After reading through every post in this thread, I don't think it's been made clear as to how "dropping" (i.e. using it as a counterweight) assists in balance or power.
This is a fairly complex physics question, involving rotational inertia, precession and other effects. I'll try to streamline it as follow:
Angular kinetic energy ("K") is what we're looking for. . . the kick's power.
The angular speed ("ω") is the speed of the moving leg (probably the shin, but striking surfaces may differ).
The moment of inertia ("I"), also called rotational inertia, measures an object's (i.e. the leg's) resistance to change in its rotation rate. Roughly, this is "balance," since a kick-through MT style kick should have enough rotational inertia to swing the kicker around in a complete circle.
Because,
K = 1/2 x I x ω^2
power increases as balance increases.
But what about the counterbalancing hand? Three considerations: 1) the axis of pivot is vertical along the support leg; 2) the kicking leg for a Thai roundkick loses speed, inertia and power after it passes the target; and 3) a high roundkick follows a more non-horizontal axis (as compared to a mid roundkick) making recovery even more difficult.
Without counterbalancing, the rotational inertia would adversely affect the kicker's vertical position (due to the above factors). With good counterbalancing, the kicker will stay vertical longer, providing a better pivot. This allows for greater average angular speed (ω
, which leads to greater power (K).
In the beginning, I alluded to "precession," which is the result of an angular force (like gravity) working on a rotational force (like a spinning top, or a roundkick). I won't go into formulae, but consider the spinning top. The more force with which it spins (i.e. dropping hands), the more likely it will stay vertical.
Earlier, somebody had mentioned kinetic linking. Kinetic linking can only do so much if a striker needs to recover his or her stance/base afterwards. For example, a right cross (or straight right, if you want to get technical), is much more powerful if the puncher would over-commit and "buckle" the front leg for more forward motion. Of course, this is not advisable for fighting. If a kicker can stay vertical longer, that is better maintain balance and apply even greater kinetic linking, he or she can now initiate a kick with more acceleration than otherwise possible. Simple Newtonian physics explains the rest:
Mass x Acceleration = Force
That is all.
