FAA Flight Instructor Airplane (FIA)Aerodynamics and Principles of FlightMedium
An airplane's wing has an area of 180 square feet and a lift coefficient (CL) of 1.2 while flying at a true airspeed of 169 ft/sec in air with a density of 0.002378 slugs/ft³ (standard sea level). Using the lift equation L = CL × 0.5ρV²S, approximately how much lift is the wing producing?
- AAbout 3,650 pounds
- BAbout 1,800 pounds
- CAbout 7,300 pounds
- DAbout 14,600 pounds
Show answer & explanationAnswer & explanation
Correct answer: C. About 7,300 pounds
Compute dynamic pressure: 0.5 × 0.002378 × (169)² = 0.5 × 0.002378 × 28,561 ≈ 33.96 lb/ft². Multiply by wing area: 33.96 × 180 ≈ 6,113 lb. Multiply by CL: 6,113 × 1.2 ≈ 7,336 lb, approximately 7,300 pounds.
Why the other options are wrong
- A. Roughly half the correct value; likely from omitting the 0.5 factor incorrectly or halving CL.
- B. Far too low; likely from using velocity instead of velocity squared.
- D. Roughly double the correct value; likely from doubling CL or forgetting the 0.5 coefficient.
Lift Equation
L = CL × 0.5ρV²S; lift depends on the lift coefficient, air density, the square of velocity, and wing area.
- Lift varies with the square of velocity
- Doubling velocity quadruples lift (all else constant)
- CL depends primarily on angle of attack
Memory trick: 'CLR-V²-S': CL times half Rho times V-squared times Surface area.