Lunar distance, watch recovery and coastal sextant methods

The enhanced DE440 Sun–Moon solver includes observer-specific light time and annual/diurnal aberration. Bundled IERS DUT1 data supports high-accuracy offline calculations without downloading an update. DUT1 is UT1 minus UTC, the small correction for Earth’s rotation; it is not chart or weather data.

Under Lunar Tools → Advanced, Check / download update… retrieves the official IERS table, validates it and installs it for immediate offline use. No compiler or restart is required. This explicit button press is the only network action. Alternatively use Import local file… with an official finals2000A.all file copied from another computer. Current coverage is shown on the tab. Data is selected for each sight’s date, not the computer’s date.

The plugin has no data-expiry lockout. Outside all available coverage it continues using UT1 = UTC and warns of reduced accuracy. Failed downloads, invalid data or failed saves retain the previous valid table and the bundle. The bundled table ends in September 2027, but that is not an end date for the plugin. Downloaded tables can extend it; fallback solving remains available beyond it. Future fallback is not guaranteed to match dated-data precision.

The mathematical problem is a coupled three-equation solution. For each trial clock correction the plugin evaluates the Moon and selected body at all three corrected epochs, reduces each altitude at its own epoch, transports the observer when requested, and forward-models the raw lunar distance. It solves the common clock correction, reference latitude and reference longitude together. The reported one-sigma UTC and position uncertainties come from the local weighted numerical covariance of the three raw angles; weak or highly correlated geometry therefore produces a larger estimate. These estimates describe the entered random angle uncertainties, not unmodelled systematic effects such as an incorrect index correction, abnormal refraction or COG/SOG error.

Choose Check at entered UTC to hold UTC fixed (including the existing manual correction) and examine position candidates and model-minus-observed lunar distance residuals. This mode does not solve or save an additional clock correction. Compare a published position at its stated UTC, not automatically with a position at a different recovered UTC.

The Sun/Moon calculation uses the local JPL DE440s kernel when it has already been installed for the eclipse module. Its separation and geographic positions use the same apparent directions, including light time and annual aberration. Other bodies, or an installation without DE440s, use the bundled offline analytical ephemeris. The results window identifies which source was used. NASA LOLA terrain is unrelated to ordinary lunar-distance clearing and is not used.

When more than one time matches, the plugin does not silently choose a remote root. Narrow the approximate date/time, or use a second lunar observation. Geometry where lunar distance changes slowly is reported as weak. A one-second-rate watch does not by itself produce one-second recovered UTC: sextant, limb, altitude and refraction errors normally dominate.

Once a lunar recovers UTC, the accompanying corrected Moon and body altitudes provide position constraints. Spherical altitude-circle intersections seed the WGS84 refinement. In separate-time mode the constraints are evaluated at their individual epochs and numerically reduced to the lunar-distance reference epoch. Position candidates, including longitude, are reported. This is a direct joint position calculation; the plugin does not use the invalid shortcut of multiplying watch error by 15 degrees per hour.

Two circles generally have two mathematical intersections. A rough hemisphere/DR position selects the nearer one. If absolutely no positional knowledge is available, retain both candidates and resolve them with a third altitude sight, a second lunar, the observed sky orientation, or another independent constraint. After selecting a UTC candidate, Save lunar solution stores a named derived result with immutable input snapshots and its report. It changes neither raw readings nor the global clock correction. Review saved records from Saved lunar solutions in Lunar Tools. In the Fix dialog, explicitly select the saved correction for visible altitude sights from the same watch/clock. Only working copies are recalculated; sights more than 12 hours from the solution’s recorded reference epoch are rejected.

Both modes show joint position uncertainty as horizontal RMS, not the radius of a 68% confidence circle. WGS84 is a reference ellipsoid, not a local geoid or vertical-deflection model; eye height approximates ellipsoidal height. UT1 is approximated by UTC. These and unmodelled systematic effects are not included in the formal measurement uncertainty.

For an object whose waterline is visible, enter the sextant angle from waterline to top, the charted top height, water level above the chart height datum, height of eye and index error. The solver includes Earth curvature and a selectable standard terrestrial-refraction model. The result is a range circle centred on the charted object, not a fix.

For an object whose base is hidden beyond the sea horizon, select Sea horizon to top. This uses the refraction-aware formula underlying Table 15 of the American Practical Navigator (Bowditch). Abnormal refraction can produce large errors. Charted height and tide datum must refer to compatible datums.

In 2.8.5.3 this mode accepts zero and negative dip-corrected angles. The index-corrected measured angle must still place the top on or above the visible sea horizon. Waterline mode still requires a positive angle; the two measured baselines are not interchangeable and the plugin never changes modes or corrects the raw reading for you.

Visibility guidance shows the observer’s horizon, the target’s estimated geographic range, and the waterline-to-top angle at the waterline horizon. These are standard-refraction estimates, not guaranteed visibility or a light’s nominal/luminous range. Bowditch mode uses the effective curvature implicit in its published constants; waterline mode uses its own terrestrial refraction coefficient. A zero dip-corrected angle is not the visibility limit. Both implemented range methods require the target top above the observer; waterline mode also requires positive eye height. Lower targets can produce ambiguous waterline ranges and are rejected rather than choosing a branch.

Use the height of the actual sighted feature: for a light this may be focal height, not the height of its tower. Water level must be expressed relative to the same height datum (it may be negative). Select target waypoint…​ copies coordinates from an OpenCPN mark or route point. Coordinates remain editable; the picker does not supply or change the target height.

An optional true bearing turns the range into an estimated position. A raw magnetic compass bearing is converted with explicit east-positive variation and deviation. Its accuracy is limited by the bearing as well as the vertical angle. Record the bearing at effectively the same instant as the vertical angle, or reduce it to that position epoch before entry.

Target coordinates and measured angles start blank. Closing the window retains an unfinished observation; choose New / clear observation before starting a different one. That action also clears results and plots and reloads the current central index-error and eye-height defaults.

Variation and deviation are disabled and ignored for true bearings. For a magnetic compass bearing they are editable, and Use WMM at current boat/time can fill a clearly labelled variation estimate for the current boat position and UTC. Compass deviation remains a manual vessel/instrument input.

One included angle between two charted objects defines a curved line of position. Enter three objects in their observed left-centre-right order and the left-centre and centre-right measurements to obtain two independent loci. Landmark positions and measurements initially remain blank so plausible defaults cannot be mistaken for observations. The central sextant index-error default is applied to both measurements. The plugin solves their intersection on the sphere from the supplied approximate position and reports residuals, a geometry condition indicator and an estimated one-sigma uncertainty.

The left, centre and right waypoint buttons reuse the searchable OpenCPN waypoint picker; cancelling leaves existing coordinates untouched. Choose by coordinates as well as name when names repeat.

The uncertainty entry is in arcminutes (60 arcminutes = 1 degree). The reported value is formal angular-input uncertainty, not total fix accuracy: it excludes landmark-coordinate errors, misidentification, shared instrument errors and unmodelled vessel motion. Coordinates rounded to 0.1 arcminute cannot justify interpreting a small formal error as metre-level accuracy. Increasing the entered angular uncertainty changes the uncertainty estimate, not the best-fit position. Independent observations and a maintained DR remain essential. Dedicated radar-bearing/range input is not implemented; ordinary radar range is not a vertical-angle measurement.

The approximate position chooses the intended solution; poor or tangent geometry may have other solutions or fail to converge. The plotted individual loci are coastal-scale charting aids, while the reported numerical fix uses exact spherical bearings.

If the two horizontal angles were read sequentially while underway, enable Advance the vessel between the two HSA readings. Enter the second reading’s signed interval from the first, plus COG true and SOG. The numerical solver evaluates each angle at its own vessel position and reduces the resulting fix and chart loci to the first-angle reference epoch. With no vessel motion, the times of observations of fixed terrestrial objects do not change the geometry.