Cross-Country Ski Glide Physics (3D)

Technique

Race Controls

Kick Effort 70%

Glide Wax Quality 60%

Course Hilliness 50%

Live Readout

Speed

0.0 km/h

Slope

0.0°

Distance

0 / 420 m

Elapsed

00:00

Energy Reserve

100%

How it works

The skier moves along a 3D hill profile h(x) built from three sine harmonics (amplitude set by the hilliness slider). Every physics step (60 Hz, fixed dt) sums the real forces along the slope tangent:

slope angle   θ = atan(dh/dx)
gravity       F_g   = −m·g·sin(θ)
glide drag    F_f   = −sign(v)·μ·m·g·cos(θ)
air drag      F_d   = −sign(v)·½·ρ·Cd·A·v²
propulsion    F_p   = effort · F_max(tech) · fatigue

a = (F_g + F_f + F_d + F_p) / m
v += a·dt ;  x += v·dt

μ (glide friction) runs from 0.10 (cold wax mismatch) down to 0.02 as the wax-quality slider improves. Each technique sets its own F_max and drag area Cd·A: Classic diagonal stride trades power for a tall, upright, higher-drag posture; Skate skiing has the highest peak force but burns energy fastest; Double poling is the most metabolically efficient but weakest on steep climbs. Energy reserve E drains at a rate proportional to propulsive power output (F_p·v / efficiency) and regenerates slowly whenever effort is low; fatigue = 0.3 + 0.7·(E/100) scales the propulsive force down as you tire, so redlining early costs you on the final hill.

Speed: 0.0 km/h

Grade: 0.0%

Dist: 0 m

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