Astronavigation by sextant

[Malcolm3]

Why are there no plotting sheets made for north of 70 degrees.Is it because no one goes there or is astro more inaccurate as longitudes converge making it impractical. Or is it that even at noon highest would be about 30 degrees and less than 20 has high refraction. Im talking about summer in artic when sun never sets
Malcolm

 

[Simes]

Why are there no plotting sheets made for north of 70 degrees.Is it because no one goes there or is astro more inaccurate as longitudes converge making it impractical. Or is it that even at noon highest would be about 30 degrees and less than 20 has high refraction. Im talking about summer in artic when sun never sets
Malcolm

Yes to all of the above. The universal sheet only goes to 70 degrees but you can produce your own for any latitude including 70 to 90 degrees. The Nautical Almanac has a table to deal with increased refraction, so there is no reason other than market forces controlling how useful it would be to produce at a good element of cost a plotting sheet for north or south of 70 degrees.

 

[AndrewB]

I believe atmospheric refraction can be higher at the poles because of a mass of cold air close to the surface. But for astronavigation following the usual rule of not observing objects within 10° of the horizon, I've never heard that it makes a serious difference.

Rather than standard plotting sheets, I prefer to use a nice empty area of sea on a small-scale chart covering the latitude where I am currently. That way the scales are ready printed for you, you don't need to work them out.

 

[jdc]

Here's one I prepared earlier

Why are there no plotting sheets made for north of 70 degrees.Is it because no one goes there or is astro more inaccurate as longitudes converge making it impractical. Or is it that even at noon highest would be about 30 degrees and less than 20 has high refraction. Im talking about summer in artic when sun never sets
Malcolm

Here are some for the polar regions I made last year.
http://www.awelina.co.uk/sextant/plotting_sheets/

They use Transverse Mercator projection so you can plot intercepts on them directly. There is nothing very special about the corrections, except that one tends to use the sun when at low angles, which would normally be avoided when in temperate latitudes. This:
http://www.awelina.co.uk/sextant/JavaScript_Sextant_calcs_2013.html

has corrections which make explicit pressure and temperature and should be good for low altitudes (down to a couple of degrees). The semi-empirical correction formula is described here:
http://en.wikipedia.org/wiki/Atmospheric_refraction#CITEREFGarfinkel1967

Go for that midnight sun shot - it's fun at least!

 

[AntarcticPilot]

Here are some for the polar regions I made last year.
http://www.awelina.co.uk/sextant/plotting_sheets/

They use Transverse Mercator projection so you can plot intercepts on them directly. There is nothing very special about the corrections, except that one tends to use the sun when at low angles, which would normally be avoided when in temperate latitudes. This:
http://www.awelina.co.uk/sextant/JavaScript_Sextant_calcs_2013.html

has corrections which make explicit pressure and temperature and should be good for low altitudes (down to a couple of degrees). The semi-empirical correction formula is described here:
http://en.wikipedia.org/wiki/Atmospheric_refraction#CITEREFGarfinkel1967

Go for that midnight sun shot - it's fun at least!

Just a word of warning about Transverse Mercator near the poles. The mathematics of the Transverse Mercator projection for the ellipsoid is intractable, and the usual algorithms (Taylor Series expansions) are only good for less than about 10 degrees of longitude away from the central meridian. Further away than that, the conversion from lat/long to cartesian coordinates may not be accurate. There are more accurate expressions available, but I don't know what Matlab uses, and I'd be a bit surprised if it was one of the better (more complex) expressions.

It probably doesn't matter for the purposes of a plotting sheet for astro-navigation, but it is worth noting that Transverse Mercator can be a bit of a can of worms!

 

[jdc]

Just a word of warning about Transverse Mercator near the poles. The mathematics of the Transverse Mercator projection for the ellipsoid is intractable, and the usual algorithms (Taylor Series expansions) are only good for less than about 10 degrees of longitude away from the central meridian. Further away than that, the conversion from lat/long to cartesian coordinates may not be accurate. There are more accurate expressions available, but I don't know what Matlab uses, and I'd be a bit surprised if it was one of the better (more complex) expressions.

It probably doesn't matter for the purposes of a plotting sheet for astro-navigation, but it is worth noting that Transverse Mercator can be a bit of a can of worms!

I agree that the spherical T-M projection is only good a few degrees either side of the central meridian, but a plotting sheet is only a few degrees wide anyway - at least up to well north of 80 degrees. I'm sure we can agree tho that it's better to use a transverse projection than a normal Mercator one once in high latitudes, but I'd be glad to be told of a better one to use.

Nor do we really have to worry about the earth not being spherical: as I think about it, we navigate on an an imaginary sphere of 'unit' radius, and when using a plotting sheet, plot relative to angle subtended at the centre of the earth. There is no notice taken or required of the earth being an oblate spheroid. In this way a mile is defined as 1 arc-minute.

The fact that the mile varies a little bit bit (0.3%) with latitude could be allowed for easily enough but is probably not worth bothering with as few logs are as accurate as that anyway and it's not a cumulative error in sun-run-sun fixes.

The problem would only be that the derived astro-nav position would not quite tally with the land plotted on the (WGS84) navigational chart, do you know how big this error can be?

PS: I don't have the Matlab mapping toolbox, so don't know their algorithms. When I did a coordinate conversion from scratch (once, not recently) I used the Helmert transformations published by the OSGB.

 

[AntarcticPilot]

Nor do we really have to worry about the earth not being spherical: as I think about it, we navigate on an an imaginary sphere of 'unit' radius, and when using a plotting sheet, plot relative to angle subtended at the centre of the earth. There is no notice taken or required of the earth being an oblate spheroid. In this way a mile is defined as 1 arc-minute. I understand this to be the Geocentric definition of latitude.

The fact that the mile varies a little bit bit (0.3%) with latitude could be allowed for easily enough but is probably not worth bothering with as few logs are as accurate as that anyway and it's not a cumulative error in sun-run-sun fixes.

The problem would only be that the derived astro-nav position would not quite tally with the land plotted on the (WGS84) navigational chart. The difference must be the difference between Geocentric and Geodetic latitudes, do you know how big this is (I'll work it out this evening if I get a chance).

I was being rather pedantic - the errors in astro-navigation from a yacht far exceed the likely errors in the plotting sheet!

I did once work out the correspondence between geocentric and geodetic latitudes; it isn't hard, but I forget what it is!

I've just looked it up in Snyder (Map projections: A Working Manual, USGS Professional Paper 1395, page 17 equation 3-28)

Geocentric latitude = atan((1-e*e)*tan(geodetic latitude))

where e is the eccentricity of the ellipsoid, 1/298.257.

Doing a quick spreadsheet shows that the maximum difference between geocentric and geodetic latitude (geocentric is always less) is .000322 degrees at 45 degrees, diminishing to zero at the equator and the pole. That's around 35 metres.

 

[Mariner69]

Since the best accuracy you're likely to get is around 2 miles I used to use the back of a chart for my plotting and mucked around with the 'C' correction if really keen.

Managed to keep the old man happy with my daily sights before we enjoyed the introduction of Transit. Letting both chronometers stop at sea did not however endear me to him; he read my fortune and parenthood long and distinctly.

Great days!