Discussion
For \( L_\beta = -20 \), \( N_r = -0.40 \), \( N_\beta = 3.0 \) and \( L_r = 2.0 \), all in consistent units, the spiral mode is
Answer: D
Evaluating the criterion:
\[ \begin{aligned} L_\beta N_r &= (-20)(-0.40) = 8.0 \\ N_\beta L_r &= (3.0)(2.0) = 6.0 \\ L_\beta N_r - N_\beta L_r &= +2.0 \end{aligned} \]
Positive, so the aeroplane is spirally stable, though not by a wide margin. Reducing the dihedral effect to \( -15 \) would take the first product to 6.0 and put the mode exactly on the boundary. Roll damping does not enter the criterion, so the last option is wrong on the face of it, and the sign errors in the other two come from mishandling the product of two negative derivatives.
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