Question on Celestial Navigation

[jeffrwatts]

Hi all,

I've been reading and working through a few problem in David Burch's Celestial Navigation Home Study Course.

One thing I'm noticing is that my the fix I calculate by sextant measurement appears highly dependent on my DR.

Since:
1) fix is made on two (or more) lines of position (Zn and a).
2) Each line of position is dependent on Hc and Z
3) Hc and Z are then dependent upon my DR latitude and LHA (which is computed using DR longitude).

Note: I'm using both assumed lat and long for tables, and precise lat and log (for formulas).

Meaning if my DR position is reasonably off, then my fix is likely equally off. So, how does this tell me what my true position really is?

Hoping someone can help me build some better intuition here, as obviously people have been doing this successfully for a few hundred years

Thanks much in advance

[SeanPatrick]

Are you saying that you are getting different fix locations when using different APs/DRs? Or are you just having trouble understanding how the fix could be the same using different positions? If it is the former, then it would really help if we could see all of your work.

How far away from the fix is the DR? What are the altitudes of the bodies? What is the time interval between shots? These and other factors can influence how accurate the fix is.

As long as the DR/AP is within a reasonably short distance to the fix (say 20 miles or so), you should get a fairly consistent position. Lines of position are plotted from an azimuth and intercept. The azimuth changes very little with changes in position, so the calculated azimuth is used. But the intercept will change more rapidly with a change in position. One DR/AP may produce a positive intercept (toward), while another may produce a negative one (away) for the same shot. But the LOP should end up in the same position no matter which DR/AP you use.

If the fix is more than 20 miles from the DR/AP, then it is recommended to set the fix as the DR/AP and then do the whole process over again. This can be repeated as many times as necessary to refine the fix until it is less than 20 miles from the DR/AP. (See: the Nautical Almanac; Sight Reduction Procedures.)

[Adelie]

Originally Posted by jeffrwatts

Hi all,



I've been reading and working through a few problem in David Burch's Celestial Navigation Home Study Course.



One thing I'm noticing is that my the fix I calculate by sextant measurement appears highly dependent on my DR.



Since:

1) fix is made on two (or more) lines of position (Zn and a).

2) Each line of position is dependent on Hc and Z

3) Hc and Z are then dependent upon my DR latitude and LHA (which is computed using DR longitude).



Note: I'm using both assumed lat and long for tables, and precise lat and log (for formulas).



Meaning if my DR position is reasonably off, then my fix is likely equally off. So, how does this tell me what my true position really is?



Hoping someone can help me build some better intuition here, as obviously people have been doing this successfully for a few hundred years



Thanks much in advance

DR position and AP are very different things.
DR is your best guess as to where you are.
AP is a location near your DR chosen so the AP-Lat is a whole number of degrees and AP-Long is a whole number of degrees different from GP-long or GHA. That is AP-long has the same minute of arc as GHA so LHA is a whole number.

AP-lat should be the same for all the sights, AP-Long will be different for each sight.

[Rumrace]

I’m happy you got polite intelligent conversation and help. Sextant threads usually trigger the competition squad who arrive with insults assumption and other things stupid people do.
I’ve listened to my 15yr old grandson try to teach his 5 year old brother how a sextant works. We found it entertaining to follow Jupiter every evening two summers ago as one fix. That July Jupiter got hit with a huge asteroid protecting earth. I think it’s a great teaching tool for many things.inside the heliosphere.

[ChrisJHC]

You can pick anywhere for your AP, however the closer to your actual position the better.
Some of the assumptions regarding straight lines and curved surfaces start to fall down if you’re too far away from your AP.

As previously said, you will be adjusting your AP longitude anyway.
You don’t have to pick your AP latitude on a whole degree value, but it does make for easier plotting.

At the end of the day, all you are doing is saying:
1. If I was standing at the AP, what angle should the sun have been from the horizon? And what would the bearing to the sun have been? (Hc)
2. What angle to the sun did I actually measure? (Ho)
3. Based on the difference between 1 and 2, how far towards or away from the AP is the LOP?

The rest of it is just doing the adjustments and calculations then drawing lines on a piece of paper.

Then you get to do it again to get a fix!

[goboatingnow]

Originally Posted by jeffrwatts

Hi all,



I've been reading and working through a few problem in David Burch's Celestial Navigation Home Study Course.



One thing I'm noticing is that my the fix I calculate by sextant measurement appears highly dependent on my DR.



Since:

1) fix is made on two (or more) lines of position (Zn and a).

2) Each line of position is dependent on Hc and Z

3) Hc and Z are then dependent upon my DR latitude and LHA (which is computed using DR longitude).



Note: I'm using both assumed lat and long for tables, and precise lat and log (for formulas).



Meaning if my DR position is reasonably off, then my fix is likely equally off. So, how does this tell me what my true position really is?



Hoping someone can help me build some better intuition here, as obviously people have been doing this successfully for a few hundred years



Thanks much in advance

The Hilare method works by computing the error between your assumed position and the celestial one.
It’s merely a “technique “

[jeffrwatts]

Wow... thanks everyone for the quick responses!!!!

Thanks to SeanPatrick's prompt to show my work, I went back and scrutinized my calculations and found my issue. I do see a pretty consistent fix within 20 nm or so. Posting the results here for the next doubting soul

For reference. I'm using an example from the Celestial Navigation book for inspiration: exercises 7.4 (Altair) and 7.5 (Antares), both taken at the same time UTC.
UTC:
7/25/78 at 04:07:22.
Altair:
GHA: 66 degrees; 55.18 minutes
dec: 8 degrees; 48.87 minutes
Ho: 30 degrees; 31.8 minutes (Hs, ic, DIP, refraction omitted for brevity)
Antares:
GHA: 117 degrees; 19.98 minutes
dec: -26 degrees; 23.05 minutes
Ho: 18 degrees; 49.5 minutes (Hs, ic, DIP, refraction omitted for brevity)

Original DR and LOPs / Fix
dr_lat: 44 degrees; 36.0 minutes
dr_lon: -122 degrees; 14.0 minutes
Altair
Hc: 30 degrees; 31.89 minutes
Azimuth: 109 degrees; 22.52 minutes A; Intercept: 0 degrees; 0.09 minutes
Antares
Hc: 18 degrees; 52.48 minutes
Azimuth: 175 degrees; 21.67 minutes A; Intercept: 0 degrees; 2.98 minutes
Fix is Lat:44 degrees; 39.07 minutes; Lon:-122 degrees; 12.61 minutes

Variant 1 DR and LOPs / Fix:
dr_lat: 44 degrees; 16.0 minutes
dr_lon: -122 degrees; 34.0 minutes
Altair
Hc: 30 degrees; 24.95 minutes
Azimuth: 108 degrees; 54.65 minutes T; Intercept: 0 degrees; 6.85 minutes
Antares
Hc: 19 degrees; 11.21 minutes
Azimuth: 175 degrees; 2.18 minutes A; Intercept: 0 degrees; 21.71 minutes
Fix is Lat:44 degrees; 39.11 minutes; Lon:-122 degrees; 12.7 minutes


Variant 2 DR and LOPs / Fix
dr_lat: 44 degrees; 56.0 minutes
dr_lon: -121 degrees; 0.0 minutes
Altair
Hc: 31 degrees; 14.42 minutes
Azimuth: 110 degrees; 36.62 minutes A; Intercept: 0 degrees; 42.62 minutes
Antares
Hc: 18 degrees; 36.24 minutes
Azimuth: 176 degrees; 32.04 minutes T; Intercept: 0 degrees; 13.26 minutes
Fix is Lat:44 degrees; 39.59 minutes; Lon:-122 degrees; 12.7 minutes

I've written some python code for these experiments. Feel free to fork and take if you find value:
https://github.com/jeffrwatts/celestial-navigation

[jeffrwatts]

Thanks Sean!

I found the issue while preparing the post to show my work.

Appreciate the insight to do iterative fixes when DR/AP are greater than 20nm

[Adelie]

Originally Posted by ChrisJHC

You can pick anywhere for your AP, however the closer to your actual position the better.
Some of the assumptions regarding straight lines and curved surfaces start to fall down if you’re too far away from your AP.

As previously said, you will be adjusting your AP longitude anyway.
You don’t have to pick your AP latitude on a whole degree value, but it does make for easier plotting.

At the end of the day, all you are doing is saying:
1. If I was standing at the AP, what angle should the sun have been from the horizon? And what would the bearing to the sun have been? (Hc)
2. What angle to the sun did I actually measure? (Ho)
3. Based on the difference between 1 and 2, how far towards or away from the AP is the LOP?

The rest of it is just doing the adjustments and calculations then drawing lines on a piece of paper.

Then you get to do it again to get a fix!

The only generally published and relatively modern sight reduction method I know of that allows AP-lat to not be a whole number is Ageton/HO-211 and it's variations which uses the DR-lat. The Hav-Dinoil method may use DR-Lat (but you need to be plugged into the CelNav community to even know of it's existence let alone how to use it), and very old methods using lookup tables for trig functions may also allow it.

All the modern methods are lookup tables (214, 229, 249) where AP-lat is in whole degrees to reduce the size of the tables. You could use an interpolation table such as is used for Declination but that would take extra time and add extra potential for errors which is why it never was done.

My recollection of Davies/NASR and HO-208/Driesenstock are that they use whole number AP-lat too.

There may be some French or Soviet systems that use DR-lat. I haven't been able to figure out how Norries tables work so I can't address that. 229 & 249 are joint US-UK products so there may be an older UK method but I'm not aware of it.

[Adelie]

Originally Posted by jeffrwatts

Wow... thanks everyone for the quick responses!!!!

Thanks to SeanPatrick's prompt to show my work, I went back and scrutinized my calculations and found my issue. I do see a pretty consistent fix within 20 nm or so. Posting the results here for the next doubting soul

For reference. I'm using an example from the Celestial Navigation book for inspiration: exercises 7.4 (Altair) and 7.5 (Antares), both taken at the same time UTC.
UTC:
7/25/78 at 04:07:22.
Altair:
GHA: 66 degrees; 55.18 minutes
dec: 8 degrees; 48.87 minutes
Ho: 30 degrees; 31.8 minutes (Hs, ic, DIP, refraction omitted for brevity)
Antares:
GHA: 117 degrees; 19.98 minutes
dec: -26 degrees; 23.05 minutes
Ho: 18 degrees; 49.5 minutes (Hs, ic, DIP, refraction omitted for brevity)

Original DR and LOPs / Fix
dr_lat: 44 degrees; 36.0 minutes
dr_lon: -122 degrees; 14.0 minutes
Altair
Hc: 30 degrees; 31.89 minutes
Azimuth: 109 degrees; 22.52 minutes A; Intercept: 0 degrees; 0.09 minutes
Antares
Hc: 18 degrees; 52.48 minutes
Azimuth: 175 degrees; 21.67 minutes A; Intercept: 0 degrees; 2.98 minutes
Fix is Lat:44 degrees; 39.07 minutes; Lon:-122 degrees; 12.61 minutes

Variant 1 DR and LOPs / Fix:
dr_lat: 44 degrees; 16.0 minutes
dr_lon: -122 degrees; 34.0 minutes
Altair
Hc: 30 degrees; 24.95 minutes
Azimuth: 108 degrees; 54.65 minutes T; Intercept: 0 degrees; 6.85 minutes
Antares
Hc: 19 degrees; 11.21 minutes
Azimuth: 175 degrees; 2.18 minutes A; Intercept: 0 degrees; 21.71 minutes
Fix is Lat:44 degrees; 39.11 minutes; Lon:-122 degrees; 12.7 minutes


Variant 2 DR and LOPs / Fix
dr_lat: 44 degrees; 56.0 minutes
dr_lon: -121 degrees; 0.0 minutes
Altair
Hc: 31 degrees; 14.42 minutes
Azimuth: 110 degrees; 36.62 minutes A; Intercept: 0 degrees; 42.62 minutes
Antares
Hc: 18 degrees; 36.24 minutes
Azimuth: 176 degrees; 32.04 minutes T; Intercept: 0 degrees; 13.26 minutes
Fix is Lat:44 degrees; 39.59 minutes; Lon:-122 degrees; 12.7 minutes

I've written some python code for these experiments. Feel free to fork and take if you find value:
https://github.com/jeffrwatts/celestial-navigation

20nm is pretty good for a beginner. On a small boat at sea in moderate weather I would expect an experienced practitioner to get down to around 5nm.

[SeanPatrick]

Jeff,

As you can see from the screenshot below, the data generated by my spreadsheet mostly matches your figures. (I used a height of eye of 0 ft., no index correction and standard temperature and pressure, since those bits of information were not provided. I had to fudge the Hs to get the Ho to match.)

By my calculation, your first fix is about 3.2 nautical miles from the original DR. Your second fix is only 0.1 NM from the first fix and your last fix (using an AP 56.2 NM from the DR) is only 0.5 NM from the first fix. I'd say that's about as good as you can get. Well done!

[Adelie]

Originally Posted by SeanPatrick

Jeff,

As you can see from the screenshot below, the data generated by my spreadsheet mostly matches your figures. (I used a height of eye of 0 ft., no index correction and standard temperature and pressure, since those bits of information were not provided. I had to fudge the Hs to get the Ho to match.)

By my calculation, your first fix is about 3.2 nautical miles from the original DR. Your second fix is only 0.1 NM from the first fix and your last fix (using an AP 56.2 NM from the DR) is only 0.5 NM from the first fix. I'd say that's about as good as you can get. Well done!

Do you mean the the OP has multiple fixes, are do you mean the OP has multiple lines of position that are close to the DR position?

[SeanPatrick]

Multiple fixes.

He gives three examples, each with different DRs - but the same sight data. Apparently, he was experimenting with varying the DR (or AP) by about 20' in all directions (N, S, E & W), perhaps to see what effect that would have on the fix. His fixes for the three examples were:

• 44°39.07' N, 122°12.61' W
• 44°39.11' N, 122°12.7' W
• 44°39.59' N, 122°12.7' W

The differences in the fixes are in line with the shortcomings of the traditional methods when using different DRs/APs.

[Rumrace]

Here is an interesting history on the topic from a local retired teacher.

https://owlcation.com/stem/History-o...ow-to-Make-One

[Rumrace]

I have a few replicas and original navigation tools. I have a replica from Iran of and astrolabe, a moon gauge (works) , but the real weirdo is the Radhost Complector. The Complector navigates to other dimensions and is powered by orange quartz
Ago had an ancient navigation tool I believe fell under early astrolabe from goths.