NavList:

Hello Chris Smith.

Welcome aboard :). Sorry for the slow replies here on the NavList message boards. We'll do better.

You wrote:
"I can use a running fix and then the HSC method to get a fix but I have been looking at some emergency navigation techniques where if you only had a chronometer with known error and a bris sextant could you get a longitude by double sight on the sun with the Bris sextant and time offset from LAN  and UTC LAN to get longitude. I have been having moderate success with this in a fixed location but am wondering about underway and how to deal with any changes in lat and long. "

Aha! Thank you for the clarification. If I am reading this correctly, your question isn't about Bris sextant sights specifically, but more about "fixed" or "constant" angle sights... You take a Sun sight at some hardware-fixed angle before an hour or several before local noon. Then at about the same time after noon, you take another sight using the same fixed angle sextant with the same altitude as a result. For example, I shoot an altitude of 33°15' before noon. I wait some hours and get another altitude of 33°15' after noon. Of course we may have to make the usual corrections for dip, refraction, and semi-diameter (or maybe not, since this method is about determining the central time --the time of "true" noon-- and so long as the corrections are the same before and after noon, we can skip them). But how do you correct for the motion of the observer and the change in the Sun's declination?

We know that we can solve this by standard methods. We could ignore the fact that the sights were taken with a fixed-angle sextant and instead treat the identical values as a "mere coincidence". Then we work up the sights as a standard pair of Sun lines of position with some dead reckoning connecting them. That works just fine, and for many navigators, that's the optimal solution. Nothing new to learn, no tricks. But this method does depend on access to complete navigation tables or calculated values. What's the alternative?

You suggested getting the "time offset from LAN  and UTC LAN to get longitude", and that's absolutely right. If we can adjust one or both of the sights for observer motion and changing declination, then we can restore the perfect before-and-after symmetry between the two sights. Then the time of local apparent noon is exactly the time in between the two sights. That's 12:00:00 in local apparent time, which isn't much use... But of course we have the UT of the original sights, so we just split the difference in UT between them, and that is the UT when the Sun and our vessel were aligned on the same meridian, the same longitude. Then we calculate the GHA of the Sun at that UT, and the result is our longitude. Note that this would be the longitude of the vessel at local noon. So from there we advance it by usual dead reckoning estimation which will give good results over a period of time as short as would be likely in a scenario like this.

That leaves the main problem: how do we "adjust one or both of the sights for observer motion and changing declination"? In some methodologies of air celestial navigation, this is a MOO and MOB problem. MOO is the "motion of observer" correction, and MOB is the "motion of body" correction. I am short of time to continue with this, and this post is getting long anyway, so I will leave this for any fans of MOO and MOB to describe how it's done. I will also try to get back to add more on the computation side later this evening.

Short answer: yes, it can be done. And yes, there are relatively easy calculations.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA