โœ… Sway with Foot Rise

Weโ€™ve previously explored how Sway, without Foot Rise, risks imbalance during rotation. You can review that analysis here:
โžก๏ธ Sway with No Foot Rise

Now letโ€™s explore what happens when Foot Rise is added โ€” and why it changes everything.

๐Ÿงญ The Big Idea

When the Leader initiates a Natural Turn (or any figure involving sway combined with foot rise), the system transitions from a simple pendulum to an energy-stabilized gyroscopic maneuver.

This is the biomechanical version of "Why This Works, Every Time."

๐Ÿ“Œ Key Principles

1. Progressive CBM

  • The Leader should not try to complete rotation "on 1."
  • Instead, CBM must occur as a smooth curve โ€”
    a progressive dฮธ/dt over the 3 beats of the figure.
  • This delays peak torque and gives the Follower time to respond.

2. Sway as COG Compensation

  • The leg swing generates outward force.
  • Sway acts like a counterweight โ€” keeping the Center of Gravity (COG) over the Center of Support (COS).
  • Itโ€™s dynamic feedback: sway grows in response to the legโ€™s torque.

3. Foot Rise as an Energy Injector

  • Foot rise lifts the system vertically, reducing vertical load briefly.
  • This reduces static friction just enough to increase turning speed.
  • It also compresses the required radius for the turn.

โš–๏ธ Supporting Math

Torque Cancellation:

\[ T_{\text{leg}} + T_{\text{sway}} \approx 0\]

If sway matches the torque created by the leg extension, the net tipping moment is canceled.

Vertical Force Reduction via Rise:

\[ F_z = mg - F_{\text{rise}}\]

Where:

  • \(mg\) = dancerโ€™s weight
  • \(F_{\text{rise}}\) = force applied during foot rise

Less pressure = more maneuverability.

Increased Rotational Energy:

\[ E_{\text{rot}} \propto I \cdot \omega^2\]

Where:

  • \(I\) (moment of inertia) drops slightly due to foot rise and narrowing base.
  • \(\omega\) (angular velocity) therefore increases, helping rotation.

๐ŸŸข Why This Cannot Fail

  • The sway ensures balance.
  • The rise adds energy.
  • The progressive CBM times it correctly.
  • The Follower is carried, not dragged.

This is a self-stabilizing, biomechanically justified system.

โœ… No awkward shove on beat 1.