Astro nav - what is the accuracy of this method

[bbg]

OK, here is a method I used to plot my position. It was pretty accurate East-West. Of the three times I did it I was about 63 miles out north (twice) and five miles out north (once). I think the problems north might have been mis-reading by a minute on a very faded sextant.

Anyway, here is the technique and I am interested to know - from people who REALLY understand astro nav - what they think of the accuracy on a moving boat. I gather it can be very accurate when you are on land.

The idea is to take a noon sight for latitude and also for longitude. Getting the height of the sun for latitude is not so difficult, but getting the time of the meridian crossing to the second is obviously much much more difficult because the curve is so flat.

So here was the technique I used. Knowing the expected time of the meridian crossing, I started taking sights about 60-90 minutes before noon. I took a series of about 5-8 sights about a minute or two apart, and took a very careful note of the time of each.

Then took the noon site.

Then, 60-90 minutes after noon, I took a corresponding series of sights. Set the sextant to the last pre-noon altitude and waited, then noted the time. Set it to the next one and noted the time. Etc.

This gave me pairs of sights before and after noon. For each pair of sights I averaged the time between them to find when "noon" was according to that pair of sights. Typically I would get four out of five, or five out of six, that were pretty close, and one outlier. I threw out the outlier and averaged the rest, to give me noon.

It seemed to work pretty well. Possibly not well enough to find an atoll in the Pacific, but probably well enough to find Martinique.

I know the movement of the boat between the pre-noon and post-noon sights will have an effect, but are there any thoughts on whether this would be a "good enough" approach if all else fails?

 

[skyflyer]

Assuming you have a reasonable DR position why do you not look up in the almanac the time or meridian passage (which of course is NOT 12.00 exactly, not even on local time) and then start taking sights a few minutes before hand. You will constantly need to 'rack down' the sun to the horizon until suddenly you don't; it has 'bottomed out" - that is meridian passage and you can note the time accordingly

It should be easily possible to discriminate to a minute of arc, which IIRC equates to 4 secs of time.

 

[AndrewB]

'Bracketting' noon is a well-established method of determining the exact time of local noon, usually done by sights about 10 minutes either side. Your method will be good for latitude, and will also give longitude provided you know GMT precisely. (Plus, as skyflyer points out, you need to know the "equation of time" to convert local noon to the mean time noon, as well as the sun's declination).

As you say, this method is not in practice as accurate as the more usual method based on a pair of observations at different times, but because it greatly simplifies the calculations, found favour with the old-time sailing ship masters. A table showing the "equation of time" is often found enclosed in sextant boxes, for emergency use.

 

[bbg]

Thanks to both. Of course when I did the sights I was familiar with the equation of time and knew that noon is not always 12:00.

Perhaps I didn't need to go as much as 60 minutes either side of noon, but did so on the basis that the curve was much less flat and therefore easier to be precise about the time that the sun was at a certain angle.

FWIW I was required to demonstrate that I could find my position by astronav before I did the MiniTransat, and bracketing was the method I used and it seemed to be OK. And quite honestly I am pretty confident I could have found Brazil if my GPS had failed.

I am glad to hear it was used as a simple method in the past, but I guess what I am trying to understand is how much less accurate it is (in theory and practice) than sun-run-sun. And if the difference is not that great (particularly in practice) why do people still learn sun-run-sun?

 

[Birdseye]

Maybe a similar reason as why they use a sextant at all. Now gps handhelds are so cheap and there are three independant sets of satellites and the accuracy is to meters not miles, why bother?

You use a watch not a sundial dont you?

 

[AndrewB]

Maybe a similar reason as why they use a sextant at all. Now gps handhelds are so cheap and there are three independant sets of satellites and the accuracy is to meters not miles, why bother?

No romance in your soul, Birdseye. Picture this: BBG has been bobbing about in his life-raft in the middle of the Pacific for a month; his last GPS battery faded away several days ago; he's sucking at the dew on his canopy; somewhere out there Tahiti lies, but where?? He takes out his trusty sextant .... OK, I better get back to the day job.

 

[Talulah]

You use a watch not a sundial dont you?

Didn'y you watch the training video 'All is Lost' with Robert Redford?

 

[dolphin]

the way you are doing the observation is ok but you can improve if you use the 3 (three) lines of positions as follows, one about 1.5 - 2 hrs before the noon, noon and 1.5 - 2 hrs after .
adjust the first and third observations for the time of noon position and you will have a three lines crossing in fairly acceptable triangular and the mistake from the dead reckoning will be small as between the first and the last observation,
the time is only about 3-4 hours or the distance of about 20-30 nm !

 

[capnsensible]

Maybe a similar reason as why they use a sextant at all. Now gps handhelds are so cheap and there are three independant sets of satellites and the accuracy is to meters not miles, why bother?

You use a watch not a sundial dont you?

Why bother going sailing when you can get a plane.......

 

[martyn78]

Why bother going sailing when you can get a plane.......

I don't believe you just said that!!!!!!

 

[AntarcticPilot]

To answer the OP's question about accuracy, 1 nautical mile should be attainable under good conditions. Of course, conditions aren't always good! Land-based surveyors using essentially the same techniques with a theodolite routinely achieve accuracy to a few hundred metres (typically 100-300 m). Of course, a full-blown astronomical observatory does much better than that; WGS84 (the datum we all know and love) is based on radio astronomical observations that are of millimetre accuracy. But you won't achieve that without access to radio interferometry of Quasars and suchlike .

My favourite error in astro observations was on-shore. A team out on an ice cap had surveyed in locations for 4 radio transponders being used by an airborne navigation system - long before GPS was around. The system didn't read out a location; it simply recorded distance to each transponder, and yours truly had to post-process these distances into aircraft positions; simple geometry, but with some interesting edge conditions to handles. It should have been OK, but I found that the error involved when one particular transponder was being used was far too high. Anyway, I contacted the survey team (based in Norway), and of course they said, no, the position is fine - that can't be the problem. But I reworked the numbers, and still got crazy results. So, using the few places where more than two transponders were received, I back-calculated the location of the transponder, and got an answer substantially different from where they said it was. Got back to the survey team with this result, and they re-examined their calculations. Still no error - until one of them noticed that the change in bearing from the base station was 15 degrees. Suddenly light dawned - the only person in the group with a watch had happened to be one of the British members of the team, and his watch was set to BST, resulting in an hour's error in their azimuth calculations! When that was taken into account, and the position was recalculated, all was well.

 

[Bilgediver]

No romance in your soul, Birdseye. Picture this: BBG has been bobbing about in his life-raft in the middle of the Pacific for a month; his last GPS battery faded away several days ago; he's sucking at the dew on his canopy; somewhere out there Tahiti lies, but where?? He takes out his trusty sextant .... OK, I better get back to the day job.

Thats when you realise what the piece of wood with knotted string is for in the Grab Bag

 

[bbg]

AntarcticPilot, I know from your other posts that you are probably the best person to ask, so the real aim of my question was based on the fact when I bracket the sights before and after noon, I have moved. So what might give very good accuracy ashore will necessarily degrade when afloat, but I'm not sure how much of a real difference it will make.

 

[AndrewB]

To answer the OP's question about accuracy, 1 nautical mile should be attainable under good conditions. Of course, conditions aren't always good! Land-based surveyors using essentially the same techniques with a theodolite routinely achieve accuracy to a few hundred metres (typically 100-300 m).

Accuracy to within 1 nm by this method??? Respect, if you can do it, from a yacht. It implies, among other things, that local noon can be determined to an accuracy of 4 seconds, and that will mean a sextant accuracy of better than 0.1'. I've heard 20 miles accuracy is more realistic with this method. 1 mile accuracy is pretty good going even with a conventional sun-run-sun observation.

 

[AntarcticPilot]

AntarcticPilot, I know from your other posts that you are probably the best person to ask, so the real aim of my question was based on the fact when I bracket the sights before and after noon, I have moved. So what might give very good accuracy ashore will necessarily degrade when afloat, but I'm not sure how much of a real difference it will make.

Well, I am a theoretician rather than a practical navigator; others will far exceed my practical skills! However, it will entirely depend on how long the interval is, how fast you're moving and in which direction. At sailing boat speeds (at least, those most of us encounter ) I can't imagine it making much odds. Your method is, I think, the method of equal altitudes, which is a venerable and well-known technique to make the determination of "noon" more precise. You need to remember that you're not the only thing that is moving; the Earth has also moved on in it's orbit round the sun in the interval between your sights, and that could be a significant effect near the equinoxes when day-length is changing most rapidly. I've never heard of that being regarded as a problem for this method. I think you will find that the way you are doing it averages all the various effects so that you do indeed get the nominal position at the moment of noon. Of course, you probably could stymie it by doing a radical change of course and speed during the period of the sights, but as long as you're making a steady speed and constant course, I think that your method will average it out.

 

[brokethebox]

I love using my sextant, and found over the whole of our down the world trip, taking sights every day that we could we were almost always within 10 miles, and i remember my examiner saying that it's not knowing where you are that's important, it's where you're not.

the one thing i'd point out is to that it's better to have your sights more than 90 minutes after or before your noon, and know your run during that time.

Enjoy, and good luck

J

 

[Porthandbuoy]

Romance be damned! I know selectaive availability is now "Off", (the only decent thing Dubya did while in the White House), but before then the GPS satellites were owned by the US Dept of Defense. When Gulf War 1 kicked off they dicked around with the GPS clocks and the platfrom I was on, firmly secured to the sea bed off Tunisia, appeared to be doing 17kts across the Libyan desert. Solar flares or an act of war could render the entire GPS constellation useless. IMHO of course.

Besides, astro delivers a great deal of satisfaction when your destination appears over the horizon when and where expected.

 

[prv]

Romance be damned! I know selectaive availability is now "Off", (the only decent thing Dubya did while in the White House), but before then the GPS satellites were owned by the US Dept of Defense.

They still are owned by the DoD, though of course there is now also the Russian system and will soon be the European one too.

Pete

 

[maxi77]

Sun run mer alt and perhap another run sun was a traditional pattern along with morning and evening stars. It had the advantage of almosr always presenting a good horizon, not always as easy at dusk. You of course need to transfer position lines to get the best results.

As for accuracy I was taught an everyday deck officer should achieve 5 miles and an experienced expert 1 mile.

 

[Sinbad1951]

I would expect to be within a mile. Each site simply gives a position line at approximately right angles to the heavenly body (ie sun). Thus a noon site when the sun is either south/north will give you an east/west position line. So the earlier or later you leave your morning or afternoon site the greater the angle of that line and hence the more accurate the point of intersection of the two lines.
However for pure astro pleasure use star sites. Take half a dozen at sunset or sunset using stars 50-60 degrees apart then you have 6 intersecting position lines and accuracy down to less than half a mile.