RYA Yachtmaster Ocean. Sun Sights and Plotting

Transcription

1 RYA Yachtmaster Ocean Sun Sights and Plotting

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3 Sun Sights and Plotting What will I learn in this lecture? This lecture covers parts of topic 6 of the RYA syllabus and is the most intensive. You will learn how to reduce a sun sight using the AP 3270 tables. You do not have to know any mathematics for this section. Working on this topic This lecture follows on from the lecture on Meridian Passage. You should also have completed RYA exercises 1 to 3 and 5. RYA exercises 4, 5, 6 and 7 should be completed when prompted to do so. The RYA syllabus includes a section on the use of calculators for working out sights. Our experience is that this is of little real assistance. These days, if you want to work out a sight electronically, there s a range of programmes available for a variety of computers. We suggest that you work everything out manually during this course using the tables that are supplied. You will understand the processes this way and might even find it quicker! Suggested time Based on the RYA syllabus we suggest you allow around four hours of study time plus time for the RYA coursework. Sun Sights Page 1 of 36

4 Finding your way around this lecture CHAPTER 1 - MORE ON THE THEORY... 3 SIMPLE PRINCIPLE... 3 WE NEED A BIT MORE THEORY... 3 CHAPTER 2 - GREENWICH HOUR ANGLE AND LONGITUDE... 5 LOCAL HOUR ANGLE... 8 CHAPTER 3 - USING THE SUN AT ANY TIME OF DAY CHAPTER 4 - CALCULATED ALTITUDE THE BASICS GENERAL PRINCIPLES - A REMINDER SOLVING THE PROBLEM INTRODUCING THE AP TABLES THE CHOSEN POSITION CHAPTER 5 - CALCULATED ALTITUDE - APPLYING THE TABLES CHAPTER 6 - PLOTTING PLOTTING SHEETS AND CHARTS PLOTTING A POSITION PLOTTING OPTIONS CHAPTER 7 - THE PLOTTING SHEET WITH THIS COURSE CHAPTER 8 - USING THE SHEET IS STRAIGHTFORWARD STEP 1 - CUSTOMISE THE SHEET (PAGE 27) STEP 2 - PLOT THE CP (PAGE 28) STEP 3 - PLOT Z N (PAGE 28)...21 STEP 4 - PLOT THE POSITION LINE (PAGE 29) SOME HINTS AND TIPS CHAPTER 9 - PLOTTING A POSITION SUN SIGHTS STAR SIGHTS TRANSFERRING A POSITION LINE RUNNING FIXES ASTRO NAVIGATION IMPLICATIONS: CHAPTER 10 - PLOTTING SHEET WORKED EXAMPLES CHAPTER 11 - SUN - RUN - SUN CHAPTER 12 - TRANSFERRED POSITION LINES AND EP S CHAPTER 13 - CAN YOU HELP FRED? CHAPTER 14 - ANSWERS Sun Sights Page 2 of 36

5 Chapter 1 - More on the Theory First, let s take a breather; you ve worked on a number of new concepts so?? How much can you remember? 1 1. Describe how time is handled worldwide. 2. If it is 22:00 in Zone + 10 on November 30 th what is the UT and GD? 3. Describe the steps to convert an SA to a TA as concisely as you can. 4. Can you define a Zenith and a ZD? Simple principle Think for a moment about the Zenith. It is the point on the celestial sphere vertically above the observer and this means that there is a straight line between the centre of the earth, the observer and the point on the celestial sphere above him or her. We could reverse that and say that for each body on the celestial sphere there is a point on the earth s surface lying on the straight line between the body and the centre of the celestial sphere (which is also the centre of the earth). This is called the Geographical (or sometimes the Ground) Position (GP) of the body. Once we know the GP of a body we can use some sleight of hand to work out how far we are from it and use that information to work out a position line. If we have two position lines we have a fix and the problem has been solved for the general case. It allows us to use a sight of any astronomical body at any time to derive a position line. Think about the Meridian Passage sight in this light for a moment.?? What, in terms of a position line, does it give us? 2 We need a bit more theory Geographical Position GP GP - the point on the earth s surface on a line between the centre of the celestial sphere and the body GP - has a Latitude & Longitude Tiller School Hang on to the simple concept as you study some more astro theory. Remember that if we know where the GP of our observed body is, then we can use it to work out a position line (NOT, directly, a position) which we can use conventionally on a chart. That s the goal but how do we do it? The movements of the astronomical bodies (sun, moon, planets, and stars) are both predictable and accurately tabulated for us. This means that if we can measure, or deduce, the angles accurately enough we can work out our position or, at least, a position line. Sun Sights Page 3 of 36

6 It is all based on the ability to measure angles and times very accurately and everything else we need is tabulated for us. The process of reducing a sight is little more than filling in a form and adding and subtracting a few numbers. Unfortunately it has its own terminology and it definitely helps if you have an understanding of what you are doing. It helps you to avoid silly errors and also allows you to make reasonableness checks as you proceed. It is time to learn a little more Astro Theory. We left it at the point where you had gained an understanding of Hour Angles - Greenwich and Local or GHA and LHA, the Zenith and the Position Circle.?? First a little exercise to help you remember the definitions because we then strayed onto more practical topics such as Time and the Meridian Passage sight. Are the following statements true or false (if false try to correct them)? 3 1. The GHA of a body is the angle, relative to the appropriate (North or South) pole between the Prime (Greenwich) Meridian and the meridian of the body. It is measured only in a Westward direction 2. The SHA of a star shares the definition of GHA except that it is measured relative to the First Point of Aries 3. FPA rotates 360 every 24 hours relative to the Greenwich Meridian 4. GHA of a body minus LHA of the same body always equals the observer s longitude 5. GHA star = GHA of FPA + SHA star 6. The declination of a star is, to all intents and purposes, unchanging Don t worry too much if the next bit of theory appears to be a bit jargon prone and complex to understand, it is quite a common reaction! The concepts, at the level we study them, are most definitely within your grasp even though the mathematics would be completely incomprehensible to most people. Luckily, we don t need mathematics to handle astro navigation, just the concepts and the terminology. If you remember that in astro a distance and a position can both be defined as angles then all should be well. In the classroom we often revisit the theory after completing the work on sun sights. You ll be pleased to know that this is a subject where you can learn WHAT to do to calculate a position without understanding WHY you have done it. Learning how to do it often helps you to understand the theory. Sun Sights Page 4 of 36

7 Chapter 2 - Greenwich Hour Angle and Longitude Angles are key to this topic and here is what we need to know. We can t progress to real astro navigation quite yet but we are getting there. Longitude is measured to the East or West of the Prime Meridian (Figure 1). We know that the limits are 180 W and 180 E and as we cross from one to the other so our longitude switches from one NAME (East or West) to the other and the date changes. This picture introduces a new format to you. We are looking vertically downwards towards the North or South Pole and the limit of what we can see is the equator (take an apple or orange, treat the stalk as the North Pole and you can see what we mean). This is the Gnomonic projection.?? Incidentally can you remember what happens when going from W to E across the International Date Line at midnight? 4 Equation of Time The relationship between longitude and time is that we define a day as being exactly 24 hours long. The conversion of arc to time table on RYA page 19 helps us make the calculations. Predictably perhaps, the real universe doesn t exactly follow a 24 hour day. The Equation of Time block (bottom right of RYA page 13 for example) tells us one particularly useful piece of information and that is the time of Meridian Passage for the sun (and the moon).?? Can you define what this means? 5 For example, 12h 13m is the LOCAL time of Meridian Passage on February 24 th. This means that at the moment of Mer Pass on February 24 th the time, to the observer, will be 13 minutes past 12 wherever he or she might be. Strictly speaking the Equation of Time is the excess of Mean Time over Apparent Time and can be a positive time (February and June in the RYA booklet) or negative (September). It tells us how much the assumed 24 hour day differs from real world (the earth s rate of rotation and orbit around the sun). Greenwich Hour Angle Here s the problem. We define a position on earth in familiar terms using Latitude and Longitude. We are comfortable with the use of angles to define the position and accept without a second thought the two measurement datums of the Equator and the Prime Meridian. Longitude We are looking DOWNWARDS at the N Pole Prime Meridian Terrestrial Equator Figure 2 - GHA Astronomical longitude is very similar to longitude but uses a new term the Hour Angle. It is measured from the same arbitrary reference point - the Greenwich or Prime Meridian and Figure 2 both gives you W 90 0 Measure WEST Figure 1 - longitude revisited North Pole The Prime Meridian is an artificial reference point which, by agreement, passes through Greenwich E 90 0 Measure EAST Astro Longitude - the GHA GHA = Greenwich Hour Angle - the angle at a point in time between the prime meridian and the meridian of the body North Pole Celestial Equator Looking down from above the N Pole Prime or Greenwich Meridian GHA is only measured clockwise Sun Sights Page 5 of 36

8 the general idea and continues with the same format as Figure 1. Hang on to the concept as we investigate hour angles in a bit more detail. We need to find how to define the position of a heavenly body at a moment in time. We can use this information to determine our position on earth but only after we apply some cunning logical trickery to solve the problem. When considering Hour Angle we are looking DOWN from outside the Celestial sphere to the North (or South) pole of the earth and seeing as far as the equator. This format allows us to correctly show meridians of longitude as straight lines. GHA Greenwich Hour Angle In Figure 2 a GHA for the body of 110 is exactly equivalent to a Longitude of 110 W. It would be WRONG to write an hour angle with a NAME and so the GHA is 110. GHA is measured clockwise and Figure 3 makes the point - the body concerned has a GHA of 220. It does NOT have a GHA of 140 E. Greenwich Meridian Figure 3 - GHA GHA Handling the stars There is just one difference with the stars. You may recall that the stars are assumed to be glued to the celestial sphere but, to us, they rotate. This gives us a clue - the celestial sphere, in our theoretical world of astro navigation, is rotating. Actually, of course, it is the earth that is doing the spinning. There is a reference point for stars (Figure 4) called the First Point of Aries and usually referred to as FPA or the Greek symbol of a ram s horn. FPA isn t a physical entity, we can t touch it or feel it but it does provide us with a reference point or datum when working with the stars. There s a slightly more formal definition in the Glossary. Its formal definition (Figure 5) is meaningful in the sense that it is defined as the point where the sun's path crosses the celestial (or earth's) equator. It therefore rotates at 360 per day. The definition doesn t matter much to us but it does mean that FPA has a GHA but not a declination.?? Check this on page 12 of the RYA booklet now. We can measure the angle from FPA to any star and be confident that it will remain essentially constant for quite long periods of time (many years). This angle (Figure 6) is called the SIDEREAL HOUR ANGLE (SHA) and is a constant for all practical navigational Sidereal Longitude Sun Sights Page 6 of 36 Sidereal Hour Angle Similar concept for the stars. First Point of Aries (FPA) is a reference point from which we measure the longitude of a star. The SHA changes very slowly over time. Figure 4 - Sidereal longitude North Pole First Point of Aries First Point of Aries Celestial Equator S FPA - the point where the sun s ecliptic crosses the celestial equator. FPA rotates around the earth in 24 hours approximately. Figure 5 - FPA North South Celestial Equator Greenwich Meridian Ecliptic N

9 purposes. There will be a slow drift of the stars and the tables we use have a limited life of about ten years.?? Look at page 12 onwards in the RYA booklet and make sure you can find the SHA and declination for a star. Also prove for yourself that the changes are very slow and of the order of a few 1/10 of a minute over the six months or so covered by the tables we have. The significance of this is that FPA gives us (roughly speaking) a stellar equivalent of the 'Prime Meridian'. It is moving but we can position a star in terms of its Declination and SIDEREAL HOUR ANGLE (SHA) relative to FPA. This gives us a convenient way to locate stars (Figure 7) but only if we can find FPA at any point in time. The declination and SHA of a star change but very slowly so we can treat them as constant for quite long periods of time.?? Do we know where FPA is at any time? 6 Figure 7 puts it together for you and we now have an easy way to define the position (in terms of angles) of any astronomical body. Figures 8 to 10 summarise matters so far. The sun, moon and planets are relatively close to the earth and 'move' fairly rapidly across the celestial sphere. We define their position in terms of DECLINATION and GREENWICH HOUR ANGLE (longitude). The only difference with the stars is that we have a GHA for FPA plus a fixed 'offset' called the SHA and fixed declination for each star. Does this last paragraph make sense? It should and Figure 7 - heavenly position you are beginning to develop the vocabulary and concepts which will allow you to understand astro. If you cannot remember the terms then now is the time to go back and work through this material again. Incidentally in a 24 hour period the sun s GHA moves through VERY NEARLY. We know that every four years there is a leap year and that from time to time there is a time 'correction'. The purpose of all this is to ensure that our earth time, which is based on a 24 hour day, stays acceptably in line with more accurate and stable time measurements based, these days, on atomic clocks. If this were not done then we would experience a slow drift of the seasons. The assumption is that all astronomical bodies operate at a convenient 15 per hour EXACTLY. They do not and it is in the nature of things that the heavenly bodies do not follow prescribed orbits for our convenience. There are inconsistencies and Star s Meridian Sidereal Hour Angle Celestial equator Sun Sights Page 7 of 36 SHA Figure 6 - SHA First Point of Aries Celestial North Pole GHA of FPA Prime Meridian GHA of Star = GHA FPA + SHA for star The position of a heavenly body Grid reference Declination = Latitude N and S reference is celestial equator Greenwich Hour Angle = Longitude Measured clockwise from Greenwich Meridian For stars the First Point of Aries is a moving point for which we have a GHA. The position of a star is fixed relative to FPA. The heavenly bodies Stars constant SHA and declination relative to FPA slow change over time fixed to the celestial sphere GHA for FPA is tabulated for us Sun, Moon and Planets move across celestial sphere GHA and declination tabulated for specific times in Almanacs Figure 8 - the heavenly bodies

10 'wobbles' in their orbits, which mean that we cannot use the 15 per hour assumption for accurate navigation. We can and do use it for sight planning and many other purposes.?? Test yourself. 7 Define Declination SHA If someone tells you the SHA is 120 E Is that valid? If not how should it be expressed? What will the sun s GHA be at 15:00 GMT? 09:00 GMT? Local Hour Angle A GHA reminder?? Look on pages 12 and 13 of your RYA study pack and you will find the GHA tabulated for each of the planets, the sun, the moon and FPA. For all practical purposes we can see that if the GHA of a body at NOON GMT is 0, then after 4 hours it will be 60, after 12 hours it will be 180 and, after 24 hours, it will be 0 again. Finding the sun Declination and GHA are tabulated in Nautical Almanac. GHA is relative to GMT Local time of Mer. Pass is required calculate by adding (W longitude) / subtracting (E longitude) the Longitude in Time use arc to time table to convert angles to time or vice versa Figure 9 - finding the sun What about the observer then? We can extend these concepts to include us - the observer. Wherever we are on the earth we are going to have a longitude. Looked at another way we all have an hour angle which is dictated by our position RELATIVE to the PRIME meridian. The LOCAL HOUR ANGLE (Figure 10) of a body is the same as the GHA but measured from the observer's meridian rather than the Prime Meridian. This has great significance to astro navigation. Observer s Local meridian is 56 0 W. Local Hour Angle Greenwich Meridian Figure 10 - LHA 1 LHA GHA Sun Sights Page 8 of 36

11 ?? If we know the LHA of the body and its GHA we can calculate our longitude - can you work out how? 8 Figure 11 introduces you to the final wrinkle on LHA and it is to do with the NAME of the observer's longitude. It is actually easy to work out and remember - study Figure 10 again and we can see that the LHA of a body based on an observer with a Westerly Longitude is LESS than the GHA. Conversely it will be greater than GHA with an Easterly longitude. If you are not sure then draw the equivalent diagram to Figure 10 for an Easterly longitude. We now have two hour angles (Figure 12). 1. GHA measured from the Prime Meridian applies to all bodies and to FPA. For stars their GHA is GHA for FPA plus the SHA for the star in question. 2. LHA is measured from the observer's meridian and is otherwise the same as GHA.?? Work through this exercise. It is designed to test your conceptual knowledge rather than your maths so everything is in whole degrees. If you are unsure try drawing some simple pictures The sun has a GHA of 130 degrees. What is its LHA if we are at: a. 30 West? b. 40 East? 2. What is our longitude if the LHA is 100? 3. SHA of a star is 135 a. If FP Aries has a GHA of 135 what is the star s hour angle? b. If FP Aries has a local hour angle of 090 what is our longitude and what is the star s local hour angle??? Try the exercise below before we move on. 10 Local Hour Angle The angle measured westwards between the observer s meridian (longitude) and the astronomical body in question. GHA is relative to the Greenwich Meridian There is a LOCAL meridian for every location on earth LHA body = GHA body -West Longitude or +East Longitude. Figure 11 - LHA 2 Hour Angles The measurement datum Some change Local Hour Angle Sun, Moon, Planets, FPA Fixed (in effect) Greenwich Hour Angle Relative to a fixed arbitrary meridian Sidereal Hour Angle Fixed relative to FPA (which moves) 1. Local noon is at 16:45 GMT. At that time Figure 12 - hour angles summarised a. What is our longitude? b. What is the sun s GHA and LHA? 2. A star has an SHA of and FPA is a. What will be its LHA if we are at 15 W? b. If SHA was what would the LHA be? Sun Sights Page 9 of 36

12 Chapter 3 - Using the Sun at Any Time of Day It is time to put our new found theory into practice. One of the most useful navigation bodies is the sun. We can see it for long periods of time and, by definition, when we can see it we can also see the horizon. What more can one want in astro terms? We already know that it is quick and easy to use the sun to work out our latitude.?? How can you describe it in one sentence? 11 It would be very desirable to be able to observe the sun at any convenient time, for example through a break in thick cloud, and work out a position line. The sun has one other very useful property for the navigator and it is to do with the length of time for which it is visible during the day. Think for a moment.?? In what direction does the sun rise and set? 12 During its passage from sunrise to sunset we perceive the sun as swinging from roughly East to roughly West and in the N hemisphere the bearing of the sun goes via due South (and vice versa in the S hemisphere). We know that our position line is going to be at 90 to the sun s azimuth and this means that during the day the position line is also going to rotate. The net of this is that if we observe the sun in the morning at, say, 08:00 local time, again at midday and finally at 16:00 we can arrange to get a good angle of cut between the three position lines. Using standard plotting techniques we can transfer the first to the second or even transfer the first two to the third and thereby obtain our position.?? In the example above what will be the angle between each pair of position lines? 13 The sun s bearing changes during the day This drawing applies to the N hemisphere The sun s azimuth changes during the day from roughly E at sunrise to roughly W as it sets. Position lines from the sun This drawing applies to the N hemisphere This means that the position line also rotates so by choosing our times we can get a good angle of cut. This is a technique called sun - run - sun and, as the name implies, all we need to know is the distance run and estimated track between sights to be able to establish a position. It doesn t matter when the sights are taken and nor must it include Mer. Pass. although that is a useful and easy sight. The only thing that matters, and it is no different from any other sight, is the angle of cut - too narrow and our sight s positional accuracy becomes suspect. This doesn t sound too bad does it? We ve narrowed the problem down to deriving a position line from a sun sight and then plotting it. Both are straightforward. Sun Sights Page 10 of 36

13 Would you like some good news before we delve into the detail? In fact, as you will soon find out, once you have mastered the technique for one body, in our case it is the sun, you have mastered it for all observable bodies. The process of calculating the TA may differ slightly but the tables and techniques for all bodies are then essentially the same. There s only one exception and that is with the stars - use the recommended ones and it is actually EASIER! Sun Sights Page 11 of 36

14 Chapter 4 - Calculated Altitude the Basics To make wider use of the sun we need to be able to use the PZX triangle in a different way. Our aim is to be able to establish a position line from a sun sight taken at any time. General principles - a reminder The tools of the trade are: 1. A set of sights and times from which we choose an accurate one or derive an ideal sight and calculate the observed true altitude H o. 2. Accurate knowledge of UT and Greenwich Date. 3. A DR or EP to give us our chosen position Z. 4. A way to compute the calculated true altitude H c. We can use either the AP3270 Air Navigation Tables or their equivalent or a scientific or programmable calculator. Our recommendation is to use the tables - they are easy, quick and accurate once you know what you are doing. Solving the problem We know about the first three. What of the fourth? The objective is to solve the PZX triangle. To do this we need to know the position of X - the GP of the body. We also need to know where Z is and this is easy because we can use our DR or EP as a good working assumption. Once we have values for Z and X we can calculate the azimuth and altitude based on Z - our CHOSEN POSITION or CP. There are numerous programmes which will handle the mathematics for us on a variety of calculators and computers. Alternatively we can use tables to perform this function. Tables The choices are essentially Air Navigation (AP3270) or Marine Navigation (NP401). For yachtsmen the normal tables are the AP3270 set because: They permit us to plan sights as well as reduce them. The use of a consistent set means we have less to remember. They were developed for hard pressed aircraft navigators and this means that they are very likely to be both simple and rapid to use. We ll be finding that they do, indeed, meet these criteria. We could also use haversine and log tables. We ll focus on the AP tables since these are best for yachtsmen and are the preferred RYA method. If you intend to use a computer or calculator we still suggest you understand how to do it manually. Electronics can fail. We ll consider, in turn, the tables and what they contain, the CP and how to select it to make the tables usable and using the tables to work out the intercept and azimuth that are the goal of all this hard work. Introducing the AP tables Let s look at the AP3270 extracts we have available to us. They are on pages 26 to 47 of the RYA booklet.?? Open the booklet and find them now. Pages are extracts from Part 1 of the tables and are used for sight planning and star sight reduction (covered later in the course). Our extract covers latitude 50. In the real world there is a similar set for each degree of latitude. Sun Sights Page 12 of 36

15 Pages 30 to 45 are from Volume 3 of the tables and give us the calculated altitude Hc and azimuth Z of the observed body from the chosen position. d is the difference in Hc between successive pairs of declination columns. The tables use Declination (horizontal axis) and LHA (vertical axis) for each degree of latitude - we only have it for 50 and for each intersection of a row and column we find values for H C, d and Z. Pages 30 to 33 cover declinations of 0 to 14 with SAME name declination as latitude. Pages 34 to 37 cover the same range of declination but with CONTRARY names. Same for declinations 15 to 29 on pages 38 to 45. You may have noticed that both LATITUDE and LHA are given in whole degrees. This is to reduce the size of the table to a manageable set of volumes. Imagine similar tables for every 1/10 th of a minute of latitude, declination and LHA and it would be difficult to get them on board many yachts, let alone keep her afloat with the weight of paper! The consequence of this is that it imposes some constraints on how we choose the latitude and longitude of Z our Chosen Position or CP. The Chosen Position Our goal is to select a CP that is close to our DR and meets the requirements of the AP tables. We need to consider both latitude and longitude. Latitude The easy one - simply round it to the nearest whole degree and keep the name (N or S). Longitude The relationship between LHA, GHA and Longitude is that LHA = GHA + - Longitude. The NAME (East or West) determines whether we add or subtract. Our goal is to find a longitude that gives an LHA with a whole number of degrees for the body in question AND is as close to the DR longitude as possible. We do this by ensuring that our CP is never more than 30 from our DR position. That doesn t sound too painful and the next section gives you some general rules for working out the longitude of our CP. Remember that our goal is an LHA with a whole number of degrees and no minutes AND the longitude of our CP is as close to our DR or EP as we can make it. Chosen Longitude We can restate the requirement very simply. We have to choose a longitude which, when added to, or subtracted from, the GHA will yield an LHA in whole degrees. Westerly Longitude: The rule is simple and easy to understand: Chosen LHA = GHA - nearest longitude to DR which will give a whole number LHA For example: If our DR is W and GHA then the precise LHA would be (97 03 minus ). The Chosen LHA would be 47 ( ) and the Chosen Longitude W. Sun Sights Page 13 of 36

16 We want the CP to be as close to the DR or EP as possible and sometimes we may have to adjust the CP s degrees to achieve this. In the example above it would be WRONG to choose an LHA of 46 because the CP would then have to be W ( ). So to put it another way if GHA is we chose our longitude as W (within 30 of W) and subtract it to give an LHA of 47 Here s another example: The Sun s GHA is and DR Long. is W, work out the chosen LHA and CP. The accurate LHA is (i.e. GHA ( ) DR Long (14 27 ). To meet the requirement for a whole degree LHA we have to modify the DR longitude. In this case it becomes W (we have to use a value for the minutes that makes the LHA a whole number of degrees). The LHA is 221 ( minus ).?? Had our DR long been W what chosen longitude and LHA would you use? 14 Easterly Longitude Arithmetically speaking we must use the complement of the minutes (subtract minutes from 60) in the GHA and add GHA to chosen Long to get a whole number of LHA degrees. This isn t nearly as difficult as it sounds as this example makes clear: DR is E GHA is CP Long E. We have worked this out by taking the minutes of the GHA (3 ) and subtracting them from 60 to get 57. This is the value of the minutes in our CP Longitude. LHA 147 ( ). Note that is a better CP Long than because it is within 30 of our DR Long. There are occasions, and this is one, when we need to adjust the CP longitude s degrees. In this example we could have used a CP of E by not making this adjustment. Far better to take a moment to work out the degrees of longitude that will result in a chosen longitude that is as close as possible to the DR s longitude. Clearly is a lot nearer to than either or so we choose E as the best CP Longitude. The chosen DR dictates the value of the LHA that we will use in the tables You might ask whether the degree in our CP actually matters. The answer is that if you do not make the adjustment to get the nearest CP Longitude you could introduce an error of many miles in calculating the intercept distance (see later). Your answer probably will not be wrong, but the intercept will be longer and this makes the process of plotting a bit harder. It is not good practice for this reason alone. Doing it the simple way There s a lot to be said for making this a systematic process and a good sight form will help you to systematise the whole process. Here are some simple rules for you: DR Long. W 1. Put in CP long. minutes THEN 2. Put in CP long. degrees which make CP long. Within 30 of DR long. DR Long. E 1. Put in CP long. minutes calculated as (60 -GHA minutes) Sun Sights Page 14 of 36

17 2. Put in CP long. degrees to make CP closest to DR longitude.?? Now have a go at filling in the blanks in this table: 15 GHA DR Long LHA for AP tables W W E E Chosen Longitude?? Now try a more realistic exercise - use values for the sun. 16 We ve given you a date and a time so you can work out the GHA for the sun from the tables to be found on RYA pages 12 to 17. Date Time - UT GHA sun DR Long LHA for AP tables 21 June h 34m 5s W 25 Feb h 28m 10s W 22 Sept h 31m 43s E Chosen Longitude Sun Sights Page 15 of 36

18 Chapter 5 - Calculated Altitude - Applying the Tables?? Look at the AP 3270 part 3 tables. Suppose we know the body we have observed, the date and time of observation, our DR and a derived CP are we ready to use the tables? 17?? We know about declination - you ve used it for the Mer. Pass calculations - so, if need be, go back and refresh your memory now. Now, at long last, we can solve the problem and obtain the values we need for navigation. Volume 3 of the AP tables gives us our calculated altitude Hc and azimuth Z. Let s take an example and work it through step by step. We will not use a sight form at this stage. A sight was taken and after due calculation the CP was calculated as 50 N, 17 4 W, Sun s declination N 12 37, LHA 310.?? Find the intercept and azimuth that should be plotted. Here are the steps to follow: 1. Find the right table. It is on pages ?? Can you work out why? 18 Note that the columns running across the page cover declination and give values of Hc, d and Z for both the left hand and the right hand LHAs.?? Check for yourself that if you entered the table with a declination of 10 and LHAs of 305 and 55 you would get values of 29 45, +47 and Enter table with the values for our problem. We need the column for a declination of 12 and the row corresponding to an LHA of 310.?? What values did you get? 19 We now have tabulated values for Z (the azimuth) and a value for Hc (the calculated altitude). Neither is directly usable at this stage.?? Can you work out why? Work out the correct H C We obtained a value of +48 for d. It helps if we understand what this means so look at the value of H C for declinations of 12 and 13.?? Work out the difference in minutes? Once again you can work out the correct value arithmetically or use a table. The latter is the way that most people prefer so turn to RYA pages We know the minutes of declination and that H C changes by 48 minutes per degree of declination at this LHA. We could guess that H C will be a bit more (37 sixtieths) than half of 48 minutes so somewhere in the high twenties is a good reasonableness check. Now enter the table with arguments (values) of 48 for d (the top row of the table from 1 to 60) and 37 for minutes (of declination down both sides of the table) and we find a value of The correction to be applied is therefore 30, the sign of d is positive so we ADD this correction. H C therefore becomes (34 18 plus 30 ). 4. Convert the tabulated Azimuth (Z) to a True Bearing (Z n ). It is called Z n to differentiate it from the Z we find in the tables. The true bearing will vary depending on whether the Azimuth is to the East or West of the observer s meridian. It is not a toss of the coin exercise and the rules have been handily included for us on the tables themselves.?? Take a look now at the top and bottom of the table on page 30. Sensibly the formulae for the Northern hemisphere are at the top and for the Southern at the bottom of the page. Our latitude is 50 N so we use the top of the page. LHA was 310. Z was 115 so in this case we see that Z N = Z so Z N has a value of 115 T. Sun Sights Page 16 of 36

19 It s not a hard exercise so have a go now (use a sight form from the Form Pack if it helps).?? CP is 50 N, W; LHA 055, Declination N Work out the H C and Zn. 22 Here s a common source of error - don t forget which hemisphere you are working in! Now we ll take this example the final step. We know the calculated altitude. If we also know the observed altitude (i.e. TA from the sextant) we can calculate the intercept and its direction. Do you remember GOAT? It simply says that if the observed altitude is greater than the calculated altitude we are nearer to the body s GP. Fairly obviously if the reverse applies then our observed position is further from the GP than the CP. The naming makes sense, for once, and GOAT is a useful and memorable acronym. For example, if our H O were then GOAT tells us that the intercept is AWAY (observed less than calculated). The length of the intercept is simply the arithmetic difference between H C and H O so in this case it is 10 miles.?? Can you work out why this arithmetic works and is not affected by the latitude? 23 Hint think about the azimuth and intercept - is it part of a great circle and what does this mean? The next stage is to put it all together. We know the basics but can we use a sight form? The answer is YES, there is one in your Form Pack and also on the back of the plotting sheets. You should use sight forms from now on.?? Before you use it test your knowledge by writing your own. How much of the Meridian Passage sight form can you reuse??? Try a sun sight reduction now. Work out RYA Exercise 4 Question 1. Key steps in working out the answer are given in the endnote so if you are having a problem you should be able to work it out backwards'. 24?? Now work on and complete RYA Exercise 4 and send it to us. Sun Sights Page 17 of 36

20 Chapter 6 - Plotting We cannot proceed until we know how to plot a position in mid ocean. Here s the problem; by using a very clever logical trick we now have a way to establish a position line that will be on a bearing (Z N ) and at a distance (Intercept) relative to a known position (the CP) on the ocean. How can we make use of it in practical navigation? The intercept is unlikely to be more than a few miles long and yet our vessel may be thousands of miles from the shore and sailing on a featureless void from the chart maker s point of view. Plotting sheets and charts Few skippers are going to be thrilled at carrying a huge pile of charts containing nothing but empty sea so that they can plot some position lines. Accurate plotting in a passage chart covering, for example, the entire North Atlantic Ocean is not practical. The answer is to customise a general blank chart to meet our needs. This allows us to carry a small number of reusable charts at a scale that allows us to plot the intercept and position lines reasonably accurately. The blank chart is, these days, usually called a plotting sheet and you have some with your course pack. There s no difference in principle between this, and the familiar process of switching between charts to use the one with the most appropriate scale, as we move from pilotage to passage and back again. The only difference is that we are going to make our own customised large scale chart and use it to establish a position which can be plotted on the small scale passage chart (which might span a whole ocean on one standard sized chart). As we close the land the navigator will automatically switch to a pilotage chart and the position can then be plotted on that. The only thing to bear in mind is that a position based on astro navigation is likely to be several miles in error and so care is required as land is approached. Plotting a position Once we have customised the plotting sheet by inserting a latitude and longitude we can plot our chosen position (CP), bearing and intercept and draw the position line as a short straight line at right angles to the bearing.?? True or false? The position line is a portion of a position circle centred on the ground position of an observed body 25 If we can plot two or more position lines then we have a position and that, really, is all there is to it, except to remind you that a position line is just that, a position line. Its source doesn t matter so we can cross our astro position line with another from ANY valid source. We could use a line of soundings, a shipping lane or any other source to give us a position line. On this course we are going to restrict ourselves to position lines derived from astro navigation but we don t have to. Incidentally it is all downhill from now, on as we study the use of stars. There s no more new theory to be learnt. In mid ocean there is little point in trying to plot position lines on a chart. The accuracy would be hopeless because of the scale of an ocean chart and the chart would, anyway, show little more than 'sea'. The normal technique is to use a plotting sheet and the one we prefer (and it is the one that 'Ocean Sailing' also uses) is the American version. The same plotting sheet is in the pad of Imray plotting sheets included with your course. When you work on the exercises this is the one to use, unless you have a strong preference and experience with another. Sun Sights Page 18 of 36

21 Everything that follows relates to the version we recommend. Plotting options There are a variety of ways to plot a position. They include: 1. Plotting on a chart - the problem is that most passage charts cover a very large area of water so the scale makes accurate plotting very difficult. This is not true when closing a coast and using passage charts. We may even be able to cross an astro position line with a depth or other position line to get a position. 2. Plotting sheet - there are various ones but the one we will be using is easy and straightforward to use. It employs a constant latitude scale - we add the units - and a variable longitude scale. A different type of sheet has a variety of Latitude scales and a single Longitude scale. 3. Squared paper - the problem with this is that although the DIFFERENCE OF LONGITUDE (angular distance) between meridians of longitude is constant with latitude the physical distance (DEPARTURE) reduces for a given longitudinal difference as the latitude increases. The Imray plotting sheet is one way to allow for this. An alternative is to use traverse tables. To use squared paper we mark a latitude and longitude in degrees to suit our assumed position. This might be our DR or it could be the CHOSEN POSITION (CP) that we used to enter the AP3270 tables. You will sometimes find this referred to as the AP (Assumed Position). Latitude is plotted conventionally. Traverse tables allow us to work out the Longitude as a DISTANCE so we can use the same units for latitude and longitude on the paper (e.g. 1 square is 1 minute of latitude or 1 mile). The CP can then be plotted correctly and the intercept measured as usual from the latitude scale. Squared paper - without traverse tables - requires us to, in effect, create a local traverse table in the form of a graph. There is not much merit in using squared paper or traverse tables. Although the techniques are reasonably straightforward a plotting sheet is both easier and eliminates one source of error! We can use the sheet directly with a minimum of preparation. Sun Sights Page 19 of 36

22 Chapter 7 - The Plotting Sheet with this Course The pad of plotting sheets we supply should be ample for this course. If you need more we can supply them - please check with us for the cost including post and packing.?? Look at a sheet now from the pad with your course - there is an extract on page 26. It has three working parts: 1. A TRUE compass grid in the centre. 2. A LATITUDE scale running from top to bottom. This is a fixed scale and spans any five degrees of latitude or 300 miles. 3. A LONGITUDE scale in the bottom right hand corner. This is the key to using the plotting sheet. You will recall that on a Mercator chart the Latitude scale is expanded as the latitude gets higher (i.e. farther from the equator) so that the Longitude scale stays the same and the meridians and parallels remain at 90 to each other.?? Suppose we fixed the latitude scale. What will then happen to longitude on this variation of the Mercator projection? 26 The fixed latitude scale runs conventionally from North to South through the True compass rose. Bear in mind that DISTANCE is measured on the LATITUDE scale. The unusual feature is that the longitude scale has to be derived from the block at the bottom right. With a latitude of 0 one degree of longitude should equal one degree of latitude.?? Check it now for yourself. Normally the latitude scale expands as latitude increases on a Mercator chart. If we keep the latitude scale constant the longitude scale must reduce as latitude increases.?? Think about it and then check with the plotting sheet. You will find that the longitude scale changes with latitude and that there is a graph spanning latitude 0 to latitude 70. Make sure you can spot this and also that you can identify how the longitude is made up from 5 blocks of 10 of longitude marked (confusingly) from 0 to 50 plus one more finely subdivided area with each line spanning 2 and again marked from 0 to 10. One of the more common errors is to set your dividers on 0 and 50 and then assume you have measured a degree of longitude. YOU HAVE NOT!?? What have you measured? 27 Sun Sights Page 20 of 36

23 Chapter 8 - Using the Sheet is Straightforward?? Take a plotting sheet now and follow these steps to plot the example below. The plotting sheet copies from page 27 onwards show you how the plot is built up. We need to plot the following position line. CP is 49 N 29 W, Z n is 315 T and intercept is 15 miles away.?? Make sure you know what these terms mean if you have forgotten then go back to the appropriate lectures and revise before proceeding. Step 1 - Customise the sheet (page 27) The objective is to decide on the latitude and longitude scales that are most appropriate for our plot and annotate the plotting sheet. 1. Mark the LATITUDE in whole degrees and mark that against the central East - West line on the plotting sheet. We can now plot any latitude relative to this that fits on the sheet and page 27 shows you the end result. Remember that we do not have to plot our CP at the centre of the plotting sheet. We can adjust the sheet to suit our needs and if our vessel were on a NW course we might well want to plot our CP off centre to allow for her movement. This would be the case if, for example, we plan to use a transferred position line (covered earlier). 2. Mark the LONGITUDE in whole degrees - usually we will use the centre of the sheet but, once again, any point will do. 3. Identify the longitude scale to use (on this course it will always be the one for 50 North or South but don t be fooled; in real life it will often change during a long passage). Step 2 - Plot the CP (page 28) The technique we are using gives us an azimuth and intercept from the Chosen or Assumed Position.?? Can you correct this statement? The CP always has a latitude and longitude which are rounded to the nearest whole degree to make plotting easy Mark in the latitude and longitude for the CP. 2. In our case for simplicity we have a CP longitude as a whole number of degrees. Normally the minutes of longitude will not be zero. 3. Page 28 shows you this stage with a CP of N, W. Step 3 - Plot Z n (page 28) Take another look at page 28. We have plotted our CP and the next step is to plot Z n. In our example it is 315 and we have plotted it correctly. Step 4 - Plot the position line (page 29) 1. We have an intercept of 15 miles AWAY. This means that we need to plot the position lines 15 miles from our CP and that it is 15 miles further from the observed body s GP than the CP. In other words it is AWAY from the GP so we extend our bearing line in the opposite direction. Page 29 shows you this step. Sun Sights Page 21 of 36

24 2. The intercept is 15 miles so we measure 15 miles or minutes of latitude USING THE LATITUDE SCALE OF THE PLOTTING SHEET (This is the North - South centre line) and mark it on the plot. 3. The final step is to mark in our position line. Page 29 shows you all the final steps. Some hints and tips The common problems that most people have with a plotting sheet revolve around the scale of the sheet and the confusing number of lines. Here are some hints. 1. The intercept may be a very short line on the plotting sheet so use a sharpened pencil and work accurately If you have access to an enlarging copier you can expand the plotting sheet. 2. One position line does not make a position so we are going to end up with a confusing plot. The example overleaf shows you a convention that will help: 2.1. MARK each CP with a label (Sun 09:00, Moon 1, Polaris etc) 2.2. Plot the Z n as a dotted or dashed line to differentiate it from the position line. In the example on page 30 there s a plot of the sun t 09:00 with an azimuth of roughly 210 T and an intercept of 70 miles AWAY Mark the position line as shown in the picture. The arrows on the position line point to the observed body s GP. 3. On a voyage you can expect to be working in a particular hemisphere and with an East or West longitude. In this course you could be working with any combination. Before you plot anything do please stop and think! For example - Latitude in the Southern hemisphere increases in a Southerly direction! This is one of the most common plotting errors. Sun Sights Page 22 of 36

25 Chapter 9 - Plotting a Position Sun sights The sun is available to be used throughout the day and so it is particularly convenient. It is common practice to take a sun sight, wait for a few hours and take another. This is in contrast to a set of star sights which are taken, to all intents and purposes, at one time (morning just before the sun rises or in the evening just after it sets). Sun sights demand a different plotting technique called a running fix and it is described below. Star sights We will have a number of sights taken at roughly the same time. At yacht speeds we will make no significant error by plotting a set of sights taken over a period of several minutes as though they had been taken simultaneously. Because the set of sights will use a number of observed bodies it is almost certain that each will have its own CP, Zn and intercept. Repeat the process for each observation and our position is where the group of position lines. There s likely to be a cocked hat and the usual rules apply but with an added twist. It will not usually be possible to nip up on deck and retake the sights. Fortunately in mid ocean even quite a big cocked hat will usually be acceptable and a twelve hour wait till the next star sight window will not cause too many problems. Transferring a position line We could well have a position line from a morning sight, a latitude and, in an ideal world, a position line from an afternoon or evening sight. We need a technique to allow us to use all three position lines (remember that a Latitude is no more than an East - West position line) to establish the vessel s position and the running fix is the technique to use.?? If you know how to plot a running fix you can skip the next section. We are making assumptions about our vessel s speed and course and any ocean current that may be present (though that is ignored in this course). We can make a good stab at the first two.?? Can you think of a way, on passage, to establish the current? 29 Running Fixes Let s start with the technique in general and familiar terms by thinking about coastal navigation. We ll look at a couple of ocean points later on. Figure 13 shows the basic approach. The technique is summarised in Figure 14 and Figure 15. A running fix starts like any other with a position line. It is absolutely vital to note the time and log reading as well as the bearing. Plot the first position line. It is then necessary to wait until the position has The assumed EP is a standard EP taking full account of tidal drift and leeway. Assumed EP 11:00, log 170 Second position line Running fix 220 o M Chosen object Transferred line (mark with a double arrow) passing through assumed EP Figure 13 - The running fix Tower. 09:30, log 163 First position line Sun Sights Page 23 of 36