All you Astro Navigators out there

[AntarcticPilot]

I certainly do not dispute that such charts do ignore the fact that meridians are not pararrel, but for those working in the majority of the oceans other that the very high latitudes those errors are to small to worry about in the scale that these plotting sheets are used. In the prehistoric days before GPS it was accepted that astro was imprecise and the objective was to keep ones errors below 5nm, quite satisfarorary in mid atlantic, one was advised never to aim directly for the destination landfall, but to one side or the other, by more than your expected error so you knew which way to turn. I sometimes think we crave too much accuracy at times these days, but then I am an old fart who survived walking to school by myself at the age of 5, drank unpurified water as a child etc etc.

High latitude navigation and in particular charts and their projections is a special case, one I never had to deal with and I must admit I have no intyentions of starting now. Thus if I do find myself having to do a bit of astro then those hand made plotting sheets will suffice.

Well, look at my username to understand why I worry about high latitudes And I realize that for most people I am nit-picking, but it happens to be something that falls squarely in one of my areas of competence. I earn my living working with maps of high latitudes, and detailed knowledge of the properties of maps and projections goes with the territory.

Just for completeness' sake, someone voyaging to Svalbard - not an impossible destination for a European yacht - would be well advised to take account of chart distortions caused by the high latitude.

 

[maxi77]

Well, look at my username to understand why I worry about high latitudes And I realize that for most people I am nit-picking, but it happens to be something that falls squarely in one of my areas of competence. I earn my living working with maps of high latitudes, and detailed knowledge of the properties of maps and projections goes with the territory.

Just for completeness' sake, someone voyaging to Svalbard - not an impossible destination for a European yacht - would be well advised to take account of chart distortions caused by the high latitude.

I had made that lateral leap concerning the user name, I think the real point is that we should always try to use the most appropriate tool for the task, and be aware of the potential errors. One of the problems with digital read outs is they by their nature tend to lull you into believing they are accurate. When I first used the likes of Decca, Loran A etc you plotted on lattice charts and they did give you a visual feel for the scale of the fixed errors you knew existed, when you change that to a digital display with a resolution of 10 feet people tend to expect it to be accurate to 10 feet, even when you are outside the accurate ground wave pattern.

 

[stephenh]

Maxi77 :
“The RN produced a standard plotting chart which you applied the scaling to. They came on a pad and were used once”

AntarcticPilot :
“It is still mathematically incorrect”

I am confused.

I use Admiralty chart D6018 which I think is the plotting sheet that Maxi refers to.
It is drawn up for 1 degree of latitude of one’s own choice and I do not understand how it can be ‘mathematically incorrect’.

Granted its scale is not that large but it has worked for me at 66 N ( not the North Pole admittedly ) and is probably to a greater degree of accuracy than my sights!

APilot - please would you explain, at ‘O level’ standard rather than ‘Phd’ !!!!!

Thanks Stephen

 

[AntarcticPilot]

Maxi77 :
“The RN produced a standard plotting chart which you applied the scaling to. They came on a pad and were used once”

AntarcticPilot :
“It is still mathematically incorrect”

I am confused.

I use Admiralty chart D6018 which I think is the plotting sheet that Maxi refers to.
It is drawn up for 1 degree of latitude of one’s own choice and I do not understand how it can be ‘mathematically incorrect’.

Granted its scale is not that large but it has worked for me at 66 N ( not the North Pole admittedly ) and is probably to a greater degree of accuracy than my sights!

APilot - please would you explain, at ‘O level’ standard rather than ‘Phd’ !!!!!

Thanks Stephen

Basically, on a Mercator chart the linear scale of the chart varies with latitude. One of the Mercator projection's bad properties is that the scale varies rapidly and (more crucially) non-linearly with latitude. The rate at which scale varies is latitude dependent, being zero at the equator and infinite at the poles. In temperate or equatorial latitudes, the rate of change is not large, and can be disregarded. However, in high latitudes, the scale changes very rapidly, and even over a small span of latitudes is significantly different between the north and south extremities. The scale factor varies according to 1/cos(latitude), and between 65 and 66 degrees it changes from 2.36 to 2.46 - about 5%, or 3 nautical miles of potential systematic error over degree. Between 75 and 76 degrees it goes from 3.86 to 4.13 - about 10%, or 6 nautical miles. At 85 and 86 degrees it is 11.47 and 14.34 - more like 30%, or 18 miles potential error! And for pure silliness, between 88 and 89 degrees it is 28.65 and 57.30; 50%! At 90 the scale factor is infinite.

Just for completeness, the rate of change of scale with latitude is given by tan(latitude)/cos(latitude). I attach a jpeg image showing the way in which scale factor (blue line) and rate of change of scale factor (red line) change with latitude. Note that the vertical axis is logarithmic!

 

[stephenh]

AP - thank you very much indeed, not the sort of detail you would get in evening classes.

Again thanks , especially for the simplicity...
Stephen

 

[JayBee]

Re: AntarcticPilot

......which brings us conveniently on to the interesting subject of meridional parts and the measurement of rhumb line courses and distances on a mercator chart......

 

[AntarcticPilot]

......which brings us conveniently on to the interesting subject of meridional parts and the measurement of rhumb line courses and distances on a mercator chart......

Why isn't there a "tired smile" icon? One thing I regularly have to make clear to people is that there is no such thing as a map projection that allows you to accurately measure distance from the map, except in very specialized cases. It is, for mathematical reasons, impossible. We can make maps that preserve shape OR we can make maps that preserve shape, but these two properties of maps are mutually exclusive. What we can't do is create a map where distance is always scaled correctly (think about it - if you peel an orange, there is no way of flattening the peel without stretching it).

On large-scale charts, the error is tiny, and unlikely to be a problem when you do distance off your favourite light-house. But you certainly can't measure ocean-crossing distances from a chart with any hope of getting an accurate answer.

If anyone really wants accurate great circle computations, may I recommend this ? The "geod" program does great circle computations. It is accurate to geodetic levels, and takes account of the shape of the oblateness of the earth. [GEEK WARNING]This is a command line utility[/GEEK WARNING]

 

[mattonthesea]

Thank you all for this thread. For th first time in my life I understand how this all works. I had the concept OK but the workings now make sense too!

Next question: is the principle the same for using other stars than th sun? Ie do you take readings from known stars and plot them using the same methods? (I assume the pole star would not be useful for this!) And then do you do a running fix and/or a 3 point fix?

I'm doing an atlantic crossing next year and will prob oly use sun-run-sun but itmight be useful to know.

BTW Sod's law: this thread starts at a period of daily sunshine in theUK and guess what; can I get hold of a (very) cheap sextant? Of course not

 

[JayBee]

Why isn't there a "tired smile" icon? One thing I regularly have to make clear to people is that there is no such thing as a map projection that allows you to accurately measure distance from the map, except in very specialized cases. It is, for mathematical reasons, impossible. We can make maps that preserve shape OR we can make maps that preserve shape, but these two properties of maps are mutually exclusive. What we can't do is create a map where distance is always scaled correctly (think about it - if you peel an orange, there is no way of flattening the peel without stretching it).

On large-scale charts, the error is tiny, and unlikely to be a problem when you do distance off your favourite light-house. But you certainly can't measure ocean-crossing distances from a chart with any hope of getting an accurate answer.

No need for any "tired smile icons" methinks.

Perhaps I should have said the calculation of rhumb line courses and distances. We're not talking geodesy or surveying here, just practical navigation.

Day's run type calculations at sea usually involved mercator sailing, where the differences in latitude were converted into units of longitude (aka meridional parts) for the trig. GC routes were divided up into rhumb line segments as a practical necessity.

All good practical stuff - as is the use of the simple, large scale plotting sheets described above. Granted - not for v.high latitudes.

 

[snowleopard]

I have in front of me a pad of plotting sheets produced by Imray. It has a linear latitude scale up the centre and a series of curves which you use as a longitude scale so you can get an exact ratio of lat to long at any given latitude. Here it is. No mystery, no approximations. Simples.

And it has nothing to do with trans-ocean distances. The distances plotted here are less than 100M.

 

[JayBee]

Imray plotting sheet

Peering at the small print at the bottom, I see that Imray got it from the Celestaire astro-navigators in Kansas - slightly let down by some of the spelling in the labelled steps!

Still reckon it's easier to make one's own, with a fixed longitude scale.

 

[timbartlett]

Next question: is the principle the same for using other stars than th sun? Ie do you take readings from known stars and plot them using the same methods? (I assume the pole star would not be useful for this!) And then do you do a running fix and/or a 3 point fix?

The basic principle is the same, but the way the position of stars is presented in the Almanac is different. You can use planets, too. But if you use the Air Sight Reduction tables the sight reduction process for stars is different, (very much simpler).

Yes, you normally plot star sights using azimuth and intercept derived from each star, just as for the sun.

The calculations using the Pole star are completely different, but the answer is your Latitude -- no need to plot anything other than a line of latitude!

Strictly speaking, any three point fix is "wrong" (even one taken using three visual landmarks and a compass) unless you take all three bearings at once. The same thing applies to star sights: unless you somehow take all three/four/five/six sights simultaneously there will be an error caused by your own movement. But in practice, for yottigation, so long as you travel less than a couple of miles between the first sight and the last, it is hardly worth losing much sleep over.

 

[maxi77]

Strictly speaking, any three point fix is "wrong" (even one taken using three visual landmarks and a compass) unless you take all three bearings at once. The same thing applies to star sights: unless you somehow take all three/four/five/six sights simultaneously there will be an error caused by your own movement. But in practice, for yottigation, so long as you travel less than a couple of miles between the first sight and the last, it is hardly worth losing much sleep over.

Indeed, but as a yacht is unlikely to travel more than a mile whilst taking the sights an academic point when getting an astro fix from a yacht to less that 5 miles is hard going. I have vague memories of having it explained to me how you could shift the position lines to account for the different times each was taken but I never actually did it. On a yacht I suspect the unkown deviation in you hand held compass probably contributes more error than any boat movement.

 

[snowleopard]

I have vague memories of having it explained to me how you could shift the position lines to account for the different times each was taken but I never actually did it. On a yacht I suspect the unkown deviation in you hand held compass probably contributes more error than any boat movement.

Transferring a position line is simple stuff if there is a significant time between sights, but what has a hand compass have to do with it?

 

[maxi77]

Transferring a position line is simple stuff if there is a significant time between sights, but what has a hand compass have to do with it?

I was not talking about transferred position lines rather resolving the impact of each position line of a sight having been taken at a diferent time, which would equally apply to resolving thcocked hat of a visual fix taken with a hand held, hence the reference to to the handheld. I believe aircrew did this to compensate for the distance moved between individual sights where the impact will be noticeable at several hundred knots.

 

[timbartlett]

I was not talking about transferred position lines rather resolving the impact of each position line of a sight having been taken at a diferent time, which would equally apply to resolving thcocked hat of a visual fix taken with a hand held, hence the reference to to the handheld. I believe aircrew did this to compensate for the distance moved between individual sights where the impact will be noticeable at several hundred knots.

You don't have to be doing several hundred knots: the effect is quite noticeable at typical ship speeds, and is potentially noticeable even at yacht speeds (say 6kts) if you take more than about 15 minutes to complete a series of sights. Whether it is worth bothering with at 6 knots is a completely different matter.

As Snowleopard suggests, the principle is similar to a transferred position line, but the practicality is slightly different. Not sure whether I can attach a diagram, and its difficult to explain without, but I will do my best:-

In a "normal" plot (i.e one that does not account for movement during the shoot), you typically end up with a number of chosen positions (one for each heavenly body) strung out along a parallel of longitude, and you plot the intercept and azimuth for each one, measuring from the CP.

Suppose, for instance, that
(a) you are heading SW at 8 knots:
(b) you shot Venus at 1933 and Arcturus at 1951 and
(c) for some reason) you want to plot your position at 1945.

In the 12 minutes between 1933 and 1945, the boat moved 1.6 miles SW, so you "run on" the Venus CP by draw a line from the original Venus CP, 1.6 miles in a SW direction. The end of that line is an adjusted Venus CP: you plot your intercept and azimuth from the adjusted CP instead of from the original CP.

Similarly, in the six minutes between 1945 and 1951, the boat moved 0.8 miles SW. So you adjust the Arcturus CP by "running back" the CP by drawing a line from the original CP, 0.8 miles in a NE direction. The end of that line is the adjusted Arcturus CP, from which you plot the intercept and azimuth.

 

[Neil]

I have in front of me a pad of plotting sheets produced by Imray. It has a linear latitude scale up the centre and a series of curves which you use as a longitude scale so you can get an exact ratio of lat to long at any given latitude. Here it is. No mystery, no approximations. Simples.

And it has nothing to do with trans-ocean distances. The distances plotted here are less than 100M.

Thank you very much for this! I was struggling with Cunliffe's very sparse explanation of the plotting sheet - the above is as clear as crystal, and I managed my own worked example (using Cunliffe's data) following your method. Excellent!

 

[bastonjock]

ive just bought my first sextant,and to go with it i downloaded an Ebook called "celestial navigation for the clueless" so far it makes sense.

 

[smartcom]

If you want to check your sight reduction calcs, download a free 30 day trial of WinAstro.
It gives your LOP as a bearing and distance from your initial EP, so you can plot it on a normal chart or a plot sheet without any problems.
Tim

 

[Lady Campanula]

....you typically end up with a number of chosen positions (one for each heavenly body) strung out along a parallel of longitude, and you plot the intercept and azimuth for each one, measuring from the CP.

Just 'cos I'm feeling 'nitpicky'. what on earth is

a parallel of longitude

when it's at home....?

Armchair bluddy admirals! Nearly made me drop my toast! H'rumph!