A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?
Now I don’t have any aerospace/aero-dynamics training, but this is the logical deduction I have made. I say Yes, the plane although moving relatively at speed will remain static due to the coveyer belt matching its speed, and therefore would create the lift needed to create sustainable flight.
Assuming windless conditions, you’d be correct. Lift requires wind resistance. If your plane is not moving forward through the air, it isn’t pushing through an air mass.
The cross-section of a plane’s wing is such that when it flows through air, the relative air pressure above the wing is less than the relative air pressure below it, thus lift. It’s why the top of a wing, from front to back, has more of a curve than the bottom. Since the wing is moving through the air, adjacent air pockets that the wing touches will move over and under the wing at differing rates in order to be left by the wing still adjacent (airstream observations support this), and the air pocket above the wing must travel faster in order to traverse the larger curve of the top of the wing and still arrive at the back of the wing at the same time the bottom air pocket does. I’d drop Bernoulli’s Equation on you at this point if I wanted your head to explode, but suffice it to say that pressure and velocity are inversely proportional per B’s Equation, so if you increase velocity, you gots to decrease pressure. So, your wing pulls upwards and takes the fuselage with it.
Another example is a truck bed with a tarp over it: the tarp pops up because the faster moving air over the tarp is inducing a pressure drop.
Yes, because taking flight is not primarily a measure of the friction between the plane’s wheels and the ground, but rather, between the plane’s wings and the air. And when the plane is going 200+ mph (or whatever it’s takeoff speed is), the wings will generate sufficient lift to take off. The effect of wheels on ground is fairly neglible.
Phil has pretty much said it, the fact that the conveyor belt is clocking along real fast backwards under the wheels isn’t going to make any difference to the actual acceleration of the plane, which is being pushed by the turbines on the wings. The wheels will spin twice as fast, though.
Because the wings aren’t moving relative to the air! Groundspeed != Airspeed. Sure, the wheels are turning like mad, but unless there’s an external source of wind, airspeed is going to measure 0!
That diagram is dumb. Anyone who has ever read a flight-sim manual from Janes or Microprose knows that there are 4 forces for a plane (going clockwise from top), Lift, Thrust, Gravity, and Drag.
There is no lift in the diagram! Sure, you’ve got a shitpile of thrust going on, but that doesn’t help you.
It all gets back to (as referenced in the straight dope message board link) that it’s really a question of what the conveyer does. My interpretation is that the aircraft is stationary on the treadmill, no matter the thrust applied.
The belt matches the speed and acceleration of the plane. So if the plane is moving FORWARDS at 10mph, the belt is moving at 10mph, making the wheels spin at 20mph minus some small fraction for friction. Let’s say 20%. So if the belt is cranked up to 10mph, the plane will only “feel” 2mph of that. The rest will be the wheels spinning freely.
Or think of it this way. Lets put YOU in an office chair with wheels on it, and lets put the chair on a conveyer belt. We’ll give you a steel bar that you can hold on to for support that is not connected in any way to the conveyer belt.
Lucy cranks up the conveyer belt to 50mph and it moves underneath you. But, to stay still, you just have to hold on to the steel bar. Indeed, you can actually push off the steel bar and move in whatever direction you want, because your wheels are just spinning under you.
The aircraft engines are like that steel bar that you’re pushing yourself against. Pushing against the steel bar generates thrust, just like an aircraft engine pushing against air. Your arms only have a reach of about three feet, though, and that’s the extent of your thrust. A plane can generate thrust for as long as it needs to.
So you see, what the conveyer belt is doing is only imparting a little bit of extra drag at the wheels. The plane will not be held in place, but will move forward at 80% of it’s normal acceleration for a given throttle setting.
Actually, reading the question again, it’s rather mudane.
The conveyor matches the speed and acceleration of the plane. If the plane is not actually moving, then the conveyor belt wouldn’t be moving either. But if the plane starts to accelerate at 1G, that indicates forward motion. At that point, the speed of the conveyor belt is not relevant: the plane is in motion and air is passing over the wings.