Basic Latitude by Local Apparent Noon (LAN) Sun Meridian Passage

[Music] when calculating latitude by local apparent noon or meridian passage we need a nautical sextant to take a reading of the Sun and we need to correct that reading for a dip index error and main correction refer to an earlier video if necessary we also need the nautical Almanac there's one conceptual piece that we need to talk about first and that is the fact that the Sun is up there somewhere in space and if you were to stand on it and drop a line right down to the earth it would impact in one particular spot that spot is called the declination of the Sun its measured north or south of the equator and that spot moves over the course of the day as the Earth rotates up from underneath it now you can also imagine that somewhere on the earth our vessel has a position and that position is defined as its latitude well there's one time each day when the Sun and us are on the same meridian or line of longitude so as the Earth rotates beneath the Sun once each day the Sun is on the same line of longitude as us or it's on our meridian and that's called meridian passage it also happens when the Sun is at its highest point in the day if you can form a relationship between these positions then we can really quickly use meridian passage to our advantage so if that's our latitude and this is the declination of the Sun if we can just measure something to relate these two things mathematically we can calculate our latitude and we can do that by measuring something called Zenith distance right so if we can obtain Zenith distance we can look up the declination of the Sun we can use a mathematical relationship to find our latitude at meridian passage once per day so what is zenith distance well it's best to think about it like this right here's you with your Sexton the spot directly over your head is called your zenith and if this was the horizon typically what we do with the sextant is we measure the angle from the horizon to the Sun and that's called our height observed and we'll use that in all of our mathematical relationships going forward in the advanced stuff but it turns out that if you can kind of take the inverse of that angle if you take this angle right here that's called Xena distance and that's really fundamental concept in kind of the theory of celestial navigation not necessarily the practice of it but if you take the height observed and subtract it from 90 because this is a right angle you can get your zenith distance so for instance if your height observed was 40 degrees above the horizon then the zenith distance is 50 degrees right so it's just 90 minus the height observed is your zenith distance and so back here you can use that zenith distance plus the declination which you look up to obtain your latitude and really you're going to end up in kind of one of three cases in the first case latitude in red will be equal to Z naught distance in green - declination in blue in the second case latitude in red is equal to Z natha's sense in green plus declination in blue in the final case latitude in red is equal to declination in blue - zenith distance all of these examples are just hypothetical cases and it's really going to depend on your ships dead reckoning position in terms of what relationship you can form between the declination of the Sun the Z existence and your latitude we observed the Sun at 75 degrees above the horizon right well according to our diagram and that would make the zenith distance 15 degrees in this case because the zenith distance is always just 90 minus the height observed well that's good if we were to look up in the nautical Almanac the declination for the Sun and we'll show you how to do that in a minute might get 10 degrees north as an example well what would the latitude be in that case well it really depends on the situation that we have so if we had a situation in which we were in the northern hemisphere and the Sun was also in the northern hemisphere but just below us then that would mean this is declination this is zenith distance so that means latitude should just be zenith distance plus declination so our latitude in this case would be 25 degrees north how about another basic example in this case we observe the Sun above the horizon at 43 degrees above the horizon so in this case the zenith distance would be 90 minus 43 or 47 degrees for the zenith distance and again using the nautical Almanac if we had a declination of say 10 degrees south then again if we're in the northern hemisphere what kind of situation are we in in this case we are in the northern hemisphere and the Sun is in the southern hemisphere so latitude is going to be equal to Zenith distance minus declination so latitude is equal to Z no distance minus declination in that case and so if we did zenith distance minus declination we should end up with a latitude of 37 degrees north what about an example when say we're in the northern hemisphere but near the equator in the summer so the Sun is to the north of us so here we are on 21 August 1981 and it is 1600 GMT Greenwich Mean Time or universal coordinated time how do we find out the information that we need from declination well if we flip to the day in question August 21st and we look down here is 21 August this is GMT so we come down to 1600 GMT and then the declination column is right here so come down to the day 1600 declination is 12 degrees and it's North North 12 degrees well that's convenient so the declination in this case is 12 degrees north and if we observed the Sun above the horizon at 85 degrees above the horizon that would make the zenith distance in this case would be 90 minus 85 or 5 degrees now here's where we need to think about the situation in this case it looks like the Sun is a little bit to our north in this case so the sun's declination is higher than in our potential latitude so in this case latitude would equal declination minus zenith distance the latitude equals declination minus zenith distance and so if we do all that math out declination minus zenith distance we end up with a latitude of 7 degrees north all right so that's another kind of basic example but finally let's do one where it's a little more complicated what if it is 21 August 81 but it's 16:30 gmt so now we can't just look up the declination and what if we observed the height of the Sun at 55 degrees 37.8 minutes above the horizon right well the first thing we could do very easily is get our Zenith distance by saying 90 - that would be the zenith distance one quick trick if you're doing this by hand is to say 90 is equal to 89 degrees and 60 minutes it makes the hand math a little bit more straightforward so in this case the zenith distance would be equal to 34 degrees 22 point 2 minutes okay great and now we need to look up the declination so again we go to the correct day and we come down to 21 August there's no 1630 here there's 1600 and 1700 so if we have a declination at 1600 of 12 degrees north and a declination at 1700 of 11 degrees 59.2 our time in question is 1630 so we could interpolate this and take the value halfway between those alternatively you can use the D number down here 0.8 minutes and use the increments and corrections pages in the back of the nautical Almanac for 30 minutes 0.8 and find a correction to use in that case so the correction would be 0.4 so either way our declination is going to be 11 degrees 59 0.6 minutes north and that's right out of the nautical almanac so the last step is to think about the situation that we're in and I didn't give you a D our position but in this case we're kind of back where we started we're in the northern hemisphere the Sun is also in the northern hemisphere but lower than us so latitude this value should be equal to Z Neph distance which is this value plus declination it's the latitude equals zenith distance plus declination and if we add these two values together zenith distance and declination then we should get 46 degrees twenty one decimal eight minutes north right so the process was to take the height observed turn it into a Zenith distance right and then find the declination and then compute latitude based on the situation and just as a recap of the lesson in the beginning we said that at one time during the day the sun's declination or its latitude north or south to the equator passes our meridian or our line of longitude and everything kind of lines up nice and easily so we could then define our latitude by the mathematical relationship between the declination of the Sun and the zenith distance zenith distance once again was just the complement of what we measure with our sextant right so 90 degrees for a right angle minus the height observed yields the zenith distance and then finally we just need to think of what situation we're in based on our dead reckoning position and the declination of the Sun and then work through examples such as this also remember that when we are using our height observed those are corrected values in other videos we talked about how to correct a sextant to get the height observed [Music]

Channel: Practical Navigator

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Keywords: LAN, meridian passage, local apparent noon, coast guard, navigation, celestial, sextant, noon sight, noon latitude, practical navigator, celestial navigation, sextan, how to navigate, boat, sailing

Id: HrH1vQrIFcs

Length: 11min 55sec (715 seconds)

Published: Wed Sep 27 2017