Forehand Degrees of Freedom

Skyward C-loop takeback (κ), cylindrical spine coordinates (z, θ, r), passive wrist whip, forearm roll & 4.5 ms stringbed collision

Racket Whip & Takeback ATP ~33 m/s

31.6 → 18.6 m/s

Sky takeback +86° ↑ · Max lag 99°

Outgoing Ball IN

96 mph

Launch +4.8° · Kick 82 cm

Topspin Rate ATP ~2,708 rpm

2,435 rpm

Plane β +1,638 (67%) · Whip+Roll +797 (33%)

Contact Window MODEL 5 µs

4.61 ms

Squash 26 mm · Bow 21 mm · Carry 8.7 cm

Live Pose (z, θ, r, Sky) LIVE POSE

z 82 · θ -106° · r 51

Tip +85° ↑ sky · Lag 28°

t = -620.0 ms · Tip +74° ↑ sky Drag stage to orbit · Scroll to zoom

Stroke Time -620 ms

Stringbed Footprint & Grip Bevel Cue feel (throat→tip)

23.8 m Court Flight (Drag + Magnus Spin) 1.8× Z-scale

Tune Dials & Degrees of Freedom

Double-click any dial/slider to reset

Reference Presets (or tune any dial/number below):

Primary Rotary Dials Drag up/down · Scroll · Dbl-click

κ Sky Tip 85°

θ₀ Unit Coil -106°

ω Spine Spin 745 °/s

Δz Squat 14 cm

Δφ Reach 88°

β Plane Tilt +26°

1. Skyward Takeback & C-Loop (κ, θ_back)

Takeback Racket Sky Angle (κ)

deg

85°–90° points racket head straight at the sky during unit turn; 0° = flat stick

Unit-Turn Coil Depth (θ_back)

deg

How far shoulders coil back around spine (-90° = side-on, -115° = deep tour coil)

Takeback C-Loop Hand Lift

Hand height during high preparation before dropping into the low slot

2. Cylindrical Spine & Legs (z, θ, θ_hip)

Altitude Squat Depth (Δz)

Knee-bend drop during coil and upward leg drive through contact

Contact Base Altitude (z_drive)

Pelvis height at contact (lower = deep sitting stance, higher = tall strike)

Spine Uncoil Speed (ω_trunk)

°/s

Peak torso angular speed around spine · Measured ATP mean: 745 °/s

Pelvis / Hip Lead (X-Factor)

0% freezes hips; 100% fires pelvis ~18 ms ahead of shoulders

3. Arm Lever & Swing Plane (r, α, β)

Takeback Elbow Bend (φ_load)

deg

Elbow flexion tucked in during unit turn (smaller = wider arm takeback)

Radial Elbow Extension (Δφ → r)

deg

Unbends arm into slot (88° = straight-arm ~77 cm reach; 45° = double-bend)

Reach Timing vs Turn

Negative = early arm cast; 0 ms = synced slot drop; positive = late jam

Shoulder Forward Release (α)

Horizontal shoulder adduction driving upper arm ahead of chest

Swing-Plane Tilt (β Low-to-High)

deg

0° = level drive (~740 rpm); 24°–30° = heavy tour topspin (~2,500 rpm)

4. Wrist Whip, Roll, Grip & Ball (λ, ρ)

Wrist Stiffness (Whip vs Lock)

0% = loose passive hinge whipped to ~96° lag; 100% = rigid locked wrist

Forearm Doorknob Roll Rate (ρ̇)

°/s

Pronation wiper rate peaking +24 ms post-impact (ATP mean: 794 °/s)

Forehand Grip Bevel (or click 1–8 octagon)

String Face Tilt Offset

deg

Auto-close string face as swing plane β tilts upward

Impact Spot Along Strings

Incoming Ball Pace

m/s

0 m/s = drop-feed · 10 m/s = 22 mph rally · 25 m/s = 56 mph heavy ball

Cylindrical Body Pose (z, θ_spine, θ_hip)

z — Pelvis Altitude (Squat)

θ_spine — Torso Spin

deg

θ_hip — Pelvis Spin

deg

Shoulder, Elbow & Plane (α, η_ua, φ, η_fa, β)

α — Shoulder Horizontal Angle

deg

η_ua — Upper-Arm Elevation

deg

φ_elbow — Elbow Bend (Sets Reach r)

deg

η_fa — Forearm Loop Pitch

deg

β — Swing-Plane Tilt

deg

Wrist Sky Cocking, Lag, Roll & Bevel (κ, λ, ρ)

κ — Wrist Sky Cocking (Tip Up)

deg

Positive κ cocks wrist upward so racket head points straight at the sky

λ — Wrist Lag (-) / Flexion (+)

deg

ρ — Forearm Doorknob Roll

deg

Grip Bevel ("Hand & Strings" view shows finger wrap)