NavList:

Diego,

NavAlm uses an iterative numerical forward model. It calculates the sextant distance expected at a trial UTC, then adjusts UTC until that distance matches the observation. It does not use Borda’s or Young’s clearing formula.

The positions come from NOVAS C3.1 and JPL DE440s, calculated for the observer’s location and elevation. Parallax is included in those topocentric positions. Bennett refraction, scaled for pressure and temperature, raises each direction toward its zenith. The program then computes the angular separation using three-dimensional vectors. This accounts for how the two altitude corrections project onto the measured distance.

For limb contacts, it searches the refracted disc circumference, including differential refraction across the disc. Both complete discs must remain above 5° geometric altitude; lower trials are rejected. Atmospheric variability remains a limitation near that boundary. The model uses smooth limbs and does not model lunar terrain, planetary oblateness, or phase/photocentre effects.

Yes, the uncertainty includes distance-to-time amplification. With AP held fixed, it evaluates the predicted sextant-distance rate numerically at the solution:

Time sigma in seconds = 60 × distance sigma in arcminutes ÷ absolute distance rate in arcminutes per minute of time.

Thus it uses the actual geometry rather than assuming a constant lunar rate. With two measured altitudes and position refinement enabled, it propagates all three entered angular uncertainties through the local position/time Jacobian. Synthetic altitudes supply geometry only; they do not count as independent observations.

Your numerical example is right: at 33′/hour, a 1′ distance error corresponds to about 109 seconds of time, or 27 nautical miles of equivalent longitude error at the equator. More generally, a clock uncertainty of σ seconds corresponds to approximately σ/4 nautical miles at the equator, or σ cos(latitude)/4 along the local parallel.

The displayed sigma is a formal measurement uncertainty, conditional on the model and entered errors. It excludes AP uncertainty in fixed-position mode, atmospheric-model errors, and instrument or limb systematics. A small residual does not establish observational accuracy.

Showing the equivalent longitude error in nautical miles would be a useful addition, clearly distinguished from total position uncertainty.

I have been able to (by very careful interpolation on my sextant micrometer) get lunars that are 10~20s off of UTC.  Planets seem to work better as tangency is more obvious, but lunars are so picky that you have to consider the SD of the planet.  I am also going to be getting some bifocals instead of using progressive lenses for this.  But I am happy I can recover time without WWV now.

Chris