Discussion
With \( C_{n_\beta} = 0.12 \ \mathrm{rad^{-1}} \), dynamic pressure \( 5000 \ \mathrm{Pa} \), \( S = 25 \ \mathrm{m^2} \), \( b = 10 \ \mathrm{m} \) and \( I_{zz} = 150\,000 \ \mathrm{kg\,m^2} \), the value of \( N_\beta = C_{n_\beta}\bar q S b / I_{zz} \) is
Answer: B
Dimensionalising the coefficient:
\[ \begin{aligned} N_\beta &= \frac{0.12 \times 5000 \times 25 \times 10}{150\,000} \\ &= \frac{150\,000}{150\,000} = 1.0 \ \mathrm{s^{-2}} \end{aligned} \]
so 1.0 per second squared and a Dutch roll frequency near 1 rad/s. The 0.12 option is the coefficient itself, which carries different units. 10 slips a decade. 0.5 halves the result. Note the structure: frequency rises with dynamic pressure and fin volume and falls with yawing inertia, exactly as the pitch case does with its own quantities.
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