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General Sight Reduction

Below is a form using JavaScript that performs general sight reduction :
[to be used in conjunction with nautical almanacs]

Dead Reckoning Position

Latitude : degrees minutes
Longitude : degrees minutes

Celestial Body's Information

Declination : degrees minutes
Greenwich Hour Angle : degrees minutes
(or Local Hour Angle if DR Longitude is left blank)


Calculated Azimuth :
Calculated Altitude : degrees minutes

Sight Reduction - a brief history

Quoted from "The Calculator Afloat - a Mariner's Guide to the Electronic Calculator"
by Captain Hernry H. Shufeldt, USNR (Retired) and Kenneth E. Newcomer

Sight reduction is defined as the process of deriving from a sight the information needed for establishing a line of position. This entails computing the body's altitude or azimuth, using either the estimated or an assumed position.

As we know it, sight reduction is a comparatively recent development, whether the computations are made by log tables or sight reduction tables; the concept of the position line dates back only about 140 years.

For centuries, the only sights the navigator could use were those of bodies transiting his meridian; from these he could obtain his latitude. Otherwise, with the exception of Polaris, which served to indicate latitude and direction in the Northern Hemisphere, without an accurate time source, the celestial bodies were of little use except as steering reference.

The need for developing a method of determining longitude became ever more urgent as longer voyages of commerce and exploration were undertaken. During the fifteenth through the eighteenth centuries, the best mathematical and scientific minds in Europe worked on this problem. It was known that the apparent motion of the heavenly bodies was extremely regular, and that the Moon changed its position relative to the Sun and the stars at a constant rate.

It was apparent, therefore, that there were two possible solutions; either the Moon must be made to furnish time, and therefore longitude, or an accurate time piece must be designed and built. The latter choice was long unattainable; the great majority, therefore, turned their attention to the Moon.

The Moon's rate of motion, as it crosses the sky, differs by roughly 30' per hour, about the Moon's diameter - or 12° per day - from the motions of the Sun and stars. If the exact angular difference between the center of the Moon and the center of some other celestial body could be measured, the time of the observation, and therefore the longitude, could be determined.

The first determination of longitude by lunar distance is variously attributed to Regiomontanus in 1472, Amerigo Vespucci in 1497, and John Werner in 1514; however, for centuries it was very little used, because of lack of accurate ephemeral data on the Moon, poor instruments, and the complexity of the necessary computations.

In 1675 the Royal Observatory was established at Greenwich, England, and accurate ephemeral data on the Moon were slowly accumulated there, as well as at various observations on the Continent. In 1767 the English Nautical Almanac appeared, combining much astronomical data in a single source. Incidentally, this publication eventually led to the universal adoption of the meridian of Greenwich as the prime meridian for establishing longitude.

The advent of the Nautical Almanac facilitated the working of lunar distance observations, and the invention of the sextant in 1730 made it possible to obtain such observations with considerable, accuracy. On his first voyage to the Pacific, 1768-1771, Captain James Cook did not carry a chronometer, and determined his longitude by lunar distances. In 1769-1770 he charted New Zealand with remarkable accuracy. Observations were all made afloat by Cook, himself, and Charles Green, an astronomer, using Hadley sextants.

By our standards, these instruments were quite primitive; however, the latitudes obtained were all very accurate. The longitudes were somewhat more uncertain. The South Island he placed about 25', or 18 miles, too far to the East; one of the greatest errors was 40'.

However, the lengthy mathematical calculations involved deterred many navigators from making use of lunar distance observations, and the bait of coming to the latitude of the vessel's destination, and then sailing down the easting or westing to the port, remained in wide use. The simplification of the lunar method by Nathaniel Bowditch in 1802 considerably widened the use of the lunar distance observation.

Even with a chronometer on board, lunar distance observations continued to be used in isolated areas as a check on chronometers until the invention of radio. The lengthy tables of "Maritime Positions," listed in Bowditch through the 1962 edition, were included primarily to permit checking the accuracy of the chronometer by means of celestial observations.

John Harrison developed a prototype chronometer in 1720, and submitted a perfected instrument to the Royal Navy for sea trials in 1735. Improved models were produced by him over the next 40 years; they ran well, but were extremely expensive, and their use was long highly restricted. Only in this century did the chronometer come into wide use, greatly facilitating the determination of longitude. The invention of radio permitted a regular and easy check on its accuracy.

With the invention of the chronometer, when the latitude was known, it became possible to compute the longitude, using the time sight method; this method of navigation remained popular into this century, as a position could be determined without plotting. The discovery of the line of position by Captain Thomas H. Sumner in 1837 heralded a new era in navigation. The Sumner line of position was originally obtained by reducing the same sight twice; the estimated latitude was used for the first reduction. A slightly different latitude, say, 10' or 20' from the first, was then selected to reduce the sight a second time; a line of position was then drawn through the two positions on the chart. With the invention of azimuth tables in the latter part of the nineteenth century, it became possible to work only one time sight, and then draw a line through the resulting position, perpendicular to the body's azimuth.

The era of the "new navigation" came with the introduction of the altitude- difference method of determining a line of position by Commander Adolphe-Laurent- Anatole Marcq de Blonde de Saint-Hilaire, of the French Navy, in 1875. This method remains the basis of almost all celestial navigation used at sea today.

The Marcq Saint-Hilaire method, as it is generally called, remained in common use on board U.S. Naval ships through the first decades of this century. Computed altitude and azimuth angle were calculated by means of the log sine, cosine, and haversine, and natural haversine tables included in Bowditch.

Subsequently sight reduction was greatly simplified by the coming of the various so-called short-method tables - such as the Weems Line of Position Book, Dreisonstok's H.O. 208, and Ageton's H.O. 211. Even greater simplification was achieved when the inspection tables, H.O. 214, H.O. 249, and H.O. 229, were published.

The final step is use of the electronic calculator. However, the wise navigator will always have familiar back-up methods to rely upon if necessary; he may even need to find his longitude by a lunar distance observation on occasion.


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