Reed's Astronavigation Tables

[figue]

The Reeds tables do use the Marcq St. Hilaire method; they output an azimuth and an intercept. The difference between Reeds and, say, the Air tables is that the former uses the versine method; this removes the need to identify an assumed position, allowing the use of the DR position and is really no different to using one of the calculator reductions.

Personally, I find the number of lookups needed in Reeds over burdensome and prefer the fewer lookups (and greater physical volume) of the Air tables.

I struggled through many celestial navigation texts (Blewitt, Cunliffe and many more) until I attended the Rubicon 3 training course - very highly recommended.

 

[GHA]

I keep saying I should learn the calculator way, so I know it but I'm not sure if that's cheating or not?

Using one of the many programs is handy for banging out dozens of sights just to practice taking sights and get instant feedback. Opencpn has a good plugin which show the position line.

 

[DMN]

I like Reeds tables.

All current methods but one use MStH, ie an intercept and azimuth to draw a perpendicular position line. The one that doesn’t is a CTS and I’ll explain that below.

For MStH, two approaches are in use: 1) use your dead reckoning position from which to draw the azimuth and 2) use an assumed position as close as possible to to your DR but one that results in integral values of Lat and LHA.

With Reeds tables you can use 1). This also applies to using the haversine formula and Nories tables and also if you use a calculator. They can all cope with non integral inputs.

More commonly, tabular methods require integral inputs of Lat and LHA so as to make the size of the tables manageable. Some tables are quick to use but voluminous. Others are more compact but more complicated to use, eg the concise tables in the back of the nautical almanac.

The advantage of using your DR position is generally shorter intercepts. The plotting of position lines, and the interpretation of them, is simpler. Reeds tables are unusual in that they facilitate use of the DR position but are also compact. They are my preferred method.

A CTS is a chronometer time sight. You can do this with the NAO concise tables but it is not easy. You can do it with Reeds, although you will need to be familiar with the formula and how to evaluate it. A CTS rearranges the formula for solving the triangle. It is useful when: a) you know your Lat and Long (eg in a harbour) and want to check your watch error, or b) you know your Lat and the time and want to calculate LHA hence calculate Long. In this second case, positions are found with no plotting, just calculation. However, you may have to transfer a position by DR if you observe a morning Sun due East for Long and then get Lat from a noon sight.

 

[Frank Holden]

Looks like I am a few days late and a few dollars short but nothing new there.

I reckon this is pretty good but then I would say that wouldn't I.
Offshore Navigation.pdf
Published 30 years ago in Australian magazine 'Cruising Helmsman'.

If just taking sun sights I see no point in using any air tables or similar.
Simply use the Haversine Formula . Buy a second hand copy of Nories, download the daily pages for the voyage in prospect from here The Nautical Almanac.

Take altitude, correct
Look up Log Hav LHA, Log Cos Lat, Log Cos Dec.
Add the three together, convert product to Nat Hav

Look up Nat Hav of Lat ~ Dec, add this to the above

Convert from Nat Hav to Degrees. Bingo! Zenith distance.

And yes, I could have someone taking and reducing sun sights within a few hours from a cold start.
Getting them to understand what they are doing may take the rest of the week.

 

[DMN]

Looks like I am a few days late and a few dollars short but nothing new there.

I reckon this is pretty good but then I would say that wouldn't I.
Offshore Navigation.pdf
Published 30 years ago in Australian magazine 'Cruising Helmsman'.

If just taking sun sights I see no point in using any air tables or similar.
Simply use the Haversine Formula . Buy a second hand copy of Nories, download the daily pages for the voyage in prospect from here The Nautical Almanac.

Take altitude, correct
Look up Log Hav LHA, Log Cos Lat, Log Cos Dec.
Add the three together, convert product to Nat Hav

Look up Nat Hav of Lat ~ Dec, add this to the above

Convert from Nat Hav to Degrees. Bingo! Zenith distance.

And yes, I could have someone taking and reducing sun sights within a few hours from a cold start.
Getting them to understand what they are doing may take the rest of the week.

Nories tables are a bit bulky and heavy for my liking. Too many decimal places, I think. As for the Nories traverse table, puhleese! I made my own traverse: 1 page double sided, course angles every 2.5 degrees. Plane sailing solutions on one laminated sheet that tucks into my Reeds booklet. Lightweight and compact. No other tables required.

 

[Skylark]

…….Plane sailing solutions on one laminated sheet that tucks into my Reeds booklet. Lightweight and compact. No other tables required.

Plane sailing is very good for establishing, for example, the morning DR position after an overnight run following the last fix. Need only course steered and log reading.

Convert course to a quadrant bearing notation, dLat is simply Cos(course) x distance, Departure is Sin(course) x distance and dLong is Departure / Cos(mean Lat).

I still use 4-figure Log Tables that I bought for engineering college in the 1970s.

Good fun for the recreational navigator while long distance sailing.

 

[Frank Holden]

Nories tables are a bit bulky and heavy for my liking. Too many decimal places, I think. As for the Nories traverse table, puhleese! I made my own traverse: 1 page double sided, course angles every 2.5 degrees. Plane sailing solutions on one laminated sheet that tucks into my Reeds booklet. Lightweight and compact. No other tables required.

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.

 

[st599]

Can't comment on Reeds as I've never used it but bear in mind the following:
Per Skylark's comment above, the RYA in the yachtmaster ocean shorebased reference the nautical almanac and sight reduction tables. You may consider being conversant with the alternatives a good thing or a complication.
The admiralty publications (NP314/303v1-3) are 50% more than the commercial editions. Moreover they're an awkward size which won't fit conveniently on your bookshelf. Unfortunately I learned this the hard way so my NP303v2-3 will continue making stowage awkward
vols 2-3 of the sight reduction tables are a one-time purchase. Vol 1 is every 8 years so after initial outlay you mostly have the annual cost of the commercial edition of the nautical almanac which is pretty similar to your Reeds almanac
And of course you don't necessarily need vols 2 *and* 3, for example if you just wanted to sail canaries to the caribbean

Bottom line: NP314+NP303v1-3 are well over £130 but go with the commercial editions and you're looking at about the same price as reeds (annual cost of almanac + depreciating selected stars over 8 years) plus the £40 one-time outlay for vols 2 and 3 of the sight reduction tables.

The US NOAA publish the same data in the same format for free, and you can buy them from various print on order sellers on Amazon for about £12-15.

 

[srm]

I keep saying I should learn the calculator way, so I know it but I'm not sure if that's cheating or not?

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.

 

[jdc]

I always use a calculation program for teaching since it allows the learner to get useful results within a few minutes, which is so encouraging. The looking up of GHA and DEC plus the sight reduction stuff is really off-putting when the person doesn't yet have any confirmation that they've read the sextant correctly, so I always teach that bit later once the position is shown to be usefully accurate (2 or 3 miles is achievable in the first 20 mins of picking up a sextant).

Then, if interested, some are, some aren't, they can go on to do the look up and interpolation of the GHA and DEC (or the identification of the star or planet). And finally the sign reduction by whatever method.

I don't care for either Cunliffe's book nor Mary Blewit's - but worked it out from scratch for myself, but YMMV. And it is entirely possible for anyone to get it in a couple of hours: last summer I crewed for a couple doing their first 'blue water' passage and they both got the taking of sights in 20 mins and the working out in an hour. So I don't think that using a calculator is cheating at all but is rather a near essential teaching aid. FWIW I use this one¹ (which can be downloaded as a smart-phone app).

1. Disclaimer: I wrote it

 

[zoidberg]

Quite a few years back, I was summoned to South Wales for my YM(O) viva - which didn't get off to a good start as I was an hour late due to 'motorway accident' and no phone.

The known-to-be-gruff examiner suppressed his irritation and was meticulously fair. We discussed my 'journal' and that I'd done the whole 1500nm trip using astro and trad nav - not just a measly single sun sight - then he turned to my record of daily Compass Checks by Sun's Amplitudes. "How did you manage those," he growled, "on a conventional sailboat?"- clearly suspecting a 'fiddle factor'.

I grinned, and pulled from my bag a hefty 'Pelorus' I'd made up from a spare destroyer's bridge Dumb Compass, used for taking bearings, which I'd modified to clamp onto the yacht's cabin top. He was intrigued, quietly examining it, then rummaged in a cupboard behind him and produced a perspex facsimile of much the same thing.

"Here's one I made earlier' he laughed - in the buzzword of the moment - and we spent the rest of the exam period comparing 'Pelorii'....

No more questions.

 

[DMN]

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.

I agree that using a calculator is not cheating. Log tables and slide rules are both calculators, just not electronic. I programmed my calculator to allow quick and easy sight reduction and the convenience is undeniable. But I keep regressing to paper. It’s not easy to explain why but I think in the main because it is tangible and also leaves a record of how the position line was attained. It enables self checking more easily. Checking when using a programmed calculator means plugging the numbers in and running it again, which is not really checking very much at all.

 

[Buck Turgidson]

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?

 

[DMN]

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?

The ABC tables are merely for calculating the azimuth angle. That is, they are a central component of the MStH method.
Enter table A with LHA and Latitude. Enter table B with LHA and body declination. Be careful of signs (n or s, + or - depending on table version). Add the numbers and use the answer to enter table C according to Lat. Result is Z, the azimuth angle. The true azimuth, Zn, is then Z east or west, depending on LHA, of your meridian reckoned from either N or S. The rules are clearly stated on each page.

 

[zoidberg]

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.

Odd.

Last time I headed south from 'somewhere beyond Ireland', the top left corner of Spain turned up 'zackly where it was before, and more or less right in front of us..... using LtCdr Harry Baker's 'Heavenly Bodies' as advertised.

I'd managed a decent astro fix to update my DR plot rather earlier in the day, so I was not really in need of the late twilight 'offerings' which included the moon. Anyway, several of the high coastal lights were distant-visible so I could revert to LOPs using my handbearing compass.... but I gave myself a shake and geared up for a tricky moonshot to the WSW. Peering down the tube, I struggled to decide on a true horizon, as there was a broad 'river of silver' stretching from us to where the near-full moon would be brought down.

Then, right in cue, a family of whales surfaced, sounded and dived - black shapes one-by-one right across the view in my 'silver river'. If I hadn't got my act together and tried for the shot, I'd have missed witnessing that. One of the most precious memories of all my sailing years....

Oh, and the moonshot worked out quite agreeably.

 

[Frank Holden]

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?

What is this ABC method of which you speak? The only ABC tables I know are the ones in Nories etc used for working out azimuths. I recall using them to correct longitude for errors in latitude or v/v when using 'long by chron' but how that worked has long since departed my memory.

 

[DMN]

There is another useful feature of the Reeds tables for those of us who like lightweight and compact nav books to carry around: log tables.

1) Reeds includes versines and log versines. From this table, you easily read 4 figure log tables. eg look at 30 degrees, 0 minute. The natural versine is given as 0.1340 and the log ver is given as 9.1270. So, you now know that the log of 1.340 is 0.1270, log of 13.40 is 1.270, log of 134.0 is 2.270 etc. The log of 0.0134 is 8.1270 etc. If you need to know the number whose log is 9.456, scan the log ver columns and you find 0.2857. On occasion you may have to interpolate by eye for the fourth figure.

2) Reeds also provides log cos and log sin tables. You can also work out log tan from these two, since tan = sin/cos, log tan = log sin - log cos. I think with all these log tables, most, if not all, navigational problems can be solved manually if that is your preference without carrying additional volumes.

 

[Frank Holden]

There is another useful feature of the Reeds tables for those of us who like lightweight and compact nav books to carry around: log tables.

1) Reeds includes versines and log versines. From this table, you easily read 4 figure log tables. eg look at 30 degrees, 0 minute. The natural versine is given as 0.1340 and the log ver is given as 9.1270. So, you now know that the log of 1.340 is 0.1270, log of 13.40 is 1.270, log of 134.0 is 2.270 etc. The log of 0.0134 is 8.1270 etc. If you need to know the number whose log is 9.456, scan the log ver columns and you find 0.2857. On occasion you may have to interpolate by eye for the fourth figure.

2) Reeds also provides log cos and log sin tables. You can also work out log tan from these two, since tan = sin/cos, log tan = log sin - log cos. I think with all these log tables, most, if not all, navigational problems can be solved manually if that is your preference without carrying additional volumes.

No Nat & Log Haversines? Thats a shame. I am unfamiliar with Reeds having only strayed north of the equator on two occasions in the last 30 years. As I already have 2 copies of Nories, one ashore and one on my boat, I shall live with the bulk and leave my money in my pocket.

 

[AntarcticPilot]

No Nat & Log Haversines? Thats a shame. I am unfamiliar with Reeds having only strayed north of the equator on two occasions in the last 30 years. As I already have 2 copies of Nories, one ashore and one on my boat, I shall live with the bulk and leave my money in my pocket.

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.

 

[Frank Holden]

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.