Kinematic Distance Breakdown ($D_{total}$) $d_1 + d_2 + d_3$
Takeoff Distance ($d_1$)
Foul board edge to COM projection at takeoff
0.32 m
Flight Parabola Distance ($d_2$)
Airborne COM trajectory with aerodynamic drag
7.17 m
Landing Extension ($d_3$)
COM at initial sand touch to heel imprint
0.48 m
Total Official Mark ($D_{total}$)
Simulated competition measurement
7.97 m
Trajectory Kinematic Formulation:
$d_2 = \int_0^{t_{land}} v_x(t) \, dt \approx \frac{v_0 \cos\theta}{g} \left( v_0 \sin\theta + \sqrt{v_0^2 \sin^2\theta + 2g(h_0 - h_{land})} \right) - \Delta d_{drag}$
$v_0 = \sqrt{v_x^2 + v_y^2}, \quad v_y = \frac{\int F_{ground} \, dt}{m} - g t_c$
$d_2 = \int_0^{t_{land}} v_x(t) \, dt \approx \frac{v_0 \cos\theta}{g} \left( v_0 \sin\theta + \sqrt{v_0^2 \sin^2\theta + 2g(h_0 - h_{land})} \right) - \Delta d_{drag}$
$v_0 = \sqrt{v_x^2 + v_y^2}, \quad v_y = \frac{\int F_{ground} \, dt}{m} - g t_c$