WILL IT FLY?

It's a good thought to try to take out the components that are complicating the problem and then reexamine it, but in this case it fundamentally changes the problem. The point of wheels on landing gear is to significantly reduce the frictional force between the airplane and the ground.

In order to bring this entire discussion to a point, we must start with the equation:

F=ma (1)

with F being force, m being mass, and a being acceleration. The reason this equation is so important is that the fundamental question is whether or not there is acceleration. With that known, let's breakdown the forces on the airplane. If I were face-to-face with you right now, I would simply draw you a free body diagram, but due to the medium, my explanation will have to due.

A few assumptions: up is up, +j is up, down is down, -j is down, right is forward, +i is forward, left is backwards, -i is backwards, gravity goes down.

Now, we all can agree that there is gravity acting on the airplane and that the acceleration due to gravity is constant at g = -9.81 m/s^2. Using equation 1, the force due to gravity is the mass multiplied by g and is constant, W. The ground exerts a force on the plane equal to the force the plane exerts on ground. This is called the normal force, N. Lift, L, works in the same direction as the weight and normal forces. The only important part of the lift calculation in this problem is that there has to be some sort of freestream velocity, therefore, a positive velocity experienced by the plane will translate into lift. That is everything in the j-direction. Adding all the forces together and using equation 1 gives us equation 2:

maj = Wj + Nj + Lj (2)

In the i-direction there is thrust, T, friction, Ff, and drag, D. Since we are looking the airplane from rest to take-off, drag will be considered negligible since it is dominated by the velocity term which will be relatively small when compared to the friction and thrust terms. Friction is determined by using equation 3:

Ff= -Cr*N (3)

where Cr is the coefficient of roll friction. Cr is determined by the materials involved. It would be very unlikely for it to be anything greater than 0.05, therefore, we can safely say that Ff=-0.05N. The i-direction equation is:

mai = Ffi + Ti = -0.05Ni + Ti (4)

In order for the plane to take off, maj > 0 and therefore, mai must be > 0. While I do not know what the thrust of the hypothetical plane is, I am certain that it is greater than 1/20th of the weight of the plane. If the plane does indeed generate thrust greater than 1/20th of the weight, that will result in acceleration which will steadily increase the velocity creating lift and thus allowing the plane to take off.

I hope that makes sense to everyone. Again, tell me if there is anything that is unclear or you might feel is dubious. Thank you.
 
wait, wait, wait. Is the entire key to this problem the concept that the treadmill moving backwards does NOT actually move the plane backwards at the same speed that the treadmill is moving? And if so, why didn't anyone say that clearly like 10 pages ago so I didn't have to waste an hour of my life on this thread, lol;_;. Nekio said something of the sort like a page ago and it was the first thing anyone had said that appeared relevant to me.

-benny
 
...If you want to recreate the wheels, drag your feet on the bottom of the pool while you swim, you'll still move.

No, you won't move. Because, as you stated in the first post, the floor is moving BACKWARDS at the same rate you're moving FORWARDS. YOU'RE GOING NOWHERE.
 
i think Manikalas nailed it. If you have a long enough treadmill and enough thrust the plane will take off. As soon as the force of the jet engines is greater than the force exerted on the plane due to gravity you will move forward.
 
i think Manikalas nailed it. If you have a long enough treadmill and enough thrust the plane will take off. As soon as the force of the jet engines is greater than the force exerted on the plane due to gravity you will move forward.

Theres no mention of the runway being on a downward slope. This was all that was mentioned:
the runway is more like a giant treadmill, and has a system in place to constantly monitor the exact speed of the airplane on it. As the plane moves forward, the treadmill moves rearward, in the opposite direction the plane is moving, at the same speed.

Given only that information. The plane will not take off. AGAIN, for every instance of the plane gaining forward momentum, the treadmill runway exerts the exact opposite force. It can be concluded that the treadmill will NOT let the plane take off because as stated in the first post:
A jet plane is sitting on a runway
The treadmill can exert force on the plane because the plane is clearly ON the treadmill runway.
 
Yes you will move foward. No one is saying you won't. When you run on a treadmill do you stay in the EXSACT same place? Of course you don't. You move foward and backward some. A passenger plane needs about 150 MPH of wind going over the wings to generate enough lift to take off. Lets say the treadmill is infinte lengeth. Lets say the plane and landing gear is indestructible. Lets say the plane has no limit to what speed it can get and same for the treadmill. While you will keep going faster and faster. You will move foward. But if the treadmill is monitoring the speed of the plane and is matching it. The plane will never be moving down the treadmill at over 150 MPH. Yes the wheels will going 10,000,000,000,000,000 MPH but that doesn't matter. You still don't have 150 MPH of air flowing over the wing to give it lift. There for it will never take off.
 
Given only that information. The plane will not take off. AGAIN, for every instance of the plane gaining forward momentum, the treadmill runway exerts the exact opposite force.

This is where you have it wrong. It exerts the exact opposite velocity. Force can only be created from velocity by applying friction. However, there are only 2 wheels on the ground, each of which has a very small amount of surface area in contact with the ground. This small amount of friction will never produce enough force to counteract that of the engine thrust, and then plane should end up skidding forward along the track.
 
But if the treadmill is monitoring the speed of the plane and is matching it. The plane will never be moving down the treadmill at over 150 MPH.

I think what they're trying to say is, it doesn't matter the treadmill's matching it, it'll keep accelerating anyway (with respect to the ground) because the engines are pushing backward against the air, not the ground. So they'll start at 0 and both keep going faster and faster and the plane will still be moving forward anyway (comparative to the ground) just cause what it's pushing against is in fact the air.

Takes a bit to wrap your head around, but I can see where theoretically it makes sense. In practical application I doubt it because the plane IS pushing against the ground too. Hello gravity.

In all honesty, the only way I can see this taking off, is with the engines underneath the wing. Thankfully the majority of modern passenger jets have their engines there (back to my favorite example of the Boeing 737).

Pluna.jpg


How flight is achieved is thanks to the Bernoulli effect where air pressure under the wing is higher than that of over the wing. If engines are under the wing, their force creates pressure under there. And the non-moving air over the wing, by virtue of not moving, is lower pressure.

So it boils down in my mind, to is the pressure difference from engines alone enough to overcome gravity? Only way I can think to test this is find a model plane that somehow has under wing jets. Tie a rope to its ass somehow that doesn't inhibit airflow. Pull the rope taught, and let the engines rip. If she takes off vertically and is holding there fighting the rope, but airborn, then yes. The engine force alone is enough.

Man, why am I still here? lol
 
This is where you have it wrong. It exerts the exact opposite velocity. Force can only be created from velocity by applying friction. However, there are only 2 wheels on the ground, each of which has a very small amount of surface area in contact with the ground. This small amount of friction will never produce enough force to counteract that of the engine thrust, and then plane should end up skidding forward along the track.

Whoops, yes, velocity. But read the first post. The treadmill is matching the velocity of the plane, thus keeping it still.

As the plane moves forward, the treadmill moves rearward, in the opposite direction the plane is moving, at the same speed.

It doesn't mention where the speed is measured. It only says that the forward speed of the plane is matched by the rearward speed of the runway. Plane goes nowhere.
 
Whoops, yes, velocity. But read the first post. The treadmill is matching the velocity of the plane, thus keeping it still.

It would only keep it still if the friction between the wheels and the surface created enough force to keep it from skidding. It's like when you slam on the brakes, you don't stop instantly you skid along the road a little ways. If you give yourself sticky tires, you can stop even faster but still not instantly.

The same concept applies here. The force from the engines is so great that the friction is not enough to counteract it, even if the treadmill is going a million miles per hour.
 
It would only keep it still if the friction between the wheels and the surface created enough force to keep it from skidding. It's like when you slam on the brakes, you don't stop instantly you skid along the road a little ways. If you give yourself sticky tires, you can stop even faster but still not instantly.

The same concept applies here. The force from the engines is so great that the friction is not enough to counteract it, even if the treadmill is going a million miles per hour.

Yes but that is not the only force holding the plane down. You have 4 forces. 1. the treadmill 2. gravity 3. friction 4. Air causing some resistance for movment speed. Take any one of those factors out and yes the plane will fly. And like stated before that the system matches it perfectly. Remeber no lols the system is broken.
 
Yes but that is not the only force holding the plane down. You have 4 forces. 1. the treadmill 2. gravity 3. friction 4. Air causing some resistance for movment speed. Take any one of those factors out and yes the plane will fly. And like stated before that the system matches it perfectly. Remeber no lols the system is broken.

1. and 3. are the same thing. How is treadmill and friction holding the plane down? The only force that exists due to the treadmill is a force of friction. There is no other force from the treadmill. Furthermore, kinetic friction forces have a maximum value that is dependent only on the physical properties of the two surfaces in contact. As such, the velocity of the treadmill is completely irrelevant, because there is a velocity at which point the coefficient of friction reaches the maximum value for the surfaces of "treadmill" and "wheel". The result is that no matter how fast the treadmill is moving in reverse, the force of friction never exceeds a certain value, and the net force on the plane will be positive.
 
The treadmill is backwards force not allowing it to gain lift. the friction happens even if there isn't any treadmill. its happens when landing gear is on normal runways. Its just the force of the plane going faster is causing a lot more friction then normal along with the treadmill pulling the plane backwards.
 
The treadmill is backwards force not allowing it to gain lift. the friction happens even if there isn't any treadmill. its happens when landing gear is on normal runways. Its just the force of the plane going faster is causing a lot more friction then normal along with the treadmill pulling the plane backwards.

All forces that are a result of the surface are considered frictional forces, and as such all properties such as maximum coefficient value, etc apply.

When the plane is moving very slowly (very slowly) the net force of the plane will indeed be 0. In this case (even though technically the plane has a non-zero velocity), calculations will be done with the force of static friction. Once the force of the plane is high enough the force of kinetic friction will be used, and the plane will start sliding.

Sorry, but that's just the way it is.
 
I decided to put this into perspective by using the actual weight of a 747-200 and the actual thrust used by its engines. As I showed in my calculations, takeoff will eventually occur if the thrust, T, is greater than the force of friction, Ff. The actual equation is:

For takeoff to occur: T > 0.05N (5)

where N is the normal force. N will be analogous to the weight in this problem. (As the plane moves down the runway/treadmill, the magnitude of N will decrease as lift is generated by the wings.)

Now, the 747-200 has a weight of 833,000 lbf when fully loaded. It has 4 engines which together produce 52,500 lbf of thrust. If equation 5 is shown to be true using these values, then the plain will takeoff.


(52,500 lbf) > 0.05(833,000 lbf)

52,500 lbf > 41,650 lbf True

Therefore, the plane will overcome the force of friction with ease and eventually takeoff. Furthermore, using equation 1, we can divide the resultant force by the mass of the plane to find that it has an acceleration of 0.42 ft/s^2

If there is anything that is unclear or you may think dubious, tell me and I will try to explain in further detail.
 
After some major thinking about I get it now and feel really retarted now lol >.>

Best way I can think of explaining this is get a skate board and treadmill. Stand on the skateboard on the treadmill and hold your arms on the handle bars. Doesn't matter how fast the treadmill moves if your arms are strong enough to hold the force of the friction from the treadmill and the skateboard you won't move. Now while the treadmill is moving pull yourself foward with your arms. You will go foward. Same exsact thing happens with the engines on a plane. It will eventully be moving down the treadmill fast enough for take off speed.
 
^^/ Nice Heie

The main 'problem' with this question is really focusing on the correct frame of reference, and how the forces work. Once people get that, it becomes a lot easier. It can seem like there is no way possible in any world any way if you are focusing on it differently, however (like a car, for example)

It doesn't mention where the speed is measured. It only says that the forward speed of the plane is matched by the rearward speed of the runway. Plane goes nowhere.

Hm... but I think you are confusing the issue. Just because the treadmill matches the speed of the plane doesn't mean it matches the force. The treadmill can go as fast as it wants to, its the force on the wheels (and thus the force pushing the airplane backwards, against the force of the engines) that matters. Now, if I said that the treadmill was 'holding the airplane in place', then yes, I could see. As said before, its a matter of seeing 'past' the assumption that this is the case, and asking, does it really.
 
As the plane moves forward, the treadmill moves rearward, in the opposite direction the plane is moving, at the same speed.
Both speeds with respect to the ground, not the speed of the plane with respect to the treadmill. ^_^b
 
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