Freekick Lab | Dr. Loveless Curiosity Lab

Explore a Bending Free Kick

Start with the real kick, then move into the model. The page shows how gravity, drag, and spin combine to make a ball curve, and then lets visitors experiment with the launch vector and spin-axis vector themselves.

Concept 1: Beckham Model + Real Kick

A tuned 3D model is synchronized with a real Beckham free-kick video.

Original Video

Shared time 0.00s

Loading Beckham free kick model...

Desmos 3D model

Real kick reference

Concept 2: Build Your Own Free Kick

Change the launch vector and spin-axis vector to build a shot that bends into the goal.

Preset

Clean bending goal. Use the sliders below to tweak the shot, then press Play.

Start x 5.00

Start y -9.13

Speed 24.59

Elevation 0.196

Aim 0.459

Spin 40.11

Spin tilt 0.888

Spin turn -0.750

Spin direction +

Purple = initial velocity. Orange = spin axis. Presets are starting points; the sliders above send values directly into Desmos.

Loading interactive free kick model...

Interactive free-kick challenge

Concept 3: Arjav’s Prototype

A future-facing prototype showing where this project can grow next.

Open Arjav’s Prototype

Arjav built this early Lovable prototype as a concept sketch for the next version of the project. It is still under construction, but it shows several goals we want to build toward: famous kick presets, side/top views, and live slider controls.

Screenshot of Arjav’s Freekick Lab prototype with trajectory views and slider controls

Core Model

The model tracks the center of the ball:

\[ \mathbf r(t)=\langle X(t),Y(t),Z(t)\rangle \]

Newton's law is written as:

\[ m\mathbf r''(t)=\mathbf F_g+\mathbf F_{\text{drag}}+\mathbf F_{\text{spin}} \]

Gravity \(\mathbf F_g=\langle 0,0,-mg\rangle\)

Drag \(\mathbf F_{\text{drag}}=-\frac12\rho C_D A\|\mathbf v\|\mathbf v\)

Magnus / Spin \(\mathbf F_{\text{spin}}=c(\boldsymbol\omega\times \mathbf v)\)

Velocity \(\mathbf v(t)=\mathbf r'(t)\)

Concept 2 Controls

In the interactive graph, the purple vector is the launch vector and the orange vector is the spin-axis vector. They are drawn off to the side so the ball and goal remain visible.

\(V_0\): launch speed

\(A_0\): elevation angle

\(B_0\): left/right aim angle

\(S_0\): spin amount

\(D_s\): spin direction

\(A_s,B_s\): spin-axis orientation

Numerical Path

The Desmos model uses Euler's method: acceleration updates velocity, and velocity updates position.

\[ \mathbf v_{n+1}=\mathbf v_n+\mathbf a_n\Delta t \]

\[ \mathbf r_{n+1}=\mathbf r_n+\mathbf v_n\Delta t \]

Goal Feedback

The interactive graph uses a simple goal detector. The target panel turns green for a goal and red for a miss.

What to Notice

Spin does not push the ball forward. It changes the direction of the aerodynamic force. That is why two shots with similar speed can have very different paths when the spin axis changes.

Drag shortens the flight, gravity lowers the arc, and the Magnus force bends the shot sideways.

Where It Started

Arjav began with the question of how a soccer ball curves through the air. His paper models the flight of a spinning soccer ball using gravity, quadratic drag, and the Magnus force, then connects the model to famous free kicks such as Beckham against Greece.

The visual page turns that model into an interactive lab: first match a real video, then let visitors change the speed, aim, elevation, spin amount, and spin axis themselves.

Future Additions

Future versions will add a famous free-kick gallery with Beckham, Roberto Carlos, and knuckleball examples, plus supporting views for top-down curl, side-view height, spin axis, and force diagrams.

This first version focuses on the two central experiences: matching a real free kick and building your own bending shot.

Explore a Bending Free Kick

Where It Started

Future Additions

Links & Resources