I will leave it to someone better able to explain, but NO..It will NOT fly. (The way you have posted the question)
The Mythbusters bit was so flawed I'm surprised they aired it.....they used an ultralight aircraft that became "light" after about two seconds, hence started to develop lift and wasn't even in constant contact with the "conveyor belt" being towed behind the truck.
jonsad: You are correct in your statement that the plane gains it speed through the prop; however, the wheels are on the plane to roll the plane until it develops enough speed for lift to carry it off the ground. With the speed of the "conveyor" and the speed of the planes forward motion matched, it will not develop the needed airspeed to lift off the ground.
This guy does a great job of explaining....
Read the entire explanation...The answer to the question, THE WAY YOU ASKED IT, is NO, it will not fly. If the treadmill or conveyor ALWAYS MOVES AT THE SAME SPEED, THE PLANE CANNOT DEVELOP LIFT.
The reason so many people say it will fly is because they are conceding the fact that no conveyor/treadmill in the world can accomplish the feat of exactly matching a planes forward rolling speed. The question is inherently flawed, but to answer it in the spirit of the way the question is intended....NO!!
P.S. I love it when someone gives a "thumbs down" to a correct answer....
Thank you jttexas!!! I imagine the people that think it willl fly also feel a strong 20 mph wind on their face when they are at the gym "going 20" on a stationary bike!!.....Or when they put their car on blocks and rev the engine until it says 100 mph, they put their arm out the window and expect it to blow back!!
Good job, Louis!!!
You can lead the horse to water.....
Again, those of you that belong to "the plane doesn't need friction on the ground" camp; you are correct, but there IS friction and it is not a factor in the question you can choose to ignore. It's like asking someone "How fast could a Nascar car go?" I answer aproximately 210 mph....you reply: "No, I'm saying with no friction in the wheels, no energy loss in the conversion of fuel to h.p., no wind resistance, no ground resistance, etc." Friction IS a part of the equation; if anything, the question shows how much actual energy it takes to overcome it's effects in everything we do.
You are changing the question to suit your answer....if the "conveyor" belt exactly matches the speed that the plane would normally achieve during run-up...IT SIMPLY WILL NOT FLY. (It doesn't move) A plane cannot fly until it builds up enough speed ON THE GROUND to develop lift. I guess I'm wondering why in the world we have 8,000 foot long runways if all we need to do is put a 747 on a football field-size belt and flip a switch? (It really wouldn't be that hard to engineer and build, just expensive..) The hundreds of millions of dollars saved in real estate would surely be enough for airports to lower ramp fees and save money for airlines, thus saving the airline industry. All of you in the "it will fly" camp should get together and make some money!! Why do aircraft carriers use a launching system to get jets off the short carrier jets? According to your theory they don't need any friction on the ground do they?
A boat doesn't need friction on the ground to move either, does it? So if a boat is moving nicely along a river at 10 kts and suddenly a current of 10 kts in the opposite direction develops; according to you the boat will keep going at 10kts, right?.?.?.? (Remember, the boat doesn't need friction from the ground to move)
Dennis (below) also explains nicely...but again, in the question the "asker" never says "imagine a plane with 100?fficient wheels, bearings, (they don't exist) and a conveyor belt that has unlimited speed and a 100?rictionless surface".
So I now will add to my previous statements; According to the laws of physics as we know them, and the physical and mechanical limitations of technology we have available to us, it is impossible for the plane to fly off the conveyor belt, as the question is posed.....If you are able to develop a totally frictionless (100?fficient) wheel/bearing and a conveyor belt coated with Clark Griswold's cooking spray (think Christmas Vacation), not only will you be a ga-billionaire, I will admit defeat!!
Anyway...great question, great answers (wrong or right), I'm moving on to the "chicken or the egg"!!!!:)