Loading Aircraft…
A wing on its own answers what one surface does. An aircraft is a moment balance: the weight at the CG, lift on every surface at its own arm, the drag of everything in the flow, and a thrust that closes the sum. This page draws that balance as a free-body diagram in the x–z plane and solves it, for a hydrofoil with the rider a metre above the foils as readily as for a light aircraft.
Two equations in two unknowns: lift equals weight, and the moment about the CG is zero. The unknowns are the body angle of attack and the stabiliser incidence (the CG-for-a-fixed-tail inverse is in the connector tool and comes to this page next). The moment sum is (z − z_cg)·F_x − (x − x_cg)·F_z for every force, pitch-up positive, so a CG well above or below the wing is first order: the lift's body-axis component times that height scales with the lift coefficient and bites at low speed. Each row reports its residuals, and a speed the craft cannot fly is refused with a reason rather than trimmed silently.
All surfaces are meshed into one lifting line with the wake aligned to the flow, so the stabiliser flies in the main wing's downwash rather than in free air. That matters: on a Cessna-class layout a stabiliser adds barely half the lift in situ that it adds alone, and a strip-theory method that sums surfaces independently reports the craft a quarter more stable than it is, in the dangerous direction. Sections are viscous through NeuralFoil; drag is the Glauert induced term plus the section profile drag. Trim angles agree with the single-wing analysis on this site within half a degree at the same lift.
The neutral point is found by a central finite difference of the pitching moment about the trim point and cross-checked against the library's own stability derivatives; the difference is shown in millimetres. The static margin is that point's distance aft of the CG as a fraction of the main wing's mean aerodynamic chord. It is the wing-plus-tail figure: a fuselage is destabilising and moves the neutral point forward by roughly 0.05–0.10 chords on aircraft, and on a hydrofoil the rider is the controller, so the margin is reported as computed with no verdict attached.
Non-lifting parts enter as drag elements with a height: a mast or strut is a section solved at its own Reynolds number, drag q·c·L·Cd along the flow; a board, pod or fuselage is a drag area CD·A. Each adds a moment through its height above or below the CG and adds to the thrust the balance demands, but not to the pitch stiffness, so the static margin is unchanged by them. The free surface, cavitation and a mast's own side force are not modelled.
The tail-volume card from the wing designer is evaluated for the same geometry and shown beside the solve: the tail volume coefficient, a momentum-theory downwash and a stick-fixed neutral point from four numbers. It has no z-arm and no downwash solution, which is exactly what the solve adds. Building the craft and reading the estimate are free; a solve is 2 credits at one speed or 3 across a range, with no free monthly allowance.
Balance a whole craft in the x–z plane: lift, weight, drag and thrust, and how stable the balance is. Pick the wings, set the CG, solve.
Freeride wing template, a 150 cm² stabiliser on a 700 mm arm, an 80 kg rider a metre up on a 900 mm mast. Replace the surfaces with your saved designs.
x is 30% of the front wing MAC. Both directions matter: the z-arm is first order when the CG sits well above or below the wing.
Momentum-theory downwash, no z-arm, no fuselage or mast. The same card as on /wing; the solve on the right replaces it.
Both surfaces are solved together on a lifting line with the wake following the flow, so the stabiliser sees the front wing's downwash. Section drag is viscous; the mast is a 2D section at its own Reynolds number. Cavitation, the free surface and the mast's own lift are not modelled.
Solve to get the trim angle, the stabiliser setting that balances the moment, the load on every surface, the thrust the x-balance demands and the static margin.
Building the craft and the estimate are free. The solve is 2 credits for one speed, 3 for a sweep.