Many syllabus-based ballroom figuresβsuch as the Reverse Turn in Smooth Waltz or Smooth Foxtrotβare traditionally described as having a 3/8 turn distributed over 3 steps, specifically:
The first mention of this (that we are aware of) is in 1948 with the first edition of "The Ballroom Technique" by the legendary Alex Moore. It has stayed with us virtually unchanged over the subsequent 77 years or so during which things might have changed in the light of new knowledge.
This analysis explores the biomechanical and logical implications of this structure, and provides a superior alternative based on movement science and partner dynamics.
The turn is heavily front-loaded, requiring:
This creates inconsistent motion and instability, especially for the follower.
In reverse figures:
The follower must rotate around the Leader rapidly during step 2, then suddenly stop rotation and close feet at the end of step 3.
Because the movement cues for the abrupt final 1/8 turn are weak and late:
Since the most frequent consequences are:
This fixes the amount of turn at 1/4 spread evenly over steps 1-3. The traditional (book) alignments are commencing DC and ending DW whereas this will end FW. This is easily corrected by turning 1/8 to DW during the "lowering phase" of the next beat.
| Step | Turn Amount | Description |
|---|---|---|
| 1β2 | 1/8 turn left | Begins rotation gently |
| 2β3 | 1/8 turn left | Continues rotation smoothly |
Let total turn be \(\theta = 135^\circ = \frac{3\pi}{4} \text{ rad}\)
Over 3 steps (t = 3):
\(\omega_{avg} = \frac{\theta}{t} = \frac{3\pi/4}{3} = \frac{\pi}{4} \approx 0.785 \text{ rad/step}\)
This version maintains constant angular velocity, resulting in:
To better understand why the ERD method outperforms the Book version, we can compare their angular velocities and assess how the distribution of rotational effort affects movement.
The Book Version demands a sudden burst of rotation (Ο/2) in Step 2, which creates torque spikes, balance challenges, and poor responsiveness for the follower.
The ERD Method distributes the rotation evenly (Ο/4 across each interval), minimizing angular acceleration spikes and maintaining flow.
In biomechanical terms: A dancer's ability to rotate fluidly is proportional to how consistent the applied angular velocity is. Sudden increases (as in the Book version) create strain and instability, especially for the partner on the outside of the turn.
Below are the step-by-step breakdowns: Angular velocity \(\omega\) is defined as:
\[ \omega = \frac{\Delta \theta}{\Delta t}\]
Where:
| Step Interval | Turn | \(\Delta \theta\) | \(\omega\) |
|---|---|---|---|
| Step 1 β 2 | 1/4 turn left | \(\frac{\pi}{2}\) rad | \(\omega = \frac{\pi}{2}\) rad/step |
| Step 2 β 3 | 1/8 turn left | \(\frac{\pi}{4}\) rad | \(\omega = \frac{\pi}{4}\) rad/step |
| Step Interval | Turn | \(\Delta \theta\) | \(\omega\) |
|---|---|---|---|
| Step 1 β 2 | 1/8 turn left | \(\frac{\pi}{4}\) rad | \(\omega = \frac{\pi}{4}\) rad/step |
| Step 2 β 3 | 1/8 turn left | \(\frac{\pi}{4}\) rad | \(\omega = \frac{\pi}{4}\) rad/step |
Yes, the ERD method will result in an ending alignment and Travel Vector (Tvec) of FW. This is easily corrected by turning 1/8 left to DW during the "lowering phase" of the next beat.
Any figure in Closed Position that asks for 3/8 of a turn over 3 steps, without the use of a Heel Turn or staggered timing, inherently violates the biomechanical constraints of partnered motion.
Yes, we are aware of the implications of this proof.