00 / OVERVIEW · BODY-VS-KICK MISMATCH

The Anomaly

A physics-based reading of an anatomically anomalous free kick. Atlas's body is rotated 66° from the goal direction; the ball departs 55° off body forward; the Magnus deflection brings it home.

Top-down geometry showing Atlas perpendicular to the kick line

Setup

Atlas faces 26° azimuth. The goal lies at 92°. The ball must curve through space to reach a goal the body is not pointing toward.

Data

Launch speed26.43 m/s

Lateral curl2.4 m

Flight time1.05 s

Spin rate6.4 rev/s

Claim

Off-axis strike geometry, hard impulse, sidespin. The ball travels past the goal frame and curves back to find the post.

FIG · BODY-VS-GOAL VECTORS Annotated geometry — body forward (cream), to-goal (teal dashed), 66° mismatch arc, ball trajectory. REFERENCE

Body one way. Ball another. Goal found.

configuration → impulse → trajectory → evidence ATLAS

01 / CONFIGURATION · BODY-VS-GOAL GEOMETRY

The Stance

Atlas's body faces 66° from the line to goal — nearly perpendicular. A flat rectangular foot (28 × 10 cm, near-rigid sole) makes off-axis contact possible.

Atlas at strike — body forward arrow and to-goal arrow

Geometry

Body forward26°

Line to goal92°

Off-axis66°

Ball departs81° · 55° off body

Surface

Atlas D1's foot is a flat plate, 28 × 10 cm. Where a human curved instep would constrain contact along body forward, the flat plate can deliver impulse at any angle to body orientation.

Why

A human kicker must align hip and trunk to the kick direction. Atlas does not.

FIG · KICK BIOMECHANICS Five-phase standard kick (Approach → Plant → Loading → Strike → Follow). Lees & Nolan 1998. REFERENCE

The body faces away. The kick still finds the goal.

configuration → impulse → trajectory → evidence ATLAS

02 / IMPULSE · OFF-AXIS POWER TRANSFER

The Strike

A single 8.33 ms contact frame delivers the energy and angular momentum of the next 1.05 s of flight. 1.36 kN average force, 95 % energy transfer, 6.4 rev/s implied spin.

Foot velocity, ball velocity, spin axis at contact

Force

Foot impact14.8 m/s

Impulse11.4 N·s

Avg force1.36 kN

Contact8.33 ms

Energy

Ball KE gain150 J

Foot KE lost159 J

Transfer95 %

Launch speed26.4 m/s

Spin

Rate6.4 rev/s

RPM384

C_L0.62

F_M avg0.73 N

FIG · MAGNUS EFFECT Pressure differential around a spinning ball — lateral force F_M perpendicular to flight. REFERENCE

Off-axis impulse loads angular momentum.

configuration → impulse → trajectory → evidence ATLAS

03 / TRAJECTORY · MAGNUS ARC

The Curve

Out to peak X = +2.4 m at t = 0.4 s — wide of the goal — then 1.82 m of lateral curl back across the goal mouth in 0.65 s.

3/4 rear view showing the curving trajectory toward goal

Arc

Peak X+2.40 m

Lateral curl1.82 m

Peak height2.80 m

No-spin miss2.57 m

Magnus

F_M avg0.73 N

C_L0.62

Spin6.4 rev/s

Flight1.05 s · 10.7 m

Evidence

Spiral mechanism from free kick (Dupeux et al. 2010) as the ball decelerates, the Magnus radius shrinks — the trajectory bends harder near the end.

Roberto Carlos spiral reference (Dupeux et al. 2010)

FIG · MAGNUS DEFLECTION Right-foot free kick. Outside-of-foot spin curves the ball back toward goal. REFERENCE

The ball travels past the goal, then returns.

configuration → impulse → trajectory → evidence ATLAS