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Aerodynamics Advanced

04 Capstone: Size a Wing

Time to run the machine in reverse. Instead of computing lift from a given wing, you choose the wing: find the area from the constraint that actually binds, then audit what that choice does everywhere else. This is how real sizing works: one requirement sets the number, the rest sit in judgment on it.

Step 1 / 1

Size the wing for a two-seat light aircraft. Requirements: maximum weight W = 10800 N (about 1100 kg); stall speed no more than V_s = 25 m/s in sea-level air, ρ = 1.225 kg/m³ , with flaps delivering C_L max = 1.6 ; cruise at V = 55 m/s, sea level. Deliver: (1) the required wing area S , with working; (2) the cruise lift coefficient that area implies, and whether it is sensible; (3) a wing-loading sanity check against a comparable aircraft; (4) an aspect-ratio choice with the tradeoff argued, not asserted. State your assumptions.

Hints

Start from the constraint that binds. At the stall the wing is at C_L max and lift still equals weight, so S = 2Wρ V_s² C_L max .
Then run the lift equation forward at cruise to find the C_L the wing actually sits at. Light aircraft cruise happily around 0.3 to 0.5; far outside that band, something upstream is wrong.
Wing loading W/S is the classic cross-check: a Cessna 172 carries roughly 65 to 70 kg per square metre.
Aspect ratio: span cuts induced drag but costs spar weight and stiffness. Argue from this mission, not from a formula.