This is the 2D companion to the 3D "1000× kick force" laboratory, rebuilt directly from the impulse-momentum theorem instead of an arbitrary force multiplier: the leg's momentum at the instant of contact is transferred to the target over a short contact window, and the shape of that transfer (modelled as a half-sine pulse, the standard approximation for short impacts in biomechanics) sets the peak force.
Momentum: p = m · v
Impulse: J = p (leg decelerates to ~0 at full transfer)
Avg. force: F_avg = J / Δt
Peak force: F_peak = F_avg · (π / 2) (half-sine impact pulse)
Energy: E_k = ½ · m · v²
- Leg mass — the effective swinging mass (shank + foot for a normal kick, far more for the "augmented" end of the slider); more mass carries more momentum at the same speed.
- Swing speed at contact — foot speed the instant it strikes the target; force grows linearly with speed for a fixed contact time, since momentum is proportional to velocity.
- Contact time — how long the foot stays in contact while momentum transfers; a stiffer, shorter impact concentrates the same impulse into far higher peak force — this is why a rigid strike hurts more than a padded one carrying the same energy.
- The × baseline human kick readout compares your peak force to a typical trained kick (12 kg effective mass, 20 m/s foot speed, 8 ms contact) — the same "how far past human" framing as the 3D lab's multiplier, but produced by real inputs instead of a slider labelled ×.
Real-world relevance: this is the same impulse-momentum relationship (F = Δp/Δt) that determines strike force in martial arts, the peak load a shin guard or crash pad must absorb, and why extending stopping time (padding, follow-through) is the standard way to cut peak force without changing the energy delivered.