Having just completed learning a bit of CelNav I thought I might throw up a summary of my very broad level understanding of it…just to ease the way for anyone who wanted to give it a try. I’m going to try to avoid getting too in the weeds, in part because smarter people than me have done it better, but mainly because, with surprisingly little effort, I could say something incredibly wrong.
So, take what I say with a grain of salt and back it up with some of the good tutorials out there. My personal recommendation is to use Eric van der Veen’s
excellent tutorial contained in the Cel Nav download for MSFS…
which is necessary to perform celestial navigation in MSFS anyway (and is where I shamelessly cribbed most of my information and pictures from…my thanks to Mr. van der Veen for his great work and explanation!).
OK, here we go!
In the simplest possible terms, celestial navigation follows five simple premises:
At any given date and time there is a place on the Earth where a given celestial object will be straight overhead.
With a sextant (or other angular measuring device) an observer can measure the angle from the observer’s present position to that celestial object.
Knowing 1 and 2, you can draw a cone, with the angular height (AKA Altitude) the same as your sextant reading and with the object as your apex. As shown below.
The base of the cone is a circle. The observer must be somewhere on that circle for 1 and 2 to be true. This circle is what can be considered your Line of Position (LOP).
If you can determine your direction to that celestial object, your cone basically flattens into a triangle (essentially a slice of the cone). Theoretically, the observer’s position would be in the acute Earthbound corner of that triangle (shown by the biplane in the picture).
The concept of finding your celestial position isn’t quite as straightforward as that however.
If I could distill it down to a single sentence, I think it would be correct to say that:
“You find your celestial position by determining the angle(s) and direction(s) to a celestial body (or bodies) from a known point near you (i.e. the Assumed Position [AP]), then compare the computed angle(s) to the angle(s) you observe and correct the difference between the two, from the AP, to find your actual position.”
As a approximate example, let’s say that you think you’re on the cone above. But your observed altitude (angle) is greater (steeper) than the one you calculated. You must be closer to the point where the object is straight overhead (like standing more directly under a lightbulb). So, you calculate the difference between the two angles and that is the distance closer you are!
Now, in reality you don’t calculate the angles from where you are. You do that from the Assumed Position, which is explained below, but is derived from your DR position. But the concept still applies.
From this all else follows and is mostly math and corrections for physics and geometry.
There are two ways (that I’m aware of) to calculate your position in Cel Nav. I’m just going to call them the “Easy Way” and the “Old School Way”
Bear in mind that, these methods are examples of sighting a single object, like the Sun. Triangulating via multiple objects (like stars at night) is based on the same concept, just with the calculations being a bit different.
A. The Easy Way
The Easy Way is easy in large part through the use of a Web Based Sight Reduction (WBSR) tool that does away with a lot of table referencing and math. You can find it here.
You will also need the Nautical Almanac for the current year:
For this, I’d recommend the series of videos by P Gatacomb:
The one thing I’d mention is that the video author does make a sign error when plotting his position in the second video. I’ll address this below at the appropriate point.
With these two tools in hand:
1. Create a Dead Reckoning (DR) Position.
As death and taxes are unavoidable, so is DR when doing either kind of Cel Nav if for no other reason than that you need a position to start from. It goes without saying that the quality of your DR work will reflect on your Cel Nav accuracy, but probably less so using the Easy Way.
2. Create an Assumed Position.
I already know what you’re going to ask:
“Wait, isn’t our DR position basically an assumption of our position already?”
To which I reply, excellent question conveniently inquisitive reader!
The best pilot friendly definition that I can come up with for Assumed Position is this: An Assumed Position is your DR position rounded to make the math easy which I think is something any pilot can appreciate!
In the case of the WBSR tool for example, you are required to round to the nearest minute. However, considering that the size of a minute of Latitude/Longitude is only around 1 Nautical Mile, this means that your DR position and AP will probably be quite close to each other.
This is not the case for the Old School Way.
3. Enter the known data into the WBSR tool
I’d watch the videos in the above links to see what he enters and what he doesn’t. Fundamentally though, we are telling the tool that we are at Lat/Long X (the AP) and the body we are interested in is defined by Greenwich Hour Angle Y and Declination Z. The few other things we are telling the tool are specifics about us, the observer.
4. Take the Sextant Shot
Follow the instructions that come with the Cel Nav app.
5. Enter the Instrument Reading into the appropriate box and click Reduce Sight
The WBSR tool will immediately calculate your Observed and Calculated Altitudes (angles) and will populate the Azimuth and Intercept fields.
6. Plot the Azimuth and Intercept to find your celestial position.
The Azimuth is the direction that the celestial object you sighted is from the AP. The Intercept is the distance. Be careful! The Intercept can be negative in which case you need to plot the Intercept in the OPPOSITE direction!
And that’s it! Pretty straightforward once you try it a couple of times.
B. The Old School Way
The Old School way is primarily different from the Easy Way in that you are using traditional tables to look up the same data that the WBSR tool would look up for you. Because these tables are, as they traditionally were, published in book form, it was/is necessary to publish the information in larger increments and then allow the user to adjust these values through a series of corrections.
For this method, I learned primarily by using the excellent tutorial that the Cel Nav author publishes with his app.
Solely by way of comparison, I’ll give the high level overview of that process.
1. Create a Dead Reckoning (DR) Position.
Step 1 is the same and for the same reasons…you need to base your calculations on somewhere. But, DR plays a much more significant role in the Old School method because, in the end, you’re going to use it as a second position reference.
So, if your DR position is wonky, it can really mess with your final position.
2. Create an Assumed Position.
Step 2 is also the same, and will follow organically from filling out the Celestial Precomputation form, but I mention it separately because it is a significant cognitive concept and functions a little differently than with the Easy Way. Since the tables in the Nautical Almanac are only published to the closest degree, your Latitude must also be rounded to the nearest degree. Your Longitude is a little more different still. Your Longitude is actually chosen so that the minutes can be added to or subtracted from the Greenwich Hour Angle with a result that comes out to a whole degree. This will result in your Local Hour Angle (LHA).
In case you are wondering why, my best guess goes back to the sheer size of the data set involved in publishing every minute of Lat/Long which would have had to have been carried in book form by every navigator out there.
The upshot of this is that your AP (which was in the previous method probably within a mile of your DR position) can be quite far away from it now, which will affect the geometry of the entire process.
This is important because your eventual sighting will result in an Intercept that is along the Azimuth from the AP, not necessarily from you! I believe that this is one of the reasons that your DR position is so important…because your correction can potentially be based on an AP that is so far away.
3. Complete the pre-sighting portion of the Celestial Precomputation form.
You will have started your Celestial Precomputation form already in order to create your AP. Most of the rest of the form will be finding your Azimuth and applying any of a number of potential corrections for the time of sighting (which must be corrected if not on the whole hour), the Coriolis Effect, refraction, etc.
But, in the end you will wind up with an Azimuth and a Calculated Altitude. Note that you get both of these before rather than after you make your sighting, unlike the *Easy Way but they mean the same thing.
4. Take the Sextant Shot and Finish the Precomputation Form to calculate the Intercept
The tutorial has you preplot the AP (corrected for Coriolis Effect) and Azimuth on your chart before the sighting (along with a 10% circle of error estimate on your DR position), but I think that is primarily to save time.
In any case, when the time comes, take your sighting and complete the form to determine your Intercept.
5. Plot the Azimuth and Intercept solution
Functionally, this works just like the Easy Way. The only difference is that this doesn’t quite complete the process in this case.
6. Plot a Line of Position at a right angle to the Azimuth at the Intercept
This is a bit of supposition but, because your Azimuth and Intercept can potentially be nowhere near your DR position in this method, you can’t simply accept the Intercept as your final position. You need to use a second source. And the only one you have available is your DR plot.
So, remember way back to the base of that cone that we determined we were on? The Azimuth and Intercept was a point on the triangle at the base of that cone. This right angle line that we draw from the Intercept represents a wider section of that same circle (cone). We are somewhere along it.
And, since we are accepting that our DR position is a valid secondary position, our final calculated position, our FIX in other words, is where that right angle line (the LOP) passes closest to our DR position.
Now you can see why the quality of our DR position was so important in this method!
Well, this was a lot longer than I’d intended, but it’s just not a short subject unfortunately.
This doesn’t really address multi-body shots, except to say, as I had earlier, that the basic concept/plotting is very similar.
As I also said, I’d highly recommend the sources that I listed above for exactly HOW to use either of these methods. What I hope I’ve accomplished here is to maybe explain just a little of the WHY, which took me a bit to piece together as I was learning it (and continue to learn it) myself.
It can be quite satisfying to plot your position this way. I highly encourage trying it!