I do realize the tires generally have little to do with it beyond initial movement and that it will take off. Restating: if there is EVER any differential in inertia/speed between the two then it will take off. BUT, and that is a big but, if speeds are matched to the billionth power, exactly, totally, nothing different to the point that NO differences, then no.
If the plane does start moving forward (or backwards due to wheel friction) in relation to the ground or tower, then it IS moving faster/different) than the rolling runway, it broke the inertia/kenetic energy (lost my long ago physics terminology) barrier of a standstill.
Look at it this way, suppose the runway starts backwards first at 10 mph, after the plane has moved backwards 100 yards, the engine accelerates to bring it up to 10 mph making it effective ground speed as "0"; Keep doing this - accelerating the runway first until the plane is catching up with the runway speed on a 100 mile long runway. Eventually the runway will be doing 100mph, the plane is slowly catching up and finally reaches 100mph on the runway, the weight and minor wheel friction will still keep it on the runway because no wind is flowing over the wings yet.
IF the plane were to speed up 1/10 of 1 mph faster than the runway, then it would begin forward movement and take off.
HOWEVER, with the specific question that was asked, until a canceling inertial difference is overcome, it won't take off. But once an inertial difference is overcome, it will take off, - but then they are not equal.
If a runway was 1000 miles long and was going 150 mph in one direction, could a 120 mph Cessna setting on it facing the other direction get up enough speed to ever take off?
This is the OTHER side to the main question. Everything being exactly equal, no, but that kind of precision measurement doesn't exist, so for the question - no, for reality - yes - unless the runway does go backwards faster than the plane can accellerate.
Lastly, if the plane is allowed to move forward as much as one inch, you should allow the possibility for the runway to move in the reverse at the beginning - faster than the plane can accelerate forward, taking it backwards. If this statement is considered not to be fair, then neither is a plane that accelerates forward beyond the speed of the runway. It boils down to timing - which comes first. If equal, no. If unequal, it is possible.
If the plane does start moving forward (or backwards due to wheel friction) in relation to the ground or tower, then it IS moving faster/different) than the rolling runway, it broke the inertia/kenetic energy (lost my long ago physics terminology) barrier of a standstill.
Look at it this way, suppose the runway starts backwards first at 10 mph, after the plane has moved backwards 100 yards, the engine accelerates to bring it up to 10 mph making it effective ground speed as "0"; Keep doing this - accelerating the runway first until the plane is catching up with the runway speed on a 100 mile long runway. Eventually the runway will be doing 100mph, the plane is slowly catching up and finally reaches 100mph on the runway, the weight and minor wheel friction will still keep it on the runway because no wind is flowing over the wings yet.
IF the plane were to speed up 1/10 of 1 mph faster than the runway, then it would begin forward movement and take off.
HOWEVER, with the specific question that was asked, until a canceling inertial difference is overcome, it won't take off. But once an inertial difference is overcome, it will take off, - but then they are not equal.
If a runway was 1000 miles long and was going 150 mph in one direction, could a 120 mph Cessna setting on it facing the other direction get up enough speed to ever take off?
This is the OTHER side to the main question. Everything being exactly equal, no, but that kind of precision measurement doesn't exist, so for the question - no, for reality - yes - unless the runway does go backwards faster than the plane can accellerate.
Lastly, if the plane is allowed to move forward as much as one inch, you should allow the possibility for the runway to move in the reverse at the beginning - faster than the plane can accelerate forward, taking it backwards. If this statement is considered not to be fair, then neither is a plane that accelerates forward beyond the speed of the runway. It boils down to timing - which comes first. If equal, no. If unequal, it is possible.
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