Rhumb Line Error
The straight Coriolis table in Figure 13-9, found in the Air Almanac or Pub. No. 249, has a limited application. As long as a constant TH is flown, the path of the aircraft is a rhumb line. Because a rhumb line on the earth’s surface is a curve, it is also a curved line in space. If the aircraft is headed in an easterly direction in the Northern Hemisphere, the apparent curve is to the left and becomes an addition to the Coriolis error. By the same token, if headed in a westerly direction in the Northern Hemisphere, the apparent curve is to the right, or opposite that of Coriolis force. [Figure 13-10] There are notable exceptions to this. When flying north or south, the aircraft is flying a great circle and there is no rhumb line error. Also, when steering by a free-running, compensated gyro, the track approximates a great circle and eliminates rhumb line error.
At speeds under 300 knots, the error is negligible. However, at high speeds or high latitudes, rhumb line error is appreciable. For example, at 60° N latitude with a track of 100° and a GS of 650 knots, the Coriolis correction is 15 nautical miles (NM) right, and the rhumb line correction is 10 NM right. Use the following steps and Figure 13-11 to determine the correction for rhumb line error and Coriolis correction.
- Enter the nearest latitude on the left side. Interpolate if necessary.
- Enter the nearest track across the top of the chart. Interpolate if necessary.
- Choose the closest GS and extract the correction; 50N, track 080°, GS 500 knots = 14.3 Right.
Groundspeed Acceleration Error
Changes in airspeed or wind velocity cause this error. Prevent changes of airspeed through good crew coordination.
Changes in wind velocity with resultant changes in GS are more difficult to control. The change in GS causes the liquid to be displaced, with the subsequent shifting of the bubble creating a false horizon. Notice in Figure 13-12 how the horizon is automatically displaced by keeping the bubble in the center while these changes are taking place. A very simple rule applies to acceleration and deceleration forces. If the aircraft accelerates while a celestial observation is in progress, the resultant LOP falls ahead of the actual position. Accelerate—Ahead. The more the LOP approaches a speed line, the greater the acceleration error becomes. Refer to Figure 13-13.
- Enter with Zn–Track.
- Extract acceleration error and apply sign.
Example: Track = 080°, Zn = 060°, Beginning GS –500 knots, ending GS –515 knots.
060° – 080° = 340° = –1.40
515 – 500 = 15 knots
–1.40 × 15 = –21 correction to the Ho
A change in track can be produced by changes in the wind, heading changes caused by the autopilot, changing magnetic variation, or by heading changes caused by pilot manual steering errors. As with the Coriolis force and rhumb line errors, correction tables have been developed for wander error. Values extracted from the wander correction table, shown in Figure 13-14, are to be applied to the Ho.
Use the following information as entering arguments for the determination of the correction taken from the table:
- The heading at the beginning of the observation was 079°.
- The heading at the end of the observation was 081°.
- The observation was taken over a 2-minute period.
- The GS was 450 knots.
- The Zn of the body was 130°.
Following the instructions shown at the bottom of the table, enter the numerical portion of the table with the values of GS and the change of track per 2 minutes. In this case, the GS is 450 knots and the change in track per 2 minutes is 2°. Since the heading at the end of the observation is greater than the heading at the beginning, the change is 2° to the right. Notice that you must know whether the change is to the right or to the left to determine the sign of the correction. The factor obtained from the table is 12 × 2 = 24.
Next, enter the graph portion of the table with the value of the factor (24) and the value of the azimuth of the body, minus the value of track. The graph is so constructed that it must be entered with Zn – Tr.
Zn – Tr = 130° – 080°; so use 050°
Following the rules in steps two and three in the table; the correction is 19′. Since the change in track is to the right, the correction is subtracted from the Ho. This is determined by referring to the signs shown at the ends of the arc in the table. Figure 13-15 shows the effect of this correction.
If the track and groundspeed are the same at the beginning and the end of a shooting period, there is no wander error.
Index error is usually the largest mechanical error in the sextant. This error is caused by improper alignment of the index prism with the altitude counter. No matter how carefully a sextant is handled, it is likely to have some index error. If the error is small, the sextant need not be readjusted; each Hs can be corrected by the amount of the error. This means that the index error of the sextant must be known to obtain an accurate celestial LOP. Another mechanical error found in sextants is backlash. This is caused by excessive play in the gear train connecting the index prism to the altitude counter.
Usually, index and backlash errors are nearly constant through the altitude range of the sextant. Therefore, if the error at one altitude setting is determined, the correction can be applied to any Hs or Hc. The correction is of equal value to the error, but the opposite sign.
The sextant should be checked on the ground before every celestial flight. Preflighting the sextant can determine the sextant error of an individual instrument. The sextant error can also be determined in-flight and a correction can be applied to the precomp to compensate for the error. To determine the error and correction in-flight, one must have a celestial LOP, a Zn, and the actual, or best-known, position of the aircraft at the same time. [Figure 13-16]
The fix symbol represents the best-known position at the time of the celestial LOP. To determine the actual value of the correction, measure the shortest distance between the position and the LOP. This tells you how many minutes of arc (NM) the Ho must be adjusted on subsequent shots to get an accurate LOP. In this case, the value is 10′. To determine whether this value must be added or subtracted, note whether the LOP needs to be adjusted toward the Zn or away from the Zn. Remember the rule HOMOTO? It applies here, too. If the LOP needs to be moved toward the Zn in order to be made more accurate, the Ho needs to be made larger, thus, the correction is added to the Ho to make the Ho value increase. If the LOP needs to be moved away from the Zn, the correction is subtracted from the Ho to make the Ho less. In Figure 13-16, the LOP needs to be moved 10 miles toward the Zn in order to be accurate; thus, the sextant error correction is +10 to the Ho and can be used on subsequent shots obtained from the same sextant.
An important thing to remember is that the sextant error correction assumes conditions are consistent. As a technique, it is wise to obtain several LOPs with a sextant, noting the sextant errors on each, before establishing a value to be carried on the precomp. Once using that correction, make sure you use the same sextant.