Originally posted by SFRT - Frenchy
Wow ... those videos were amazing! I do have no clue of what you guys are talking about:confused:
... I just hope it's not about "would my 16,000lbs Metroliner get airborne if the wheels are spining at 115 knots, but my relative wind and Ground Speed are 0".
Here’s the original AH BBS question:
Originally posted by rabbidrabbit
A plane is standing on a runway that can move like a giant conveyor belt. The plane applies full forward power and attempts to take off. This conveyor has a control system that tracks the plane's wheel speed and tunes the speed of the conveyor to be exactly the same but in the opposite direction, similar to a treadmill.
The question is:
Will the plane take off or not?
Read and answer this to see a force you have not considered:
Here’s a story that simplifies the problem: (Note that the term wheels in this story refers to wheels and tires)
Identical triplets Al, Bob and Chuck buy three identical bush planes. Since they live in Alaska, all three brothers buy and install large balloon “tundra tires” and wheels. The wheels, planes and brothers are identical. All three planes will take off from a normal runway in exactly 100 feet and at exactly 50 mph. The brothers fly their planes to an air show in Wisconsin. At the air show Bob finds and buys a set of fantastic wheels. These wheels are exactly like the wheels he has on his plane in every way except they have half the mass. Their mass is distributed in the same proportion as the wheels that he plans on replacing. Al thinks Bob is silly and is content with his old wheels. Bob thinks that Al will eventually want a set, so he buys a second set to give to Al on their birthday.
Bob finds a buyer for his old heavy wheels and installs a set of his new lightweight ones. He loads the second set into his plane so that it is balanced just as it was before. Bob’s plane now weighs exactly the same as Al’s and Chuck’s, but its wheels have half the mass.
Meanwhile, Chuck runs into a magician who sells him a set of magic wheels. These wheels are exactly like the wheels he has on his plane in every way except they have no mass. Chuck installs his magic wheels. He loads his old set into his plane so that it is balanced just as it was before. Chuck’s plane now weighs exactly the same as Al’s and Bob’s, but its wheels have no mass.
When the brothers leave the air show they request a formation take off. They line up wing tip to wing tip and apply power at exactly the same time. All three planes weigh exactly the same and must hit 50 mph to lift off. When Chuck’s plane lifts off his wheels stop spinning instantly since they have no mass. Since they have no mass, they also have no rotational inertia. When Al’s plane lifts off his heavy wheels are spinning at 50 mph and have considerable rotational inertia. When Bob’s plane lifts off his half-weight wheels are spinning at 50 mph and have exactly half the rotational inertia as Al’s wheels.
Where did the rotational inertia and energy in Bob’s and Al’s wheels come from?
How did the rotational inertia and energy now stored in Bob’s and Al’s wheels affect the take off distance of their planes?
We know that Al’s plane will still take off in exactly 100 feet; where will Bob’s and Chuck’s planes take off?
