Discussion
Assertion (A): Lanchester's phugoid formula contains neither the wing area nor the pitching moment of inertia of the aeroplane.
Reason (R): The idealised phugoid is derived by assuming a lossless exchange between kinetic and potential energy at constant lift coefficient.
Select the correct answer from the options below.
Answer: C
Both are true and the second explains the first. Lanchester's derivation treats the aeroplane as a point mass trading height for speed with lift held proportional to the square of the speed at fixed incidence; no rotation about the pitch axis enters, so inertia in pitch cannot appear, and wing area cancels with the weight through the trim condition. What survives is \( \omega_n = \sqrt{2}\,g/u_0 \), a function of trim speed alone. It also explains the formula's limitation: having thrown away the loss mechanism, it says nothing about damping.
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