Question 55 ONC05 - Master or Mate of LT 200 GRT

The Correct Answer is B **Explanation for Option B (Correct):** Quadrantal error in a gyrocompass is a type of steady-state error that results from the damping mechanism (the control force designed to bring the gyro spin axis into the meridian). This error is proportional to the sine of twice the vessel’s heading ($E \propto \sin(2\theta)$), where $\theta$ is the vessel's heading. This trigonometric function ($\sin(2\theta)$) reaches its maximum absolute value (1 or -1) when $2\theta$ is $90^{\circ}$ or $270^{\circ}$. This occurs when the vessel's heading ($\theta$) is $45^{\circ}$, $135^{\circ}$, $225^{\circ}$, or $315^{\circ}$. These headings correspond precisely to the **intercardinal headings** (Northeast, Southeast, Southwest, Northwest). Therefore, the quadrantal error has its greatest numerical effect when the vessel is sailing on these headings. **Explanation of Incorrect Options:** **A) When the vessel is in high latitudes:** While other gyrocompass errors (like latitude error or steaming error) are significantly affected by latitude, the *maximum magnitude* of the quadrantal error is primarily determined by the heading, not the latitude. Latitude does affect the natural period of oscillation and the damping coefficient, but the heading is the direct variable that maximizes the $E \propto \sin(2\theta)$ term. **C) When the vessel is on north or south headings:** North ($000^{\circ}$ or $360^{\circ}$) or South ($180^{\circ}$) headings correspond to the cardinal directions. At these headings, the $\sin(2\theta)$ term becomes $\sin(0^{\circ})$ or $\sin(360^{\circ})$ or $\sin(360^{\circ})$, all of which equal zero. Therefore, the quadrantal error is actually **zero** or negligible when sailing directly North, South, East, or West (the cardinal headings). **D) When the vessel is near the equator:** Similar to Option A, the proximity to the equator (low latitude) has a major effect on other errors, but it does not maximize the angular term ($\sin(2\theta)$) that defines the quadrantal error. Quadrantal error is maximized specifically when the heading is intercardinal, regardless of the latitude.