Not a war, just a sextant question.

[johnnyandjebus]

Originally Posted by Minnewaska

I will take a crack at celestial nav 101 over a cup of coffee. For starters, forget the sextant.
Learning how to use it has nothing to do with understanding what is going on.

You are trying to figure out two things. First, your distance north or south of the equator (latitude). Second, your distance east or west from an artificial starting point on the planet (longitude) That was arbitrarily set at Greenwich England.

Latitude first. This would be easier with a model, but can you picture yourself standing on the equator and pointing at the sun high in the sky at noon? Now picture yourself standing in Canada at the exact same time on the exact same day and point at the sun. The angle of your arm would change because you moved but what you are pointing at didn't. You don't need to know much math. The angle changes as you move away from the equator. Once you know that angle, you can look up in a published table to know how far you are from the equator.

Now longitude. Set your watch to noon when the sun is at its highest point in the sky as you are standing in Greenwich England. Now, wherever you are on the globe, just check your watch when the sun is at its highest point. That will tell you how long it has been since it was noon in Greenwhich England. If your watch says 3:00, the sun has traveled for three hours since it was right above Greenwich. Since the sun travels fully around the earth in 24 hours, you are 3/24ths of the distance around the globe from Greenwich. Again, you just look that time up in a table and it will tell you how far you are west of Greenwich.

The sextant is only a device to measure that angle for latitude. When that angle reaches its highest for the day, it is noon and you check your watch to see how far from Greenwhich you are.

The techniques for doing this precisely with a sextant are a separate matter, but have nothing to do with the concept.

How was that?

Minnewaska.
The above is about the most useful, basic, simple and easy to understand explanation of CN I have ever read. It ought to have a sticky attached to it.


John

[chrisncate]

First, thank you for the great explanation. It's really good.

Latitude first. This would be easier with a model, but can you picture yourself standing on the equator and pointing at the sun high in the sky at noon? Now picture yourself standing in Canada at the exact same time on the exact same day and point at the sun. The angle of your arm would change because you moved but what you are pointing at didn't. You don't need to know much math. The angle changes as you move away from the equator. Once you know that angle, you can look up in a published table to know how far you are from the equator.

So this angle is determined by the sextant - you read the degrees and note the exact time you are reading the degrees as soon as you have lined up your sight? Am I understanding this correctly?

Now longitude. Set your watch to noon when the sun is at its highest point in the sky as you are standing in Greenwich England. Now, wherever you are on the globe, just check your watch when the sun is at its highest point. That will tell you how long it has been since it was noon in Greenwhich England. If your watch says 3:00, the sun has traveled for three hours since it was right above Greenwich. Since the sun travels fully around the earth in 24 hours, you are 3/24ths of the distance around the globe from Greenwich. Again, you just look that time up in a table and it will tell you how far you are west of Greenwich.

So.. you need the sextant for latitude, and the tables for longitude - is this correct? What happens next? How do you combine both pieces of data in order to find where you are? I realize you probably put this answer in here already, I'm really trying to understand exactly what you are saying.

The sextant is only a device to measure that angle for latitude. When that angle reaches its highest for the day, it is noon and you check your watch to see how far from Greenwhich you are.

[SlowButSteady]

Good summary, Minnewaska. The only problem with "the noon sighting" is that it actually consists of a series of observations as the sun rises and then falls around local noon. And, of course, it only can be used with the sun. This means that the sun and horizon must be visible and clear for about 10 or 20 minutes (or more, depending on how accurate ones dead reckoning has been) around local noon.

The "line of position" method is what I outlined above. It was first developed (using slightly different methodology) around the middle of the 19th century (rather fortuitously, and under the most challenging of circumstances; see here) and allows one to fix position any time two or more celestial bodies and the horizon are visible (usually dawn and dusk). With practice, one can fix position in 5 minutes or so twice a day, usually with a bit higher accuracy than the noon position method.

Even if just the sun and horizon are visible, one can still combine ones dead reckoning position with a single line of position to get a pretty good estimate of ones actual position (although, this is not an actual "fix" of position).

[PaulfromNWOnt]

chrisncate:

My understanding is that you take a series of sights, and mark down the time for each of them. If you plot these sights and times on a graph, you will then be able to eyeball the time when the sun was at it's highest point overhead. Using the appropriate almanac/table/form that time will indicate your longitude.

Let me see if I can confuse myself even more:

You use the sextant to determine latitude directly-ish with one sight, but you take multiple sights to make sure that your solar noon is correct to determine longitude accurately...???

Kinda??

Sorta??

Hmm...

[PaulfromNWOnt]

Originally Posted by SlowButSteady

Good summary, Minnewaska. The only problem with "the noon sighting" is that it actually consists of a series of observations as the sun rises and then falls around local noon. And, of course, it only can be used with the sun. This means that the sun and horizon must be visible and clear for about 10 or 20 minutes (or more, depending on how accurate ones dead reckoning has been) around local noon.

The "line of position" method is what I outlined above. It was first developed (using slightly different methodology) around the middle of the 19th century (rather fortuitously, and under the most challenging of circumstances; see here) and allows one to fix position any time two or more celestial bodies and the horizon are visible (usually dawn and dusk). With practice, one can fix position in 5 minutes or so twice a day, usually with a bit higher accuracy than the noon position method.

Even if just the sun and horizon are visible, one can still combine ones dead reckoning position with a single line of position to get a pretty good estimate of ones actual position (although, this is not an actual "fix" of position).

Dood.... I love the idea of accuracy, and not having to rely on only one time of day, but I'm still at the baby steps and hand-holding stage. I'm going to add your post to Minne's for future reference.

Thank you.

[SlowButSteady]

Originally Posted by PaulfromNWOnt

Dood.... I love the idea of accuracy, and not having to rely on only one time of day, but I'm still at the baby steps and hand-holding stage. I'm going to add your post to Minne's for future reference.

Thank you.

I'm not knocking Minnewaska's post at all. Conceptually, that is how celestial nav was done for about 100 years. However, once the line of position methods were developed they were used almost exclusively until electronic navigation (LORAN, GRS, et cetera) were developed.

[smurphny]

I have a cheap plastic sextant in case GPS ever disappears. Being math-challenged, I had a hard time understanding the concepts. Some publications that focus on the trig make my eyes glaze over and I'm convinced they are written by people whose mission it is to discourage most people from attempting celestial nav. There is no way I will EVER understand the math. BUT, understanding the basic idea of the navigational triangle is not too difficult. Once I understood the 3-D picture of global position, assumed position, zenith distance, azimuth, and the hard-to-get-your-head-around idea that the rays of a body hit the entire surface of the earth in a parallel fashion, the actual process slowly became clear. Understanding the triangle is the basis for all of it. I also bought the great little computer program by Omar Reis which has everything needed to accomplish the task of figuring out where you are.

A good publication is Mary Blewitt's Celestial Navigation for Yachtsmen although imo it could explain some concepts a little better.

[AdamLein]

I like Minnewaska's explanation as well. A noon sighting---which I really don't think fell out of use at all (all the cruising books I've read mention noon sights or no sights)---is one example of a special special case of CN, which is the meridian passage---the point when a star crosses a meridian.

Meridians are lines of longitude. At any point in time, a given celestial body's center is over exactly one meridian. "Noon" is when you and the sun are on the same meridian, so noon is the sun's meridian passage. But every star has a meridian passage, and you can do a "noon sight" for any star.

The other method mentioned here is the "line of position" method. This method is based on more complex math that simplifies to basic addition in the case of a meridian passage. You may have heard about the navigational triangle. Imagine taking an orange and drawing two dots somewhere on the skin, but not on the stem or navel. One of the dots is your position on the Earth and the other is the star's position in the sky (or rather, the spot directly below it on the Earth). You can now draw a triangle on the orange by connecting the navel (aka "north pole") with these two dots using great circles. That's the navigational triangle. There's some fancy math for solving these triangles, or you can use tables. Either way, a lot of work.

But not in all cases is the resulting triangle really a triangle. The special case is when the navel and the two dots are lined up. If you draw a great circle through those three points, you are drawing a meridian; both the meridian you are on, and the meridian the star is on. So this is a meridian passage. Now instead of this crazy curvy triangle and the complex math/tables that you need for it, you just have a simple line. Here's how you solve it:

The distance on the line from the north pole to you is CL = 90° - your latitude, or "colatitude".
The distance on the line from the north pole to the star is CD = 90° - the star's declination, which is just a fancy word for latitude on the sky; this is "codeclination".
The distance on the line from you to the star is ZD = 90° - the star's altitude in the sky, measured by your sextant; this is "zenith distance".

Depending on the order the points come in, you may end up adding or subtracting, but once you have this picture in your head, it should be easy to follow. For example if you're farther north than the star (i.e. you're looking south the see the star), then CD = CL + ZD. If you're looking north, there are two possibilities, based on whether the star is higher or lower in the sky than Polaris. You can just draw the picture to figure out the formula, or you can stick to using stars in the south*.

This is how you get latitude from a meridian passage; longitude is conceptually even simpler and has already been explained. Note that it works regardless of whether the star is the sun, a planet, or any other very distant light source (more corrections are needed for the moon). So if I were navigating by CN, I would go for three sights per day: meridian passage of a bright star or planet in the morning and evening twilight (you need to be able to see the horizon) and a noon sight. If I were feeling particularly masochistic I might do the fancy intercept method, but not if I had any real responsibilities at the time, which I expect would be always.

I admit I'm being a bit hard on the intercept method. You don't actually have to do any of the fancy math, because it's all in the tables for you. You only have to do basic arithmetic. But it still is more work than a meridian passage.

*I am simplifying a bit. In principle if you're in the southern hemisphere you will probably be looking north for noon sights, and if you're in the tropics, your noon sights might be any which way. In any case, having that picture in your mind of those three points---north pole, you, star---lined up on a meridian tells you everything you need to know to do CN by meridian passage.

[killarney_sailor]

The best way to learn celestial is to actually do it. Take a sight and one of the standard ways of reducing it and see how you do. Likely there will be some issues with the calculations or perhaps the actual sight (it is a bit of an artform on a small boat). Then take some more sights and keep plugging away at it. When I tried to learn it from a book I found it quite hard to visualize everything. When you do it, step-by-step it makes much more sense and it is easier.

[Minnewaska]

Originally Posted by SlowButSteady

Good summary, Minnewaska. The only problem with "the noon sighting" is that it actually consists of a series of observations as the sun rises and then falls around local noon. And, of course, it only can be used with the sun. This means that the sun and horizon must be visible and clear for about 10 or 20 minutes (or more, depending on how accurate ones dead reckoning has been) around local noon.

The "line of position" method is what I outlined above. It was first developed (using slightly different methodology) around the middle of the 19th century (rather fortuitously, and under the most challenging of circumstances; see here) and allows one to fix position any time two or more celestial bodies and the horizon are visible (usually dawn and dusk). With practice, one can fix position in 5 minutes or so twice a day, usually with a bit higher accuracy than the noon position method.

Even if just the sun and horizon are visible, one can still combine ones dead reckoning position with a single line of position to get a pretty good estimate of ones actual position (although, this is not an actual "fix" of position).

I agree, although, this alternate method is much harder for a 101 level course.

I also agree that you must take several sites around noon, to determine exactly when local noon ocurred. As the angle keeps increasing, it must be getting closer to noon and once it begins to decrease again, you've passed noon. However, I was trying to avoid how to use the sextant when trying to explain why this all works.

We're on the same page, I know.