Ready Speed 0 km/h Distance 0 m Above hill 0 m Time 0.0 s FPS 0
Solid jumper: current jump. Translucent jumper and orange curve: previous jump (ghost). Cyan curve: predicted path for the current settings. Arrows (optional): blue velocity, green lift, red drag, white weight. Red line on the hill: K-point; blue line: hill size HS. Drag to orbit, wheel or pinch to zoom.
Jump! Reset Slow-mo: off
Ski Jump Flight Lab
A point-mass ski jumper: curved in-run with friction and drag, take-off, then flight with quadratic drag and lift down to a landing hill. Virtual model with illustrative aerodynamics: no rotation, no real hill homologation.
Jump! Force arrows: off Ghost: on Quality: High
Overview Follow jumper Take-off Landing zone
In-run (gate to take-off edge)
Take-off
Flight
Air and gravity Sea level, 15 C (1.225 kg/m3) High altitude, about 3000 m (0.909 kg/m3) No air, Earth gravity Moon-like: no air, g = 1.62 m/s2
Landing hill
Live readouts (current settings)
Height against distance Speed against time Lift and drag in flight Missions
Mission 5: predict the body pitch angle (degrees) that gives the longest jump with the current settings Check
Hint: lift grows with the angle but so does drag. Run the sweep below to see the measured optimum.
Experiment: which pitch angle maximises distance?
Headless: repeats the whole jump (same in-run speed, same take-off) for pitch 0 to 60 degrees in 2.5 degree steps, refines the maximum with a parabola through the three best points, and cross-checks it with an independent golden-section search. Distance is measured on the hill, so the curve has a kink where the path crosses from the steep hill onto the flatter transition.
Sweep body pitch
Independent numerical checks
Controls Sliders change the prediction at once (cyan curve, readouts and graphs). Press Jump to watch the jump: in-run, take-off, flight, landing. The previous jump stays as a ghost. Drag or one finger: orbit; wheel or pinch: zoom. Space on the focused scene: jump; R: reset. Headwind is positive (air moves against the direction of travel), tailwind negative. Take-off angle is the angle of the velocity just after the edge, measured from the horizontal. The jumper pops up relative to the table: the implied pop speed is shown in the readouts. The science
In-run. Along the track (arc length s, heading angle φ below the horizontal) Newton's law gives m dv/dt = m g sinφ − μ N − ½ ρ (Cd A)in vr |vr | with N = m (g cosφ + v²/R) on the concave transition of radius R = 80 m and air speed vr = v + w cosφ (w > 0 is a headwind). The crouched drag area (Cd A)in = 0.18 m² and the friction range μ = 0 to 0.08 are typical order-of-magnitude values, not measurements. The track is a 35° straight, the transition, and a 6 m table inclined 10° down. Without friction and drag, energy conservation gives v = √(2 g h), where h is the gate height above the edge.
Take-off. The take-off speed is the in-run speed plus the trim. The flight-path angle γ0 is set directly; the pop speed relative to the table is v sin(γ0 + 10°). Jumper and skis are one point mass of 70 kg (typical, equipment included).
Flight. With relative air velocity v r = (vx + w, vy ): m dv /dt = mg − ½ρ Cd A |vr | v r + ½ρ Cl A |vr | R90 v r , where R90 turns a vector by +90° (lift is perpendicular to the air flow). The coefficients are illustrative, not wind-tunnel data: with body-ski angle of attack α, Cd = 0.30 + 1.05 sin²α, Cl = 1.2 sin 2α, reference area A = 0.65 m². They reproduce the qualitative trade-off (lift rises then falls, drag keeps rising) and a jump of a believable length, nothing more. The angle α is held constant; there is no pitching moment, no rotation and no ski-body interference.
Terminal speed. For a body falling with drag only, vt = √(2 m g / (ρ Cd A)); the check table compares the integrator with this and with v = vt tanh(g t / vt ).
Numerics. Fixed-step classical RK4 (flight 1/480 s, in-run 1/500 s). The landing instant is found by bisection on the sub-step where the height above the hill changes sign. The page shows the independent checks: drag-free flight against the closed-form parabola, frictionless in-run against √(2gh), terminal velocity, and the landing root find against a separate brute-force integrator.
Landing hill. A simplified FIS-style profile: convex knoll (slope grows from 11° to 35°), a straight 35° section, a concave circular transition starting at the K-point, then a flat outrun. The K-point is the point at chord distance K from the edge. Jump distance is the straight chord from the edge to the landing point (the real rule measures along the slope). The hill-size line HS = 1.16 K uses a typical ratio and is only a marker. This is not a homologated hill. The normal impact speed is the velocity component perpendicular to the surface; the equivalent drop height is vn ²/2g; a concave transition makes it small.
Simplifications. Point mass, uniform steady wind, constant air density, no snow resistance on landing, distance points are not computed. Assets built with Blender; scene by Three.js.