There are two completely distinct ways to swing on a swing- You can rotate your body relative to the seat-chain body at the same frequency as your swinging but out of phase, or move your center of mass up and down the chain at twice the frequency. The power of the former is ~ torque applied to chain \* angular velocity, the power output of the latter is radial velocity of your body \* (angular velocity ^2 \* chain length).
To get to any height, you have to switch from one to the other once the angular velocity ^2 term dominates- this is why learning to swing is so unintuitive.
There are two completely distinct ways to swing on a swing- You can rotate your body relative to the seat-chain body at the same frequency as your swinging but out of phase, or move your center of mass up and down the chain at twice the frequency. The power of the former is ~ torque applied to chain \* angular velocity, the power output of the latter is radial velocity of your body \* (angular velocity ^2 \* chain length).
To get to any height, you have to switch from one to the other once the angular velocity ^2 term dominates- this is why learning to swing is so unintuitive.