FoilVision · Biomechanics Module

Fencing Lunge — Joint Impact Force Simulator

A classical-mechanics model of the ground reaction force and the load transmitted to the knee and ankle when the front foot lands in a lunge. Tune the athlete and the technique, watch the figure and force vectors respond, and explore what drives injury risk — impulse–momentum and Newton's laws only, no deep learning.

Presets:

Lunge & force vectors

Front-knee bend tracks lunge depth; stride tracks speed. Arrows show force magnitude at each joint.

GRF Knee Ankle

Parameters

Everything updates live.

Body mass

40120 kg

Fencer height

150200 cm

Lunge speed (forward velocity at landing)

slow · 1 m/sexplosive · 5 m/s

Lunge depth (center-of-mass drop)

shallow · 5 cmdeep · 45 cm

Landing technique (base contact time)

stiff · 20 mssoft · 150 ms

Foot strike angle

flatheel-first 40°

Braking fraction f

glidehard brake

Surface

Impact pulse shape Sets k = peak ÷ average force — see “What is the pulse factor k?” below.

Estimated impact loads

Peak values during landing.

Peak ground reaction force

×BW

Knee joint force

×BW

Ankle joint force

×BW

Knee flexion at landing

effective contact

Velocity arrested (Δv)

m/s

forward + vertical

Landing impulse (J = m·Δv)

N·s

momentum removed

Knee impact risk (illustrative)

A qualitative band based on peak knee load in body-weights — for comparing techniques, not diagnosis.

08×BW16×BW24×BW+

Vary one parameter; all others stay at current values. Dashed line = now.

Sweep:

Ground reaction (×BW) Knee (×BW) Ankle (×BW)

Body-segment masses

From your body mass using standard anthropometric fractions (Winter). These weight the joint-load model.

Segment	% of body mass	Mass

The physics

Vertical landing speed from the COM drop h, boosted slightly by a steeper foot strike:

v_vert = √(2 g h) · (1 + 0.2 sin φ)

Velocity the front leg arrests (braked forward + vertical):

Δv = √( (f · v_fwd)² + v_vert² )

Effective contact time (surface & strike), then force (impulse–momentum + Newton II):

Δt_eff = Δt · s · (1 − 0.25 sin φ) F_avg = m Δv / Δt_eff + m g F_peak = k · F_avg

Joint loads — knee amplified by flexion, ankle ≈ full GRF:

F_knee = F_peak · (1 + 0.9(1 − cos θ)) F_ankle = F_peak · (1 − m_foot/m)

What is the pulse factor k?

When the foot lands, the ground reaction force is not constant — it climbs from zero, peaks, and falls back to zero over the contact time Δt. That curve is the impact pulse. Two facts about it matter:

The area under the curve is fixed by physics — it equals the impulse, the momentum the leg removes (J = m·Δv plus the weight term). You can't change it for a given landing.
But for the same area, a spikier curve reaches a higher peak — and it's the peak force, not the average, that stresses the joint.

k is the ratio that captures this — the peak force divided by the average force:

k = F_peak / F_avg ⟹ F_peak = k · F_avg where F_avg = m·Δv/Δt_eff + m·g

You don't choose k freely — it is derived from the pulse shape. The average force is the area under F(t) divided by Δt, so each geometry fixes its own peak-to-average ratio:

Pulse shape	Force over time F(t)	Average force	k = peak / avg
Rectangular	constant = F_peak	F_peak	1.00
Half-sine	F_peak·sin(π·t/Δt)	(2/π)·F_peak	π/2 ≈ 1.57
Triangular	up to F_peak at Δt/2, then down	½·F_peak	2.00

How each value comes out: for a rectangle the average is the peak, so k = 1. For a half-sine bump the mean height is 2/π of the peak, so k = π/2 ≈ 1.57. For a symmetric triangle the mean is exactly half the peak, so k = 2. Take-away: same impulse, spikier pulse → higher peak joint load — which is why a smoother, more absorbed landing lowers force without changing the athlete's speed or mass. Watch the Force–time pulse tab: its shaded area stays equal to the impulse while the peak rises and falls with k.

Model & assumptions

g = 9.81 m/s²; body weight BW = m·g. Peak factor k = peak force / average force is set by the impact pulse shape so the area under F(t) equals the impulse (rectangular 1.00, half-sine π/2 ≈ 1.57, triangular 2.00). A spikier pulse means a higher peak for the same landing.
Braking fraction f is how much forward momentum the front leg arrests on contact — the rest carries the body through the lunge.
Foot strike angle φ steepens the impact: it nudges vertical velocity up and shortens effective contact time (a heel-first landing is sharper than a flat one).
Surface multiplies contact time (a soft mat lengthens the deceleration, lowering peak force).
Knee amplification 1 + 0.9(1 − cos θ) reflects quadriceps/patellar load rising with knee flexion; θ maps from lunge depth (≈30° shallow → ≈110° deep). Ankle sees essentially the full ground reaction force.
Single rigid point-mass impact — no soft tissue, muscle co-contraction dynamics, or multi-segment inverse dynamics. Trends are reliable; absolute numbers are estimates.

Educational estimate, not a clinical measurement. This simplified classical-mechanics model shows how lunge parameters influence joint impact loads. The qualitative trends — stiffer, faster, deeper, sharper landings raise joint force; softer surfaces and longer contact times lower it — are robust. Absolute values are approximate; a validated study would use force plates and multi-segment inverse dynamics.