🧩 A Fully Defined Timing Model for Follower Response in Swing Dances

In the Ballroom 'Swing' dances (Waltz, Foxtrot, Quickstep, Viennese Waltz), the follower’s movement on Beat 1 is governed by both musical cues and biomechanical constraints. Here's a clearly defined timing model that explains when, why, and how followers move — and how long they have to do it.

⏱️ Timing Phases

Phase Duration (ms) Description
Pre-lowering -200 to -50 Calm stillness; follower is poised and waiting.
Lowering Cue -50 to 0 Leader lowers center slightly — this is a ‘get ready’ signal.
Early Prep overlaps -50 to 0 Follower may begin retracting the RF, prepping subconsciously.
Decision Window 0 to ~300 Follower commits to where the RF will go. Pizza slice is locked.
Step Execution 300 to 667 RF travels. COG begins transitioning. No turning back!

🔄 Action Types on a Beat

For any given beat of music, the following actions may occur:

  • No action
  • Start of an action
  • Continuation of a previous action
  • Completion of an action

These actions are informed by preparation, perception, and reaction timing.

🧠 Delay Model: Instinct + Physics

Let:

  • T_s = Time spent preparing to act
  • T_e = Time required to end/reset after movement
  • T_p = Perception + Reaction delay
  • T_b = Duration of a beat (in ms)
  • T_a = Available Action Time

General Equation:

T_a = T_b - (T_s + T_e + T_p)

⏲️ Real-World Waltz Example

Tempo: 30 MPM (Measures per Minute)
Time Signature: 3/4
→ T_b = 667 ms per beat

Let’s assume:

  • T_s = 150ms (preparation)
  • T_e = 100ms (cooldown or reset)
  • T_p = 50ms (reaction time)

Then:

T_a = 667 - (150 + 100 + 50) = 367 ms

The follower has ~367ms of usable time to execute their movement.

📏 Travel Distance Example

If the follower travels at 1 meter/second, then:

d = v × t = 1.0 × 0.367 = 0.367 meters

So a typical follower could step just over one foot’s length in that time.

⚡ Kinetic Energy Example

Let:

  • Mass m = 70kg
  • Velocity v = 1.76 m/s

Then:

KE = ½ m v² = 0.5 × 70 × (1.76)² ≈ 108.6 Joules

This energy:

  • Drives movement across the floor
  • Must be redirected or dissipated between steps
  • Can support flow, or cause collisions if unmanaged

Levels of uncertainty

As the follower travels they have increasing options as to where to place their moving foot. This is shown in the diagram below where Follower is moving backwards (from their perspective) and their moving foot has increase options as to where it can be placed.

Followers increased foot placement options over time

🧠 Why This Matters (to you)

Most dance instruction focuses on what to do — not why it works.

This model:

  • Explains the mechanics of follower response
  • Reveals how long they have to act
  • Helps instructors avoid vague cues like “just feel it”
  • Creates a foundation for biomechanical choreography and teaching

💬 Quote of the Day

“Here’s the math. Prove it wrong.”
— A Confident DanceBot (and probably HAL)