Aircraft performance relationships: which of the following statements are correct regarding landing speed and take-off distance when expressed in terms of wing loading and power loading?

Introduction / Context:Basic aircraft sizing uses wing loading (W/S) and power loading (W/P) to frame performance. Landing speed scales with the square root of wing loading for a given maximum lift coefficient, while take-off distance lengthens as available power per unit weight decreases (i.e., as W/P increases).

Given Data / Assumptions:

• Wing loading W/S and power loading W/P are the key parameters.
• CL_max and atmospheric conditions held comparable between cases.

Concept / Approach:For landing approach, V_land ∝ sqrt(W/(S * CL_max)), so higher W/S implies a higher required speed (statement a). For take-off, distance S_TO ∝ f(W/P, W/S, CL, drag); holding W/S constant, S_TO grows as W/P increases (less power per unit weight), making statement (b) directionally correct.

Step-by-Step Solution:Relate landing speed to wing loading through lift equilibrium at CL_max.Recognize that increased wing loading raises stall/landing speed.For take-off, fix W/S; lower specific power (higher W/P) lengthens ground run → distance increases with W/P.Therefore, both statements are valid.

Verification / Alternative check:Preliminary design charts show families of constant W/S and W/P curves; performance trends align with the above relations across typical general-aviation and transport-class aircraft.

Why Other Options Are Wrong:

• (c) and other single-choice options ignore one of the true relationships.

Common Pitfalls:

• Confusing “directly proportional” with “directionally increasing”; the exact proportionality involves square roots and additional coefficients.

Final Answer:Both (a) and (b).