NavList:

David P, you wrote:
"I wouldn’t be too worried about using fancy maths inside a cocked hat."

But what if there's no fancy math! The procedure in the Nautical Almanac is "obscure". And some of the attempts to simplify it, like procedures for drawing symmedian lines, are just too much trouble and only slightly less obscure. Yet there are tricks available --new tricks! And if they take almost no work, yet provide a better estimate of the fix, we want that, right? :)

You also noticed my 90° pair of LOPs. That's no accident. You're probably not surprised to hear that. A pair of LOPs at a 90° angle possess a symmetry that has been overlooked for too long, I would say. More later.

And you added:
"Ignoring my carefully maintained DR position, that gives me a fix 10nm up and 20nm right.  That’s Vulcan 480kts celestial.  For the boys & girls of the Bulldog Breed bobbing up and down on the sea at 4.8kts there might be more time for sophistication. "

Ha ha. Yes, they're sophistimicated.

You concluded:
"If you insist I use three position lines, I’d mark my fix along PL A halfway between where PLs B & C cross it.  That gives me 11nm up and 21nm right. My reason for doing that is the narrower the angle between PLs B&C the accuracy of the BC intersection varies greatly and pulls a centred fix too far from PL A, irrespective of which centre you use.  E.g.  If the angle between PLs B&C approaches zero, they would eventually intersect at infinity, so your fix would be half-way to infinity (joke)."

Exactly. And there's an even better way to express this. The fix should be close to the short side. How close? Under what circumstances? And how do we know? 

More later today.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA