im in the top of a tower and two cannons are shot underneath me, one to the left and one to te right, im united to the cannonballs by a cable and i give away cable or take it with a spool lests look at the drawing:
the cannonball i shot in trajectory 3, a straight one, i give away as much cable as needed so the tension of the cable is 0
the tension in trajectory 1 the circular one the tension is constant of 10000 N so the tension is the same the one that pulls up that the one that pulls down
but in the trajectory 2 the one that is first an otwards spiral and then and inwards one the tension that pulls down is of 1 N while the one that pulls up is of 10000 N
i would be virtually shot up in trajectory one with almost no reaction
besides conservation of energy predicts that once the cannonbal is spinning in this spiral shape it will last forever with no friction
so i just would have to keep this spiral trajectory to go as high as wanted by only having used the initial energy of the cannons
i could maybe then use this upwards thust to feed a motor that made the cannonball spin faster what would increase the upwards thrust which would increase again the spin