Wing Planform Designer — Aspect Ratio, Sweep & Induced Drag

Wing Planform

Wingspan 10.0 m

Root chord 1.8 m

Taper ratio (tip/root) 0.50

Leading-edge sweep 5°

Angle of attack α 6.0°

Presets

Wing Metrics

Aspect ratio AR

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Wing area S

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Oswald efficiency e

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Lift coeff. C_L

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Induced drag C_Di

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Lift / drag L/D

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How it works

A finite wing's lift-curve slope is reduced from the ideal 2D value by three-dimensional flow spilling around the wingtips (Prandtl lifting-line theory):

C_L,alpha = a0 / (1 + a0 / (pi * AR * e))    [a0 = 2*pi per radian, thin airfoil]
C_L       = C_L,alpha * alpha   (alpha in radians, zero-lift angle = 0)
C_Di      = C_L^2 / (pi * AR * e)            [induced drag]
L/D       = C_L / (C_D0 + C_Di)              [C_D0 ~= 0.02 fixed parasite drag]

The Oswald efficiency factor e captures how far a real planform's span-load falls short of the ideal elliptical distribution (e = 1). This sim uses Raymer's design-chart approximation:

Straight wing:  e = 1.78*(1 - 0.045*AR^0.68) - 0.64
Swept wing:     e = 4.61*(1 - 0.045*AR^0.68)*cos(sweep_LE)^0.15 - 3.1

Aspect ratio (AR = b²/S) — a long, slender wing (glider) has less induced drag than a short, stubby one (fighter) for the same lift, because tip vortices are relatively weaker.
Taper & sweep — a linearly tapered planform never matches the true ellipse exactly (that costs a few points of e); sweep trades efficiency for high-speed compressibility margin and structural reach.
Wingtip vortices — high pressure under the wing spills around the tip into the low pressure above it, rolling up into the trailing vortex pair you see streaming downstream. That rotational energy is exactly the induced-drag penalty.
Past the stall angle the flow separates and this simplified model rolls C_L back down — real stall behaviour depends on airfoil and Reynolds number, this is illustrative only.

⚠ STALLED

Local lift (span load) Wingtip vortex

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