Reed's Astronavigation Tables

[Frank Holden]

Tongue in cheek, I point out that all you really need for celestial navigation is the ephemeris of astronomical objects, sine, cosine, arc sine and arc cosine. The last four are functions to be found on any cheap calculator. Those in conjunction with the Sine and Cosine rules of spherical trigonometry will get you a position line. Haversines merely confuse the basically simple mathematics to make the arithmetic simpler.

I would take the opposite view - that the Haversine formula - as taught and practised for many many years before the coming of the calculator is the superior method of working with PZX triangles..

Try using the sine formula without your electrickery!

Simple arithmetic is, was, and always shall be the friend of the simple sailorman.

 

[DMN]

The second copy of Nories came as part of a deceased estate I bought just under 30 years ago, $Australian 500 for a swag of nautical books and a dutch 'Observatuer'(sp) sextant. Didn't like the sextant sold it on for $500 - kept most of the books.

My Nories hasn’t left my bookshelf at home for at least 20 years. Mostly Reeds goes to sea, although some years I just use the Nautical Almanac blue book with its concise sight reduction tables. However, since most nav is dead reckoning corrected occasionally by a terrestrial cross bearing, a squint at the GPS or a celestial sight, my 1 page compact traverse table gets more work than anything. I have a Celestaire astra iiib sextant. I took a Frank Reed course on lunar distances and have completed a few lunars at home. None at sea, yet. The rigmarole of the sight and the mathematics of the clearing could well be too much on a yacht unless conditions were particularly benign.

 

[AntarcticPilot]

I would take the opposite view - that the Haversine formula - as taught and practised for many many years before the coming of the calculator is the superior method of working with PZX triangles..

Try using the sine formula without your electrickery!

Simple arithmetic is, was, and always shall be the friend of the simple sailorman.

Yes, but I used to write computer programs to handle this kind of maths, and I did say that I was speaking tongue in cheek! For me, Sine and Cosine rule are "built in" so to speak, and providing you avoid edge cases where you are taking the difference of two large numbers, give a clearer view of what you're actually doing.

I find Haversines and sight reduction tables "difficult" because they hide the intrinsically straightforward mathematics from you. But I appreciate that simplicity and reliability of computation matters, especially in an aircraft where the aircraft may be moving many miles per minute. Also, of course, I do realize that my viewpoint is unusual!

All you are doing is computing a) the radius of the small circle on which you lie with its centre at the nadir point of the celestial object observed (which is just addition and subtraction) and b) the azimuth and distance of the nadir point from your estimated position (Sine and Cosine rule). Neither is mathematically complex, and I would be most likely to make a mistake applying the various corrections to the sight.

Of course, if you want real complexity, try doing the relevant calculations on the WGS84 spheroid...... And no, I wouldn't try it without a textbook and a computer to hand! Of course, the accuracy of marine celestial navigation is such that it would be a waste of effort anyway.

There was an occasion in Svalbard (in the 1970s, when calculators were a rarity and computers were definitely NOT portable) when we wanted to do some simple trigonometry and hadn't got the relevant tables. I sat down and hand-calculated the sines and cosines we needed from the relevant series! This was a land party, so we didn't have navigational material. But I could do it (these days I'd have to look up the series for Sine and Cosine; back then I still remembered that bit of my A-level maths!). Incidentally, before the advent of computers, most mathematical tables contained errors; that was the impetus for Babbage's work on the Difference Engine.

 

[srm]

Tongue in cheek, I point out that all you really need for celestial navigation is the ephemeris of astronomical objects, sine, cosine, arc sine and arc cosine. The last four are functions to be found on any cheap calculator. Those in conjunction with the Sine and Cosine rules of spherical trigonometry will get you a position line. Haversines merely confuse the basically simple mathematics to make the arithmetic simpler.

No need for "tongue in cheek".
Referring back to my previous post (#29) we used haversine tables for the long hand calculations under the old UK syllabus for deck officer qualifications. When the syllabus changed with STCW and allowed students to use calculators "to check their workings" we changed the calculation methods to use simple scientific calculators and the nautical almanac as you described.

 

[john_morris_uk]

Hmm. For better or worse I’ve examined someone for their YM Ocean this morning.

A few problems: they added 0.5 for d when calculating Dec even though ‘d’ was given at 0.4 per hour. (How can a proportion of ‘d’ be bigger than the value of ‘d’ but they didn’t grasp what they were doing..,)

Bigger problem was that although they could look up GHA they had no real idea what it is. They know it stands for Greenwich Hour Angle but they couldn’t draw me a picture or explain what that means. I don’t mind if people do things by rote but some understanding is helpful and the above are only two examples from a series of problems I faced when discussing ocean passage making with them.

No name’s obviously. He/she will remain anonymous.

 

[srm]

Hmm. For better or worse I’ve examined someone for their YM Ocean this morning.

A few problems: they added 0.5 for d when calculating Dec even though ‘d’ was given at 0.4 per hour. (How can a proportion of ‘d’ be bigger than the value of ‘d’ but they didn’t grasp what they were doing..,)

Bigger problem was that although they could look up GHA they had no real idea what it is. They know it stands for Greenwich Hour Angle but they couldn’t draw me a picture or explain what that means. I don’t mind if people do things by wrote but some understanding is helpful and the above are only two examples from a series of problems I faced when discussing ocean passage making with them.

No name’s obviously. He/she will remain anonymous.

Definitely a case of "not yet competent" when I was assessing students for STCW deck officer certificates, but we would have picked up on someone not understanding the basics long before they got to calculating a position line.

 

[john_morris_uk]

Definitely a case of "not yet competent" when I was assessing students for STCW deck officer certificates, but we would have picked up on someone not understanding the basics long before they got to calculating a position line.

I don’t think it’s appropriate for me to comment on the outcome. But we’ll agree on the lack of competence.

 

[Andy Johnson]

I bought these a couple of years ago along with the reeds ocean handbook which has a chapter on astro. Imagine my surprise when the astro chapter is all MStH but refers to there own astro nav book as if it uses the same method.
Anyway I couldn't get to grips with the ABC tables. Same sights using ABC 30 miles out from actual. Using MStH 2 miles. Will try again this year but will also download the full almanac again.
Interesting that I have an iPad app which agreed exactly with my MStH calculation and only required me to enter the sight. I figure if people think using a calculator is reasonable then by the same toke the app should be fine too. But I do like to try and do it all manual. The reeds tables should give me that capability if I can just figure out how to get an accurate answer. Does anyone have a link to a solid instructional source for the ABC method?

Hi Buck,
I am a newby on this forum so you might have had answers already but here's a link to an article I wrote. Hope it is of interest.
Astro Nav from Home and go to Useful Articles number 3 "Using Reeds Astro Navigation tables".
Cheers,
Andy Johnson

I bought these a couple of years ago along with the reeds ocean handbook which has a chapter on astro. Imagine my surprise when the astro chapter is all MStH but refers to there own astro nav book as if it uses the same method.
Anyway I couldn't get to grips with the ABC tables. Same sights using ABC 30 miles out from actual. Using MStH 2 miles. Will try again this year but will also download the full almanac again.
Interesting that I have an iPad app which agreed exactly with my MStH calculation and only required me to enter the sight. I figure if people think using a calculator is reasonable then by the same toke the app should be fine too. But I do like to try and do it all manual. The reeds tables should give me that capability if I can just figure out how to get an accurate answer. Does anyone have a link to a solid instructional source for the ABC method?

 

[Refueler]

The two main methods of Sun sights ..... MSH and Long By Chron.

Long by Chron was prevalent on various older shipping lines ... Blue Star ... Cunard ... etc. while MSH tended to be more used by 'younger' ...

Stars of course MSH literally ruled ...

Talking shipping not yottie....

 

[srm]

When I first started teaching fishermen for their tickets in Shetland (the old "Second Hand Full and Special" that was a skipper ticket for the smaller vessels that made up much of the Shetland fleet at the time). I had a couple of fails who then went down to Orkney to resit as the next course in Shetland was 9 months away. Capt. Robbie in Orkney was most annoyed that I was teaching MSH. Long by chron was shorter and easier he said. I think perhaps by one small set of calculations taking a few lines.
I moved to the Nautical Dept in Orkney after Capt. Robbie retired; we only taught MSH after he left for both MN and Fishing.

 

[Refueler]

I am unsure how traverse tables found there way into the conversation - however.

I find it far easier to teach people using first principles - ok not quite first principles, I am quite happy with just accepting Napier's Rules.
I do think that having over several hundred years having simplified the process to such a degree by using the Haversine formula people -as soon as they got hold of a scientific calculator - regressed back into using the Sine formula. Made no sense to me.

Now before anyone takes me for a luddite I used the air nav tables throughout the 70's into the early 80's when as 4 to 8 watchkeeper I was taking stars twice a day when at sea. I also bought a Sharp PC-1246 programmable mini-computer in about 1989 and programmed it using an article written by Mike Harris and published in PBO. His little book 'Astro Navigation by Pocket Computer' is still a worthwhile read.

So its not as if I am a 'one trick pony' touting the only method I know.

Mine was the Ti49 with Nav module.

Still works today - but battery pack is shot. And I've lost the charger anyway.

 

[Refueler]

No not cheating.

Part of my job up to retirement included teaching astro nav for UK MN and fishing deck officer exams. All we used once STCW came in was a nautical almanac and calculator, however students had to show each step of the calculations not just the final intercept. Prior to that the UK exams did not allow calculators, just nautical Almanac and Nories or Burtons tables for haversines and logs etc.

When doing my YMO passage I used a Nautical Almanc and Burtons tables. No need to carry the air, or marine, sight reduction tables. Also, shorter intercepts to plot from the actual DR rather than the rounded up assumed position used with the reduction tables. The sights were accepted even though not using the RYA method.

My MN Certs - was never examined for sight calculations .... (UK) .....

 

[Refueler]

No need for "tongue in cheek".
Referring back to my previous post (#29) we used haversine tables for the long hand calculations under the old UK syllabus for deck officer qualifications. When the syllabus changed with STCW and allowed students to use calculators "to check their workings" we changed the calculation methods to use simple scientific calculators and the nautical almanac as you described.

When I did my Tickets ... I used Burtons ... and a plain calculator .... first Ticket was in 1977.

My Burtons is still modified to allow it into the examination - the printed explanation pages were allowed - but owners notes had to be covered over or erased.

Sights ? As I mentioned earlier - they were never part of tickets I took !! Nor of the OND in Nautical Science ...

 

[srm]

My MN Certs - was never examined for sight calculations .... (UK) .....

Yes, it was all desk work, no need to produce actual sight calculations. No fisherman I met had ever seen a sextant on a fishing boat, until I took one aboard for horizontal angles having hired the vessel to lay current meters.

However, the examiners based in Aberdeen always started the final oral exam for any MN or Fishing Candidate with a demonstration of using the sextant and taking an angle. Probably, to try to get the candidate to relax.

 

[Refueler]

Yes, it was all desk work, no need to produce actual sight calculations. No fisherman I met had ever seen a sextant on a fishing boat, until I took one aboard for horizontal angles having hired the vessel to lay current meters.

However, the examiners based in Aberdeen always started the final oral exam for any MN or Fishing Candidate with a demonstration of using the sextant and taking an angle. Probably, to try to get the candidate to relax.

arrrrr Aurals ..... or Orals ??

The 'describe the three errors on a sextant and how you determine them' question !

 

[[194224]]

Sight reduction (intercept/MStH method) was certainly part of my GCE 'O' level in Navigation all those years ago.

 

[Refueler]

And 'woe betide' the candidate who 'fumbled' the sextant out of box wrong way !!

 

[srm]

And 'woe betide' the candidate who 'fumbled' the sextant out of box wrong way !!

My students were all drilled in the correct way: open the box, release the locking toggle, carefully pick up with left hand, transfer correct way up to right hand holding the handle.

I used to enjoy using a sextant, often taking around a hundred or so horizontal angles per day during inshore surveys. There was something satisfying about it. But then my intro to using the instrument was a bit unconventional.

My last sea job (during a summer off university) had been on a seismic ship in the North Sea operating one of the first sat navs, the US Navy's Transit system (that took a running fix from a single satellite in polar orbit). The next summer I got a job (having finished university) as a trainee hydrographic surveyor with a research unit that had its offices in the grounds of UK Hydrographic Office in Taunton.

My boss was with one of the teams measuring sand waves in the North Sea when I was asked to position some acoustic targets in Torbay - using a sextant. I got a book out of the library, a sextant out of the instrument store, and spent an afternoon sitting behind a tree (so I could not be seen from any of the HO windows) working out how to use it.

 

[Refueler]

Transit ............. UGH !! Magnavox !! We carried Transit on the Gas Ships Brunei to Japan with Shell .... the first ones were the two huge box units ... one was the gubbins that received the signals ... box was huge !! Second was the print out box - again not so small ... later swapped for a text screen.
Then that was ripped out and we got the all in one Magnavox Transit ... about size of a small portable TV.
Positions from it .... being Palawan Passage - an area that Transit didn't actually cover so well .. the sats positions would over days bunch up and we'd have a load over short time ... then nothing for ages .... while they then started to spread out ... to then start bunching up again.

Seismic ... I was with CGG and later Western Geophysical .... being a Deep Sea Navigator instead of the usual Coastal guys ... I was usually the one who had the job of calibrating the tail buoy angle from stern of ship ... still today I wonder how I ever saw a tail buoy at end of 2.5km seismic cable through a standard KH Mates sextant !!

As to sights ... I actually enjoyed nav .. and would when I was 12-4 take Moonlight stars ... later of course 4-8 was proper twilight stuff ...

 

[srm]

Transit ............. UGH !! Magnavox !! We carried Transit on the Gas Ships Brunei to Japan with Shell .... the first ones were the two huge box units ... one was the gubbins that received the signals ... box was huge !! Second was the print out box - again not so small ... later swapped for a text screen.

I was with SSL, UK subsidary of a US firm. They had two Norwegian stern trawlers on long term charter. At least our cable drum was a lot higher above the water than one vessel I saw in Aberdeen that had come from the Gulf of Mexico and had a very low freeboard. Even so one night I was up to my waist in seawater while recovering the cable.

I probably pre-date your Magnavox experience. A four person cabin was stripped out, fitted with AC and the electronics fitted in to a deck to deckhead rack system. We communicated with the beast using a massive free standing teletype machine and it drove a track plotter. Most of the time it must have been running on DR. We were told it was the first in the North Sea. We were comparing it with the Decca HiFix system that was the standard nav system at the time. I only did a couple of shifts as operator before leaving the company and heading back for my final year at university.