1 / A wing does not need to float to hold you up.
When water moves past the foil, pressure over its surface produces a net force. The foil also turns the water’s momentum downward. These are two descriptions of the same interaction, not competing explanations. A floating board is supported by displaced water; an airborne foilboard is supported mainly by moving-fluid lift, plus the kite’s upward pull. At zero water speed, this model produces zero hydrodynamic lift.
L = ½ ρwater Vwater² S CL(α)
D = ½ ρwater Vwater² S [CD0 + CL²/(π e AR)]
AR = span² / area
Lift is perpendicular to the incoming flow; drag is parallel to it. At the same angle, area, and coefficient, doubling water speed gives four times the lift. In level flight you instead reduce the angle as speed rises. In a bank, only the vertical component supports weight.
2 / The kite, the water, and the rider have to agree.
Vapparent = Vtrue wind − Vrider
(Lfront + Ltail) cos(bank) + Fkite,z = (mrider + mgear) g
Forward drive − total drag = 0 for steady speed
Σ pitch moments about the combined center of mass = 0 for pitch trim
The rear wing may push up or down depending on its incidence, the front wing’s downwash, and angle of attack. When it pushes down, the front wing must carry that extra load. A larger or more distant tail changes leverage and pitch-rate resistance; that does not, by itself, establish dynamic stability.
The auto-lift mode solves for angle, stopping at the assumed peak lift. It also assumes the rider banks against lateral pull. It does not silently fix your load position. The pitch cue and “Balance the pitch moment” button address that separately.
3 / What the two speed modes actually do
Hold water speed: an externally maintained test point, like a tow tank. When drive differs from drag, free motion would accelerate or decelerate; the slider deliberately holds speed. An over-lift state would climb and an under-lift state would descend. Those vertical motions are reported, not integrated.
Solve wind-driven: searches 0.5–20 m/s for a positive-speed, fully supported root where forward drive equals drag, with auto lift balance. It requires a downward-crossing force residual, less than 60° bank, no front or tail stall, and some rider load remaining. It assumes the rider is already foiling. A missing root is reported, not converted into a fictitious flight speed. Small numerical force residuals may be rounded to zero.
Minimum support speed: the first speed where the model’s maximum attached-flow lift can support the combined vertical/lateral load. It is not the minimum wind to launch, and does not verify that the kite can accelerate a board through its water-start drag.
4 / Deliberately visible simplifications
Water density is 1,025 kg/m³; air density is 1.225 kg/m³. Gear mass is adjustable. The front wing uses a finite-wing lift slope 2π / [1 + 2/(e AR)], with e = 0.82. A simple, explicitly assumed post-stall falloff replaces the linear lift curve past its maximum. Its plotted stall angle therefore changes with aspect ratio. These are not measured polars.
| Front section | CL,max | CD,0 | Zero-lift angle | CM |
|---|
| All-round | 1.20 | 0.012 | −2° | −0.035 |
| Early lift | 1.45 | 0.019 | −3° | −0.045 |
| Thin / fast | 0.90 | 0.008 | −1.5° | −0.025 |
The tail has AR 4.5, e = 0.8, CL,max = 0.95, and CD,0 = 0.012. Its effective angle is αfront + incidence − downwash, with downwash ≈ 1.6 CL/(π e AR) radians. The near-wake factor 1.6 is illustrative. The front aerodynamic center is 20 cm ahead of the mast, and the fuselage slider sets front-to-tail aerodynamic-center spacing. The combined center of mass is approximated 90 cm above the board; harness force acts 95 cm above it. Load position is a simplified combined fore/aft center of mass, not a prescription for exact foot placement.
Mast drag uses its immersed span × 0.11 m chord × CD 0.009. Fuselage drag uses an equivalent area of 0.00026 m² at 65 cm length, scaled linearly with length. Rider air drag uses CD × area = 0.45 m². If the foil cannot supply the load, board contact drag and buoyancy are not modeled; the displayed drag is then an airborne-system estimate, not total surface-riding resistance. Drawn ride height is fixed at 55% of mast length when supported and at the surface otherwise. It is not predicted altitude.
The parked-kite model converts nominal area to projected area (72% inflatable; 82% ram-air), estimates an aerodynamic resultant from apparent wind, and aligns that resultant with an assumed taut line at the selected elevation. The force component along apparent airflow equals drag. Inflatable: CL = 0.15 + 0.8 × sheet fraction, CD = 0.075 + CL²/(π × 4 × 0.8). Ram-air: CL = 0.18 + 0.9 × sheet fraction, CD = 0.05 + CL²/(π × 6 × 0.82). Sheeting is a simplified loading control: actual backstall and kite collapse are not simulated. Kite mass, line drag, loops, and wind gradients are omitted. If the requested line elevation exceeds acos(CD/√(CL²+CD²)), this parked-kite closure has no solution. The lab flags that boundary, suppresses a cruise solution, and displays a force vector clamped to the maximum feasible elevation rather than silently inventing extra force.
Incidence signs are geometric: positive means the tail’s leading edge is tilted up relative to the front-wing chord. Real brands’ “positive shim” labels can mean different things. Consult your own manufacturer rather than copying a slider value onto equipment.
The flow lines, pressure labels, force-arrow lengths, and ride height are explanatory drawings. They are not a numerical flow-field solution. The underwater view uses dimensionally scaled foil geometry; the whole-system view compresses kite-line distance. High bank, high kite unloading, and stall are flagged rather than presented as validated riding states.
5 / Sources and further reading
Sources support the governing concepts, not these specific illustrative coefficients. The numerical values above, the parked-kite closure, and the visualization are this lab’s assumptions. Model v1.0 · September 2026. The supplied X post could not be retrieved, so this is an original interactive lab, not a reproduction of its layout.