In your post
you present an excellent description of the mechanical principles found in all high level swings. I would also like to thank you for providing the links to the Nyman's simulations below. I have studied those simulations and will give a couple of my takes on his test and conclusions.
First, I must say that I wish I had acquired the program Paul used long ago. It would have been of great value to simulate the physics principles of CHP, BHT and THT. I think Paul did a good job with his first two simulations (below) where he shows the angular acceleration of the bat induced from the double pendulum effect (or flail if you wish) when the hands are propelled in a circular path.
Nyman's First Simulation
Paul's third simulation, where he attempts to show the effect on the bat's trajectory from adding torque, is highly misleading. It also demonstrates his lack of understanding of the principles involved in applying torque at the handle.
For torque applied at the handle to induce rotation about a point (between the hands), only the vectored forces applied by the hands that are perpendicular to the length of the bat are a factor. When the forces of both hands are directed down the length of the bat, as in Paul's simulation, there are no force vectors that are perpendicular to the length of the bat and therefore, as the swing is being initiated, no torque is being applied at the handle.
As his simulation shows, torque is not a factor in inducing bat rotation until the bat has rotated so that the directional force of the hands are no longer inline with the length of the bat. In his simulation, this does not occur to any appreciable degree until the bat rotated 30+ degrees. -- As an example: when the length of the bat has rotated 45 degrees, about half of the vectored force of the hands are directed down itsï¿½ length and half are directed perpendicular to the handle. With this simulation, maximum torque is not realized until the bat's length approaches 90 degrees to the forces applied by the hands.
Instead of Paul calling this a simulation of THT, it would have been more accurate to label it "Knob to the Ball." With knob to the ball, the forces of the hands are directed down the length of the bat and good bat speed is not attained until late in the swing.
With THT, the force of the top-hand is not driving forward as his simulation shows. The top-hand is pulling rearward and perpendicular to the bat's length. With efficient transfer mechanics, the direction of forces of the hands are always opposing and remain directed perpendicular to the handle from initiations to contact -- torque applied throughout the swing.
Tom, I am sure a great number of players and coaches have seen Paul's simulation of THT. I am starting this topic as a new thread so that some of them have a chance to read my reply.