Ski Carving Radius

How tight does a ski really turn? Set the sidecut, tilt the ski on its edge and watch it bend into a carved turn that is tighter than the radius printed on the ski.

Carved turn radius – R = R_sidecut · cos θ
Sidecut radius – ≈ L² / 8d
Sidecut depth – d
Ski deflection – h = d · tan θ
Bend radius – R_sidecut / tan θ

Turn seen from above

Sidecut circle (ski flat) Carved circle (ski on edge)

Ski geometry

Contact length is the running edge between the widest points – roughly 85–90 % of the ski length. The ski width is drawn 1.7 times exaggerated.

1. Sidecut

Tip, waist and tail define the curve of the edge. Its depth d is how far the waist sits behind the straight line from tip to tail:

d = (W_tip + W_tail − 2 · W_waist) / 4

The circle through these three points is the sidecut radius printed on the ski:

R_sidecut ≈ L² / (8 · d)

2. Edge angle

Tip & tail Waist Waist, bent Deflection h

Tilted by θ, the ski only touches the snow at tip and tail – the waist hangs in the air. Your weight bends the ski until the whole edge is on the snow:

h = d · tan θ

More edge angle means more bend. That is why a soft ski is easy to carve and a stiff one needs speed and pressure.

3. Carved radius

On the snow the edge now leaves a deeper arc, d / cos θ instead of d, and so a tighter circle:

R = R_sidecut · cos θ

At 60° the turn is half as wide as the sidecut radius. An idealised model: hard snow, no skidding. GeoGebra file for geogebra.org.