Wing Loading and Operating Speeds

Clean aircraft planform geometry diagram showing aspect ratio, taper ratio, wingspan, root chord, strake area, leading-edge sweep, and maximum-thickness sweep.

Clean wing diagram showing flapped area, flap geometry, hinge-line sweep, and takeoff and landing lift-coefficient increments.

Interactive lift curve

Move each control to investigate how geometry and high-lift devices change the lift-curve slope, zero-lift angle, and stall behavior. The dashed curve is the unchanged reference wing.

Selected configurationReference wing

Zero-lift angle0.0°

Lift-curve slope0.095 /deg

Stall point15.0° | 1.43

For every lifting surface

C_{L} = C_{L α} (α - α_{L = 0})

C_{L α (with strake)} = C_{L α (without strake)} \frac{S + S_{exposed strake}}{S}

C_{L α} = \frac{c_{l α}}{1 + \frac{57.3 c_{l α}}{π e AR}}

Where:

e = \frac{2}{2 - AR + \sqrt{4 + {AR}^{2} (1 + \tan^{2} Λ_{t \max})}}

C_{L} = \frac{n W}{q S} = \frac{n β}{q} (\frac{W_{TO}}{S})

C_{D} = K_{1} C_{L}^{2} + K_{2} C_{L} + C_{D 0}

D = q S {K_{1} {(\frac{n β}{q} \frac{W_{TO}}{S})}^{2} + K_{2} (\frac{n β}{q} \frac{W_{TO}}{S}) + C_{D 0}}

(\frac{T_{SL}}{W_{TO}}) = \frac{β}{α} {\frac{q S}{β W_{TO}} [K_{1} {(\frac{n β W_{TO}}{q S})}^{2} + K_{2} (\frac{n β W_{TO}}{q S}) + C_{D 0} + C_{D x}] + \frac{1}{V} \frac{d h}{d t} + \frac{1}{g} \frac{d V}{d t}}

Where is Lift?Where is C_Lmax?

It is assumed Lift = Weight, and that it can be achieved with C_L < C_Lmax.

Takeoff equation

\frac{T_{SL}}{W_{TO}} = \frac{1.44 β^{2}}{α ρ C_{L \max} g s_{TO}} (\frac{W_{TO}}{S}) + \frac{0.7 (C_{D 0} + C_{D x})}{β C_{L \max}} + μ

Landing equation

\frac{W_{TO}}{S} = \frac{s_{L} ρ C_{L \max} g μ}{1.69 β}

Wing loading, W_TO/S, links takeoff weight to the wing area available to support it. Use this lab to connect that design choice to stall, takeoff, and landing speeds.

Design response

V_Stall = √[2(W_TO/S) / (ρ C_Lmax)]

Wing loading, W_TO/S15.2lb/ft²

Stall speed, V_Stall66.9kt

Takeoff speed, V_TO80.3kt | 1.20 V_Stall

Landing speed, V_L87.0kt | 1.30 V_Stall

V_Stall (kt)W_TO/S (lb/ft²)

This wing loading resembles a typical light general-aviation trainer or touring airplane.

Interactive downwash

Adjust the wing geometry, angle of attack, and horizontal-tail position.

Wing Alpha5.0°Equal to geometric α in this model

Tail effective α2.6°Includes −2.4° wing downwash

Downwash ratio0.480δε/δα

\frac{\partial ε}{\partial α} = \frac{21 ° C_{L α}}{{AR}^{0.5}} {(\frac{c_{avg}}{l_{h}})}^{0.25} (\frac{10 - 3 λ}{7}) (1 - \frac{z_{h}}{b})