Celestial Navigation Revisited

[P_Funk]

So far I've seen you do your tests near the equator as far as I can recall, so I'm curious to know how this disparity between SH3's Longitude and the real world's, ie. the set width in SH3 versus the narrowing one as you move towards the poles, affects navigation for us. If I'm near the north pole in SH3 will this pose problems for us using existing almanac data? If so, how do you propose overcoming this, and if not... well why doesn't that change what the almanac says for our purposes?

Is everything just simply solved by converting from the spherical world to the cylindrical one as you did in your 3 point plotting demonstration?

Originally Posted by P_Funk

So far I've seen you do your tests near the equator as far as I can recall, so I'm curious to know how this disparity between SH3's Longitude and the real world's, ie. the set width in SH3 versus the narrowing one as you move towards the poles, affects navigation for us. If I'm near the north pole in SH3 will this pose problems for us using existing almanac data? If so, how do you propose overcoming this, and if not... well why doesn't that change what the almanac says for our purposes?

Is everything just simply solved by converting from the spherical world to the cylindrical one as you did in your 3 point plotting demonstration?

I saw from a thread in SH5 Mods Workshop a new figure never mentioned.
When I started chaseing down the numbers involved?
First? My head started hurting.

Then I noticed a possible scaleing number appear!


SH is a flat or tube World for the most part, correct?
Now how do you scale that to create a virtual 'round' World?

Create a Test Mission in the Northern parts.
Go from point A to point B and measure the times and distances.
Do another Test mission at the Equator and measure the same.
Compare the results and see if they workout to nearly real life figures.


I'm thinking I know the answer.

[P_Funk]

Originally Posted by privateer

Create a Test Mission in the Northern parts.
Go from point A to point B and measure the times and distances.
Do another Test mission at the Equator and measure the same.
Compare the results and see if they workout to nearly real life figures.

I believe they've already confirmed that every point of longitude is exactly 120km apart at every part of the map, whereas in the real world its actually far less at the poles meaning that it actually takes longer to go anywhere in SH3 cause you can't use the shortened circle by going around the 'curve' to the north on the globe when you're for instance sailing from Europe the NY.

Its like a used up toilet paper roll of a world.

[11Bravo]

Originally Posted by P_Funk

So far I've seen you do your tests near the equator as far as I can recall, so I'm curious to know how this disparity between SH3's Longitude and the real world's, ie. the set width in SH3 versus the narrowing one as you move towards the poles, affects navigation for us. If I'm near the north pole in SH3 will this pose problems for us using existing almanac data? If so, how do you propose overcoming this, and if not... well why doesn't that change what the almanac says for our purposes?

Is everything just simply solved by converting from the spherical world to the cylindrical one as you did in your 3 point plotting demonstration?

My demonstration was at 50°N and it revealed to me the need to shift the longitude in order to find the correct position. I went on blathering for two posts (talking to myself helps me think) and convinced myself that the shift/stretch needs to be proportional to the inverse of the cosine of the latitude. I tried it and it worked.

Then I studied cylindrical map projections and found one that had the exact same term in the transformation equations...an inverse cosine or secant which is the same thing.

Come back in a few hours and I will show you a series of 3 star shots at different latitudes that graphically demonstrates this stretching of longitude that is required when taking a spherical result and plotting it on a cylinder.

[11Bravo]

Originally Posted by privateer

Create a Test Mission in the Northern parts.
Go from point A to point B and measure the times and distances.
Do another Test mission at the Equator and measure the same.
Compare the results and see if they workout to nearly real life figures.


I'm thinking I know the answer.

I've done this and the world is flat for time speed distance, cylindrical for navigation off the map edges, and spherical for astronomical data when assumed position is on your local meridian, and cylindrical again when your assumed position is not.

It really is just a cylinder and I will post some stuff with the equations. I already posted the links to the map projection page in my reply to vanjast above if you want to study it.

I am building the time speed distance stuff at the same time as the sunrise/sunset almanac. 1° = 120 km at any latitude E-W or N-S. Probably a week away...

[11Bravo]

The U-13 is on its 3rd pre-war voyage to develop navigation tools for the war. This mission is to better understand the Nautical Chart, especially the map projection and how how it relates to Celestial Navigation.

The demonstration of the 3-star shoot at the end of the last voyage revealed that a correction factor to longitude was necessary. This mission tests that concept by conducting several 3-star shoots at varying latitudes.

I will choose assumed positions on either side of the observing position. One assumed position will be 1° West and North of the observing position, while the other will be 1° East and South of the observing position. We will plot the error triangles for both assumed positions. We will also correct the longitude of the error triangles using the 1/cos or sec of the assumed latitude.

If the assumed map transformation is correct, we should see the error triangles diverge from the observing position as we increase latitude. If the correction factor is correct, we should see the corrected positions move back to where we know they should be.

I think the map transformation is this cylindrical equidistant projection. The equations are shown on the figure.

You can read more about it at the following links

http://mathworld.wolfram.com/Cylindr...rojection.html
http://mathworld.wolfram.com/Equirec...rojection.html
http://en.wikipedia.org/wiki/Equirectangular_projection

[11Bravo]

We started on the Equator and shot 3 navigation stars separated by about 120° in bearing to get a nice shaped error triangle. All the site reductions are shown together with the almanac data from the two assumed positions. The error triangles nearly coincide and the correction at these latitudes are almost nonexistant. Also shown is a 30 km circle for reference.

I should say something about the clocks. These shots were done with the screen time at 0001, 0002, and 0003. Since I started the mission in nautical time zone +2, my base time is +2 and I need to add that to the screen clock to get GMT. The excellent results shown give us confidence in several things...the clocks, the sextant, the almanac, and the method of graphing the result.

Now we move to 45°N.

[11Bravo]

Now we see the error triangles are closer to the assumed position longitudes. The correction factors near 45° are substantial, and move the plotted position in the right directions and amounts to give us a good estimate of our position. Note that I am applying the sec LAT correction factor to each assumed LAT separately. This is a new discovery that further increases accuracy over what I demonstrated in the previous voyage.

Now we move to 60° N latitude.

[11Bravo]

At this latitude the correction factors are on the order of 2. The error triangles are clearly graphing closer to their assumed longitude lines than they should. And the correction to the longitude is taking care of the map transformation distortion.

Now we move to 75°N latitude.

[11Bravo]

The same trend is observed. At this very high latitude, the sec LAT correction factor is about 4. The error triangles are hugging their assumed longitudes and the large correction factor moves them close to the correct position. This is the largest error we have seen so far, and is probably magnified by the large correction factor at the distorted extremes of the map.

I should also point out for this position, we are in TZ +00 with a BTZ of +00, and therefore the screen clock reads GMT directly.

[11Bravo]

What do the results of this mission tell us.

Several things.

First, we would not be this accurate unless the sextant, clocks, and almanac were not very close. In celestial navigation, everything is linked together, and the result can not be right without everything else in the tool box being right also.

The error triangle behavior where it drifts toward the assumed longitude at higher latitudes is exactly what should happen on a sphere. Since we are using spherical trigonometry to find our position, the results should be plotted on a sphere. The results don't know how we are plotting them, so the error triangles go where they are supposed to on a sphere. The method works...but needs the correction because of the map projection.

The correction term certainly seems to be the sec LAT or 1/cos LAT. And this equidistant cylindrical projection is the one that provides it. It even looks right.

I think this strong evidence that we know what map projection the developers used. And I think it is strong evidence that we are on the right track here.

The greater error at higher latitudes might be a warning though of the limits of plotting positions on cylinders.

Next mission of this voyage will be a closer look at the clocks...radio messages from reaper7 and vanjast need to be answered.

[reaper7]

Originally Posted by 11Bravo

Next mission of this voyage will be a closer look at the clocks...radio messages from reaper7 and vanjast need to be answered.

Haven't received a mail, can you send it again - or PM me here.

[11Bravo]

No rest for the wicked...still working on it.

[CaliEs]

Originally Posted by 11Bravo

We started on the Equator and shot 3 navigation stars separated by about 120° in bearing to get a nice shaped error triangle. All the site reductions are shown together with the almanac data from the two assumed positions. The error triangles nearly coincide and the correction at these latitudes are almost nonexistant. Also shown is a 30 km circle for reference.

I should say something about the clocks. These shots were done with the screen time at 0001, 0002, and 0003. Since I started the mission in nautical time zone +2, my base time is +2 and I need to add that to the screen clock to get GMT. The excellent results shown give us confidence in several things...

I dont see "excellent results". What i see are posts of ambiguity and questions.
I look at your first calculation with the stars Alioth, Antares and Sirius
My result with your given data is this: 3StarFIX = 000-41.1'S 030-28.3'W, means 50.7nm (= 101.4km) from your real position 000N 031W.

Show us the concret calculation steps from the sighted position to the calculated Hc.
Also give us evidence of the taken shots of the stars. For example Sirius at 12°20 at 0203 GMT.
Why do you put in an index-error of 0.6' to the calculation?

[11Bravo]

Originally Posted by CaliEs

I dont see "excellent results". What i see are posts of ambiguity and questions.

Thank you for joining us. You certainly came to the right place for ambiguity and questions. Seeing "excellent results" comes from understanding the long challenging history of implementing in-game real navigation within SH3. Usually I just see stars though...

Originally Posted by CaliEs

I look at your first calculation with the stars Alioth, Antares and Sirius
My result with your given data is this: 3StarFIX = 000-41.1'S 030-28.3'W, means 50.7nm (= 101.4km) from your real position 000N 031W.

It looks like you took my observations and dumped them into a program that spits out a position on earth. Without having the program and understanding what assumptions it is making, I can't tell you why it gives a different result. But I can clearly explain how I am getting my results.

Originally Posted by CaliEs

Show us the concret calculation steps from the sighted position to the calculated Hc.
Also give us evidence of the taken shots of the stars. For example Sirius at 12°20 at 0203 GMT.
Why do you put in an index-error of 0.6' to the calculation?

Most of what you ask for has been covered in this thread.

Hs is the measured altitude of the star using a linear sextant with certain parameters set in the cameras.dat file of the game. Screenshots are available in earlier posts.

Index is a correction based on observing the error in 23 navigation stars from a known position with the sextant. The results are available in an earlier post. I notice that my errors largely are positive, so I subtract their average in an attempt to improve accuracy. For the flak station sextant, that is 6'.

Ha is what I am calling the apparent altitude after the index correction.

Alt is my main correction to the measured altitude. It was based on a camera calibration curve I developed for the external view at the station where the sextant is used. It depends strongly on the screen position, and therefor sextant position. Covered in earlier posts above.

And that brings us to my Ho. Let me dig out and post that Sirius screenshot. I will put the Alt correction chart on it also. Here we go.



SH3's Sirius displayed in my sextant together with the corresponding Alt correction based on in-game measurements of the display error of the horizon. Take a look at the horizon. That is a feature of how information is displayed in the game, and my Alt correction puts it in the right place after you measure Hs and optionally apply an Index correction. I squint and measure the star to the nearest 10'. Go ahead and hit "CTRL" + "+" a few times and stick your nose on the screen. How did I do?

Also notice how the SH3 clocks are handled. When you start a mission, SH3 remembers your starting nautical time zone and applies that as an offset to the "local time" and the "screen time". I determined how to handle that by making observations of sunrise/sunset data. Also covered in detail in this thread. I have a few more hours of testing ahead of me for that though. That will be the next post.

Now we have everything we need to plot the Sirius line of position on the nautical chart. Here is my result.



Celestial navigation works by comparing the altitude or height above horizon of a body from your unknown position to a value calculated from an assumed position nearby. Here I have created a test mission that puts me at 0°N 30°W. I shot the star. I consult an almanac for an assumed position AP of 1°N 31°W.

Here is what I know.

1. If my boat was at the assumed position AP, the star Sirius would be observed to be 12°19' above the horizon at a bearing of 253°.

2. From my real position, I observe the star Sirius to be 11°40' above the horizon which is lower by 39'.

3. Things further away look smaller and lower in the sky.

4. My position must be further away from Sirius than the AP at 1°N 31°W is from Sirius.

5. Planet SH3 has 1° = 120 km so that 39' difference in altitude would be 78 km is distance.

6. There are an infinite number of positions on planet SH3 that are 78 km further away from Sirius than is the AP. But the ones near my boat run on an almost straight line at right angle to the Sirius bearing.

7. I must be on that line.

Using the ingame mapping tools, this is what I do.

I plot the bearing from AP to the star. I advance or retreat with the ruler the distance toward or away from the star. I draw a right angle and call it the Line of Position for the star.

Repeat two more times and I get the error triangle that should contain my position if everything was done right and everything was right.

Read the whole thread. I went into this thing with my eyes open. I am attempting to quantify the errors. I am stating my assumptions and I am showing my results, including the errors.

My mods are available for download, link in my signature.