The Wright Flyer II could reach about 20 mph of airspeed on the track alone. The aircraft needed an airspeed of about 30 mph to make a proper takeoff (without hanging in ground effect). Before the catapult was developed, the Wrights needed at least a 10 mph heawind in order to reach the proper airspeed.
My question is: suppose the airplane reached 20 mph after 250 feet (76 meters) of track, which was the longest track length they ever had. No wind is present. Now suppose the track is not 250, but 500 feet (150 meters) in length. Would doubling the track distance allow the airplane to compensate for the lack of the 10 mph wind it normally needed?
I know that aerodynamically speaking for an airplane performing a takeoff, if you have 30 mph of airspeed, it doesn't matter if this airspeed was obtained by partially using a headwind or not. Airspeed is the only thing an aircraft "feels" for takeoff purposes. What I'm really in doubt for my hypotetical scenario is about the acceleration. Since the acceleration is non-linear for an airplane taking off, I'm not sure if by doubling the length of the takeoff distance the aircraft would be able to compensante for the 10 mph headwind it normally relied at the start of the takeoff.