WingHopper · Designer · Guide · Sections · Reef · Methods · Pricing · FAQ
Every calculation in Winghopper, with its assumptions and limits stated. The honest summary up front: these are design-stage models, validated against classical references, not certified engineering. Verify with a qualified engineer before anyone rides what you build.
Straight from the lift equation, V = sqrt(2W / (rho * S * CL)), with your all-up weight W, the integrated planform area S, and preset lift coefficients: CL 0.8 for takeoff/pump, 0.5 for cruise, 0.3 for fast. Those presets match how the foil community actually rides (back-computed from typical rider weights, areas, and speeds). Fluid density and viscosity come from the selected fluid preset (seawater 15 C: rho 1025 kg/m3). Reynolds number is computed on the mean aerodynamic chord at the cruise speed. This is arithmetic on the geometry, not a flow simulation.
Area is integrated from the actual LE/TE curves plus the rounded tip cap (a root-to-tip trapezoid under-reads curved planforms by several percent). MAC uses the standard definition, the integral of c-squared over the integral of c. Wetted area integrates real section ring perimeters spanwise by trapezoid, tip cap included. The pitching-moment reference point is the chord-weighted mean quarter-chord (Etkin, Dynamics of Flight, Appendix C), which is the aerodynamic center to first order for swept and unswept planforms alike.
The fast LLT solver samples the same span, rounded tip reach, interior twist curve and blended section camber as VLM. Section zero-lift angles use thin-airfoil integration of the sampled camber line. A Fourier lifting-line solve provides lift and induced drag. This is a planar, attached-flow approximation: it does not solve swept or nonplanar aerodynamic interactions, stall, viscous separation or free-surface effects. Changes to manufacturing settings do not change this wing model.
A classical VLM (Katz and Plotkin formulation): the camber surface of your actual blended sections is paneled chordwise and spanwise, each panel carrying a horseshoe vortex with the bound leg at the panel quarter-chord and the control point at three-quarter chord. The wake trails straight along the freestream. Twist and dihedral are baked into panel normals; angle of attack tilts the freestream. Forces come from near-field Kutta-Joukowski on the local velocity; the pitching moment is taken nose-up positive about the quarter-MAC; induced angle of attack uses the trailing (wake) system only, which is the lifting-line definition.
Validation, run continuously: three planforms against an exact Glauert lifting-line solution (64 Fourier modes), plus six exact invariants (zero lift for a symmetric wing at zero alpha, antisymmetry in alpha, even positive induced drag, nose-down moment for a cambered section matching thin-airfoil theory, and moment independence from lift about the quarter-MAC on unswept and swept planforms). Current accuracy: CL within about 2.5 to 4.6 percent of exact LLT (VLM reads low, the expected lifting-surface direction), induced drag 8 to 11 percent low (a known property of near-field force integration; a Trefftz-plane evaluation would tighten it). Mesh convergence spread is under 0.7 percent.
Not modeled: viscous/profile drag (the polars shown for 2D sections come from foil.tools data instead), stall, free-surface effects, ventilation, and cavitation. Potential flow only. Displayed lift-to-drag figures (best glide, the L/D polars, the glide score) do add a fixed 0.009 section-drag allowance to the induced drag. Without it, L/D diverges as CL approaches zero; with it, the peak lands where real foils live.
The three 0–10 bars are normalised reads of the polar, not measured ride data. They exist to separate one shape from another, so each is scaled against a value the solver can reach but rarely does.
Pump is lift-to-drag at the lift-off CL. Pumping is fighting drag to make the lift that carries you at low speed, so the efficiency that counts is the one at the top of the polar, not the peak L/D you cruise at. A wing can glide well and still pump poorly if its best L/D sits at a CL you never ride. Carve is an agility proxy, linear in aspect ratio: AR 4 (a dedicated surf wing) reads 10 and AR 15 reads 0. Sweep belongs in this number too and is not in it yet. Glide is peak L/D.
The fixed bands were calibrated on 846 shapes before the LLT geometry and equation correction: L/D at lift-off from 10 to 29, peak L/D from 20 to 36, aspect ratio from 4 to 15. VLM is unchanged. The corrected LLT uses these same comparison bands; the earlier saturation statistics do not establish its current coverage. The L/D figures are potential flow plus a fixed section-drag allowance, with no mast, fuselage or real profile drag, so they run higher than a real foil’s; the scores compare shapes inside this model.
Treat them as a ranking between your own shapes, not as absolute numbers to compare against a manufacturer’s spec sheet.
The stab is solved as its own VLM lifting surface at two angles, fit as a local lift line (so an inverted cambered stab carries its real zero-lift angle). Downwash at the stab is sampled from the main wing’s induced-velocity field at the stab quarter-chord, averaged across its span. The moment balance about your CG is closed for the required stab lift; induced drag at trim uses a parabolic polar (CDi = k * CL^2) fitted through the two solves. Assumes rigid geometry, no free-surface interaction between surfaces.
Load case: design load equals the load factor (default 3.5) times all-up weight, all carried by the front wing, distributed elliptically along the span. That puts the root bending moment at halfLoad times 4/(3 pi) times the half-span. The 3.5 factor sits in the aerospace band (2.5 limit times 1.5) and under the marine composites fatigue factor of 4. Sandwich construction assumes skins carry all bending with structural depth 0.85 times section thickness and an effective flange half the chord wide; solid construction uses the exact integrated section (see below). Deflection is Euler-Bernoulli cantilever integration of M/EI along the span.
Material allowables are deliberately heavy-knockdown design values, not ultimates (woven carbon wet layup 150 MPa against roughly 600 ultimate; aluminum 6061-T6 at 60 MPa because salt-water corrosion fatigue, not yield, governs and 6061 has no endurance limit; PVC 80 core shear at 0.475 MPa for peak load and 0.314 MPa at high cycles, both taken off the same 0.95 MPa minimum datasheet value rather than multiplied together, because peak load and fatigue are alternative governing cases and stacking their factors fails every sane foil). Modeled: spanwise bending against a vortex-lattice load distribution; core shear along the whole span, on a peak-load basis and a high-cycle fatigue basis; tip flex; torsion about a solved shear centre; skin wrinkling into the core; and torsional divergence. Not modeled: slam and impact loads, skin fatigue counting, bondlines, and joints other than the root bolt line. Real wings fail at the fuselage joint and from slam more often than in spanwise bending; reinforce the joint locally and treat the bending check as necessary, not sufficient.
The mount check integrates your actual root section geometry in chordwise slices for area, centroid, and second moment about the true neutral axis, then removes vertical bolt-hole strips and re-solves the neutral axis for the net section. Stress is the root moment over the net section modulus. The open-hole stress concentration (Kt of about 3) is reported separately rather than hidden in the margin: metals redistribute at the peak, composites are notch-sensitive. The integration is verified against closed-form rectangle and ellipse sections and an independent polygon (Green’s theorem) method, agreeing to 0.002 percent. Hole positions are defaults; match your fuselage.
Ply outlines come from unfolding the triangulated surface to the flat; the in-plane shear demand at each point is the difference between the flat and true corner angles. Thresholds shown: woven cloth shears comfortably to about 15 degrees and locks around 30 to 40 degrees (tight plain weaves closer to 20); UD tape effectively cannot shear. These track published forming-limit measurements for woven composites.
The operating band is the Ride tab’s arithmetic; the structural floor is the conservative root-bending model above. The thickness-to-chord goal bands track shipping foil practice; manufacturers rarely publish camber, so the camber bands are our recommended starting range, stated as such. Catalog polars come from foil.tools (XFOIL-class 2D data).
When a model changes, the validation harness has to pass first (the three LLT cases and six invariants above), and the change is logged. Found a number that looks wrong? Use the feedback widget; wrong numbers get fixed at the source, never papered over.