I'm writing a little piece of code for preliminary design that can calculate the ideal wing area for a given load, cruise speed and aspect ratio or span. It seemingly works well on the A380 data:
# A380 CONSTRAINS Load: 475000 Cruise Speed: 907.48 Span: 80 Aspect Ratio: 7.5
GEOMETRY Airfoil Lift Coef: 0.20400000000006546 Total Mass: 613525.1510617425 Lift Area: 851.9381984117002 m² # <--- perfect Average Chord: 10.666666666666666 m
However, I have a little issue relating to the attack angle with small airplanes:
# Cessna CONSTRAINS Load: 1157 Cruise Speed: 226 Span: 16 Aspect Ratio: 7.3 ERROR: Lift Coefficient was re-adjusted: 0.8950000000000661 GEOMETRY Airfoil Lift Coef: 0.8950000000000661 Total Mass: 6796.908900200735 Lift Area: 34.68578659410046 m² # <-- wrong supposed to be 16 Average Chord: 2.191780821917808 m # <-- wrong
Now, we know the Cessna has a large attack angle, which increases the Lift coefficient to 1 and enables short distance takeoff capabilities at the cost of thrust. This incidentally reduces the Lift Area to 16m².
However, the same happens with the Piaggio and there is no explanation there.
My question is: How is the lift_coef and attack_angle chosen? There seems to be loads of variables at play.
Is it because the average chord is higher than what the wing can handle structurally?