Celestial Navigation (written by a) Dummy

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…

CelNav for MSFS for Microsoft Flight Simulator | 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!

I. PREMISES:

In the simplest possible terms, celestial navigation follows five simple premises:

  1. At any given date and time there is a place on the Earth where a given celestial object will be straight overhead.

  2. With a sextant (or other angular measuring device) an observer can measure the angle from the observer’s present position to that celestial object.

  3. 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.

  1. 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).

  2. 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).

II. CONCEPT:

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.

III. METHODS:

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.

Sight Reduction Calculator (celnav.de)

You will also need the Nautical Almanac for the current year:

Everything You Need For 2023 (thenauticalalmanac.com)

For this, I’d recommend the series of videos by P Gatacomb:

MSFS - Celestial Navigation Introduction and Tools (youtube.com)

MSFS - Celestial Navigation Part 1 (youtube.com)

MSFS - Celestial Navigation Part 2 (youtube.com)

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. :+1:

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!

IV. CONCLUSION

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!

Good luck!

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Damn… it’s 11h45pm here and I am just heading to bed…

I guess not yet? :rofl:

Thank you, @Deacon211!

Should this thread fit better under the Article section?

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That has exponentially increased my admiration of those adventurers who did (and do :wink: ) venture forth over open oceans without modern nav aids.

And

Although you did a much better job of explaining that than my high school trigonometry teacher did in explaining whatever the hell he was trying to teach me…

I yet again find myself curled up in the foetal position on the floor mumbling “na, na, na, na…”

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If I might recommend the following visual explanations of the basic trig functions:

Visualizing Trigonometry: Sine Function - YouTube
Visualizing Trigonometry: Cosine Function - YouTube
Visualizing Trigonometry: Tangent Function - YouTube

I’ll see if I can find it again, but a gentleman on YouTube had an excellent series on real world use of a sextant when sailing for both sun and start shots. The altitude and speed differences in an airplane require differences in procedure and calculations, but the concepts and principles are the same.

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Great post, @Deacon211!

I may have told this story before, but this reminded me about the Navigation teacher at my flightschool. He had served in the merchant navy during WWII and as a navigator with Scandinavian Airlines on DC-4, 6 & 7 and some other types.
On the first lesson he asked us if we had gotten our tables… We looked at each other and nobody had heard of any tables. He stormed out, went to the school admin department and came back with copies of…sine, cosine and tangent tables…!
The man remembered the coordinates for every major city in the world, but he never accepted using calculators.
I had a great time learning how to plot dead reckoning tracks.

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So I shortened my sleep today by some 30 minutes because of this thread (and by some other 30 minutes because of our youngest one but that is a different story) and then saw some weird lines drawn on a map in my dreams :dizzy_face:

The tutorial shed some light on few aspects of CelNav which were not entirely clear to me, like the difference between the Easy Way and the Old School Way in plotting the fix (in that the Old School Way relies much more on DR than the Easy Way).

Btw. there may be actually Even an Easier Way since Mr Umland (the guy behind the Sight Reduction Calculator) created also Sight Reduction for the Sun calculator

https://www.celnav.de/sunsight.htm

which requires the user to input just the day and exact time of the Sun shot and it looks up the tables automatically (so no need for an almanach).

It probably does not get any easier than that. How much of the CelNav legacy is left though is another discussion :slight_smile:

Either way, I think I will go the Even an Easier Way since I enjoy rather the plotting the fixes and calculating new headings and such rather than looking up the tables and filling in the forms.

Interestingly enough, it seems that the CelNav mod v3 is introducing some error into the measurements. When I played a bit with the tool trying to get a fix when sitting on an airport, I made three Sun shots with three slightly different results (same AP, same UTC time). The difference between the three was of course just the intercept. To be honest, I did not get the fix reasonably close to my real position. Need to play more and understand more…

And the last thing before I shut up finally - on fs.to there is a CelNav mod v4 which actually makes you take the celestial body shot on your own :slight_smile:

Not a big fan of it but it may be appealing to some for sure.

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I love an Even Easier Way! Especially to start out. I kind of jumped in the deep end by trying such a long leg to start, but I think the Sight Reduction Calculators really help getting the essentials cemented in your mind. Then, if you have an interest, you can always add to it from there.

The reason that I moved on from the calculators was that there was so much that I didn’t understand about what I was doing and why I was doing it.

Though my tutorial up top is kind of average at best, I was hoping to just explain things like, Why do you use an Assumed Position instead of just using your DR position? and What IS the Azimuth and Intercept really?, which I wish someone had explained to me before I started as I would not have plotted my Intercepts backwards just because the YouTuber had made a mistake! :laughing:

There’s some really interesting math there that I just don’t have the skills to intuit unfortunately.

For instance, I recall seeing in one of those Army Air Corps manuals that an object is better for position determination at some angles, but better for speed determination in others. This makes sense since all your readings are plotted along your Azimuth. So, at some angles it would be like trying to determine the winner of a foot race with a finish line that ran diagonally rather than perpendicularly to the race course. The sensitivities are just different.

And I also sometimes just got weird results from the calculator. I honestly don’t know if this is some kind of built in uncertainty or if, literally, the sensitivities and complexity are such that a 0.001 somewhere results in miles of difference! :person_shrugging:

Yeah, you and me both! :laughing:

By all means! Like I said, I kind of jumped in the deep end and would have benefitted from a few pictures and a little dumbing down at first (and still). :wink:

@Troll

Great story! Sounds like you could add some sage advice to this thread. Dead Reckoning is about as close as I got to old school navigation. We had dumped our sextants by the time my instructor (an old Corsair pilot with a AMAZING mustache) taught me! Though, that might have also been a short range aircraft thing too.

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I’m actually a big fan of tables and printed nomographs versus using calculators for a lot of things. Reading a table or using a nomograph will usually get you in the ball park of the right answer unless you manage to do something very incorrect procedurally (ie wrong page/book of tables, wrong scale on the nomograph). It’s much easier to miss key on a calculator, and depending on where in the number string it happens the resulting error can be minor to massive.

When learning the user really doesn’t have a frame of reference to know if that answer is correct, barely wrong, or really wrong. Even if they are following all the correct procedures, entering a digit wrong can be a massive mistake. Where as reading the wrong line on the table or wrong tick mark on the nomo will get them in the ball park and provide a traceable point of error to correct.

Also calculators are very handy for doing a whole lot of things with numbers. They are not optimized for doing certain specific things however. Back before calculators were everyday items, there were an awesome array of “mechanical” (if you want to call a nomograph mechanical) aides to solve problems very quickly and efficiently. If you have a spare half hour, this 1950’s training film about USN Maneuvering Boards has several great examples.

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Still wondering why in The Easy Way the DR position is not used in determining the fix in the same way as in the Old School Way?

The only difference between the two is that the sight reduction tool automates the table looking up and form filling part with the other steps equal, right?

Am I missing something?

I wondered the same thing and, barring the possibility that the YT author did it incorrectly (his is the only example I’ve ever seen), my guess is as I said above, error sensitivity.

Since the web based method only requires you to round to the nearest minute, your DR position basically is your AP. This is actually the ideal situation because all those example pictures of cones and Lines of Position circles show a solution from the AP, which, once you go to the table method, might not be where you are.

In fact, if we take the case where your DR position is 30 minutes from the nearest degree of latitude, your AP will be at least 30NM away from you, and farther unless the longitude just happens to work out to be the same as your longitude (remember it has to be added/subtracted to the GHA) which is unlikely.

I even think that it could be worse when adding in the effect of Azimuth, because the Azimuth only points from the AP to the celestial object, which may not be towards you.

So, with the table method the best thing you can say is that you are on the Line of Position (that perpendicular segment that you draw from what would be your “solution” in the Web based method.

Since you can’t say where precisely on the LOP that is, you need a (theoretically) known position to narrow down that solution.

That’s just a guess of course, but I do think the geometry can greatly affect your solution, particularly in the Old School case, where you and the AP are not in the same place.

Like you and a friend standing far apart and trying to describe where something is to the other based on distance and angle.

Of course, I could be completely wrong! :rofl:

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Thanks for your reflection.
I suppose it does not do any harm if I use the DR in the Easy Way as well.

Well, I wonder if that doesn’t depend on how good your DR is.

At its simplest, the web based method says “You thought you were here, but you’re actually X distance on Y azimuth away”.

So, if you average it, then you are basically halving your correction. Sort of.

I think the effect of this is worse the worse your DRing is. I also found that errors compound. In my case, since I was plotting the Intercept backwards, I kept reducing my ground speed estimate, which made my next DR plot worse, which, etc,

I’ll be curious to see what your experience is as you go along. :slightly_smiling_face:

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You shall see soon :grinning:

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Good luck! It’s pretty rewarding.

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Only slightly related to this topic but I figure we’re talking fundamentally about not being lost…

Recently created a DCS scenario set in a pre-GPS/Moving Map era (just a TACAN and buried somewhere in there possibly an ADF).

Think it was in the F-5. So used to relying on the gizmo’s I just jumped in and took off. The F-5 was fun! Last time I flew it was in 2D. In VR it was - felt like - being in a go-cart with an anemic 2-stroke engine. And cozy, like I was wearing it…

Required me to go to a bombing range NW of Groom Lake. At low level.

Played that map a lot but I found out how much I was a GPS cripple from flying Gen-4 platforms. Lot of mental cycles spent keeping track of where I was (or thought I was); flipping to the F10 map and back; comparing it to the view out the window, etc.

My position was not displayed on it of course. Got lost not long after the TACAN went away (LOS).

Reverted to ‘best guess’ navigation based on time flying there. Then at some point I rolled over and saw “the farms”. Good to go! Managed to [just] miss flying into the “box” (the scripts will bark at you if you do).

Guess back in the day you had to do more map study.

Reminded me of treks in the woods/mountains way back, and going offshore in my boat (fiberglass skiff with a motor really). I was using DR then, before I knew what it was called I guess (dumb teenager).

LORAN was a thing but beyond my budget.

Plot a course on a [paper] map beforehand; hoist the anchor; line up some points on the shore; compass + time + speed. The day I could afford a ‘flashing’ depth finder made it a bit easier; had another dimension to reference.

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@jross Great stuff. Yeah it is sooo easy to become a GPS/HUD cripple as they used to call it.

But you’ll be surprised at how quickly you get good at it.

@apollon01

You know, the more I think about it, the less luck I think your going to have with using the DR to improve your position.

When you think about it, if you’re rounding to the nearest minute, you’re AP is never really more than half a nautical mile in either Lat or Long away from your AP.

Unless you’re either really lucky or good, your Cel Nav position will probably rarely be close enough to get any serious triangulation (or biangulation I guess) from that relationship.

Essentially, what you will do is plot the Intercept distance along the Azimuth, then top it with a T to show the LOP segment. Then you would follow along that T top until you were at the closest point to your DR position.

But, considering how close the AP is to the DR, you’re already there. Following along that LOP in either direction will almost always take you further away from your DR.

If you’re really close, then maybe you could tighten up the position a bit. But, since there will almost certainly be an inherent level of error in the whole process anyway, you may be “Measuring with a micrometer, marking with chalk, and cutting with an axe! :slightly_smiling_face:

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Nicely put :+1:

And all you say (AP inevitably being close to DR) makes sense.

I think first time I will go really simple so no messing with DR when determinig the fix anyway.

Already working on slashing the DC-6 checklist down to bare minimum so that I can manage all that on my own.

A Superpilot, you see?

Plane Thumbs Up GIF

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I didn’t mention that this was a quarter century ago, and I have never used dead reckoning since… :wink:

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Sounds like the impetus for a X-country multiplayer meet up: go from A → B, where A is a random aerodrome for each player. Using only the cel-NAV gear…hmm…

Cel-Nav…this brings me back to watching the nav trainees (in some version of a B737, military, don’t recall the actual type). I imagined them all taking turns peeking out the ‘porthole’ to take a reading. really NO idea what they actually did. They were allowed to deviate some amount. Memory is foggy here

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