Celestial Navigation Qs. Simulated sights, long term almanac

[ohthetrees]

He has two versions. The longer is advertised as more accurate than the original tables.

The regular one is 90 pages:
https://www.celnav.de/tables.zip

The compact one is 15 pages (accuracy suffers of course):
https://www.celnav.de/compact.zip

I found them on this page: https://www.celnav.de/page3.htm
which has some cool single-file html (javascript) based calculators, including sight reduction that you can download locally, and work on any browser. Phone, laptop, whatever. It has a long term almanac and corrections internal. I like it, but I'm trying to find the absolute easiest emergency nav setup that requires no electricity or batteries.

FYI, I had a hard time expanding the zip files with the regular default Mac archive unzip utility. The command line version works, or you can download mac utility like BetterZip or the like.
I tried to email Henning about it, but he has removed his email address from his website and materials, and only provides a fax number, which is more than I'm willing to do

[SeanPatrick]

There are several non-electronic emergency nav kit ideas in the NavList archives.

[Gruz]

Originally Posted by ohthetrees

I'll pick Kolbe up! Would it be possible to use the Kolbe almanac with something like Henning Umland Ageton tables? Or any other arbitrary tables or even direct calculator solution? Or is the almanac layout specific to the provided reduction tables? Forgive the naive questions, I'm very new to this stuff.

What do you think of his Ageton tables by the way? I haven't tried them yet, having a hard time because he asks for 't' which he describes as meridian angle, which seems like it should be similar to LHA, but is apparently something different?! He doesn't explain how to calculate it.

We chose a parallel of latitude (Lat1) north of our estimated latitude. Preferably, Lat1 should be marked by the nearest horizontal grid line on our chart or plotting sheet.

From Lat1, Dec, and the observed altitude, Ho, we calculate the meridian angle,t, using the following formula:



t= +/- arcos (sin Ho - sin Lat x sin Dec) : (cos Lat x cos Dec)




In all calculations, the sign of Long and t, respectively, has to be observed carefully.


Easter longitude: positive

Western longitude: negative



Eastern meridian angle: negative

Western meridian angle: positive

[ohthetrees]

Originally Posted by Gruz

From Lat1, Dec, and the observed altitude, Ho, we calculate the meridian angle,t, using the following formula:

t= +/- arcos (sin Ho - sin Lat x sin Dec) : (cos Lat x cos Dec)

That method of finding t would require a calculator, at least for me! Which I'm trying to avoid. If I had a calculator, I could just sight reduce directly with:

Hc = sin-1(sin(Dec) x sin(aLat) + cos(Dec) x cos(aLat) x cos(LHA))
Z = cos-1((sin(Dec) - sin(aLat) x sin(Hc)) / (cos(aLat) x cos(Hc))


I found an easy definition of t in Siranah's version of the Ageton tables Ageton Tables.

The meridian angle "t" is calculated from "LHA" according to the following rule:
if LHA < 180° t = - LHA (GP is WEST of AP)
if LHA > 180° t = 360° - LHA (GP is EAST of AP)

[Gruz]

Originally Posted by ohthetrees

That method of finding t would require a calculator, at least for me! Which I'm trying to avoid. If I had a calculator, I could just sight reduce directly with:

Hc = sin-1(sin(Dec) x sin(aLat) + cos(Dec) x cos(aLat) x cos(LHA))
Z = cos-1((sin(Dec) - sin(aLat) x sin(Hc)) / (cos(aLat) x cos(Hc))


I found an easy definition of t in Siranah's version of the Ageton tables Ageton Tables.

The meridian angle "t" is calculated from "LHA" according to the following rule:
if LHA < 180° t = - LHA (GP is WEST of AP)
if LHA > 180° t = 360° - LHA (GP is EAST of AP)

So, what you are going to use to write it down, papyrus and charcoal or wax tablet and stylus.

[Adelie]

I’d use wet or dry erase markers on laminated workforms and plotting sheets.

[Adelie]

Originally Posted by ohthetrees

He has two versions. The longer is advertised as more accurate than the original tables.

The regular one is 90 pages:
https://www.celnav.de/tables.zip

The compact one is 15 pages (accuracy suffers of course):
https://www.celnav.de/compact.zip

I found them on this page: https://www.celnav.de/page3.htm
which has some cool single-file html (javascript) based calculators, including sight reduction that you can download locally, and work on any browser. Phone, laptop, whatever. It has a long term almanac and corrections internal. I like it, but I'm trying to find the absolute easiest emergency nav setup that requires no electricity or batteries.

FYI, I had a hard time expanding the zip files with the regular default Mac archive unzip utility. The command line version works, or you can download mac utility like BetterZip or the like.
I tried to email Henning about it, but he has removed his email address from his website and materials, and only provides a fax number, which is more than I'm willing to do

The extra accuracy of the bigger tables really don't get you much. There are still big problems associated with the tables being a step function that overwhelm the improvements from using the bigger tables.

See attached search from NavList discussing the accuracy of Ageton (HO-211). Paul Hirose has done a lot a error analysis of Ageton results.
NavList Message Index: January, 2014 to December, 2019

Using the original tables you can expect RMS average altitude error of 1.23', 14.6% exceeded half a minute, and worst was 31.3'. Azimuth RMS error was 2.76', 0.184% exceeded 0.5°, worst was 2.0°.
NavList: HO 211 (Ageton) sight reduction accuracy (135559)

Using the Bayless or Pepperday tables you can expect altitude RMS error = 2.02', 43.0% exceed 0.5° altitude error, worst altitude error = 43.4'. Azimuth RMS error = 4.56', 0.503% exceeded 0.5' error, worst was 2.4°.
NavList: HO 211 (Ageton) sight reduction accuracy (135559)

If you use a table compiled for every 0.1' then RMS error is 0.60', 3.24% exceed 0.5' error in altitude and max error is 21.2'. For azimuth RMS error is 1.43', 0.037% are in error over 0.5°and max error is 1.153°.
NavList: Re: HO 211 (Ageton) sight reduction accuracy (135690)

There are several things that can somewhat improve the results. Interpolating A when determining R and then interpolating that to get B. There is the Stadler method that can improve results when t, K or LHA are in the range 87°-93°. All these involve a somewhat increased workload during the reduction with an increased potential for math error on your part.

The best move seems to be to limit the ranges of observations. Using the Ageton tables if Declination is limited to less than 75° (includes the 57 traditional navigational stars), latitude is less than 70° (Unless you are with Shackleton you aren't going to be above 70°) and limit t or LHA to less than 82° or greater than 98° then RMS average altitude error is approximately 0.6' , 9% are more than 0.5' in error and max error is 2.4'.
NavList: Re: HO 211 (Ageton) sight reduction accuracy (135578)

Using a 2102D star finder you can preplan your sights to avoid sights with t or LHA 82°-98° or 262°-278°.

[ohthetrees]

Adelie (and anyone else) how do you feel about HO 208? I'm reading "Self Contained Navigation with H.O. 208" by Letcher, and enjoying it a lot. He's a very clear writer. He sings the praises of 208, and it is very compact, doesn't expire (I think), and is quicker to use than the Ageton tables.

[SeanPatrick]

I have not used HO 208 and am not familiar with it. But, any [pure] sight reduction method doesn't "expire". HO 229 (Sight Reduction Tables for Marine Navigation), HO 249 (... for Air Navigation) Vols. 2 & 3*, the concise tables in any edition of the Nautical Almanac, the Bygrave [flat or otherwise], a scientific calculator, etc ... none of these methods "expire". (I am familiar with all of these.)



It all comes down to two things: 1) What you are comfortable with, and 2) What compromises you are willing to make (e.g. size/weight vs. complexity/accuracy). Generally, the more compact the sight reduction method - the more complex and/or the less accurate it will be. My personal opinion is to become as proficient as possible with as many varied methods as you can so that you may take advantage of whatever situation you find yourself in - although you should nota bene that you will [should] most likely never find yourself in a situation requiring the use of celestial if you have taken the proper precautions. (I.e. carrying multiple GPSs, EPIRB, etc.) But, I always advocate using celestial as yet another means of verifying all other sources of information.



Having said all of that - HO 208 is a perfectly acceptable and useful form of sight reduction for marine navigation. As are all of the examples I have listed here ... and more. Bottom line: there are many "flavors" of sight reduction available. Choose which flavor you like best - for whatever reason - and learn it by heart so that you will reduce the likelihood of making a mistake when it counts.



*Vol. 1 has some ephemeris data "baked in" to make the reduction process quicker and easier. (This was handy for navigators in aircraft because of the limited time available to spend on the process due to the higher speeds involved.) Therefore, this volume must be updated every few years to be useful.


PS


My personal favorite is a scientific calculator using the formulae found in the Nautical Almanac (plus a few more), followed closely by HO 229. But, that's just me.

[Gruz]

For Sun, planets and selected stars (up to 29° declination) I am using "Sight reductoon tables for air navigation" (PUB. NO. 249) this days known as a Rapid sight reduction tables.

For stars which have declinations above 29° I am using "Sight reductoon tables for marine navigation" otherwise known as a PUB.NO.229 or this formula.

Cos(Zenith Distance) = Sin(Lat) x Sin(Dec) + Cos(Lat) x Cos(Dec) x Cos(LHA)


Tan(Azimuth) = Sin(LHA) : (Cos(Lat) x Tan(Dec) – Sin(Lat) x Cos(LHA))


Sometims, just for fun, norie's nautical tables.

[Adelie]

Originally Posted by ohthetrees

Adelie (and anyone else) how do you feel about HO 208? I'm reading "Self Contained Navigation with H.O. 208" by Letcher, and enjoying it a lot. He's a very clear writer. He sings the praises of 208, and it is very compact, doesn't expire (I think), and is quicker to use than the Ageton tables.

So there are 4 or 5 major steps in celestial navigation:
1. Shoot the heavenly bodies (i.e. measure their angular altitude above the horizon while also recording time of sight to the nearest second). Then correct the Heights recorded by the sextant (Hs) for all related errors to get Height Observed (Ho)
1a. Identify the stars shot if that was not already known.
2. Using time and body shot determine Geographical Position (GP) for each of the stars using an almanac that has a shelf life of 1 to 50 years depending on the almanac.
3. Using GP and your Assumed Position (AP) reduce each sight using the method of your choice (these do not expire). This produces a calculated altitude (Hc) and an azimuth for each star that would match reality if you were standing at the Assumed Position at the time the star was shot.
4. Using AP, Ho, Hc and Azimuth plot a line of position for each start.

There are a number special systems like Volume 1 of HO-249 that expire, but they were intended for specific uses, in the case of 249-V1 it was to speed results for air navigation at the expense of accuracy.

Generally the only part of this process that depends on something that has a shelf life is step 2, determining where bodies are at any given second.

If you are doing celestial for a living you plunk down money every year to buy the Nautical almanac which is good for 1 year, includes sun, moon, stars, and planets, usually with some corrections baked in like the Semi-diameter of bodies and how the earth's motion around the sun changes star locations depending where we are in orbit. For professional use the NA has too many advantages of convenience and decreased likelihood of error not to use.

If you are doing CelNav for personal reasons then other considerations come into play in choosing an almanac. Cost, size, shelf-life.
-The Bowditch long-term almanac is 3 or 4 pages, good for 10 years or so, are free and work for Sun and stars.
-The Kolbe Long-term almanac is about 50 pages, good thru 2050, $35 and works for Sun and stars and comes with sight reduction tables.
-You could also use any number of online products to print pages of almanac laid out similar to the NA for whatever time period you like, 1 page for every 3 days of time, all bodies, software and print costs vary.


For sight reduction, if you are doing this professionally you have all 6 volume of HO-229 because that's the standard.

For personal use other considerations come into play: cost, size, complexity.

HO 9: Bowditch, Tables of logarithms & haversines,
HO 208: Dreisonstok, Navigation Tables For Mariners and Aviators 69 pages
HO 211, Ageton, Dead Reckoning Altitude and Azimuth Table 36pg
HO214: Tables of Computed Altitude and Azimuth. 9 volumes,
HO 229: Sight Reduction Tables for Marine Navigation. 6 Volumes.
HO 249: Sight Reduction Tables for Air Navigation. 2 volumes for sight reduction and 1 volume of precomputed star sights valid for 5 year intervals. Declination limited to 29*. The UK Hydrographic Office published a follow-up version entitled “Rapid Sight Reduction Tables for Navigation” beginning in 2003. [http://astro.ukho.gov.uk/nao/news/ap3270/]
Concise Sight Reduction Tables, Davies, 1984. 32pg. Printed in the Nautical almanac since 1989. [http://www.usno.navy.mil/USNO/astron...-naut-almanac]
Bayless Modified HO-211, 18pg, 2nd edition has Stadler method in it.
Schlereth - Modified HO-229, 280pg.
S Tables (1992): Pepperday, shorter modified version of HO 211, 9pg
Bygrave sliderule(1920): A tubular slide rule 2-3” in diameter and about 12” long. Needed 3 steps, similar to table entries, but requiring the adherence to a number of rules for special cases. Accuracy in the 1’-2’ range, but results were quick to obtain. Used primarily by aircraft 1930’s thru 1970’s. [http://www.rechenschieber.org/Positi...lideRules.pdf]
Brown-Nassau (1940ish) - 13" square plastic slide rule. DIY
LaPook(2007): 2 pages. DIY Modified Bygrave, used pretty much like the sliderule but using flattened scales, one expanded and the other printed on transparency. [https://sites.google.com/site/fredie...ve-slide-rule]
Hav-Doniol (2010s) - 2-3 pages. Requires multiplication.

Letcher sailed to Alaska and Hawai'i on a very small boat during the 1960s and the other methods available to him were either bulky (214, 249), limitations on declination (249) very time consuming (HO-9) or had significant issues with error (211) which is why he became enamored of HO-208: smallish, no big random accuracy problems, works for all declinations and latitudes.

I learned HO-208 once out of curiosity. Seemed an OK system to use.

In recent years the accuracy issues with 211 have been characterized so it is possible to know which sights are likely in error or not worth taking in the first place. This is not to push 211 but to point out that one of it's problems has been reduced if not eliminated.

You want an all paper system to use. I feel the same way, if I'm going to do it, I'm not going to use electronics. If you mean this as a back up in case of GPS failure that's the way to go but then you need to keep in mind secondary issues namely timekeeping. Check out this link for a full backup system:http://www.cruisersforum.com/forums/...ml#post2723304
ALSO
http://www.cruisersforum.com/forums/...ml#post2733360

I can't write more now, need to go to work.

[Gruz]

"If you are doing CelNav for personal reasons then other considerations come into play in choosing an almanac. Cost, size, shelf-life".


I am doing CelNav for "personal reasons" and still buying nautical almanac every year plus brown's nautical almanac.

[Adelie]

Gruz, I did not mean to imply that one couldn’t use the NA when doing CelNav for personal use, only that professional standards of practice do not trump other considerations such as cost and size.

[ohthetrees]

Adelie, thanks for the astonishingly thorough answer. I've been doing lots of practice sights and reductions, and so far I've tried:

iphone app
scientific calculator (trig)
henning umland's amazing html calculators (download them to phone for offline use!)
Pub 249
Ageton Tables
H.O. 208

I think my personal emergency navigation kit will end up containing a battary-plus-solar powered Casio fx-300ES Plus calculator ($12 on amazon), a spare calculator vacuum packed in plastic, H.O. 208, and the Kolbe Long-term almanac.

[hellosailor]

Trees-
If you can find an old Palm for $25, you can also get Eveready Lithium AAA cells (with a reliable storage life of over ten years) to bag with it, and John Manson's Pilot Navigation app suite for it should still be around. (I checked, that's the correct author and program name.) Much smaller and more precise than packing almanac sets, probably would run for two months on two AAA cells, and of course, if you can find a motherload of old apps...it eliminates the opportunity to make a lot of simple math errors by doing all that for you.
There's probably an Android app that will do sight reductions, after all smartphones are much more powerful computers. Nice thing about the Palm is that like the Casio, it doesn't know how to display ads or ask you to join Facebook.(G)