Which quantity is directly proportional to the weight of the aircraft and inversely proportional to the wingspan and speed?

Which quantity is directly proportional to the weight of the aircraft and inversely proportional to the wingspan and speed?

• A. Lift
• B. Drag
• C. Vorticity strength
• D. Moment

Answer: (C)

Circulation around the wing, i.e., the vorticity strength, is the quantity that matches that set of proportionalities. In the lift theory for a wing, the lift per unit span is given by the Kutta–Joukowski relation L' = ρ V Γ, where Γ is the circulation (a measure of vorticity). For a whole aircraft, the lift needed to balance weight is roughly the weight, and the lift per span is about W divided by the wingspan b. Equating L' = ρ V Γ with L' ≈ W/b gives Γ ≈ (W/b) / (ρ V) = W / (ρ V b). This shows that circulation grows with weight and decreases with both speed and wingspan. The other quantities don’t exhibit this exact combination: lift scales with dynamic pressure and area, drag depends on speed and shape, and moment depends on weight times lever arm, not directly on these inverse relationships.

Circulation around the wing, i.e., the vorticity strength, is the quantity that matches that set of proportionalities. In the lift theory for a wing, the lift per unit span is given by the Kutta–Joukowski relation L' = ρ V Γ, where Γ is the circulation (a measure of vorticity). For a whole aircraft, the lift needed to balance weight is roughly the weight, and the lift per span is about W divided by the wingspan b. Equating L' = ρ V Γ with L' ≈ W/b gives Γ ≈ (W/b) / (ρ V) = W / (ρ V b). This shows that circulation grows with weight and decreases with both speed and wingspan. The other quantities don’t exhibit this exact combination: lift scales with dynamic pressure and area, drag depends on speed and shape, and moment depends on weight times lever arm, not directly on these inverse relationships.