Deviation card, variation and an unplanned heading change
At the departure airfield the magnetic variation is 7°W. The aircraft's compass swing card gives these deviations: on compass heading 000°, 2°E; on 090°, 1°W; on 180°, 3°E; on 270°, 0°. The planned true heading for the first leg is 085°T. After departure, ATC clears you direct to a beacon and you calculate a new true heading of 118°T. At the aircraft's en-route position the magnetic variation is 4°W. You must steer compass headings, and the deviation card only lists cardinal headings, so interpolation is required. A trainee suggests using the 090° deviation figure for both headings because both are close to east. You need to decide the correct compass headings and explain the consequence of the trainee's shortcut.
1. Calculate the compass heading for the planned true heading of 085°T at the departure airfield.
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Convert true to magnetic first. With 7°W variation, magnetic heading = true heading + 7°, so 085°T becomes 092°M. The compass heading is near 092°C, so interpolate deviation between 090°C (1°W, i.e. −1°) and 180°C (3°E, i.e. +3°). The change is 4° over 90°, or 0.0444° per degree. At 092°C the deviation is −1 + (2 × 0.0444) = −0.91°, i.e. about 0.9°W. Compass heading = magnetic heading − easterly deviation; with a westerly deviation, compass heading = 092° − (−0.91°) = 092.9°C. A second iteration at 092.9°C gives essentially the same result, so steer about 093°C. The sign convention is the key: easterly deviation is added to compass heading to obtain magnetic heading, and westerly deviation is subtracted.
2. Calculate the compass heading for the new true heading of 118°T with 4°W variation, using interpolation of the deviation card.
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Magnetic heading = 118°T + 4° = 122°M. The compass heading will be near 122°C, which lies between 090°C and 180°C. Interpolating: deviation = −1 + (32/90 × 4) = −1 + 1.42 = +0.42°, i.e. 0.42°E. Compass heading = magnetic heading − deviation = 122° − 0.42° = 121.6°C. Check at 121.6°C: deviation = −1 + (31.6/90 × 4) = +0.40°E; compass heading = 122° − 0.40° = 121.6°C. The converged answer is about 122°C. Note that the variation change from 7°W to 4°W reduced the magnetic heading by 3° compared with the departure case, and the deviation changed from about 1°W to about 0.4°E because the compass heading moved through the card.
3. Explain why using the 090° deviation value for the 118°T case is wrong and estimate the resulting cross-track error over 100 NM.
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Using the 090° value of 1°W at a compass heading near 122°C gives compass heading = 122° − (−1°) = 123°C, compared with the interpolated 121.6°C. The error is about 1.4°, so the aircraft would fly a heading about 1.4° off the required heading. Over 100 NM, the cross-track error is approximately 100 × tan 1.4° = 2.4 NM. Deviation is not constant with heading; it varies as the aircraft's own magnetic field interacts differently with the Earth's field. Interpolating between the nearest card entries is therefore necessary, and the error is large enough to matter for a narrow airway or an approach. The trainee's shortcut treats a heading-dependent error as a constant, which is exactly the misconception the deviation card is intended to correct.