Other Instruments for Celestial Navigation

The Chronometer and Time-Keeping

Accurate time is the second essential element of celestial navigation after the sextant angle. The relationship between them is absolute: a 4-second error in recorded time introduces approximately 1 nautical mile of longitude error in a Sun sight. On a round-the-world passage, accumulated time error is one of the limiting factors on positional accuracy.

The marine chronometer is a precision mechanical timepiece specifically engineered to maintain stable time at sea despite changes in temperature, humidity, and the motion of the vessel. Traditional chronometers are mounted in gimballed boxes that keep them level regardless of the boat's motion. The best mechanical chronometers can maintain accuracy to within 0.1 seconds per day — a level of precision sufficient for celestial navigation.

A critical concept is chronometer rate: the predictable daily gain or loss of the chronometer. A well-regulated chronometer may consistently lose 0.3 seconds per day. This is perfectly acceptable, provided the rate is known and applied. Before departure, the chronometer's daily rate is determined by comparing it against a radio time signal or GPS time over several days. The accumulated correction is then applied to all time readings throughout the passage.

Quartz watches are the practical standard on most modern yachts. A quality quartz watch loses or gains only a few seconds per month — far more stable than a mechanical chronometer. The watch is synchronized to UTC (Universal Coordinated Time) before departure and its rate determined. A second watch as a backup is standard practice for offshore voyagers.

GPS receivers are excellent UTC time sources even when positional accuracy is not required. The time display of a GPS is derived from atomic clocks aboard the satellites and is accurate to within microseconds of UTC. Many navigators maintain GPS specifically for its time signal, independent of its positional function.

Radio time signals provide an independent UTC reference at sea. In the United States, WWV (Fort Collins, Colorado) broadcasts on 2.5, 5, 10, 15, and 20 MHz, transmitting voice time announcements and tick signals at every second. International equivalents include WWVH (Hawaii) and MSF (United Kingdom). A shortwave radio receiver capable of receiving these frequencies is a valuable backup on any offshore boat.

The Artificial Horizon

The sextant measures the angle between a celestial body and the visible sea horizon. But what if the horizon is not visible — obscured by fog, a heavy swell, or because you are practicing inland? The artificial horizon solves this problem by providing a perfectly horizontal reflective surface that serves as a substitute horizon.

A liquid artificial horizon consists of a shallow trough containing mercury or a heavy clear oil, covered by a glass roof to prevent wind from disturbing the surface. Because any liquid at rest forms a perfectly horizontal surface (perpendicular to gravity), its reflection of a celestial body provides an exact horizontal reference. The navigator uses the sextant to bring the direct image of the body (seen through the telescope) into coincidence with its reflected image in the liquid surface. The angle measured is twice the altitude — the observer is measuring from the reflected horizon below to the body above, passing through the true horizontal — so the raw reading is divided by two to get the altitude.

Use cases for the artificial horizon are important to understand. The most common scenario at sea is a heavy swell: when large swells pass under the boat, the visible horizon dips and rises with the wave crests, making it impossible to identify the true horizon. An artificial horizon eliminates this problem. Similarly, at dawn and dusk twilight when star sights are taken, the horizon quality degrades — in some lighting conditions the artificial horizon gives a cleaner observation than the sea horizon.

Inland and shore-based practice is the most frequent use for most sailors learning celestial navigation. Taking sights from a known position on land, comparing the computed LOP to the actual position, is the best way to develop sextant skill before going offshore. An artificial horizon makes this possible regardless of proximity to the sea.

Limitations are equally important. The liquid artificial horizon is sensitive to the slightest breeze, which ripples the surface and destroys the horizontal reference. It cannot be used on a moving vessel — the motion of the boat prevents the liquid from settling. It is therefore used at anchor, in port, or on land, not underway. At sea, the natural horizon must be used for all underway sights.

The Star Finder (2102-D)

Taking a round of star sights at twilight requires identifying multiple stars quickly in a sky that transitions from daylight to dark in 20 to 30 minutes. Without preparation, a navigator can waste precious twilight minutes searching for suitable stars. The Star Finder and Identifier (Pub. No. 2102-D), also known as the HO 2102-D, solves this problem.

The 2102-D is a circular star chart consisting of a base plate (the fixed star chart showing all 57 navigational stars in their correct relative positions) and a set of transparent overlay templates — one for each 10° of latitude from 5°N to 75°N and from 5°S to 75°S. Each template is a circle printed with altitude and azimuth curves appropriate for that latitude.

To use the 2102-D, the navigator first calculates the LHA of Aries for the anticipated time of star sights (usually the center of civil or nautical twilight). The appropriate latitude template is placed over the base plate, and the template is rotated until the LHA of Aries arrow aligns with the LHA scale on the base plate. Once set, every star on the chart that falls within the altitude curves of the template is above the horizon at that time — its approximate altitude and azimuth can be read directly from the overlay curves.

The navigator then selects three to five suitable stars for the round of sights. Ideal star selection follows the rules of good celestial geometry: stars should be separated by at least 60° in azimuth, should have altitudes between 15° and 75° (low altitudes increase refraction error; high altitudes make azimuth determination less precise), and should include a mix of azimuths to ensure good crossing geometry for the resulting lines of position.

The 2102-D is also used for identifying unknown bright objects. If a bright body is visible at a known altitude and azimuth, the navigator can set the template, find the intersection of those coordinates, and read off the body's name. This is particularly useful for planets, which are not plotted on the star chart but can be located if their current position is pre-computed separately.

In practice, the 2102-D should be set up in the afternoon before evening twilight, and the selected stars noted by name, approximate altitude, and azimuth. During twilight, the navigator pre-positions the sextant to the approximate altitude of the first selected star and searches at the right azimuth. This reduces identification time from minutes to seconds — critical when good sighting conditions may last only 10 to 15 minutes.

Plotting Tools and the Line of Position

Celestial navigation produces intercepts and azimuths — numbers that must be transferred to a chart or plotting sheet to produce the lines of position that make up a fix. The quality of the final fix depends not only on the accuracy of the sights but on the accuracy of the plotting. Sloppy plotting wastes good sights.

Parallel rulers are the standard tool for transferring bearings and drawing lines on a chart. A line drawn at the correct azimuth through the assumed position, then walked across the chart using the parallel rulers, maintains its direction precisely. Roller plotters (a parallel ruler with a rolling mechanism) are preferred on small boats where desk space is limited and the traditional walk method is difficult. A protractor plotter or Douglas protractor achieves the same result more directly by combining a graduated circle with a straight edge.

Dividers are used to measure distances on the chart. In celestial navigation, dividers measure the intercept distance in nautical miles along the latitude scale (1 minute of latitude = 1 nautical mile). They are also used to transfer distances when advancing a line of position for a running fix.

Plotting sheets eliminate the need to work on a chart directly. A universal plotting sheet (available from NGA and reproduced in Bowditch) is a blank sheet printed with meridians, a graduated latitude scale, a compass rose, and latitude lines spaced for any latitude band. The navigator draws in the assumed position, the azimuth line, and the LOP on the plotting sheet without touching the chart — the fix from the plotting sheet is then transferred to the working chart. This keeps the chart clean and makes corrections easy.

Sight reduction forms and sight log sheets are not technically instruments, but they are as important as the physical tools. A structured form — with labeled blanks for Hs, IE, Dip, Ho, UTC, GHA, Dec, LHA, assumed latitude, assumed longitude, Hc, Zn, and intercept — enforces the correct sequence of steps and makes errors easy to find. Every celestial navigator should use a form consistently. Improvising the computation in a notebook invites transposed numbers and skipped corrections.

When two or more LOPs are plotted from simultaneous (or nearly simultaneous) sights, their intersection is the celestial fix. In practice, three LOPs rarely meet at a perfect point — the small triangle formed is called the cocked hat. The fix is taken as the center of the cocked hat if the triangle is small. A large cocked hat indicates an error in one or more sights, and the navigator should evaluate each sight individually rather than simply splitting the difference.