WILL IT FLY?

REMEMBER THIS? It's going to be on mythbusters tomorrow night. Should be funny, like Jotaru's face after he finds out im his girlfriend.

Holy crap Soj talk about a necrobump. What time/channel for Mythbusters? I don't usually do the TV thing...
 
It's on Discovery, I don't remember what time.
 
I've been waiting for this to air. ^_^;; I hope they get it right though, because the problem isn't specified well enough. When you say "speed of the airplane", is that with respect to the air, the ground, or the treadmill? The answer will change the results.
 
This should be interesting, I'll be curious to watch it. I still say the plane will take off :P Or at the very least, it shoudl be able to take off given sufficient speed. The only thing holding the plane back is the friction of the treadmill. After the treadmill begins moving fast enough in the opposite direction, the force of static friction will be overcome, and the plane will begin skidding forward.
 
Holy shit, 4chan invaded mythbusters and had sex with adam and jamie's earpussies. The plane will fly.
 
It will fly.

Because Manikalas, Mechanical Engineer grad student, says it will.

And thats why us ARO's are better than you :P

Well, time for me to weight in.

Basically, the concept of lift is based off of creating a difference in pressure between the upper and lower surface of the wing. This is achieved by either camber and/or angle of attack, which is the angle at which the freestream velocity is in respect to the mean chord line of the airfoil.

A positive angle of attack will allow the simplest example of an airfoil, a flat plate, achieve lift. Camber allows an airfoil to achieve lift without an angle of attack. (Camber is the curve in a the airfoil).

Now, the reason that the plane wouldn't take off is because with the treadmill providing a negative velocity to the plane, counter acting the thrust by the aircraft, given that the friction in the wheels (both bearing and surface) is enough to counter the thrust, the plane is not moving relative to the surrounding air. If the plane isn't moving relative to the surrounding air, the freestream velocity equals zero, and thus there is no flow over the wing.

With no flow going over the wing, there is no pressure difference between the top and bottom surface, and thus no lift generated. The key to this debate is all in the freestream velocity, which is why I don't understand why people even argue it. If there's no flow going over the wing surface, there's no lift.

Let me say that again....


NO FLOW OVER WING SURFACE MEANS NO LIFT!!!!!!!!

Now that I've established that, let me also point out that a stationary aircraft on the ground can achieve flight with no thrust in high winds due to the flow of the air over the wing. This is a no brainer, stop the debating.
 
Sorry Byrdman, this is not really an aerospace problem. This is a vehicle dynamics problem.

From page 11.
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.
From page 12.
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 plane 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.
I think this shows that air does flow over the wings and that the plane will eventually take off barring mechanical failure. The idea of air flowing over the wings was considered. I never suggested that the plane would fly using what leading scientists call "magic".


One last thing, I know that you aerospace fellows actually look up to us MEs, so if you ask nicely, I will gladly send you my autograph for you to put up on your "Wall of Heroes".:cool:
 
the force of static friction is a constant that depends only on the nature of the 2 surfaces in question.
 
So what you're saying is that if this were a perfect system where the treadmill countered the plane's velocity with its own negative velocity at all times it would not fly, but since the MythBursters won't be able to design a perfect system it will fly?
 
Hmm. So after looking at it a different way, I unfortunately have to retract my earlier statement and say that it will take off. The reason it will is because I, like many others, took a look at the situation like it was a car. In reality, the wheels are free moving, and thus as long as the plane wasn't accelerated before the jet engines were lit up, then the plane wouldn't gain momentum that would later need to be overcome. The only force it would need to overcome in order to move would indeed be the rolling friction. The problem was that I came into the argument thinking that the thrust was in some way much like a car in that it would need to overcome the rolling (like a wheel driven vehicle) rather than an apparatus completely separate from the actual thrust component. In that case, it would lift off.
 
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