I am just taking my first steps in learning Celestial Navigation.

Some elements are becomong clear to me and with practice I will soon be able to take sights and establish the GP of a star.

However I am having difficulty with sight reduction. I have come across several ways of sight reduction, some require tables but some only require a good calculator. I have tried to understand the Haversine method but descriptions I have come across are too advanced for me. Can someone offer a simple explanation & possibly a worked example for me to follow.

Thanks

Mike

Let me start with the disclaimer that I have not navigated a boat with a sextant since about 1963.

Since WW2, most celestial navigation is done with tables. You need two types of table. One is reduction tables which simply do spherical trig for you. The other is an almanac which tells you where the line between the center of sun (I will use sun as example, same idea for stars, moon, etc) and the center of earth passes through the surface of the earth. If you were exactly there, the sun would be exactly overhead and your sextant would read 90 degrees between the horizon and the sun center. Now a minute (1/60 of a degree) of angle around the earth on a plane through the center is a nautical mile so if you measure 89 degrees, 59 minutes with your sextant, you lie on a circle one mile from that point on the surface of the earth.
However in practice there are all sorts of complicating details. What you do is assume you are at some latitude and longitude and mark that position on your chart. Then you take your sight and record the exact time (usually referenced to Greenwich England). You correct that sight for your height above water, the fact that you took measurement on the bottom (lower limb) of sun rather than the center and various other corrections I do not remember and write that angle down.
Now the almanac gives you the longitude and latitude (declination) of the sun's intersection with earth at that moment.
Now using the reduction tables you figure out what angle you should have measured with your sextant if you were at the position you assumed you were at. You also get the azimuth or direction of the sun from you. You draw a line through your assumed position in the azimuth direction. If you measured an angle smaller than what you calculated from the table by one minute, you move from your assumed point one mile away from the sun's intersection and make a dot. You then draw a line perpendicular to the azimuth line through the dot. You lie somewhere on that line, which is a local approximation of a part of the circle one mile further from the sun's intersection than your assumed position was.
If you are only taking sun sights, you must now wait and take another later in the day to get a line that crosses the first (correcting the first of course for how you think you might have moved between sights.) If you get a bunch of stars all at once, you simply cross the lines.
I know this is pretty rough and perhaps ancient technology, but perhaps it will be of some help.