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Suppose someone attached a mile-long unbreakable rope to the tail of an indestructible airplane in a way that cannot be detached, and the plane takes off and flies in a straight line. The other end of the rope is fastened to the ground at the end of the runway. What happens when the airplane reaches the end of the rope? Does it hover? Crash? Oscillate up and down? Go straight up like a helicopter, if the engine is powerful enough?

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    $\begingroup$ If I had to guess it would likely come to a sudden stop, then fall down. The wings need airflow to generate lift. $\endgroup$ Jan 29, 2023 at 6:21
  • $\begingroup$ @At0mic would the airflow from falling suffice to temporarily raise the plane again? That's what I was thinking might cause the oscillation scenario. $\endgroup$
    – Someone
    Jan 29, 2023 at 6:29
  • $\begingroup$ I guess one way to find out would be to build a model plane and fly it with a tether. $\endgroup$
    – Someone
    Jan 29, 2023 at 6:29
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    $\begingroup$ I think this setup is called a kite and you might enjoy doing the experiment yourself. :) $\endgroup$
    – TypeIA
    Jan 29, 2023 at 8:07
  • $\begingroup$ The airflow from falling would suffice to slow it down like a parachute, for sure not to lift it back (unless there's a strong enough thermic or unless it's a F-35) $\endgroup$
    – sophit
    Jan 29, 2023 at 8:40

4 Answers 4

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This is somewhat speculative b cause there are no unbreakable or indestructible objects, but if we assume that the objects in question won’t break subject to the forces in the experiment, and if we further assume that the elasticity of the rope is. Rey small then the aircraft will quickly come to a stop and will fall parachutally (in this case quite quickly but not in free - fall). The engines may provide a little airflow over the wings depending on the configuration but it will likely be far from enough to support the aircraft. If the aircraft is robust enough to withstand the rope then it may well survive the landing.

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The ultimate stall!

An airplane needs forward velocity to generate lift. No matter how powerful its engine is or how much thrust it has, if it does not have forward speed it does not have lift.

Helicopters solve this forward speed issue by spinning its rotor for lift and tilting forward a bit for airspeed. A airplane cannot do this.

After it stopped, the drag of its structure might limit the speed of its descent, but fall it will because a wing can not support the weight of the aircraft without lift.

What might be more fun is to attach a rope perpendicular to the direction of flight, giving full-scale control line flight.

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Assuming that both the rope and plane are indestructible, the biggest problem in this scenario for the people in the plane is that the rope is attached to the tail. This would rob the crew of any attitude control as long as the rope is taut.

As soon as the plane reaches the end of the rope, it will stop, wings will stop generating lift, since stable planes are nose heavy it will start falling nose first, resulting in airflow over the wings and lift. Had the rope been attached close to the CG, one could stabilize this flight condition and enter an orbit around the other end of the rope.

However since the rope is attached to the tail, the crew does not have any control over their attitude. One trick which could work is to roll to inverted before the rope gets taut, then once in inverted nose down attitude, pull as hard as you can and hope that the nose is heavy enough that you get in a straight vertical attitude before hitting the ground. Then the lift generated by the wing will start pushing you towards the center of the circle, giving the rope a little slack which you could use to pull back to nose towards the horizon.

This is actually a potential accident scenario for winch launched gliders, where a glider connected with a rope attached near the CG to a winch, which pulls the glider into the ait. If for some reason the rope release on the glider is stuck, the winch has an emergency guillotine to cut the rope. Even if that's broken, then the only solution is to enter a decaying orbit around the winch and hope you survive the landing.

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In reality snapping at the end of a rope would probably cause a structural failure of the airplane, but as we are already working with a massless, infinitely durable rope I'll assume the airplane won't suffer any damage.

The answer depends on where the rope is anchored. Airplanes fly because there's air flowing over the wings, if an airplane was to suddenly stop in mid-air then there would be no airflow to create lift, and the airplane would plummet to the ground. So, if the rope was attached to the tail bad things would happen. If the pilot has enough altitude they might be able to drop the nose and maneuver the airplane back to the airfield, or at least make an emergency landing. Most likely there's a big crunch at the end.

If the rope was attached to the underside of the airplane, or maybe the side, somewhere around the center of lift, then the airplane can still fly. If the rope is on the side the pilot would need to fly a constant turn around the rope's anchor point. If the rope is attached to the underside then the pilot would then have a very strange experience as the airplane would turn around the rope's anchor point, with the wings banked opposite the direction of the turn. In both cases the pilot would need to initiate a turn before the rope becomes fully taut, if not then the airplane comes to a sudden stops and it's crunch time again.

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