# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Sight Reduction Formula Question**

**From:**Peter Fogg

**Date:**2005 Jan 10, 16:26 +1100

George Huxtable wrote- "Now consider the other formula, deriving Z from its sine. If, in this case, that formula has given us sin Z = +0.98, what do we do then? Well, one solution is that Z = 88.5 deg, which might well be the right answer. On the other hand, sin 101.5 deg is also +0.98, so that's an equally valid answer. It could be either, then. How do we discover which is the one we want? In this case, there's no simple way, that I know of, to resolve the ambiguity by using inspection and logic to determine whether the wanted result is just North of East or just South of East." I guess simplicity lies in the eye of the beholder. There is a way to resolve the ambiguity. Since the virtue of the method is itself simplicity, this complication tends to detract from the appeal of the method, in the limited cases when it occurs. "You will find the advice, in some textbooks, "just take a compass bearing on the body, and it should be easy to distinguish which one is right". Well, perhaps that's reasonable, in that widely-spread example, but say the two possible angles were closer, say 88 deg and 92 deg. Would you be sure which was the right one then? And anyway, if you're prepared to accept a compass-bearing for azimuth, why are you bothering to calculate it?" Because each method acts as a check on the other - either reinforcing the same message or raising doubt. Its such an ingrained on-board habit, to have back up options for fail safe procedures for pretty-well everything. It tends to permeate all aspects of sailing - for example, each time the same mooring is picked up, nearly always a banal operation, its just as well to have a Plan D and then a Plan E if possible. The French version of 'to sail a sailing-boat' is 'naviguer un voilier'. In this sense 'la navigation' is what English speakers know as 'seamanship' - our more narrow sense of navigation is understood as being an integral part. "No, deriving azimuth from its sine is the worst possible option." Not if its virtues outweigh its shortcomings in the vast majority of cases. "There's a third option, that for some reason doesn't find its way into many textbooks. Get the azimuth from its tan! This formula is- Tan Z = sin (hour-angle) / (cos (hour-angle) sin lat - cos lat tan dec) and the rules for putting Z into the right quadrant, 0 to 360, clockwise fron North, are- If tan Z was negative, add 180 deg to Z. If hour-angle was less than 180 deg, add another 180 deg to Z." Sounds great. When can we expect to see a production model? Could this method be turned into a simple 'look up' table?