Celestial Navigation Made Easy

hi I'm will flesh and this is celestial navigation and we're here to introduce the subject and explain how it all works and give you a working knowledge of what's happening when you work out a site and how to use the sextant the key to celestial navigation is it's much simpler than a lot of people think and I have taught it many many times from teaching one other skipper one other sailor on the beach in the Bahamas just before he headed offshore for Canada having never used celestial navigation and he actually got to Canada successfully to teaching in formal classroom settings in Boston and Seattle with large classes and so I have taught at a number of ways and over the years I've found ways to teach it that explain it in a way that really anybody can understand it and master the subject it's often taught I actually have had an experience where I thought it took the class of celestial navigation in a very formal setting and found it quite a complex subject to understand the way it was taught the reality is it's really very simple and the concepts are very simple so if we explain the concepts and you understand how it works the then filling in the details is quite easy if you don't understand it to start with then you can just be snow balled with all the deep details and it starts to just get super confusing because your basic understanding isn't firm enough but when we clarify how it works first and you grasp that then filling in the details is easy now we're going to use three diagrams to explain the entire system how celestial navigation works it's really just three simple diagrams as we progress though this morning you'll want to make sure that you copy each of the diagrams so the most important tool for you this morning is paper and pencil if you don't do the diagrams yourself it's going to be really really hard to remember them by the end but if you draw all the diagrams on your own piece of paper as we draw them here on the whiteboard that will give you a really good working understanding of how it all works now my thinking is that if you don't understand how it works it's really hard to do it even if you have cheat sheets with 40 steps do this this this this you're gonna make mistakes if you don't understand what each step is about so the understanding comes first and then the details and then you should be able to work out a problem a celestial site just on a blank sheet of paper if you understand it you don't need little tips or cheating you know steps follow steps if you don't understand it no matter how many steps you're following you're gonna make mistakes and if you end up in the right hemisphere North versus South you'll be lucky but if you understand it the whole thing is quite simple I think one of the reasons it got complicated and seems hard to learn is because we use a lot of terms that aren't familiar we can say a whole sentence as a navigator where you might not understand a single one of the important words it's just like a foreign language not only do we use different terms but we use of three VA shion's for those terms and we use sometimes it's an abbreviation sometimes it's an acronym so we can talk in sort of this different celestial navigator and make the whole subject seaman really complicated and I think maybe that was done by the British Navy when they were pressed ganging their crews and they didn't want the crew to know how easy it was to navigate it's pretty hard to mutiny if you're out in the middle of the ocean and you have no idea where you are or how to get anywhere else because you can't navigate so maybe this was done intentionally but we'll sweep all that away I'll call things by names you'll understand and we'll make it pretty simple and obvious oh why should mention this whole series is brought to you by Tippecanoe boats that's my company and you can find us on the web at model sailboat dot-com so please visit our website and enjoy lots of fun stuff on there okay let's start well first let's figure out where you are how are you with differential calculus oh you look a little worried there oh well not to worry we don't need any differential calculus for a celestial navigation not involved at all it's not relevant but how about geometry and trigonometry are we better Oh a little stronger with that but look a little uncertain so well not to worry we don't need geometry or trigonometry for celestial navigation but now let's get to the crux of it how are you with adding and subtracting oh I see some brightening there yes good you do need adding and subtracting to do celestial navigation that's all the math you need adding instructing it's remarkably simple stuff all the difficult math is done for you by the tables and you just look in the book and it tells you the answer you don't have to do it any difficult math at all okay so a simple subject three diagrams and you'll understand exactly how celestial navigation works the whole subject and then later on in another segment we can do the details there are a fair number details but they all make sense they're all pretty well totally logical okay so let's get started we're gonna start with the first diagram and as we do diagrams I'll show you what we're diagramming on the globe and how we're looking at the globe we're going to be slicing the globe in different ways sometimes we may want to slice it right through North Pole South Pole senator the earth just slice sometimes we'll slice it at an angle sometimes they'll try to show the whole globe is a round surface so different ways and I'll show you on the globe power how we're doing our diagram the first diagram has several parts to it though and I told you three diagrams we're going to look at several aspects of the first diagram separately first these don't count us there's three diagrams they're just sort of extra the first thing I want to make sure everyone is clear about latitude and longitude you have to understand latitude and longitude in order to be able to do celestial okay let's do a diagram here the first diagram we're going to look at the globe as though we're poor easting up in space and satellite right over the North Pole looking down on the globe and that diagram will look like this because we want to take a look at longitude and how longitude works there's the earth here's the North Pole right here North Pole this would be similar to the equator looking down on the earth like that from the top and longitude here's England down here and Europe of course something over here America or Canada and North Pole longitude zero degrees of longitude goes right through Greenwich England that's zero degrees of longitude and then longitude is quite simple this will be ten degrees of longitude well let's do it 15 degrees let's call that 15 degrees because typically we talk about longitude and 15 degree increments because as there are spins the Sun moves 15 degrees per hour apparently approximately so 15 30 degrees 45 65 45 60 so each degree of longitude indicates an angle now the thing about longitude that you have to be careful with is one degree of longitude if you're standing with your feet on the North Pole really cold first of all but you can walk 60 degrees of longitude in like a fraction of a second it's only a few inches so right at the North Pole six degrees of longitude is nothing it's a few inches at the most where is it the equator to go sixty degrees of longitude is many many miles in fact at the right at the equator sixty degrees of longitude each degree of longitude at the equator is about 60 nautical miles so sixty degrees of longitude at the equator is 60 times 60 3600 nautical miles so longitude cannot be used to measure distance except right at the equator because it varies one degree of longitude doesn't equate to a certain distance unless you're right on the equator okay so that's longitude and longitude goes all the way around to 180 degrees here west longitude 180 and east longitude 180 degrees under an eighty East on an eighty west okay that's longitude any questions no good now let's look at latitude and make sure we're clear with that hopefully this is review or just so obvious you already know it give you fast-forward if you want but pause here for a minute because latitude some people miss have a misconception of latitude that makes celestial navigation impossible so latitude the misconception that some people have is that the earth is sliced like a tomato through first through the equator and then 1015 degrees of latitude 30 degrees of latitude like so no latitude and we abbreviate latitude L a T this is what some people think of as latitude here's the top of the earth and you're slicing it like a tomato in just sections here's different degrees 15 degrees sections a lot of - sliced like that here's the equator no that is not latitude latitude is not like slicing a tomato if you think of latitude this way you can't understand anything at all so erase that diagram from your mind instantly and probably even better not to put it on your paper okay so scribble it out of your paper let's look at latitude what latitude really is here's the earth keep the blue that shows up better good sort of a flat spot there huh so here's the earth now we're looking at the earth the globe from the side let's put in the North Pole here let's get a better globe actually and then we'll put in the North Pole whoops this side wants to be flat I don't know why you got a problem there bit better now we'll put in the North Pole and South Pole and the equator north pole here South Pole their equator very pissed the middle news the center of the earth okay now the way latitude works is latitude measures an angle at the center of the earth from the line right through the equator slicing right through the equator measuring up at an angle and then we'll call this 15 degrees of latitude we can measure the latitude here at the center of the earth we can measure it here at the surface of the earth it doesn't matter 15 degrees here and so latitude is not slicing it's measuring an angle up from the equator and South latitudes let's see here is 45 degrees south latitude 45 degrees south measuring an angle at the centre of the earth down to the equator or measuring it on the surface is Earth's 45 degrees it's the same angle we can talk about it either way it doesn't matter 45 degrees south now latitude we can talk about it in another way 15 degrees of latitude is exactly 15 times 60 so what is that sixty six hundred nine hundred not nine hundred nautical miles okay nine hundred nautical miles now if you ever wondered why we have nautical miles and why we don't use land miles out sailing it's because of celestial navigation nautical miles land miles would be really really complicated to use in celestial navigation because there's no direct equivalent in degrees but nautical miles translate very easily sik1 degree of naught one degree of latitude equals 60 nautical miles simple can simple conversion and that means since one one degree of latitude has 60 minutes of latitude in it one minute equals one nautical mile that makes navigation really easy and that's why we use nautical miles so 15 degrees of latitude 15 times 60 equals 900 nautical miles so we can talk about this distance in three ways we can talk about it as an angle at the center of the earth we can talk about it as an angle on the surface of the earth or we can talk about it as nautical miles it doesn't make any difference it's all the same basically okay now people may understand that fairly well but now we have to do take it one step farther because this is important now let's this time we sliced the earth right through the North Pole the South Pole the senator of the earth just sliced right through now we're going to slice the earth differently and show you that same concept how it works we're gonna slice there if that's some completely different angle right through let's go right through North America let's go right through North America and Hawaii North America we're here in Puget Sound area Northwest Washington and Hawaii's down here where is Hawaii should be there they're pretty small okay we're gonna slice the earth right to Northwest Washington Hawaii and through the center of the earth we can slice the Earth's through three points if we add a fourth point that won't be on our flat plane our plate that we've created weakens but with three points the center of the earth we always have the center of the earth on any slice we're taking Northwest Washington and Hawaii we can get those three points right on a single plane so um now we have the center of the earth Northwest Washington and Hawaii all on this slice okay it's not there's no North Pole the North Pole is North Pole is up off the board and South Poles down below the board not on this flat plane now we can do this we draw a line out through Northwest Washington and line out through Hawaii and we can measure the angle here between the two at the center of the earth the angle from the center of the earth to Northwest Washington and through Hawaii and that looks like it's about 24 degrees let's say and so we can say at the surface that that's 24 degrees and that translates into how many nautical miles 24 times 60 is going to be 1200 plus 240 so 1400 and 40 nautical miles okay any questions about this we can talk about distance on the surface of the earth as an angle we can talk about distance as an angle at the centre of the earth we can talk about it as nautical miles it's all the same and we can do that with any slice through the Earth's surface that includes the center of the earth okay this is why not celestial navigation is pretty simple because of this the way we talk about distance often we talk about distance a number of degrees degrees and minutes we tend desync degrees minutes and tenths of minutes we don't use seconds very much it's just - we're not concerned about that level back 24 degrees 10 minutes okay our ten point five minutes okay degrees minutes and tenths of minutes we don't go two seconds okay that's distance and latitude now let's take a couple more concepts and then we'll get to our first diagram and put all this together into our first diagram okay let's let's look at light here's the earth here actually let's make that even smaller a little bit smaller there here's the earth here let's put a satellite up in the sky here now that light from the satellite someone's coming straight down actually if you're standing right here let's put Joe here standing right here here's Joe he looks straight up and sees the satellite straight over his head and that's that light light actually let's put Joe standing he's lying down there let's put him standing up right there on the surface of the earth okay there's Joe right over his head he looks straight up right over his head is the satellite light that's that light light is coming down through the top of his head down through his body through his feet and continuing if it could continue like a gamma ray or something that light would continue right to the center of the earth like that now if somebody else is standing over here up in Bellingham Puget Sound area you're here that lights coming at a funny angle to you is not coming straight down on your head it's not not coming parallel to this beam of light it's coming at a funny angle okay now if we move farther out let's get the limit of them satellite that's much higher or somebody that's much farther away now the lines of light are not at such a big angle here to each other they're getting closer to parallel now let's move this farther out let's move this well the first star is four point two four light-years away four point two four light-years away that would be moving this point out almost as far as where the moon is I mean it's way farther than the east I mean it's in my diagram here we'd have to move at this point for the earth being this size we'd have to move this point as far as the East Coast or farther way out now we've got light coming in we don't have light coming in at weird angles here we have light coming in from so far away that the light that I see is coming virtually in line parallel to light the Joe sees all the light from that distant distant body celestial body are parallel to each other wherever we are on the surface of there all those lines of light are parallel now that's a bit of an approximation but they're so close to parallel that we can assume that they are parallel okay so that's how the light from the Sun the planets the Stars is coming down to the earth parallel lines if you think of the light as coming from a point that's close to the earth at funny angles all these different angles celestial navigation absolutely does not work or you'd have to correct for the angles and that is something we don't want to have to do the only time we correct for this angle what we call this parallax the only time we correct for it is with the moon the moon's not quite far enough away to assume it's infinitely far away and the beams of light are parallel with the moon we make a simple correction and say well it's a little bit too close to make this assumption so we're going to just nudge the nudge of the numbers the table does it for us well just nudge the numbers a little bit to make a simple correction for that but overall solution are even with the moon we make this assumption first the blinds of light are parallel and then we make a slight correction - because that assumption the moon is a little bit too close for that assumption to work perfectly okay parallel lines of light now let's actually leave these lines up here some of them two of them that's all we need leave those two lines up here we'll get rid of this now we're back to seventh grade seventh grade and yes you do need a little bit of geometry this is the only geometry you need right here probably the simplest part of geometry first thing you probably were told in seventh grade in geometry if you have two parallel lines and you have a single line crossing those two what can we say about the angles let's say this angle here is X or 30 degrees looks like about 30 degrees okay so that angle there is 30 degrees big question what is this angle here if this a these two one one line crunching another line this angle is X then this angle yes you're right X this is also 30 degrees okay now the big question the really big question these two lines are parallel this is a single line crossing those - what is this angle here what is that angle okay you got it X 30 degrees and now the final question and this is all we need for the first diagram to understand the first diagram which we're getting to in a second here this angle here is the same as that angle which is same as that angle which is same as that angle so this is x equals 30 degrees now maybe where I jumped ahead and put all these three these are the little diagrams together into a single diagram and what I'm about to show you which is the first diagram of the three diagrams you need to understand celestial navigation maybe you've already combined it all on your hand and it's like oh I see it but maybe not it's no more complicated than what we've just seen putting these three these several different concepts together okay and this is really what celestial navigation is about and I get excited about it because it's such a neat thing it's fairly simple but it's giving you a position on the face of the earth within half a mile based on celestial planets that are so far away we can say they're infinitely far away many many light-years away some of the stars that we use for celestial navigation or the planets not quite as far away or the Sun eight eight light minutes away pretty far so it's a neat subject it's really fun it's really cool you can understand it you can grasp it all and be an expert really in this one session you'll understand it okay so let's take a look at what we're doing here's the earth again there's the earth now let's mmm let's make that a little let's move give ourselves a little bit more room okay and this is where you want to be putting this diagram on your paper as I draw it because that's the only way you'll really understand it just looking at it is different from drawing it okay we remove this diagram over just a little bit here through a little bit more room on this side okay now this time we're slicing the earth again let's slice it let's speak consistent let's slice the earth through Bellingham and through Hawaii we're gonna slice it at the same angle and through the center of the earth okay so we'll get the center of the earth on there right there this is me having just sailed off the coast of Bellingham Seattle sailing out through the straits of Juan de Fuca out to sea and I'm trying to get to Hawaii why he's further down here so we sliced the earth at a funny angle we haven't got the equator on here we haven't got the North or South Pole we've sliced it to Bellingham to Hawaii and through the center of the earth okay and so we've made a flat plate a flat drawing Here I am just offshore off the coast of Northwest Washington here's Hawaii and here's the center of the earth three points we can always get three points on a flat plane okay mmm Joe happens to be in Hawaii already here's Joe standing in Hawaii okay he's waiting for me there actually maybe should have that be a female anyway more incentive anyway but anyway we'll call it Joe and Joe is here let's draw a line out through Joe that's not very good line there's a line out to Joe now it so happens that Joe looks straight up and sees a bright star above his head right above his head straight up over his head that star light is coming down through Joe's head to his feet and would continue down through the center of the earth to the center of the earth like that now if I'm up here in Bellingham that stars not going to be overhead for me if overhead will be up here it's going to that star light is coming in in parallel lines so it would be coming in at this angle here so this line of light from the same star that Joe's seeing dragged overhead would be parallel to this line of light okay parallel lines now let's just add one more line coming from the center of the earth right out through where my position is here's my position okay that's the start of your diagram try to get that on the paper send it to the earth Joe here with the start right over his head the two parallel lines of light coming in make sure this line of light and this line of light are parallel and then this line is just a line from from my position down to the center of the earth now when we shoot the when we shoot a star when we use the sextant and shoot the star we're shooting the heights of the star above the horizon so we take it and we get the angle that we look out at the horizon and then we look at the star and we see how high the star is above the horizon let's say it's pretty high let's say it's like 40 40 50 degrees the stars up about 50 degrees above the horizon what is our horizon here's the starlight what's our horizon in this diagram well think of the horizon is pretty clear word horizon horizontal everything that's horizontal is that's what the horizon is horizontal vertical is straight down to the center of the earth for my position this line represents vertical so that's a vertical straight down to the center of the earth straight down through my feet to the center of the earth that's vertical horizon is horizontal vertical and horizontal are always perpendicular to each other so if I want to add the horizon to this diagram I just need to do a line that's if I can do a straight line here a line that is perpendicular to the vertical and that line just barely touches the surface of the earth right where my feet are and that is actually my horizon and it's actually my horizon if my eye level is down right at water level there's a minor correction when I'm up on in the cockpit of my boat and my eye might be eight feet above water level there's a minor correction because then I'm looking down on what the real horizon is I'm looking down and the rising a little farther out but basically for now we can think of the horizon as being a line that just barely kisses the surface of the earth right here at my feet and is perpendicular to the vertical line down through the center of the earth remember this is me this is us you're on the boat too I'm going to say us that's us not us us right there okay now let's try to clean this up a little bit that'll give you time to get your diagram caught up because I want this to be really clean and and neat so here's the surface of the earth here's our horizon the line tangent to the surface of the earth and here's the perpendicular between the vertical which is straight down to the center of the earth and the horizontal which is the horizon okay now what we're trying to figure out here is our distance from this point this point Joe happens to be here let's say this isn't even Hawaii let's say this is just a point on the surface of the earth directly underneath that star Joe could be in a boat or he could be on land it doesn't matter but no he's looking straight up at that star that's where the star is it could happen to be over Hawaii it could be happened to be over some other body of land or over the ocean it doesn't matter Joe is looking straight up at that star this is the point directly under the stars doesn't matter if Joe is there or not let's take Joe out of there this is the point directly underneath the star here if Joe were there the stars right over his head that's called the ground point of the star that makes sense your Mountain point okay here now I'm sorry definitions at you and terminology but that one makes sense the ground point of the star GP and how do we know where that is well we just look in the tables we look in the nautical Almanac the nautical almanac is amazing it tells us the latitude and longitude of every star for every second of the year this is your definite this this happens to be 1992 Almanac every year you need a new Almanac it tells you where the Sun is in latitude and longitude where the moon is where the planets each planet is and where the 30 navigational stars are for every second of that year that this book is created for you can find all that online you can find exactly the pages of the nautical and I've got mine and check it out so we can work out exactly we loop in the table and find out exactly where let's call this that's well what's in this case let's just say this was the sudden s UN Sun this is the latitude and longitude of the Sun at a certain second of a certain day when we took our Sexton sight we were at this location we took a sextant sight on the Sun this is where the Sun was we looked it up latitude and launched it in the table in the nautical Almanac we don't call it latitude and longitude but it's a it's basically just life didn't lunch dude so the position of the Sun we know where that point is that's a definite point were someplace up here we don't know exactly where that is but we took a sextant sight measuring the height of the Sun above the horizon that would be this angle here the height to the Sun above the horizon from the horizon up to the light coming from the Sun this angle here that angle looks like about 50 degrees here that angle hey we don't call it sa X number this was a Victorian art science off the sextant we call it H s height sextant Heights sextant that's what we measured off the sexton when we looked out at the horizon we looked up at the Sun and measured the angle between the horizon and the Sun 50 degrees okay now what we're trying to figure out here is we know this point from the table from the nautical Almanac and we're trying to figure out how far away from this point we are we don't know where we are we just know we're someplace soft the coast of Northwest Washington we want to find out this distance between these two points a known point and distance to where we are how can we do it from this diagram well we're moments away from understanding this if you understand what we've got so far horizon light from the Sun coming in this is the point directly under the Sun the latitude and longitude of the Sun the sun's light going straight through that point on the surface of the earth down to the center of the earth this is just a vertical from where the we are break down to the center of the earth and this is the horizon horizontal and this is the angle up to the Sun all the sun's lights coming in parallel parallel lines of when we because the Sun is virtually infinitely far away okay now let's apply our geometry the geometry we just saw okay how does that fit in whoa look at this okay this is 90 degrees here perpendicular so this angle here whoa what's that angle if the whole angle is 90 this has to be 90 minus 50 the entire angle minus this part 90 minus 50 or let's think of it as 90 minus HS okay this is HS height sextant this is 90 minus HS right sextant 90 minus the section reading and now big question where are we here what is this angle here and look we've got we can continue this line so it's more like our former diagram previous diagram we've got two parallel lines just by a single woman too excited here breasts can continue this line hypothetically two parallel lines crossed by a single line let's continue that line just we don't need it the continuation but it makes it even more similar to our previous diagram two parallel lines crossed by a single line this is 90 minus HS here so this has to be 90 minus HS 90 degree 90 degrees - our Sexton reading and if that angle there is 90 minus HS the distance on the surface of the earth is also 90 minus HS and that distance from us to the point directly under the Sun the ground point of the Sun is 90 minus our Sexton reading if our section reading was 50 degrees 90 minus 50 90 minus HS is 40 degrees 90 minus HS at the center of the earth same angle as this angle here is 40 degrees 90 minus HS here is 40 degrees and the distance from us down to this point directly under the Sun the GP of the Sun latitude and longitude that distance is 40 degrees and 40 degrees if you want nautical miles 40 times 60 is 2400 and nautical miles so now from our sextant reading we know the distance from us to a known point that point directly under the Sun and if Jo is there we can call them up on our satellite phone and say hey Joe we're 2400 nautical miles away from you we'll be there pretty soon okay the sextant reading gives us the distance the point directly underneath the Sun Joe at this point looks straight up and says well right now the sun's directly over my head we say well we just got a sextant reading of 50 degrees on the Sun that means we are 40 degrees away from you or 2400 nautical miles away from you okay how does that help to have to know the distance away from a fixed point on the surface of the earth does that tell us where we are it gives us a piece of information important information about where we are does it tell us where we are well let's look at the next diagram we're going to do one more diagram and then we'll take a look at sextants and such like that any questions about this diagram let's clean it up just a little bit make sure you get it on your paper if you can't draw the diagram you're not you can't understand it you got to make sure you have all the details right parallel lines of light coming in a vertical line through our position us to the center of the earth a vertical line through the point directly the light from the Sun coming right down through the surface of the earth continuing on to the center of the earth so if Joe were here that'd be a vertical for him and then the horizon here we're measuring with the sextant angle from the horizon up to the Sun 50 degrees and if that's 50 degrees this is 90 minus the sextant reading HS 90 minus 50 with an angle parallel lines single line crossing angle at the Sun to the earth is 90 minus X and reading 99 is 50 which is 40 and the distance from us to the point on the surface of the earth we can measure distance here on the surface or the center by an angle distance on the surface 90 minus HS or 40 degrees okay this is where this is the whole subject really now you've got it now you just have to the next diagram simple next diagrams easy we're just applying this information this is where everything this is why it works this is the whole subject basically okay well let's go on to the next diagram you'll see why this has solved everything basically everything we need to know to get a position okay here we go next diagram diagram - that was diagram 1 remember there's three diagrams the first two the first diagram is the most complicated the second diagram the one we're about to do is really quite simple and I think you'll grasp this pretty quickly the third diagram is just a trick it's simply a trick to make it so we can use a small chart to do our final position is simply a trick it took mankind quite a long time after they developed concepts of sextants and everything to learn this last the last trick the trick that we'll see in the third diagram and some people have a little bit of trouble because it's a trick it's like well how can we do that it seems like a trick well it is a trick the third diagram but the second diagram is fairly simple okay so let's look at the second diagram now this time we're doing a diagram we're not slicing the earth at some funny angle so we have a flat plate that's what we did in the last diagram we sliced through Northwest Washington and through someplace out in the Pacific and to the center of the earth and we had a flat diagram this time we're going to represent the earth as a round surface so we can draw in let's put in our North Pole here and our South Pole here and draw in our quainter as a curved line like this okay so this is a sphere it comes imagine it round coming out from the board spiracle way okay now we saw the Sun let's let's progress a little bit on our voyage let's move forwards a little bit on our voyage now we're not right off the coast of Northwest Washington we're part way out to Hawaii and our dead rank we've been dead reckoning but after five six days of sailing and I know we're going nuts we're going sort of the Slover to white because you go through the doldrums if you head straight there instead of going south and then up so off to Hawaii but let's just let's just go ahead and go straight so we're here North America here we're someplace in this area off of North America on Hawaii's down over here someplace so we're in the Pacific let me take a morning sight on let's take a site on the easiest celestial body to shoot and at this point if I teach the class and that's what's the easiest body to shoot somebody's going to say the North Star and I love that great answer the north start does have some limited navigational use because you can figure out your latitude from the North Star fairly simply not not exactly precisely unless you do a little bit more calculation but the North Star is hard to shoot because it's 1/3 it's not not even as it's either third magnitude or beyond that it's very faint in other words it's hard to shoot because when you're shooting a star you have to be able to see the horizon you're measuring up from the horizon to the start or up to the celestial body the North Star barely emerges while you can still see the horizon because the sky is too light to see the North Star and then the North Stars there but you can't see the horizon so the North Star is not used very often for navigation the easiest thing to shoot because so easy to identify a three-year-old can identify it is of course the Sun there it is and you can shoot the Sun even when there's a slight overcast where you wouldn't be able to shoot any stars because of the cloud cover you can even shoot the Sun through a light light cloud cover and so and also it's during the day and the horizons there all day you can see this horizon all day long you shoot the Sun anytime you want doesn't have to be at that 15 minutes where the stars have emerged and you can see the stars and you can still see the horizon so the Sun is the easiest thing to navigate by and so often on a trip if you're short-handed you might the entire passage just take one or two star sights on series of star sights once or twice during passage and the rest of your navigation might just be by Sun sights when I sailed across the Atlantic in my 24 foot boat that was basically what I did I took 90 percent of the sights were Sun sights for fun I took some star in Planet sites and star in plan of sights you can take multiple sites at the same time a whole series like five stars and planets it gives you each one checks the for the other ones okay so sunset let's take a Sun sight let's take a Morning Sun sight this is roughly where we are off the coast partway to Hawaii The Morning Sun sight the Sun would be over here someplace looking south east towards the Sun now let's say we got a sextant reading of 50 degrees or HS height sextant equals 50 degrees when we shot the heights of the Sun this is the point directly under the Sun if Joe were here he would look straight up over his head and the Sun will be coming down on his head so the sun's position here and that sunlight would be going straight to the center of the earth we are up here we shot the height to the Sun above the horizon and we got the height - the Sun is 50 degrees above the horizon now from our last diagram we know the distance from the Sun we look up in the table the sun's latitude and longitude we don't call them that because we don't want this to seem too simple it actually is fairly simple but we don't want to seem simple we call it declination and local hour and Greenwich on our angle in the case the latitude and longitude we're just going to call them declination and Greenwich our angle just to make it a little bit more complicated it's actually just a latitude and longitude of the Sun now we don't know exactly where this point is where we are we don't know we're right there we're just dead reckoning might be there may be someplace in this area so a big area okay but we know from our sextant reading our distance from this point directly under the Sun the distance is going to be 90 minus HS that equals the distance D from this known point and how does that help us well 90 minus HS we've got HS of 50 so we're 40 degrees away from this point and that 40 degrees translates into 40 times 60 nautical miles 2,400 nautical miles and M nautical miles okay well that defines a circle around that point doesn't it a circle with a diameter of 2,400 nautical miles and we have to be someplace on that circle okay we could be anywhere on that circle based on that site 2,400 nautical miles away from Joe who is standing on a boat or on shore or wherever looking straight up at the Sun we're 2400 Hey Joe Hey Joe worth twenty four hundred nautical miles away from you right now I'm not sure where we are you know but I know we're on the circle 2,400 nautical miles away from you okay now that's helpful but not that helpful right because that's a big circle 2,400 nautical mile radius so what's the next step well next step is wait till afternoon stay still don't go anywhere stop your boat wait till afternoon and take a Sun sight after the Sun has moved the Sun now has moved to the west and is over here we take another Sun sight and this time we get an HS sub to second sight we're getting a chest of 70 degrees I'm sorry 30 degrees let's do it 20 degrees we waited pretty late in the afternoon 20 degrees that's about as low as we want to go if you go down below 15 degrees the light is bent so much by the atmosphere that your sight even though you make the correction for that an altitude correction for the bending of the light below 15 degrees the correction depending on atmospheric connect correct atmospheric conditions the correction is to be pretty much sort of an approximation at that point but at 20 degrees we'll get a good sight still the Sun is getting pretty far down 20 degrees we shoot it our distance away then we look up in the nautical Almanac for that minute and second that we took our section site and we get the latitude and longitude of the Sun right at that point late afternoon now Sun is low in the sky in the West we got a Sexton sighting of 20 degrees ours distance from the point the latitude and longitude of the Sun at that exact second that we took our site is going to be 90 our distance from the Sun will be 90 minus our sextant reading 90 minus 20 that's 90 minus HS right that's our distance from the Sun based on the first diagram and that's so 90 minus 20 there'll be 70 degrees away from the point under the Sun 70 times 60 70 degrees times sixty six seven six seven is 54 five thousand four hundred nautical miles away five thousand four hundred nautical miles away and I think you can see where we're going with this so now we have a big circle around that point that has a diameter of five thousand four hundred nautical miles and we're on that circle someplace right we have to be on this circle based on our second sextant reading in the late afternoon our distance which tells us our distance from the point directly under the Sun the latitude and longitude of the Sun at the exact minute and second that we took our minute and second that we took our second sight if we're on this circle and we're on our first circle because we stayed still we took down the sails if we're on both circles that means we either have to be here or here and if it's really hot we're sweating and in a bathing suit we're probably down here pretty close to the equator it was kind of chilly and we're thinking oh it's getting a little cool I better put on jacket we're up here you can probably tell which place you're out in this case we're up here so that's it you got it you can navigate now two diagrams and you can navigate but on a globe decides the problem is that just a pencil line on this globe we can do this just measure those distances on the globe and through all your arcs your circles and you'll have a position the problem is that a pencil line on this size globe is probably about just the thickness the width of the pencil line is probably about 60 nautical miles or not at 60 but the width of pencil line 20 nautical miles or 30 nautical mile anyway your accuracy is gonna be pretty small pretty low accuracy if you get a globe that's 8 feet in diameter you know as tall as the ceiling in here and you do this you can probably get down to a mile accuracy and that's close enough to cite an island especially Hawaii which is thirteen thirteen thousand feet tall so this all works but it's a little bit awkward right my thirty four foot boat certainly in my twenty four foot boat I couldn't fit an 8-foot globe it would have to be inflatable that would be really awkward wouldn't fit in the cabin in plays I have to be doing it on the deck and blow or roll like overboard like a beach ball it's a little impractical on my 34-foot boat it would be impractical on the 37 foot boat I'm building now steel hull beautiful cruise anywhere boat I thought it would be impractical so that brings us to our third diagram which is just a trick the third diagram is a trick we're going to pause here and look at sex since in a minute but I'll just give you a hint about the third diagram third diagram is just a trick to make the problem fit on a small nautical chart that doesn't extend as far as position of the Sun or this could be a star or the planet the point right under the Sun under the star of the planet and it doesn't fit this one's even farther away fifty four hundred nautical miles if you shot we wouldn't need our trick if you shot something that was winning up high and it fit on this chart the ground point was on this little chart because the thing was way up high you wouldn't need the trick of our third diagram you just do your circles right on the chart circle around that point circle around this point and on where the circles cross that's your position however shooting things we talked about shooting things there too low atmospheric distortion stay about fifteen degrees well shooting things that are way high is really hard you just don't do it because you can't tell where the horizon is something's way up here 89 degrees that would mean the ground point with sixty miles away from you fit on the chart 89 degrees where's the horizon is the horizon line over here over here just physically it's really really virtually impossible to get an accurate sighting up above you know I don't like to shoot about 75 degrees 70 degrees is even better you start getting way up high and your accuracy you just don't you can't do it he's not aware of the horizon this and it doesn't physically it's really hard to do so although it would work technically to get your celestial bodies way high so they fit on your chart real realistically it's it's not an option so we have to figure out a trick where we can do this whole final part of the problem where the latitude launched to the Sun or off the edge of the turn oh now one more point it was really irritating to have to take the sails down and stay in one place here right here like we wasted the whole day it was a great wind and waste the whole day and that was so irritating so let's not do that let's not stay in one place between these two sites now of course if it's star sites or planets and you're on a slow-moving sailboat you can take all the ups take all those sites fairly quickly because your horizon fades fairly quickly start your sites in the east because the western sky is still too bright to see any stars or planets you start your sites in the east where the stars emerge first and you can still see your horizon and you take those sites around the east and you finish up after that eastern horizon has become so dark you can't see the horizon anywhere the stars are bright but you can't see the horizon you finish up shooting to the west where the horizon is still illuminated and now those stars have emerged because the Sun is the sunlight is the sunset and the sunlight is diminished you can still see your horizon so you realistically you have ideally like a 15 minute window more you know really probably can extend that to half an hour window to take stars right when they emerge in the East moving around taking your stars in the West and that could be star surround moving around to the south and the north as you move around to the west but the Sun sights you think anytime during the day so star sights you can take five sites and they can all be within 15-20 minutes of each other or even closer maybe within five minutes if you're fast with your section and you don't have to worry about stings how much you move during those sites but with the Sun site where he sailed the whole day from a morning site until the afternoon covered lots of miles great wind you're flying along well that would make this whole problem less accurate because you no longer were in the same place when he took the site so what we do let's get rid of this box what we do is we just take this first problem here and move the entire thing whatever direction we sailed let's say we're sailing southeast we just and sail east southeast at 5 knots for six hours we just take this whole problem and move the whole problem southeast five times six 30 nautical miles we just move the whole problem 30 nautical miles to the southeast or let's say we're so excels to move the whole problem south and then when we do our two circles because we advanced the first sight when we do our two circles we do have an accurate position okay so that's called advancing your sight and you just use dead reckoning for that advancing and your dead reckoning is off by a mile your final position will be off by a mile but that's not a big error okay so our third die are going to be the trick and then you'll have the whole picture so take a look might be a good time to review your first diagram that first diagram explains why our distance from the point directly under the Sun or star or planet is 90 minus the sextant reading 90 minus HS that's all the first diagram does our distance any pilot we shoot any Sun we shoot our distance from that point is 90 minus the height to that planet above the horizon 90 minus the sextant reading that's all the first diagram does the second diagram shows how we use that information the distance is from the point that we known the known point underneath the Sun or planet the distance from that point describes a circle and we have to be on that circle the circle is an LLP lying of position and that's LLP one and this is a low p2 if we're on the first circle and we're on the second circle we have to be where they cross here okay and if you take star sites or planets you can take multiple ones you can take five sites and that gives you multiple ll peace multiple circles around the ground point of each individual star or planet that you shot and this multiple let's put another one pretty high one this was a high shot so that circle would be here now you have multiple ll piece crunching and they should all ideally cross exactly at the same point realistically they're not going to maybe you have one that's like 20 miles away from four of them crush within half a mile of each other really good sites and then one crosses is someplace 20 miles away say well that one I'm gonna throw out because I think you know I wave you know toss the boat a little bit and I didn't feel that was a very good site and it wasn't it was 20 miles off how did I do that I don't know I blew it the other ones are all crossing within half my that's the reason for star and planet sites each one you the first to define your position each one after that is checking those first two and just reaffirming that that is where you are and telling you how accurate those sites are oh they all crust within half a mile it was pretty flat seas and really calm and I got really good sites though it's sort of defining a mile wide area where I might be in that's because of the you know it's kind of rough or I was using a plastic section let's look at the sections in fact I think we're at that stage any questions so far look at these two diagrams maybe even pause right now look at your first diagram make sure you understand it make sure you have it right maybe back back up to the picture of the first diagram make sure you have it I look at your second diagram make sure you have it right and if you can find somebody to explain this to and show them take a blank sheet of paper say I'm going to teach you celestial navigation it's really simple here's the first diagram if you can draw it and explain it to them you'll know it for the rest of your life it's a simple diagram and then take the second turn the paper over do the second diagram say here's this here's why that works and makes it so we can navigate okay let's look at how the equipment we're going to use we have it over here I guess the fun stuff is the sextant let's look at sextants first this is the starting point this is an emergency section this is your backup emergency section that you never use you're never gonna use this accuracy is probably five miles with this Sexton you know in relatively good conditions that's not too bad if you know where you are was in five miles and you're crossing an ocean that's that's gonna work so not too bad it's not too bad if you are really little bet you get two of these one a backup and one for your primary and you'll be within five miles but the next step this probably is also pretty affordable the next step up is this level this is a plastic Sexton but it's a little bit more precise you have the burn your knob here for adjusting and leads off a little bit more precisely the filters are a little bit better remember remember when you're shooting the Sun you have to have the right filters or else you'll burn your eye if you're looking through a telescope at the Sun it's dangerous if you don't have filters you will do permanent damage so be very careful with filters to use the filters let me talk about the telescope for a minute and we'll talk about the filters the telescope increases your level of accuracy because it's very precise looking at the Sun or at a star through the telescope the trouble with the telescope with Sun that's not a problem because it's pretty easy find the Sun with a star the trouble with telescope is the telescope narrows your field of view so it's harder to find the star it's harder to search it out so sometimes you might shoot stars with just an open scope and those sexton's will have a scope looks like a telescope with a new thing in it it's just Hollow you're just looking through an eyepiece or a telescope so you have both options so sometimes with stars and planets it's easier to use an open scope even though it's slightly less accurate than the telescope and if you're using telescope especially but really anytime I just do it automatically because so much easier anytime you're shooting something it's pretty hard to find it by cranking by adjusting the Sexton sextant works this way one line of sight the straight line of sight goes straight through to the horizon the other line of sight goes through the eyepiece hits the mirror here bounces off it's this mirror and goes up to the sexta to the star or planet or the Sun and so you're measuring the angle between the horizon and the dist direction to the Sun or planet or star the celestial body so horizon celestial body light goes straight through your eye sight goes straight through to the horizon bounces it off this mirror and this mirror up to this celestial body so by looking through here you can find the horizon you see you're looking right at it but to find the store or planet by adjusting this is pretty darn hard so take it and flip your sextant upside down and look straight at son or straight at the star if it's the Sun make sure your filters are in place these lower filters okay look straight at the celestial body find it in the telescope or in the eyepiece and then adjust downwards until the horizon appears horizon is really obvious you can't miss it okay and then set it fairly accurately with the star or planet sitting on the horizon now it's hard to get an accurate sight upside down like this so at this point flip your sextant over now look straight at the horizon and your star when you're pointing the right direction your star will be right in your mirror okay so you found your star now that's the first thing now the next thing is to get an accurate sight that's not so easy on a small boat because the waves are bouncing and everything so you kind of have to grab your sight now the easiest way to take a sight is to set your sextant so the Sun or star or planet is slightly if it's rising on the ascendancy so the Sun or star or planet is slightly below the horizon and just very slightly below it and just keep watching it until now it's right on the horizon mark and either you're doing yourself with a stopwatch you push your stopwatch right when it touches the horizon or you say mark and the other person your partner records the exact time that it touched that you said mark it and touch the horizon now one of the problems with a Sexton is if you're holding Sexton and a funny angle you're not measuring accurately the height to the star you're measuring from up here down to a point over here and you're getting two bigger reading you have to have it straight down now it's hard to know whether you're holding the sexes and funny angle or straight down so what we do with the sextant is we rock it we keep the star our planet in the viewfinder the light coming down through the mirrors we keep the star plan in the viewfinder Rocking next end a little tricky to do that keeping the star right in the mirrors and now the star is doing this dip over the horizon and we can look at that I think you've got all this so let's take a look what it looks like through the sextant and this is you know this takes a little skill takes a lot of skill if it's rough and you're in a small boat like a 24 foot boat the boat I see all across the Atlantic in it takes fair amount of skill and your accuracy is not going to be quite as good but basically what you're doing is rocking it so the star is doing this kind of thing back and forth and this is right where you say mark right when the star hits that initially the star is rising and then initially you start with the star doing this kind of thing below the horizon and remarkably in an arc like this below the horizon remarkably fast through a telescope expecially these stars some planets they move they're shooting a lot they move he's like whoa can't keep up with it so remarkably fast that star will get up to this point and then all of a sudden it'll be above the horizon and you've missed it you got a crank back down if you're gonna if you didn't get your sight right here so that rocking you just keep rocking until it just just kissing the horizon right there if it's the Sun this more the details we'll get into a little bit later if it's the Sun or the moon it's no longer it's just a single point the table actually tells us different numbers for the Sun we shoot the lower limb of the Sun or if we shoot the upper limb of the Sun we'll see some change size was there dramatically lower limb of the Sun Sun sitting on the horizon just kissing their eyes and upper limb of the Sun just kissing their eyes on the top of the Sun and again you'd be doing this thing of rocking the Sexton so the Sun would be doing its that'll be shooting the upper limb it's usually easier to shoot the lower limb though usually it's just somehow visually easier to set the Sun on the horizon instead of setting the top of the Sun kissing their Eisen but either one see either ones fine same with the moon we're lower lower limb okay remember if you're shooting the Sun when you flip your Sexton over get your filters right you have to change the upper filters you're also burn your eye you're really will burn your retina looking the Sun to a telescope even for a second so make sure your filters are right be careful with air sexton's bubble sextants because they're like a camera all enclosed and you just flipped this you just turn this knob and the filters flip in front and see be careful if it's one of the ones where you go from darker filter darker darker darker darker and then you flip one more and there's no filter you'll burn your eye that way so be careful with the Sun okay to use the filters now it's hard to adjust the filters looking through the telescope out the thing because you're trying to keep the thing you know trying to keep the Sun in the mirrors and stuff so you want to use your filters this way you take your filters and you look right through that all the filters at the Sun oh I can't hardly see it I can't see anything flip one down oh that's a little too bright flip that one back up flip a different one down just keep adjusting until looking straight out the Sun through the filters without the telescope or any other part of the sextant you've got it so it's comfortable for your eye then flip those filters into place in front of the mirrors usually be three filters and one out of the way and then go ahead and do your sighting but make sure you are the right filters in place for the Sun with stars of course no filters at all unless the reason there's so many filters not just one Sun filter unless you're shooting something like Venus and or a dim star actually be more like a dim star sorry shooting a dim star - the no you're shooting a bright start and let's get this straight you're shooting a bright star with a dim horizon and you might want to filter the star with one filter just very slightly so you can still see the horizon or could be the other way around you're shooting a dim star with a bright horizon then you'd use the horizon filters here so a dim star you want to make your horizon a little bit darker and you're straight through so you can see the dim star a little easier so I might use one filter on your horizon so mostly the filters are for the Sun occasionally there's a situation where you'd use it for a star a dim star or a bright horizon okay now the other sextants now and this is a beautiful instrument now one thing about sextants in fact I might have even commented on this at the beginning of this segment but if you're watching in you watch it this far you probably agree unless you're some kind of electronic wizard if your GPS stops working it's time to take it and chuck it overboard because you're probably you take it apart you're not probably going to be able to fix it maybe if it's just the on/off switch or corrosion in the battery area battery holding compartment or something or some wiring connection maybe you can remedy it but if it's an electronic thing inside this GPS that stopped or if suddenly were you're in the ocean and we're at war on that GPS has been coded switched around so it's encoded so only in the US military can use it you're going to be out of luck yes backup GPS is are a great idea but still unless you somehow know what's happening inside that box and how to fix it you're going to be out of luck when it stops working whereas a sextant I mean the worst cases serious seriously the worst scenario with Sexton is you drop it overboard and it's gone and you didn't tell you and that was her backup one you adored Mari lost you a real one you've lost two of them now pretty unlikely your worst-case scenario is you can take your paper and pencil and still do a site it will give you some idea of where you are just look along the bottom of the paper and aim your pencil at the star or planet this is emergency navigation this lifeboat navigation and angle the pencil until this pointing the paper is pointing right at the bottom edge of the paper's pointing right at the horizon pencil is pointing right at the star or moon or bottom going to the moon or autumn into the Sun and then hold it still draw that longing along there measure the angle and you're gonna have a 30-mile accuracy 2030 mile accuracy you can still hit you still find Hawaii you're not gonna sail right past Hawaii so sextants and you know ways of measuring the height of a body or repairable you bend your sextant you can bend it back okay you drop it and it's like oh my god I bend it bend the thing back it's not like a GPS where you toss it and you've got your emergency section maybe have three sections on board these these little ones are you know 40 50 dollar range and if you find it on eBay it's in the ten dollar range and it's its lifetime never wears out no batteries lasts forever okay so now this is a high-end sextant with the first section the emergency section we're talking with paper and pencil oh we're talking about 20 minute mile accuracy maybe 30 mile accuracy with the emergency section we're talking about five mile accuracy with the better plastic section we're talking about one mile accuracy and all these depend on relatively moderate sea conditions with a high-end section we're talking about half-mile accuracy that's that's pretty accurate for crossing an ocean using stars sir minimum of four four point two four light-years away pretty amazing stuff so and this is a beautiful piece of art I mean it's a beautiful beautiful piece of equipment thunder displayed in your home it's just gorgeous it's fun to use pushing a button on a GPS is not all that exciting this is exciting because it's something beautiful if it were not so heavy there where there's a piece of jewelry it's really lovely so a high-end sextant is a nice possession unless the lifetime never wear out never never degrade telescope filters everything's the same all work the same just works a little smoother a little more accurate vernier you have to learn how to read the vernier thing but that's not too hard now the only negative of a really good citizen is this weighs approximately five times as much as the Plex plastic section if you're having a hard time getting a site because it's rough and it's you keep getting losing your balance or getting thrown sideways every time you're about to get it your arms keep your arm starts to get pretty tired with this sextant and just holding it up like this just talking it's heavy so in a small boat you may actually be better off with a light plastic sexton rather than a heavier metal sexton despite the your accuracy with the plastic one because of the lightness may actually be better than your accuracy with the heavy more precise metal one so I'm not feel badly if you don't want to put five hundred or a thousand dollars into a metal section just get a mid-range plastic one for a couple hundred bucks okay so that's sextants and then let's look at tables briefly here and then we'll get on to our last diagram May tables we talked briefly about the nautical almanac you can find this online you can look at it it tells you essentially what it does is tells you the latitude and longitude which we call declination for latitude just so we you know can confuse everyone basically declination and latitude are exactly the same declination north or south just like latitude north and south declination and Greenwich our angle which in our Western Hemisphere is exactly the same as longitude the only difference was Greenwich our angle and longitude is Greenwich our angle is measured from Greenwich England all the way around 360 degrees in one direction measuring from east to west all the way around 360 degrees whereas you remember longitude is measured 180 degrees around to the west and 180 around to the East Greenwich our angle makes more sense than longitude actually so we just have to but as long as we're in the Western Hemisphere Greenwich our angle is exactly the same as longitude the Greenwich our angle of a star or planet is the longitude of the star our planet you know the Western Hemisphere in the eastern hemisphere you just have to remember that they're measured differently one all the way around Greenwich now all right go all the way around munch dude around halfway under an eighty degrees around the other way 180 degrees okay so that's the nautical Almanac tells you the declination and Greenwich our angle basically latitude and longitude of every star and planet in the sky then we can use for navigation 30s navigational stars the Sun the moon and all the planets for every second of the year that the Almanac has been written or okay so that's the first piece of information you're going to get eyes out of the nautical Almanac now the second book that we use is gonna cite reduction tables this does all that all the tough math for you this does all the spherical trigonometry that we haven't seen yet because we haven't needed it yet all the all the math and everything has been really simple so far just ninety minus HS subtraction sexing reading fifty degrees our distance from the star plans point latitude and longitude underneath the star and planet ninety minus HS ninety minus fifty that's forty forty times 60 nautical miles twenty-four hundred nautical miles oh we need multiplication well so what you can do that okay but for the last diagram the knot third diagram the trick we're gonna be using this a little bit this is gonna help us get everything the whole problem onto a little chart little nautical chart instead of the trouble is using huge nautical chart that covers so much of the earth that the Sun our planet squared at a point the point directly under the Sun our planet or the stars is going to be on that big chart trouble with that is anytime you take the round surface of the earth and project it onto a flat surface you're gonna get distortions you can't just flatten it out so a Mercator projection of a huge part of the ocean you can't do your problem on that just measuring distances because in directions because it'll distort it you'd have to do that on a globe and then it would work out accurately but this is part of the third diagram we'll use numbers will go into this to get the information we need for our third diagram and we'll talk about that in a minute there's this is a chore to to nine ho2 to nine and we have several versions of site reduction tables that use this is a Chotu for nine the air navigation tables you can use this this one volume covers the entire surface to the earth but it's not as accurate and a little bit few more couple more steps to using this this covers 15 degrees of latitude so you need several volumes of this for the latitudes you're going to be most normally sailing and you probably need three volumes of this possibly four volumes if you get farther north so on you need several volumes of this or one volume of this but this is the easier one to use ho2 29 second production tables for marine marine navigation okay and actually there's another version of the marine navigation but that's 802 14 basically works in a similar way once you understand that you can use either one but 229 is the standard okay and last thing is the third diagram we'll get on to the third diagram here very shortly thank you okay now big question was anyone bothered by this diagram this picture here well you should have been a little bit bothered by it it looks very nice symmetrical like that and everything but in reality it doesn't happen this way it can't happen this way the lower limb picture is correct arcing the sextant swinging the sextant and you might have noticed in swinging the sextant the part that staying stationary is the upper mirror it's not the eyepiece that's the trick you have to pivot around this point here so that's what staying stationary that's why it's a little tricky to do it you can't do it like this because you lose the star you have to pivot it like this with this upper mirror staying stationary keeping the star in the viewfinder okay so lower limb shot shooting the bottom of the star of the Sun or moon and that is correct just sweeping over the horizon but this upper limb shot actually this would be nice if it worked this way because it would make the upper limb a lot easier to shoot but it doesn't work this way you can't do an arc like that so let's look at the upper limb again really quickly so the lower limb sweeping down over the horizon till the bottom edge of the Sun or the moon just barely touches the horizon and upper limb shot will look like this and this is why we don't like the upper limb as well it is a little trickier that's the upper limb shot this is the horizon here so the upper limb this the Sun or the moon is sweeping below the horizon and the top is just barely kissing the horizon here and it's just not as clean because you're sweeping through the horizon on your arc and so just a little little trickier and I would never take an upper limb shot except with the moon occasionally it's your only option if the moon is a partial moon like that you only have an upper limb and so you would take the upper limb occasionally technically if the Sun is partly partly occluded by a cloud you could take an upper limb shot of the Sun but it's better just to wait two minutes and take a lower limb when the lower limb when the cloud moves but with the moon sometimes you have to take an upper limb this it's not that usual look it's little trickier but it still works okay now our third diagram third and final diagram to understand the whole concept of celestial navigation remember our first diagram told us that the distance that we are from the ground point the point directly under the Sun or the celestial body that was shot the distance is 90 - our sextant reading ninety minus HS there are some small Corrections we make on the sextant reading to make it more accurate but basically our distance from the point directly under the Sun or planet or star is ninety minus our sextant reading our second diagram showed us that we could do two one circle that defines one circle around the ground point and that tells us we're on that circle someplace that's a line of position that circle and then by taking a second sight we have a second line of position a second circle around that second position of the new celestial body or the same celestial body when it's moved that gives us a second line of position where those two lines cross that's our location okay now the third diagram gets everything it's just a trick this is the trick and people object to it well how can that work well it's a trick and it's a trick that works it's pretty nifty actually and it took a long time for anybody to come up with this so this diagram gets us on to a chart a chart that includes our location but does not include the location the position of the Sun or planet or whatever we shot so we're someplace up in this area here but the ground point of the Sun or planet is way way off the chart maybe you know a thousand miles off the chart so how are we going to do the problem don't have this on our chart and can draw a circle around that point is off the chart so what are we gonna do well the starting point is kind of like pin the tail on the donkey just kind of make a random point o here let's say let's say let's pretend we're there we didn't know if we're there we might be over here anywhere on here let's just pretend we're here let's assume we're there let's call this an assumed position let's even label at ap we don't know if we're there maybe we're there but probably not we just picked the point okay now if we have an AP a point on the chart we can look at the turn and find out its latitude and it's longitude a known point now latitude longitude we have a known point here we have a second known point which is off the chart but wave off the chart thousands of miles maybe and we have the latitude and longitude for that second point we have two known points on the face of the earth we're off in the Pacific someplace our position and the position of the Sun we're way down south south east do we took it in the morning two known points from that we should be able to figure out we should be able to measure the distance between those two points or if we use a table we can go into a table that's designed for this and the table will tell us the distance from this latitude and longitude to this latitude and longitude if we know the distance between this point and this point how does that help us we're not really here why do we want to know the distance between the point directly under the Sun the ground point of the Sun latitude along - and the point where we're not even there we just took the point on the target at random well here it is maybe you're guessing ahead of me maybe you've jumped ahead and can see this well if we know the distance between this assumed point and the actual ground point of the Sun or let's say the Sun actual ground point of the Sun right when we took our sight if we know the distance we can calculate very easily the sextant reading we would have gotten if we were here so remember that the distance to the ground point is 90 minus our sextant reading that's from our first diagram so the sextant reading is that we would have gotten if we're here would just be 90 minus the distance between those two points so we know the two points know what sextant reading we should have gotten if we were here just from the table because we entered the latitude and longitude of our assumed position the latitude and longitude of the ground point under the Sun right at that second that we took our sight and the table computed the distance and then actually did the subtraction for us 90 minus the distance and gave us and height computed HC ice computed computed the sextant reading that we would have gotten if we had been right at this point right when we took our sight okay and if that sextant reading happens to be exactly the same as the sextant reading we actually got our height sextant that we shot with our sextant if those two are the same we might be right on that point however we might not be on that point - we might be someplace else where else go would be yes they were both the same the heights will be computed if we have been here and the heights we actually got we could be at that point but remember the distance from the ground point defines a circle around the location of the star a circle around that location of the star so we could be anywhere on this circle if our height computed was actually the same as the height that we read on the sextant okay let's look at this just a little bit longer here and then we'll take the next step the table since it knows our latitude and longitude and the latitude and longitude of the ground point of the star it can also it can tell us the distance between the two and then it can turn that into what sextant reading would have gotten just ninety minus the distance and it can tell us the direction from our latitude and longitude our position to the other position the position under the Sun it can tell us the direction right towards the Sun when we shot it because it knows those two points two physical points this is just the assumed position not a real position but if we have been here the direction to the Sun would have been this directional tell us in this in this case south east it'll tell us exactly and like you know how many degrees what is that that's 90 degrees so that looks like another 40 degrees so 130 degrees here it'll tell us that 132 piece that that's the way the Sun would have been what direction the Sun would have been if we've been there okay and then this circle right where the circle goes through our position would be at 90 degrees to that because this points right to the Sun that's the Sun over here way off the chart and the circle this is like a Radian pointing towards the Sun and the circle will be around the Sun and would be someplace on that circle ello P but yes you're right we weren't there and it's pretty pretty unlikely that we just guessed a point with our eyes closed where the sextant reading we would have gotten here was exactly the computed sextant reading as if we had been there that's pretty unlikely it's more likely the HS the sextant reading we got isn't the same as the computed sextant reading for this point and so it means we're not there so what do we do just keep trying points you know all over the place you know here here here here Oh none of them are right none of them are the section reading that we got for none of for none of these assumed positions come out with a computed sextant reading that is exactly the same as our section reading well that would take hours to just keep guessing and being wrong wrong wrong so what can we do that's gonna simplify things let's clean up our diagram first okay turns out that our sextant reading was not the same as the sextant reading which should have gotten if we'd been here our sextant reading let's put some numbers into this our sextant reading was let's say 30 degrees if we had been at this point our sextant reading would have been computed by the tables for this latitude and longitude and the other latitude and longitude of the Sun our sextant reading would have been 31 degrees so we aren't at this point we can't be at this point we're not even on a circle through that point we're either closer to the Sun or farther from the Sun the computed for this position is 31 degrees our sextant reading was less that means the Sun was lower and since the sun's now this where you have to be careful since the Sun was lower in the sky that means what means we're closer to the Sun or farther away from the Sun as the Sun gets higher and higher we're closer to the Sun as the Sun gets lower and lower we're farther away from the Sun when the Sun is directly overhead it's a really high reading so when the height computed is higher we are farther away because our section sight was lower that means the Sun was lower and we're farther away from the Sun so we're not here does that mean that we are one degree farther away 60 miles farther away from that point one degree farther away 60 nautical miles farther away well it could mean that we're there but remember what we're defining is a distance from a point which actually is an arc of a circle so now we can draw an arc of a circle that is one degree farther away from the Sun than this assumed position so one degrees further out as the Sun gets sir Sexton angle gets lower and lower that means were farther and farther away farther and farther back from the Sun so 1 degree farther one degree difference between the computed sextant reading that we would have gotten if we been here and the actual section reading means we're one degree farther out now this is sometimes hard to think this one out but you can just remember this is a nurse just a cheap system for them see Coast Guard Academy CGA Coast Guard Academy computed greeter away if the heights computed is greater than the actual sighting height then you're farther away from the Sun computed greater away so we're one degree farther away from the point here the assumed position and then and we know the direction to the Sun from this assumed position so our circle which defines our position is going to be perpendicular to the direction to the Sun because it's a big circle around the Sun and we can draw an arc through that point there and we have to be someplace on this arc someplace on that LLP ok so we have to find we're not here we just chose any random point for our assumed position doesn't matter if we chose chosen assumed position here our difference between our sextant reading and the height computer for this position would have been more like two and a half degrees which would have been 140 miles or something 150 miles it doesn't matter what assume position we choose it's all going to work any assumed position assume position here would have been a different direction to the Sun and a bigger difference between the computed sextant reading in the actual section and we would have come out to the same LLP same perpendicular line and leave me on that one okay but in reality to draw we don't know exactly how to draw this curve do we we don't know how to draw a curved LLP here well not a big problem because we have shrunk this we've moved in so close we've zoomed in so close on this problem to get it on a chart that this curved line essentially at this point we're taking such a small part of that huge arc that essentially it's a good enough approximation to draw that as a straight line that is perpendicular let's get a perpendicular first sight there's perpendicular to the direction to the stunt to the Sun or planet okay obviously not going to be perpendicular to all these now as we get farther and farther away our assumed position farther and further away from our actual position we start to get into a bit of an error because we're making a straight line out of a curved line so the closer our assumed position is to our actual position the more accurate all of this is so rather than choosing assumed our dead reckoning position let's say is up in here someplace let's choose an assumed position close to our dead reckoning position because then we'll have a higher level of accuracy and our LLP will be better LLP if we choose any assumed position on the chart it'll still work but we're introducing us a level of accuracy that's less less accurate okay so we'll choose an AP assume position that's fairly close to our lab our actual dead reckoning position and we'll get rid of these other ones okay any problems was that let's this is the trick the part that bothers people is that we aren't actually here we just chose a point on the map on the chart and it doesn't have to be very accurate but the more accurate is the better your problem you know the the closer your problem will work out to your actual position okay let's redraw this quickly and let's choose an assumed position over here in this area and then we worked out the site and everything and with our we have with the latitude and longitude of our assumed position we have the latitude and longitude of the Sun when we shot it the directions of the Sun turns out from the table to be like that south east little south southeast and the let's stick with these same numbers here where the height computed was 31 degrees if we've been here at our AP and computed the distance to the Sun its ground point its GP we would have gotten if we actually measured the distance we would have gotten 90 minus the distance and then corrected and then come out with our hike to compute let's say we've gotten numb that's at 60 59 the distance would be 59 degrees D equals 59 degrees then the table does the math for us and tells us having figured out the distance first the table then does the math force takes 90 minus the distance and gets the actual sextant reading we should have gotten we would have gotten if we've been at this location this last year in monster now that height Sexton was different by one degree so we just take the latitude scale and take one degree on the latitude scale and then go take that distance go away one degree 60 nautical miles and make a point and then [Music] do a perpendicular to that point to that line towards the Sun and then we draw a line of position approximating the curve around the Sun with a straight line and this is our L o P one that doesn't tell us exactly where we are just that we're on that line okay now the next step I think you can see ahead that's good a little space here the next step is to do a second sight if it's the Sun we're working with if we did a second sight a half hour later our new direction wouldn't be much different than someone to move very far and we get an LLP that crusts at a very slight angle here when to elbow piece cross at a slight angle if one of them is off by half a mile it moves the juncture point quite a long way you could do it like five miles just because you had a half mile inaccuracy in your sight so let's not take the Sun sight an hour later let's wait until after noon and then take our second sight let's wait until the Sun has moved way over to this direction here again it's way off our chart way down near the floor someplace or even in the basement way down so we can't get the Sun position on our chart if we could get the sun's position on the chart then we just do a circle around it that would be our LLP 90 minus HS this would be the distance the circle and we'd be at the two crossing points but we can't hit the sun's position on our chart which are not big enough sounds way off choose an AP anywhere doesn't have to be the same AP as this it's not likely to be the same AP as a section although if you use this AP you or any AP doesn't have to be the same it's going to be a different ap in most cases let Sue's this is our ATP - it has a latitude and longitude right we just made a point on the chart check the latitude check the longitude oh now we have the latitude and longitude of a guest position again we're not here we're just guessing okay now we have a direction to the Sun let's say it's early afternoon the Sun is south southeast south southwest in that direction and we have an HS Sun was higher now height sextant of 42 degrees that's what we read off our section 42 degrees we computed the distance the tables computed we entered the latitude and longitude of the Sun which is way off down there the latitude launch of the Sun we entered the latitude and longitude or guests assumed position and the table working up the distance between the two and then turn that into the sextant reading just by 90 minus the distance and gave us a sextant reading that we would have gotten of 41 degrees okay it's a 1 degree difference that means we're not what can't be at that point we'd have to be someplace else we can't be at this point because the sex is reading that we computed for this point isn't the same as the sextant reading we got well the computed sextant reading is 41 degrees ours is 42 degrees ours is higher that means as we get higher we get closer and closer right ours is higher than the computed for this position the computer for this position is 41 ours is 42 that means we got we were closer than that position because the Sun was higher so we measure latitude one degree of latitude here take that one degree and draw a line across the direction to the Sun and then a perpendicular to that direction towards the Sun that also the table told us when we enter at the table with the latitude and longitude of our position and the latitude and longitude of the ground point of the Sun the direction perpendicular to the direction and then draw a straight line through that point and that's our new L o P l LP - and we're on that line someplace we've got B on this line and we know we're on l LP one as well we're on that line and so we have to be where the two lines cross right there that's our actual fix and you put the time and date right beside that okay so these two lines crossing LP one l LP to make our position here now if we were shooting stars or something we could get a third site and that would make another line another LLP and hopefully you would cross within half a mile of these first two and we'd be within the triangle of those crossing L o piece but with two L apiece you have a position you have a definite position so that is our actual location now there are some refinements in this but this is the basic concept one of the problems that may not have occurred to you yet is that it's hard to create a table where you enter with four different variables the latitude our assumed position latitude our assumed position longitude and the assumed position or the actual ground position latitude and the ground position longitude of the Sun that's four different numbers it's hard at our table with four numbers so somehow we're going to combine some of those numbers and the problem simplify it for the table and the same with this one here love to combine some things and get it down to three things we under the table with but basically this is how it all works okay is this clear any questions about this you just grab a position any position and say what's the section reading I would have gotten at this latitude and longitude if your sextant reading is different the actual sextant reading you've got is different from the computed sextant reading in the table you're not at that point or either farther from the Sun or closer to the Sun you move the right direction distance away based on the difference between the height computed and the height Sexton you do the move towards or away remember the CG a Coast Guard Academy computed regular C computed greater away if the computed sextant reading is greater as in the first case 43 computed greater than the actual you can remove away if the computed and that's what we did here we've moved away one degree is a computed is less then it's the opposite of computed greater away and you're gonna move towards the Sun okay remember these LPS are straight lines on our diagram but they're actually just ran circles huge circles around the position that around the latitude of the ground point you'd circle around the latitude blacks didn't lunch too as a fair point okay so that's really the third diagram if you can get this and remember the first two diagrams that's all there is to celestial navigation except a few details that we can fill in once you understand what you're doing then the tables are relatively easy to use the table that we're using to get these critical numbers the height computed based on the latitude and longitude of our assumed position the lab student launched to the ground point miss the site reduction tables and these have all the information you need they tell you the heights computed and the direction there are a few details that we need to go over to make this really clear I can give you a hint about those but that's really part two of the talk I'll give you a few hints though and then we'll go then you'll know what's ahead even though we won't explain it totally in depth but you can serve look forward to the next part now let's take one of these lines out our second lopa our second site all information for our second site oh well before we go into these details I know that it's gonna be one question here so let's put this back in I'm sorry we'll put the second site back in I think we're towards on this one here's our AP and we went towards one degree and then I'll LP there okay perpendicular okay this is a low P - I know this one question that you all are kind of wondering it comes up frequently we took this site in the morning we sail all day and then we took this site what do we do about that obviously by sailing all day this LLP is not accurate anymore well it's a simple process to advance your first LLP just takes a minute less than a minute you can take any point on this line any point on your LLP doesn't matter you can take this point if you want but you can take any point on your LLP let's say we were ceiling and of course not due west but Southwest the CEREC our true course was 260 degrees so we just take a line at a direction of 260 degrees just using the use the compass rose is closest on the nautical chart and draw your line at 260 degrees that's 260 and let's say we're sailing at five knots for seven hours so be 35 nautical miles so we just go over to our latitude scale same latitude of the were talking about let's do scale on the side that's a little more than half a degree 35 nautical miles 35 minutes of latitude take that distance with our dividers mark off the distance on our direction and then we advance our LLP just by drawing a parallel line through this to our LLP through this point here and that's going to be here so that's our LLP advanced to the new time let's say was four o'clock 1600 afternoon 1600 hours okay and so our actual position is not where the first LLP one from the morning Prust LLP two from the evening our actual positions were the LLP advanced from the morning crosses the afternoon position afternoon LLP and so our actual positions right there very easy to advance an LLP okay so some sites are the easiest it's fun to take stars and planets fun to take the moon the advantage of stars and planets is you each one beyond two stars checks your position because you start having all these LPS crossing each other the other advantage is you probably if you take your sites fairly quickly and you're not sailing too fast you probably don't really have to advance your LLP Yolo technically it would advance it certainly on a ship traveling at 30 knots you'd advance your each of your L o piece to the position of the final LLP because the 30 knots you're gonna enter this fair amount of error but sailing is small as slope speed you can stake your start sites and your sentence under your star sites and your planets and your moon take them fairly quickly and just use them without any advancing so with multiple sites you're gonna get a bunch of LLP stressing and you might get one they way over here someplace and it's like whoa that one I throw that one I'm gonna throw that one out because the other four across in a really small area that defined about a half mile area so this one obviously I messed up the way you've hit the boat just at the wrong moment and I didn't even feel very good about that reading I thought that one might be off but these other ones are all right in the same area pressing really close together and that defines my position really precisely defines my position and then the other lines check it okay now let's take let's get rid of some of this stuff let's get rid of the advanced lob because I want to tell you one give you a little foresight into what we're some of the details here and if you have seen some of the stuff before you might say oh why is he leaving that out or why isn't he talking about that but I want to make sure you understand the basic principles first okay here now the first thing that we're up against is you can't even conceive of a table that you can enter with four different variables the AP latitude and longitude and the GP latitude and longitude so we're gonna have to do something to combine these because otherwise the table would be hundreds of volumes and we can't we don't have room for that if you're using a celestial calculator you can just enter with four variables but when using tables and tables are totally reliable you can get it I mean it can be wet they can be you know it's there's no way to really destroy these unless you drop it overboard that's not good whereas a celestial calculator again and we're back to electronics and batteries and on-off switches and all sorts of variables that you won't be able to repair on your own so how are the tables going to work well this problem this problem cannot be moved way up the globe if we move the problem way up the globe the distance is the difference between the longitudes becomes minut all of a sudden all the numbers are different if you move any problem up to whether the longitude lines are converging up at all or down at all the problem changes the distance would change the HC would change however if we move the problem around the globe keeping it at the same latitude the problem stays the same so here are the four things we have to go into the tables with basically we have to tell the table but we can combine two of them so ap longitude AP latitude GP latitude and GP longitude those are the four things that we want to tell the table but two of them two of these things we can combine but we cannot move the problem up or down we have to we can move it around the globe we can move the problem around the globe but we have to keep the problem at the same latitude so we can't we can't combine latitude and latitude because that could if we don't tell it it's the actual latitudes worse it doesn't know where to put the problem on the globe the tables don't know whether it's up at the North Pole or down at the equator and it's a totally different problem however we can combine the longitudes those two and tell the table the difference in longitude so the difference in longitude longitude between these two longitudes and then we can tell the assumed position latitude and the GP latitude the latitude of the Sun so now we've got it down to three things the difference in longitude and our let our soon position latitude and the ground point latitude and that now lets us get into the table the table is going to call these things slightly different things though and remember this is just an advanced preview this is starting to get we don't want to get you too confused about this but I just want to give you a preview because we'll look at the table in depth in part to the GP latitude is actually going to be called the declination declination and will abbreviate that as Dec it's just the latitude there's nothing different it's just purely latitude of the Sun or planet or star GP longitude is going to be called gh Greenwich our angle GHA not in the Western Hemisphere is just the longitude in the eastern hemisphere it's different we have to do a simple calculation because longitude is measured 180 degrees east undernea degrees west brandish our angle is measured all the way around to the west from east to west starting at Greenwich so in the Western Hemisphere GHA grants our angle is the same as longitude in the eastern hemisphere we have to correct for the difference okay when we combine the longitudes we're come up with a difference in longitude that's just called local our angle our angle makes sense Greenwich our angle because each hour the Earth spins 15 degrees so longitude talked about as an our angle from Greenwich makes sense the local our angle just means the difference between the longitude where we are or our soon position is and the longitude where the Sun is or the Greenwich our angle the Sun so just the difference in longitude okay so that's just a bit of a preview sounds a little bit comfy at this point a little bit complicated but once you grasp what the tables are doing then it's really clear it isn't complicated the math is simple it is just using the tables to solve the distance between these two points and then the table for you turns the distance into a computed computed sextant reading that you would have gotten if you'd been at the AP okay there's one more diagram that we can look at let's look at it quickly and then that'll be the end of part one and that may be you know if you're actually heading out C and planning on crossing an ocean you definitely want to stay tuned for part two but if you're interested in celestial navigation is just because you wanted to learn something new and it's an exciting interesting subject then you may not want all the details of how to get into the table some of the stuff we were talking about just now entering the table is three foot three factors as opposed to four variables but part two will guide you all through the last of the details starting with correcting your sextant site from H s height sextant to Heights observed and then I adjusted a couple of Corrections there based on how high you are above the water if you're going up on a ship's bridge looking down on the horizon you have to correct for that six feet off the water correct it's a smaller correction but is still correct for it and then correcting for altitude distortion of the light depending on the angle that you're shooting at if the Sun is low there's a higher altitude direction a bigger altitude direction because the light is bent more there's the Sun straight up the altitude correction is zero because the light coming straight through that Monsieur would be not bent at all although of course you never shoot it straight up because you can't do that it's too too awkward to do that okay so those Corrections and then there's some corrections in the nautical Almanac that you're going to use one correction is to get to the exact second that you took the site because the Almanac won't tell you every second it'll tell you the time times but then the position of the Sun at a certain time and then it'll jump to the next time and you have to correct in between those two positions to find exactly where it was at the exact second that you took your site again the nautical Almanac guides you through that it's very simple and it's an easy correction but you do have to know how to do it so that's another detail and then the last details are really how to get into the site reduction tables with the three variables the difference in longitude between the assumed position and the ground position and your latitude and the sun's latitude or declination so we'll go through that and then there's one more detail about choosing your assumed position so it's easy to go into the table it's easier if you choose your assumed position so it's a whole degree of latitude so the difference between your longitude of the longitude of your assumed position and the longitude of the Sun or planet that is shot so the difference is a whole degree you cannot change the latitude of the Sun no you can't adjust that and say well let's just round it off because in your sights off your whole problem work is off but the assumed position we can move wherever we want to make it easier to get into the table we'll go into that in detail so there's some details to add to this but we now have a framework that we can build on and this framework of the three diagrams is you want to make sure that that framework you don't want to start building on a framework that's shaky you want to make sure that that framework with these three diagrams is really solid and secure before you start adding details so make sure you understand all three of these diagrams how we did it especially that last one the trick where you just are choosing a random point that's the part that bothers people why why would I choose that point well it doesn't matter what point you choose except some points make it by choosing a point a little more carefully it makes it easier to get into the table to enter the table so we'll go over that really carefully well let's look at this last thing this last thing is pretty neat this is a very very simple application of some of what we've just learned this is taking a noon sight the noon sight is neat because there's a special it's a very special situation it only gives you one piece of information it gives you your latitude but in five minutes you can take an insight and work it out and have your latitude that's pretty neat that's pretty useful so let's take our earth let's let's draw it first and then take a look at the globe here's our world here North Pole and South Pole and the center of the earth we're slicing it now right through so we have to both poles and the center of the earth okay that's easy well let's also slice it so we have our position let's put ourselves heading for Hawaii again here we are off the west coast of North America getting for Hawaii and we sliced the earth right through our position through the North Pole through our position through the South Pole and through the center of the earth and made it into a flat plate here on the board okay now is there any way we can also get the position of the Sun on this diagram or is the Sun going to be above the board or behind the board we've just sliced the earth straight through our position North Pole South Pole center of the earth how can we get the Sun on this diagram well what is the one time of day that the Sun will actually be on this flat plane the same plane as we're on one time of day right at local noon doesn't mean your clock says 12 o'clock necessarily local noon is to find this the moment when the Sun is directly south of you do south and when the Sun is due south of you it lines up on the slice of the flat plane that we've drawn on the board and we can put the Suns GP on this diagram here's the equator we can put the equator into here's the equator and the Sun is north of the Equator it's summertime but the Sun is north of the Equator and this is our position this is us let's call that US and here's the GP of the Sun ground point of the Sun here center of the earth now let's do that let's go back to that first diagram that we had on the board and draw a line out to son remember the line to the Sun would go right through the GP Joe was standing right here at the GP looking straight up at the Sun it's right over his head and then let's add our other lines in a line that comes straight out through us that's our vertical straight down through our feet to the center of the earth and then our horizon perpendicular to the vertical horizontal perpendicular vertical here and that's 90 degrees there and then all the lines of Sun coming in parallel to that all the lines of the Sun are parallel here parallel everything's parallel because the Sun is far away far enough away to call it infinitely far away power a little line here coming in to us like so now when we take our section reading on the height to the Sun that's here HS height sextant okay now what have we got what are we trying to find we're trying to find our latitude we're trying to find this whole angle from where we are down to the equator that defines our latitude that is the latitude that's what latitude means so we want to find this angle here well here's the GP here we can look up in the table what the latitude of the GP is in fact you're getting so advanced now let's just call it the declination abbreviated Dec declination which is latitude it's no difference a lot of declination of the Sun here let's say that looks like about 10 degrees 10 degrees north declination of the Sun 10 degrees north we just call it declination just so it's separate we know when we say declination is not our latitude it's the sun's latitude that's the only reason we say declination is that latitude the same okay now what we're trying to figure out is our latitude well let's look at this this angle is HS so this angle here has to be 90 minus HS let's switch to red here so here we are this is 90 this angle here is 90 so this has to be 90 minus HS same as on our first diagram exactly the same and this line here is parallel to this line the sun's rays coming out and we won't need to extend that I can just so you can see it easier and single line crossing those two lines so this angle here is 90 minus HS okay and now what do we got this angle the sun's latitude is just this declination with 10 degrees let's give ourselves a section reading what does it look like it looks like about 50 degrees doesn't it 50 degrees so 90 minus HS equals 40 degrees so this angle here is 40 degrees and the declination the heights of the Sun above the equators 10 degrees here and what we're trying to find is the whole angle let's label this in here this is the 10 degrees the latitude of the Sun or the declination of the Sun what we're trying to find is this entire angle so it would just be this inner angle this this angle Plus this angle so that was 40 that's 10 so our latitude has to be those two angles together which would be 40 degrees plus 10 degrees our latitude is 50 degrees and you can work this whole problem out in just a few minutes three or four minutes five minutes of the most so you've just solved with one section site right at local noon you've just solved a problem and found your latitude it's pretty helpful knowing a latitude and being able to find it in five minutes is great okay now remember the table tells you the declination of the Sun on that day you don't even have to be very precise the sun's declination doesn't change much throughout a day so you don't have to do it hours minutes and seconds you just do it that hour the hour that you took the site just pull the declination out you'll find out next hour it hasn't hardly changed declination doesn't change very fast that's how the latitude of the Sun doesn't change very fast changes date from one day to the next day it will have changed enough that you need to allow for but during one day it doesn't change much okay so simple problem there's your latitude any refinements on this you still have to correct your sextant site H s 2h observed 2h adjusted still have to correct your section site but that's like you know 30 seconds correcting your section sites is really easy and then you've got it now just be a little bit careful because it's a different problem when the sun's in the northern hemisphere then when it's in the southern hemisphere let's just revise this and say the Sun is south of the Equator is winter in the northern hemisphere let's look at it there in our first case in this case we just got we found that latitude equals 90 minus HS plus declination right 90 minus HS plus the declination northern hemisphere northern atmosphere the sun's in the northern hemisphere that's your that's your equation you don't have to memorize this because the diagram is so simple just do your diagram let's put the Sun in the southern hemisphere and see what we get so now the Sun is down here GP let's put it ten degrees again declan 2 equals declination that's 10 degrees south now remember labeling is important in celestial navigation if you fail to label things you're gonna make mistakes so 10 degrees south let's get that clear 10 degrees south equal this declination now okay now the sun's light is coming in this way from outer space a new angle we'll get this all cleaned up the sun's light is coming in from here south of the equator 10 degrees south of the equator and that's the sun's light their sunlight their sunlight here coming in parallel to this ray of Sun you can get these lines straight parallel lines parallel lines Sexton sight HS 90 minus HS here now parallel lines single line be careful here it's this whole distance here that's 90 minus HS here same as this angle up here right two parallel lines crushed by a single line now our latitude is and here's the declination here declination because this is the equator right across here so now our latitude is different now our latitude is this whole angle minus the declination so we have a southern hemisphere hemisphere our latitude is equal to ninety minus HS minus declination for the noon sight you guys see the difference - declination versus + declination so rather than memorize these just learn the diagram because the diagram makes sense you can always you can sketch out the diagram in 30 seconds on a piece of paper and on a voyage you only have to do it every six months if you can take diagram every six months because the sudden only crosses the right across the equator every six months okay so that's the new insight super simple easy easy to do fast and easy oh one refinement our last note on the noon site is how do you know when it's local noon if you don't know where your position is how do you figure out when the sun's going to be due south of you at its highest point well that's a good question you can figure out based on your dead reckoning position about when you think the Sun will be due south of you and this is actually why we don't do noon sites as often as we might because it's kind of a nuisance to figure out exactly when it's gonna be the right time to do noon sight however when it's getting close you start watching the Sun and it's moving fast you cranking them away on the burn your knob pretty quickly it's going up up up well right at local noon the Sun seems to level off and for a few seconds even it just seems to be staying level and then all of a sudden it starts down again and so your highest reading is your local noon when it's gone and all that time - you're arcing you're swinging your sex in an arc making sure you're getting to the horizon and you keep following the Sun up and then you don't follow it down at all you check your section at the highest reading and that's your local noon okay so you don't have to compute the time accurately in fact because of the fact that the the Sun levels off for a few seconds it's not an accurate way to get your longitude and you could say well if I what if I record the exact second that the Sun is at its highest point they'll tell me about a lot my longitude - well technically mathematically yes would be true but it's really hard to record to know exactly when the Sun by a watch is at its highest point just by looking at it with the sextant so realistically as far as any accurate measurement getting you a lot of the noon sites really only good for your latitude and it's for the latitude though it's totally accurate within the accuracy of your sextant maybe half a mile is a good section okay so that's the noon sighting so we've covered a lot the first three diagrams explain how celestial navigation is done and then this last diagram is just sort of an offshoot of the first diagram a specific situation specific situation where the Sun is directly south of us so we but the Sun on the same plane as our position of the North Pole and South Pole so a specific application of the first concept okay part two we'll go into the details make sure this part though all these diagrams are really really clear explain them to somebody else take somebody aside and say hey let me show you this just takes half an hour and you can do all three diagrams in about 20 minutes half an hour if you know them well okay thank you very much and welcome to the world of celestial navigation by now you [Music]

Channel: Tippecanoe Boats

Views: 153,658

Rating: 4.8798585 out of 5

Keywords: celestial navigation, navigate by the stars sun moon and planets, celestial navigation explained, sextant, using a sextant, how to do celestial navigation, celestial navigation tutorial, sextant tutorial

Id: -ARXW8InStY

Length: 160min 21sec (9621 seconds)

Published: Wed May 16 2018