If collimation of the body with the bubble and reading the sextant were all that had to be done, celestial navigation would be simple. This would mean LOPs that are accurate to within 1 or 2 miles could be obtained without any further effort. Unfortunately, considerable errors are encountered in every sextant observation made from an aircraft. A thorough understanding of the cause and magnitude of these errors, as well as the proper application of corrections to either computed altitude (Hc) or Hs, helps minimize their effects. Remember that any correction applied to the Hs may be applied to the Hc with a reverse sign. Accuracy of celestial navigation depends upon thorough application of these corrections, together with proper shooting techniques. The errors of sextant observation may be classified into four groups: parallax, refraction, acceleration, and instrument.
Parallax in altitude is the difference between the altitude of a body above a bubble horizon at the surface of the earth and its calculated altitude above the celestial horizon at the center of the earth. All Hc are given for the center of the earth. If the light rays reaching the earth from a celestial body are parallel, the body has the same altitude at both the center and the surface of the earth. For most celestial bodies, parallax is negligible for purposes of navigation.
Parallax Correction for the Moon
The moon is so close to the earth that its light rays are not parallel. The parallax of the moon may be as great as 1° thus, when observing the moon, a parallax correction must be applied to the Hs. This correction is always positive (+) and varies with the altitude and with the distance of the moon from the earth. The correction varies from day to day because the distance of the moon from the earth varies. Corrections for the moon’s parallax in altitude are given on the daily pages of the Air Almanac and are always added, algebraically, to sextant altitudes. The values of parallax for negative altitudes are obtained from the Air Almanac for the equivalent positive altitudes.
Semidiameter correction is found on the daily pages of the Air Almanac. Apply it when shooting the upper or lower limb of the moon or the sun. It is more likely to occur on observations of the moon because, when the moon is not full (completely round), the center is difficult to estimate. Shoot either the upper or lower limb and apply the semidiameter correction listed on the Air Almanac page for the time and date of the observation. Subtract the correction from the Hs when shooting the upper limb; add the correction to the Hs when shooting the lower limb. Reverse the sign if applying the correction to the Hc. Listed on the same page is the semidiameter correction for the sun, which is applied the same way as for the moon.
Example: Using Figure 13-5, extract the corrections for the upper limb of the moon as observed on 11 August 1995 at 1100Z is 33° 41′.
Apply these corrections as:
Atmospheric Refraction Error
Still another factor to be taken into consideration is atmospheric refraction. If a fishing pole is partly submerged under water, it appears to bend at the surface. The bending of light rays as they pass from the water into the air causes this appearance. This bending of the light rays, as they pass from one medium into another, is called refraction. The refraction of light from a celestial body as it passes through the atmosphere causes an error in sextant observation.
As the light of a celestial body passes from the almost perfect vacuum of outer space into the atmosphere, it is refracted as shown in Figure 13-6, so that the body appears a little higher above the horizon than it really is. Therefore, the correction to the Hs for refraction is always negative. The higher the body above the horizon, the smaller the amount of refraction and, consequently, the smaller the refraction correction. Moreover, the greater the altitude of the aircraft, the less dense the layer of atmosphere between the body and the observer; hence, the less the refraction.
The appropriate correction table for atmospheric refraction is listed inside the back cover of all four books used for celestial computations; namely, the Air Almanac and each of the three volumes of Publication No. 249. It contains the Sight Reduction Tables for Air Navigation published in three volumes. Volume I, used by both the marine and air navigator, contains the altitude and azimuth values of seven selected stars for the complete ranges of latitude and hour angle of Aries. These seven stars represent the best selection for observation at any given position and time, and provide the data for presetting instruments before observation and for sight reduction afterwards. Volumes II and III cover latitudes 0-40 and 39-89, respectively, and are primarily used by the air navigator in conjunction with observations of celestial bodies to calculate the geographic position of the observer. This table, shown in Figure 13-7, lists the refraction for different observed altitudes of the body and for different heights of the observer above sea level. The values shown are subtracted from Hs or added to Hc.
Presently, the only practical and continuously available reference datum for the definition of the true vertical is the direction of the gravitational field of the earth. Definition of this vertical establishes the artificial horizon. It is also fundamental that the forces caused by gravity cannot be separated by those caused by accelerations within the sextant. A level or centered bubble in the sextant indicates the true vertical only when the instrument is at rest or moving at a constant velocity in a straight line. Any outside force (changes in GS or changes in track) affect the liquid in the bubble chamber and, consequently, displace the bubble.
When the sextant is moved in a curved path (Coriolis, changes in heading, rhumb line, etc.), or with varying speed, the zenith indicated by the bubble is displaced from the true vertical. This presents a false artificial horizon above which the altitude of the celestial body is measured. Since the horizon used is false, the altitude measured from it is erroneous. Therefore, the accuracy of celestial observations is directly related to changes in track and speed of the aircraft. Acceleration errors have two principal causes: changes in GS and curvature of the aircraft’s path in space.
The displacement of the liquid and the bubble in the chamber may be divided into two vectors, and each vector may be considered separately. These vectors may be thought of as a lateral vector (along the wings) and a longitudinal vector (along the nose-tail axis of the aircraft). Any change in GS can cause a longitudinal displacement. This change can be brought about by a change in the airspeed or the wind encountered, or the change in GS brought about by a change in heading due to other factors (gyro precession and rhumb line error). A lateral displacement results from a number of causes, most of which occur in spite of any efforts to hold them in check. These causes are Coriolis, rhumb line, and wander errors.
Any free-moving body traveling at a constant speed above the earth is subject to an apparent force that deflects its path to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This apparent force, and the resulting acceleration, were first discovered shortly before the middle of the 19th century by Gaspard Gustave de Coriolis (1792–1843) and given quantitative formulation by William Ferrel (1817- 1891). The acceleration is known as Coriolis acceleration, or force, or simply, Coriolis, and is expressed in Ferrel’s law.
You must realize that the bubble sextant indicates the true vertical only when the instrument is at rest or moving at a constant speed in a straight line as perceived in space. If the earth were motionless, this straight path in space would also be a straight path over the surface of the earth; conversely, a straight path over the motionless earth would also be a straight path in space.
When the aircraft is flying a path curved in space to the left, the fluid in the bubble chamber is deflected to the right, and the bubble is deflected to the left of the aircraft’s path over the earth. When the aircraft is flying a curved path in space to the right, the reverse is true.
In Figure 13-8, the aircraft is represented as flying on a curved path to the left. Note that in the inset representing the bubble chamber, the heavy black bubble is indicated in its approximate position representing the true vertical.
The observer always seeks to center the bubble and, on this beam shot facing to the right side of the aircraft to observe the body, tip the sextant up. This would tilt the bubble horizon from its true position, producing a smaller sextant reading than the true value. The smaller the height observed (Ho), the greater the radius of the circle of equal altitude—the LOP falls farther from the subpoint than the true LOP. Obviously, if the erroneous LOP falls farther from the subpoint, it falls to the left of the true LOP and the correction to the right is valid. Corrections for Coriolis error are shown on the inside back cover of the Air Almanac, as well as in all volumes of Pub. No. 249 published by the National Imagery and Mapping Agency.
Coriolis acceleration is directly proportional to the straightline velocity, directly proportional to the angular velocity of the earth, directly proportional to the sine of the latitude, and at right angles to the direction of flight.