Tool · Wing and tail geometry

Wing Planform Designer

The whole module on one page: describe the wing's planform, its airfoil and its cruise condition, and see it drawn to scale with its tails, its mean aerodynamic chord, its lift-curve slope, its cruise lift coefficient, the drag-divergence Mach number its thickness allows, where it stalls first, and the dihedral the guidelines suggest. Every number is shown, so you can check each one by hand.

Inputs

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Result

Figure T.1 The wing (blue) and horizontal tail (violet) to scale, nose up, on a grid of 1 m (or 5 m for large aircraft). The dashed lines are the quarter chords; the thick lines are the mean aerodynamic chords, with the aerodynamic centers marked. The horizontal tail is placed at the tail arm behind the wing's aerodynamic center.

Figure T.2 Span loading from Schrenk's approximation (blue) against the elliptic ideal (gray dashed), and the local lift coefficient as a fraction of the wing's (orange), for the planform without its sweep and twist. The dot marks where the stall starts.

Geometry
Quantity	Formula	Value

Airfoil and cruise
Quantity	Formula	Value

Dihedral and tails
Quantity	Formula	Value

How it is calculated

Planform (Lesson 6): \(b = \sqrt{AS}\), \(c_r = 2S/[b(1 + \lambda)]\), \(\bar c = \tfrac23c_r(1 + \lambda + \lambda^2)/(1 + \lambda)\), \(\bar y = (b/6)(1 + 2\lambda)/(1 + \lambda)\), and sweep at any chord line from the quarter-chord sweep.
Lift-curve slope (Lesson 4): Helmbold's formula with \(\eta = 0.95\), the sweep of the 30% chord line, at low speed and at the cruise Mach number.
Cruise (Lesson 3): \(C_L = W/(\tfrac12\gamma pM^2S)\) in the standard atmosphere; the Reynolds number on the MAC (Lesson 2); \(\MDD\) from the Korn equation with the mid-chord sweep and the thickness at the MAC, interpolated between root and tip.
Airfoil (Lessons 1 and 2): thin-airfoil theory for the NACA four-digit camber line gives \(\alpha_{L0}\) and the ideal \(c_l\); the incidence is \(\alpha_{L0} + C_L/\CLa\) (Lesson 7).
Span loading (Lesson 6): Schrenk's approximation for the untwisted, unswept planform. Dihedral (Lesson 7) and tail volume coefficients (Lesson 8) from the guideline tables; the tails use the middle of the tail aspect-ratio range for the class.

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