weight of the craft as well as the angular drag through the landing struts that everything changes. When a plane that weighs 150,000 pounds is pushing out roughly 160,000 pounds of thrust that it essentially becomes weightless to the backward rolling of the treadmill. It is in that magic moment of equilibrium that the treadmill, regardless of how fast it starts to zip backwards, will have any extra effect upon the plane. The angular momentum arrow starts to point forward.
When the plane then adds more thrust, it then starts to move forward, albiet slowly. The plane will start to speed up more and more and develop the needed speed to lift off. Granted, it will take a good bit of time and probably a 10 mile long runway and look like a sloppy iceskater all the way.
It all just depends on the efficiency power curves of the various plane/engine configurations to deliver the weight defying level of power at such a low speed. All prop planes would be able to do it. Jets, since they require forward momentum to deliver the insane pressure wave of intake air to deliver max pressure for max horsepower might be an iffy situation. Turbofans? Dunno. Scramjets? Dunno.
But this sucker is plausible in my eyes.
Hypothetical setup: 150,000 lb plane with four engines that can deliver a combined level of 200,000lb of thrust. The vector for gravity at rest is straight down. In normal thrust/driving the vector starts to go forward to reflect acceleration and the change of that vector. In the case of a reactive treadmill, the correction of the treadmill always makes this vector stay straight down as if at rest.
In the case of a car, the added momentum is added through the wheels and is always matchable by the treadmill. The treadmill can always keep up. It is different for a plane.
In a plane the thrust is through the props/jets/turbofans .. whatever. The imporant thing is that the thrust is through the body of the craft itself and independent of the wheels. The wheels just spin freely.
When the plane is undergoing greater and greater thrust it is slowly reducing the effect of the treadmill by making the backward rolling drag of the plane slowly become weightless.
It is at the magic point that the planes thrust output overtakes the weight of the craft as well as the angular drag through the landing struts that everything changes. When a plane that weighs 150,000 pounds is pushing out roughly 160,000 pounds of thrust that it essentially becomes weightless to the backward rolling of the treadmill. It is in that magic moment of equilibrium that the treadmill, regardless of how fast it starts to zip backwards, will have any extra effect upon the plane. The angular momentum arrow starts to point forward.
When the plane then adds more thrust, it then starts to move forward, albiet slowly. The plane will start to speed up more and more and develop the needed speed to lift off. Granted, it will take a good bit of time and probably a 10 mile long runway and look like a sloppy iceskater all the way.
It all just depends on the efficiency power curves of the various plane/engine configurations to deliver the weight defying level of power at such a low speed. All prop planes would be able to do it. Jets, since they require forward momentum to deliver the insane pressure wave of intake air to deliver max pressure for max horsepower might be an iffy situation. Turbofans? Dunno. Scramjets? Dunno.
But this sucker is plausible in my eyes.
chcr
Too cute for words
Now here, you just told me to ignore the paramount parameter of the problem.
Again, it doesn't say anything about the wheels, it says speed of the airplane. I understand why you (and many others) interpret it that way but that isn't what it says. What your saying is that the treadmill will turn at the speed that the plane would be going given a certain thrust (and therefore acceleration) for certain amount of time passed. That isn't the stated problem in my estimation.
Given the way you're defining the problem, it is absolutely plausible that the plane could take off. I still don't think it would because thrust is not unlimited (sooner or later you'll reach equilibrium, you won't keep accelerating indefinitely) but it certainly is plausible. The way I'm defining it it never will.
It's impossible to state which definition is right or wrong because the problem is (deliberately, I suspect) too vague.
Scn64
New Member
Now here, you just told me to ignore the paramount parameter of the problem.
Again, it doesn't say anything about the wheels, it says speed of the airplane. I understand why you (and many others) interpret it that way but that isn't what it says. What your saying is that the treadmill will turn at the speed that the plane would be going given a certain thrust (and therefore acceleration) for certain amount of time passed. That isn't the stated problem in my estimation.
Given the way you're defining the problem, it is absolutely plausible that the plane could take off. I still don't think it would because thrust is not unlimited (sooner or later you'll reach equilibrium, you won't keep accelerating indefinitely) but it certainly is plausible. The way I'm defining it it never will.
It's impossible to state which definition is right or wrong because the problem is (deliberately, I suspect) too vague.
Fair enough. As long as you understand what I'm trying to say I'm happy. We obviously have two different opinions of what exactly the question is asking and what situation it presents. I didn't write the question myself, I took it from another board, so I can't tell you what the original author meant, only how I interpret it. I do know that I have seen many other similar questions posted on other boards with slightly varying wording and the usual outcome is that most people agree it will fly in the end. That's after days of arguing of course.
chcr
Too cute for words
Fair enough. I can't say what the author intended either. I think that maybe this is what he (or she) intended. Interesting discussion in any case.
unclehobart
New Member
At least noone is shooting holes through my theory yet... which makes me feel better. I didn't know if if came off as plausible/sane when I wrote it.
wonders if this'd work on a place like OTC?
oh looksy -
3 pages already since yesterday ...
unclehobart
New Member
I haven't callen anyone an idiot yet.
A fecking loon... perhaps.
A fecking loon... perhaps.
