NavList:

Hi Josh,

You are quite right, and my apologies for the misreading!

What happened on my end came down to how I set up the simulation. To get the matrix solver to calculate an empirical uncertainty ellipse rather than collapsing to zero, I had introduced simulated deck noise of around one minute of arc across the sights.

Because the real Sun declination drifts by less than two arcminutes over that entire window, seeing those small residual offsets in my solver led me to conflate my perturbed data with your clean figures, and I made the mistake of assuming your table had used a simplified, frozen declination for classroom illustration. And you know what they say about assuming!

Re-checking your original numbers without my added noise confirms that your Ho and Zn values track the dynamic September 30 ephemeris spot on.

In any case, that two arcminute drift does not change the core outcome of your experiment at all. The geometry of the uncertainty ellipse behaves identically whether declination is dynamic or held constant.

Looking at the four panel image I posted, comparing the full run of eight sights against just three (the first, middle, and last), that long corridor along the line of sight stubbornly stays around five miles wide, dropping only from 5.1 miles down to 4.8 miles. The extra sights do valuable work across the bearing line, tightening the minor axis from 1.1 down to 0.8 miles, but along the line of sight, quantity simply cannot substitute for waiting on the Sun to travel.

It is a great, instructive problem, and thank you for keeping me on my toes with the numbers!

Marco Suadoni

River Moth (Nauticat 33), Essex, UK

www.vincenta.co.uk