Wing foil sizing calculator
What this calculates: board volume, wing area, and foil area for wing foiling, from a single integrated model spanning the float, wing-in-air, and foil-in-water regimes.
What it assumes: steady-state cruise, a 3–8 m² practical wing inventory, and rider weight/wind/skill as the only free inputs.
What it ignores: gusts, chop, and manoeuvring loads.
Full derivation and worked physics: Wing foil sizing from first principles.
Inputs
Required wing force
The wing only has to supply 193 N, or 21% of body-plus-gear weight. The foil carries the rest.
Apparent wind (beam reach)
§1 Float (Archimedes)
| Quantity | Value | Note |
|---|---|---|
| Total mass (rider + gear) | 95 kg | Rider + 8 kg gear |
| Weight to support | 932 N | m·g |
| Board volume range | 97–107 L | Buoyancy margin scales with skill |
§2 Foil in water
| Quantity | Value | Note |
|---|---|---|
| Foil feasible band | 430–2020 cm² | Solved frontier: small foil (race) → wing-floored (easy) |
| Chord | 7.3 cm | recommended foil, at AR 8 |
| Release speed | 6.5 m/s (13 kn) | Solver output, not an input |
| Slowest flight | 5.5 m/s | recommended foil, at CL_max |
| Cruise speed | 9.1 m/s | At max-L/D CL = 0.51 (solved for AR 8) |
| Cruise L/D | 21.1 | At the max-L/D cruise point |
| Foil Reynolds | 0.56×10⁶ | Chord-based, at cruise |
§3 Required wing force
| Quantity | Value | Note |
|---|---|---|
| Hull drag (F_hull) | 91 N | Planing board at the hump |
| Foil drag (F_foil) | 55 N | Induced + profile at the hump |
| Acceleration (F_accel) | 48 N | A_TARGET reserve, m·0.5 m/s² |
| Drive needed (F_req) | 193 N | at the takeoff hump (21% of weight) |
§4 Wing in air
| Quantity | Value | Note |
|---|---|---|
| Wing (recommended) | 4.26 m² | For the smallest feasible foil |
| Wing feasible band | 3.3–4.3 m² | Solved frontier: small foil → big foil |
| Solver | converged | hump @ 6.5 m/s |
| Min wind | 7.9 kn | Least true wind, solved (within inventory) |
§5 Apparent wind
| Quantity | Value | Note |
|---|---|---|
| True wind | 7.7 m/s | 15 kn |
| Boat (cruise) speed | 9.1 m/s | Foil cruise |
| Apparent wind | 12.0 m/s | 40° off the bow |
Honest limits
• Empirical drag and lift coefficients are calibrated against limited real-world data, not wind-tunnel validated for every foil/wing combination
• Surface-proximity effects on foil lift are extrapolated below h/c = 0.5, where the underlying model becomes unreliable
• The solver assumes a steady-state cruise condition; gusts, chop, and manoeuvring loads are not modelled
• Recommended sizes are clamped to a practical 3-8 m² wing inventory - the true optimum may fall outside that range
• Results are a sizing guide, not a substitute for a fitting session with real gear
How it works
A wing foiler passes through three physical regimes on every run — floating on the board's buoyancy, flying the wing to accelerate across the water, then flying the foil once enough lift builds up. The calculator solves for the smallest feasible foil and its matching wing across that whole envelope, decomposing the required wing force into hull drag, foil drag, and an acceleration reserve. See the full postfor every equation and the calibration story behind it.