The towel whipping analogy only works when you have a weapon that functions like a towel. One which you can use to create a force couple.

The whipping effect can't be applied to straight punching but it can be applied to a back fist or a snap kick.

For instance the backfist you pull back at the last moment to make you wrist reverse in direction to add force. It also works with the front snap kick but its hard to do. You force your knee down at the last minute to create a whipping movement

Didn't I say that my analogy was crude?