# Ski Jumping

> A 3D browser ski jumping game on six real FIS-homologated hills, each rebuilt from its own FIS
> Certificate of Jumping Hill, with a lifting-body flight model taken from published wind-tunnel
> measurements and scoring under the FIS International Ski Competition Rules.

URL: https://ski-jumping.skillsafe.ai/
Runs entirely in the browser. No account, no server call, no model, no cost. WebGL2 required.

## What it is

An independent reimplementation of ski jumping. Not affiliated with FIS.

The subject of the app is aerodynamics. A ski jumper and their skis are one aerofoil, and the
distance is produced by lift under the pilot's continuous control rather than by a release
condition. The player controls the take-off timing, then the angle of attack, the ski opening angle
and the body-to-ski angle through the flight, then the telemark.

## The hills, from their certificates

| Hill | Place | HS | K | FIS certificate |
| --- | --- | --- | --- | --- |
| Horecky HS106 | Frenstat pod Radhostem, CZE | 106 | 95 | 380 / CZE 1 |
| Toni-Seelos-Schanze HS109 | Seefeld, AUT | 109 | 99 | 3 / AUT 3 |
| Holmenkollbakken HS134 | Oslo, NOR | 134 | 120 | 86 / NOR 1 |
| Schattenberg HS137 | Oberstdorf, GER | 137 | 120 | 149 / GER 19 |
| Lysgardsbakken HS140 | Lillehammer, NOR | 140 | 123 | 303 / NOR 43 |
| Vikersundbakken HS240 | Vikersund, NOR | 240 | 200 | FLY IV / NOR |

## The model

Forces are lift and drag AREAS in square metres, the form the literature uses:
lift = 0.5 rho v^2 lA, drag = 0.5 rho v^2 dA. The app flies
lA(alpha) = 1.7073 sin(alpha) cos(alpha) and dA(alpha) = 0.1091 + 1.7340 sin^2(alpha), whose three
constants are least-squares fitted in code to Walter Mueller's three measured angles of attack
(CERN-2006-014). The fit is within 0.50% on lift and 0.12% on drag. Fed the mean Olympic flight
position and compared with Mueller's own reference-jump force history - data the fit never saw -
the model is within 7.8% on lift and 4.8% on drag.

## Sources

- FIS ICR Book III, edition June 2026: Art. 411 (hill construction), 415.1 (distance measured along
  the slope), 430-433 (scoring), 443 (the two rounds), 454.4.4 (ski flying).
- FIS Style Judging Guidelines, 2024-06-15: the three deduction groups and their caps.
- FIS Jumping Hills Construction Norm 2018 (Gasser) and his 2008 mathematical companion.
- Mueller (CERN-2006-014); Ryu, Cho & Cho (Trans. JSASS 58(4), 2015); Virmavirta et al.
  (Front. Sports Act. Living 7, 2025); Uhlar & Janura (Acta Gymnica 39(3), 2009).

Full source list with article numbers, and every reconstructed figure, in
https://ski-jumping.skillsafe.ai/CREDITS.txt

## Honest limits

The aerofoil's peak lift-to-drag ratio of 1.90 at 13.7 degrees of angle of attack is an
extrapolation about 30% above the CFD literature's 1.457. Its ski-opening turnover near 47 degrees
is above the 20 to 30 degrees reported. Ski roll, in-flight instability, crosswind, the suit and
BMI equipment rules and the team event are not simulated. All of this is recorded in CREDITS.txt.