sun sights and plotting

RYA Yachtmaster Ocean

Sun Sights and Plotting

RYA Yachtmaster Ocean Theory Course

Sun Sights Page 1 of 36 © Tiller School 2006 Yachtmaster Ocean Course Version 08 - j

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.



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........................................................................ 10

CHAPTER 4 - CALCULATED ALTITUDE – THE BASICS ..................................................................... 12 GENERAL PRINCIPLES - A REMINDER ............................................................................................................... 12 SOLVING THE PROBLEM................................................................................................................................... 12 INTRODUCING THE AP TABLES ........................................................................................................................ 12 THE CHOSEN POSITION ................................................................................................................................... 13

CHAPTER 5 - CALCULATED ALTITUDE - APPLYING THE TABLES............................................... 16

CHAPTER 6 - PLOTTING.............................................................................................................................. 18 PLOTTING SHEETS AND CHARTS....................................................................................................................... 18 PLOTTING A POSITION...................................................................................................................................... 18 PLOTTING OPTIONS.......................................................................................................................................... 19

CHAPTER 7 - THE PLOTTING SHEET WITH THIS COURSE.............................................................. 20

CHAPTER 8 - USING THE SHEET IS STRAIGHTFORWARD............................................................... 21 STEP 1 - ‘CUSTOMISE’ THE SHEET (PAGE 27) ................................................................................................... 21 STEP 2 - PLOT THE CP (PAGE 28)..................................................................................................................... 21 STEP 3 - PLOT ZN (PAGE 28)............................................................................................................................. 21 STEP 4 - PLOT THE POSITION LINE (PAGE 29) ................................................................................................... 21 SOME HINTS AND TIPS ..................................................................................................................................... 22

CHAPTER 9 - PLOTTING A POSITION ..................................................................................................... 23 SUN SIGHTS ..................................................................................................................................................... 23 STAR SIGHTS ................................................................................................................................................... 23 TRANSFERRING A POSITION LINE ..................................................................................................................... 23 RUNNING FIXES............................................................................................................................................... 23 ASTRO NAVIGATION IMPLICATIONS:................................................................................................................ 24

CHAPTER 10 - PLOTTING SHEET WORKED EXAMPLES................................................................... 26

CHAPTER 11 - SUN - RUN - SUN ................................................................................................................. 31

CHAPTER 12 - TRANSFERRED POSITION LINES AND EP’S .............................................................. 32

CHAPTER 13 - CAN YOU HELP FRED?..................................................................................................... 33

CHAPTER 14 - ANSWERS ............................................................................................................................. 34



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 30th 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 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.

© Tiller School 1998 31

Geographical Position GPGeographical Position GPGP - the point on the earth’s surface on a line between thecentre of the celestial sphere and the body

GP - has a Latitude &Longitude



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.



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 24th. This means that at the moment of Mer Pass on February 24th 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.

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

LongitudeLongitudeTerrestrial

Equator

Prime Meridian

W 900

Measure WEST

Measure EAST

1800

E 900

The Prime Meridian is an artificial reference point which, by agreement, passes through Greenwich

North Pole

‘We are looking DOWNWARDS at the N Pole’

Figure 1 - longitude revisited

Astro ‘Longitude’ Astro ‘Longitude’ -- the GHAthe GHA

Greenwich Hour Angle - ‘the angle at a point in time between the prime meridian and the meridian of the body’

Celestial

Equator

Prime or Greenwich Meridian

North Pole

GHA =1100

Looking ‘down’ from above the N Pole

GHA is only measured clockwiseGHA is only measured clockwise

Figure 2 - GHA



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.

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.

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

GHAGHAGreenwich Hour AngleGreenwich Hour Angle

GreenwichMeridian

00

900 1800

2700

GHA 2200

Figure 3 - GHA

Sidereal ‘Longitude’Sidereal ‘Longitude’

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.

Celestial

Equator

First Point of Aries

North Pole

Greenwich Meridian

Figure 4 - Sidereal longitude

First Point of AriesFirst Point of Aries

Celestial Equator

Eclipt

ic

North

South

230 27’ N

230 27’ SFPA - the point where the sun’s ecliptic crosses the celestial equator. FPA rotates around the earth in 24 hours approximately.

Figure 5 - FPA



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 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 360° - 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

Sidereal Hour AngleSidereal Hour Angle

Celestial equator

SHA

Celestial North Pole

First Point of Aries

Star’s Meridian

Prime Meridian

GHA of Star = GHA FPA + SHA for star

GHA of FPA

Figure 6 - SHA

The position of a heavenly bodyThe 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.

Figure 7 - heavenly position

The heavenly bodiesThe heavenly bodiesStars– ‘constant’ SHA and declination relative

to FPA • slow change over time • ‘fixed to the celestial sphere’

– GHA for FPA is tabulated for usSun, Moon and Planets– move across celestial sphere

• GHA and declination tabulated for specific times in Almanacs

Figure 8 - the heavenly bodies



'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.

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.

Finding the sunFinding 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

Local Hour AngleLocal Hour Angle

GreenwichMeridian

Observer’sLocal meridianis 560 W.

GHA 2200

LHA 1640

Figure 10 - LHA 1



?? 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.9

1. 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

1. Local noon is at 16:45 GMT. At that time a. What is our longitude? b. What is the sun’s GHA and LHA?

2. A star has an SHA of 132° 33’.7 and FPA is 073° 04’.1 a. What will be its LHA if we are at 15° W? b. If SHA was 332° 33’.7 what would the LHA be?

Local Hour AngleLocal 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 earthLHA body = GHA body -West

Longitude or +East Longitude.

Figure 11 - LHA 2

Hour AnglesHour AnglesThe measurement datumThe 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)

Figure 12 - hour angles summarised



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

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.

The sun’s bearing changes duringthe day

This drawing applies to the N hemisphere

‘The sun’s azimuthchanges during theday from roughly E atsunrise to roughly Was it sets.’

Position lines from the sun

This drawing applies to the N hemisphere

‘This means that theposition line alsorotates so by choosingour times we can get agood angle of cut.’



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!



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 Ho. 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 Hc .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 26 - 29 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.



• 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 HC, 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 1/10th 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 50° 17’W and GHA 97° 03’ then the precise LHA would be 46° 46’ (97° 03’ minus

50° 17’). • The Chosen LHA would be 47° (97° 03’ - 50°03’) and the Chosen Longitude 50° 03’W.



• 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 51° 03’W (97° 03’ -51° 03’).

• So to put it another way if GHA is 97° 03’ we chose our longitude as 50° 03’W (within 30’ of 50° 17’W) and subtract it to give an LHA of 47°

Here’s another example:

The Sun’s GHA is 235° 43’and DR Long. is 14° 27’W, work out the chosen LHA and CP. • The accurate LHA is 221° 16’ (i.e. GHA (235° 43’) – 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 14° 43’W (we have to use a value for the minutes that makes the LHA a whole number of degrees). The LHA is 221° (235° 43’ minus 14° 43’).

?? Had our DR long been 150 01’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 50° 17’E • GHA is 97° 03’ • CP Long 49° 57’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° (97° 03’ + 49° 57’).

Note that 49° 57’ is a better CP Long than 50° 57’ 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 50°57’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 49° 57’ is a lot nearer to 50° 17’ than either 50° 57’ or 51° 57’ so we choose 49° 57’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)



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

Chosen Longitude

93° 45’ 021° 34’W 86° 15’ 022°50’W 284° 45’ 033° 18’E 286° 11’ 043°10’E ?? 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

Chosen Longitude

21 June 1980 11h 34m 5s 121° 23’W 25 Feb. 1980 13h 28m 10s 026° 36’W 22 Sept. 1980 09h 31m 43s 019° 41’E



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 30 –31. ?? 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 112°.

2. 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?20

3. Work out the correct HC. 3.1. We obtained a value of +48 for ‘d’. It helps if we understand what this means so

look at the value of HC for declinations of 12° and 13°. ?? Work out the difference in minutes? 21

3.2. 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 46 - 47.

3.3. We know the minutes of declination and that HC changes by 48 minutes per degree of declination at this LHA. We could guess that HC 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 30.

3.4. The correction to be applied is therefore 30’, the sign of ‘d’ is positive so we ADD this correction. HC therefore becomes 34° 48’ (34° 18’ plus 30’).

4. Convert the tabulated Azimuth (Z) to a True Bearing (Zn). It is called Zn 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 ZN = Z so ZN has a value of 115° T.



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, 16° 45’W; LHA 055, Declination N 11° 41’. Work out the HC 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 HO were 30° 55’ then GOAT tells us that the intercept is AWAY (observed less than calculated). The length of the intercept is simply the arithmetic difference between HC and HO 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.



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 (ZN) 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.



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.



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



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, Zn 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’. 28

1. 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 49° 00’N, 29° 00’W.

Step 3 - Plot Zn (page 28) Take another look at page 28. We have plotted our CP and the next step is to plot Zn. 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.



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.

1.1. 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 Zn 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.

2.3. 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.



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

Running fixRunning fix

Tower. 09:30, log 163

11:00, log 170

220oM

‘AssumedEP’

Transferred line(mark with a double arrow)passing through ‘assumed EP’

Chosen object

First positionline

Second position line

The ‘assumed EP’ is astandard EP taking full account of tidal driftand leeway.

Figure 13 - The running fix



changed significantly. The rules on 'angle of cut' apply to this type of fix and ideally the bearing needs to change by at least 45° (three hours in astro terms) and preferably more.

Once the required change of angle has occurred another bearing is taken, time and log reading noted and the second position line plotted. It's now time to do some more chartwork.

The concept is that we are going to move the first position line by the DISTANCE and GROUND TRACK that the boat has moved between taking the two bearings of the object on shore. If we can do this successfully then the boat's position is where the two position lines cross. It is not difficult in principle though practical problems can affect the accuracy.

?? If we move the first position line in the way described above what plot do we need?30

You probably got the answer - we need to work out the boat's EP and to take as full an account as we can of the actual course steered, the leeway and tidal streams.

There's a problem though - an EP needs a starting point and we don't have one. It doesn't matter because we have a position line and, by definition, our boat must lie somewhere along that line.

So we pick any point on the line and work out our 'assumed EP' as accurately as possible from the start point we have selected.

All that remains is to transfer the first position line so that it runs through the 'assumed EP'. The boat's position is fixed where the two position lines actually cross. Remember to identify the transferred line with a double arrow and that's 'all there is to it'!

Astro navigation implications: This technique used to be used for coastal navigation and is the one we have to employ for astro navigation. Here’s a set of questions and answers that should help you.

1. Where do we start? Plot the first CP, intercept and azimuth in the normal way 2. What starting position do we use for transferring the position line? Any point on the first

position line will do. 3. How far and in what direction do we transfer the line? By the distance covered between

the first sight and the second in the direction the ship was heading. Apply any ocean current drift if it is significant (in this course it is ignored).

4. What about a third position line? Move the first two in the distance and direction the vessel travelled between the second and third sights.

5. Are there any timing implications? Yes, the normal rules apply on angle of cut so we need to time the sights to allow for this. ?? For example a morning sun sight at 08:00 transferred to a noon sight (latitude) will give an angle of cut of what?31

Running Fix (1)Running Fix (1)

Identify objectTake bearing– Note time and log– Plot it

Continue on passageWhen bearing has changed significantlyGet new position line

Figure 14 - The running fix (1)

Running fix (2)Running fix (2)

From any point on the original positionline– Assess ‘EP’ - distance, direction and tide– Move position line to ‘EP’– Plot with ‘double arrows’Fix is where ‘moved line’ and secondline crossKEY IS ACCURATE ‘EP’

Figure 15 - The running fix (2)



6. How accurate is this procedure likely to be? In the real world we would expect, and will usually find, that the plot results in a ‘cocked hat’ which may well span several miles. This would be quite acceptable in mid-ocean and the error will be of little consequence.

7. Do I place my first CP somewhere close to the centre of the plotting sheet? For a set of star sights this would normally be the best technique. If you plan to transfer a position line you may wish to offset the first fix to one side of the plotting sheet to try to get everything on one sheet. Incidentally you work out which side of the sheet to start by remembering which way the vessel is moving!

?? If you would like some practice now then try these:

Here are some important reminders: 1. The plotting sheet scale is small - use a sharp pencil and be as accurate as possible when

plotting bearings and measuring distances 2. Use the correct LONGITUDE scale on the plotting sheet. 3. Label each CP and use the correct chart annotations - even if you do not get lost we probably

will if there is a mistake in your coursework!

1. EP is 490 47’N 150 02’W. Observations were made of the sun and moon at the same time (near enough). Plot the position if: 32

Sun CP 500 N 150 18’.3 W Intercept 7’ towards 1980T Moon CP 500 N 140 56’.4W Intercept 13’ towards 1260T

2. EP 500 11’N 070 19’W. Following stars were observed. Plot the position if:33

Polaris latitude 500 07’.8N Mirfak; Intercept 3’.9 away from 0390T through the EP Arcturus; Intercept 1’.9 towards 2760 T through EP Kochab; intercept 2’.6 away from 3350 T through the EP

The next step is to work on, complete and submit RYA Exercise 6. Then return to the lecture on Sun Sights at the chapter on Sun – Run – Sun.

At long last we can combine all our hard won knowledge and start to work out AND PLOT a position; useful navigation at last.



Chapter 10 - Plotting Sheet Worked Examples



50 N

30 W

1 degree oflongitude.



50 N

30 W

1 degree oflongitude.

CP is 49 N 29 W

Zn is 315 T



50 N

Measure 15 mileson the latitudescale, mark thepoint and draw aposition line at90 degrees to Zn.

Intercept is 15miles AWAY soextend the line inthe reciprocal of315 T



Sun09:00



Chapter 11 - Sun - Run - Sun We are all familiar with the concept that the sun rises in the East and sets in the West. In the Northern hemisphere it runs to the south of us during the day. The opposite applies in the Southern hemisphere and the sun passes north of the observer.

This gives us a useful and powerful navigational technique. The sun - broadly speaking - is going to move in a 180° arc during the day although the actual angle depends on the latitude and the sun's declination (i.e. the time of year). If our boat were motionless in the water with no current affecting her movement we could establish her position with two or three sun sights.

Suppose we took two sun sights with six hours between them. The two position lines would be at 90° to each other (remember that the sun 'moves' at 15° per hour) and we would end up with a fix. Add a noon latitude sight and we end up with a pretty good fix. We could improve it a bit if we made the interval between the sights four hours - provided that the sun were visible - to give an optimum angle of cut with three position lines.

This is an invaluable concept. It is not particularly time sensitive and provided that we can get reliable sun sights separated by several hours we will get a fix - it may not be optimal in the sense of its angle of cut - but in mid ocean there will always be another chance tomorrow.

The Sun - Run - Sun fix takes this principle one step further by allowing for the vessel's movement.

?? Summarise briefly the technique for transferring a position line. If you cannot remember then it is time to revise the running fix we covered when learning about plotting.34

?? Take the example above - try extending that sun sight. Assume a meridian passage latitude of 50° 11’.1N on the same day with a ship’s course of 085°T and speed of 4.5 knots and find your position.

?? There’s an optional exercise in Chapter 13 to help you remember the theory and put it into context.



Chapter 12 - Transferred Position Lines and EP’s In the examples used by the RYA course material, the sun-run-sun sights all use pairs of sights on the same day, and with modest distances run between them. Bear in mind that, in real life, you might have been waiting several days for the sun to appear through the clouds for a second time. Alternatively you may be on a very fast vessel and have covered a great distance between sights (one reason why the plotting sheets are so big). In this case you would not think of using the Estimated Position relevant to the first sight to establish the LHA for reducing the second sight. Why should you then, when the distance is not great. Take this opportunity to become familiar with the correct practice. A logical procedure to follow is to plot the first EP (EP1) on your plotting sheet when you plot your first Position Line. On the assumption that your work is accurate, you now know that you are on this PL somewhere, so it makes sense to “improve” your EP to the closest point on the PL since, in this dimension at least, your position is no longer an estimate. From this improved EP you can draw your Dead Reckoning run, the far end of which will be your new EP (EP2), which you will use to establish the LHA and Chosen Position for the reduction of your second sight, as well as being the point through which your transferred PL will now run, parallel to your initial PL.

Now complete and submit RYA Exercise 7

then move on to Using The Stars.

Important Exercise 7 reminder!

There are two types of sun sight. We’ve just been studying one; don’t forget the other!

?? What type of sight reduction should we use for a noon sight?35



Chapter 13 - Can You Help Fred? This is an optional exercise. We'll happily mark your answers for you.

‘Fred’ (that’s not his real name of course) set sail from Falmouth (300 miles West of Greenwich for practical purposes). He is now in his fifth day of the passage and has ‘enjoyed’ a SW wind dead on the nose for the whole time. He has been struggling to make a heading (roughly) of West en route for the Azores. Not good news!

His problems started when his electronics packed up, lock, stock and barrel early on the second day. They are still dead, and so will Fred, unless he can sort himself out. A large fish ate his trailing log impeller during the second night so he’s back to throwing bits of wood into the water and timing their passage. He’s guessing 4 knots, based on past experience or 100 miles per day.

He dug his trusty (but unused) sextant out and discovered to his amazement that although he had brought the Nautical Almanac and the AP3270 books he had forgotten all his Ocean theory notes and the textbook. Never a man to give up he decided that since he was beyond VHF range he had better re-learn his astro.

After a horrendous night - rough weather and a guilty conscience had left him with nightmares about time zones, hour angles, declinations and the like - he decided to write down his problems and then start puzzling things out.

1. Here are a few of the things that he was confused about - please enlighten him.

1.1. First Point of Aries has something to do with .... 1.2. If FPA is 283° 17’.1 and SHA of a star is 183° 51’.9 what is the GHA of the star?

1.2.1. If my longitude is 7° 31’.8W what is the LHA? 1.2.2. If my longitude is 135° 15’.8E what is its LHA?

1.3. Do we need the GHA of a body to know its declination? 1.4. The GP (which means ....?) is defined by what?

2. He was puzzled to find that his first attempt at a midday sun sight (more commonly called a ................ ?) was a failure. He nipped up on deck when he was five days out (5 days of b***** SW Winds in June he snorted) and at midday on his watch was staggered to find that the sun was rising / falling? Can you explain this and help him work out the right time for the sight? Mer Pass for the day was given as 12:02 so surely that should have been the sight time? He had worked out that the distance represented by one minute of latitude was roughly 1.5 minutes of longitude at his latitude but then got stuck!

3. The following day - June 21st he managed to get a midday sun sight. The result was as follows:

3.1. SA 58° 37’.3. IE -25’.0 Height of eye was 7 ft. What was his latitude? 3.2. If the time of the sight on his watch was 14h 13m 12s and his watch was 7 seconds

fast (according to Radio 4 which he could still just receive) can you give him guidance on a suitable EP for his afternoon sun sight that same day?

3.3. How long after local midday would be a good time to plan for a sun sight? 4. As a matter of interest - Fred’s brain was beginning to work again now he had some idea of

his position - he remembered something about Greenwich Date. Should he be worried when taking sun sights in his current position?



Chapter 14 - Answers 1 Your answers should be on these lines:

1. The world is divided into 24 time zones numbered from 0 (zero) to -12 in an Easterly direction and 0 to +12 in a Westerly direction. Time zone 0 is centred on the Prime or Greenwich Meridian.

2. 22:00 in Z + 10 means that we add 10 hours to get UT so it will be 08:00. We will have to change the Greenwich Date (GD) to 1st December.

3. Sextant Angle (SA) is converted to Apparent Altitude (AA) by removing the effects of the observer’s height of eye (DIP) and the mechanical Index Error (IE) of the sextant. This applies to all observations. The tables allow us to apply all the further ‘body specific’ corrections in one, or at most two or three, steps.

4. The Zenith of any body is defined as the line running from the centre of the earth through the body concerned. The Zenith Distance (ZD) is the ANGULAR distance between the Zeniths of two bodies. It is not a physical distance measured in miles.

2 The Meridian Passage sight gives us our latitude but not, directly, our longitude unless we know the time very accurately. It means that we are SOMEWHERE along the Parallel of Latitude and all we can say with some certainty is that we are not on land (assuming the sight was taken from a boat) and we know which ocean we are in. That still leaves an awful lot of uncertainty! Mer Pass is a specialised and simple example of using a sight to obtain a position line.

3 Your answers should on these lines:

1, 2, 3, 5 and 6 are all true. 4 is incomplete and a truer statement would be “GHA of a body minus LHA of the same body always equals the observer’s longitude. If the answer is negative then the NAME (East or West) of the longitude will be E and, if positive, it will be W.” Don’t forget that hour angles are always measured in a Westerly or clockwise direction whereas longitude is measured E or W of the Greenwich Meridian.

4 The date does not change. In other words a day is ‘lost’ across the date line and gained as midnight passes. 5 Mer. Pass is the time at which an observer will see the body reach its highest angle and just begin to fall. It marks the

point at which the body being observed crosses the observer’s meridian (of longitude). 6 YES. FPA has a GHA so we can find its ‘longitude’ from the tables (page 12 of RYA booklet). 7 Your answers should be:

• Declination is the astro equivalent of latitude. It is the angle of the body relative to the celestial equator. • SHA is the 'longitude' of a star - it is measured relative to a reference point called the First Point of Aries. • SHA of 120°E is invalid. • SHA is always measured clockwise and in this case it should be 240°. • Sun's GHA. • At 15:00 = 045°. • At 09:00 = 315°.

8 Subtract a WEST longitude from GHA to get LHA or ADD an Easterly longitude to get LHA. 9 Your answers should be:

• GHA sun = 130°. • With longitude 30°W the LHA is 100°. • With longitude 40°E the LHA is 170°. • Longitude with GHA 130° and LHA 100° is 30°W. • Star's hour angle is 270°.

• Longitude is 045°W and LHA star is 225°. 10 Your answers should be:

• Local noon is 16:45 GMT so Longitude is 71° 15' W. • Sun's GHA is 71° 15' and LHA is 0°. • Star's LHA is 132° 33'.7 + 73° 04'.1 - 15° 0' = 190° 37'.8. • 30° 37'.8 - i.e. subtract 360° from an angle that is > 360°.

11 By observing the sun when it crosses the observer’s meridian, calculating the Zenith Distance and modifying it to take account of the sun’s declination.



12 Broadly speaking it rises in the East and sets in the West. There’s an excerpt from the relevant table on RYA page 25

which gives us the bearing of the sun at various declinations and we can use this information (Lecture 9) to help us check the ship’s compass for deviation when on passage.

13 60 degrees because we are making the observations at 4 hourly intervals and one hour equals 15 degrees. 14 Actual LHA is 2350 43’ - 150 01’ or 220 42’. Chosen longitude should be 140 43’ and LHA 2210. If we had chosen a longitude of 150 43’ the resultant LHA would have been 2200 and chosen longitude 150 43’. Clearly this is further from the actual DR Long than 140 43’. 15

GHA DR Long LHA for AP tables

Chosen Longitude

93° 45’ 21° 34’W 72° 21° 45’W 86° 15’ 22°50’W 63° 23° 15’W 284° 45’ 33° 18’E 318° 33° 15’E 286° 11’ 43°10’E 329° 42° 49’E 16 Using the Increments and Corrections tables on pages 21 – 23 the answers are:

Date Time - UT GHA sun DR Long LHA for AP tables Chosen Longitude

21 June 1980 11h 34m 5s 353° 5’.3 121° 23’W 232 121° 5’.3W 25 Feb. 1980 13h 28m 10s 18° 44’.3 26° 36’W 352 26° 44’.3W 22 Sept. 1980 09h 31m 43s 324° 45’.8 19° 41’E 344 19° 14’.2E Note: If you used the conversion of arc to time table you will have introduced some minor errors. You must use the right

table. 17 No, we need to know the value and name of the declination of the observed body at the time of the sight. 18 Because the latitude and declination both have the same ‘name’ - North. 19 Hc 34° 18’, d +48, Z = 115. 20 The calculated altitude is for a declination of 12°. Our declination is, and this is the norm, not a whole number of

degrees; once again we have to interpolate. The azimuth can be named either East or West and the tables cater for both. There are simple rules that we follow to obtain the correct value.

21 35° 06’ minus 34° 18’ is 48 minutes and this is the value of ‘d’. ‘d’ is telling us that HC is increasing (+) by 48 minutes of arc for a change in declination of one degree.

22 From tables:

Hc = 30° 32', d = +48, Z = 111°.

‘d’ corr’n = 33’ so Hc = 31° 05’.

LHA is 055° so Zn = 360 - 111 = 249°T - see formula at top of page for Northern hemisphere. 23 ZX is part of a great circle and by definition one minute of arc equals one nautical mile. 24 Your answer should be:

TA 54° 42’.6.

Ships time 22nd 10h 30m.

LHA 330°, Chosen Long. 6° 47'.7W and chosen Lat. 50° N.

Declination 23° 26’.1N.

Intercept 4’.6 towards Zn = 128° T. When you start plotting you will see why we would round this answer to 5’. 25 This statement is true. 26 It means that if we had a set of charts covering the same range of longitude (20 degrees, let’s say) but differing latitude

ranges the WIDTH of the charts would vary with the widest charts being at the equator where a minute of longitude also equals nautical mile.

27 50 minutes of longitude.



28 ‘The CP is always rounded to the nearest latitude in whole degrees. The longitude is calculated to give an LHA in whole

degrees. 29 It should be possible by star fixes to establish our ground position over, say, 24 hours (e.g. take sights on successive

mornings or evenings) and an EP. Given reasonably accurate water speed / distance instruments the difference is likely to be the prevailing ocean current rate and set. Passage planning books and routeing charts also give information about ocean currents and the rates and sets that can be expected.

30 This is a way of defining the boat's EP. If you think about it for a moment the EP is exactly this - the boat's water track modified by her leeway and any tidal streams.

31 4 hours at 15 degrees gives an acceptable angle of cut of 60 degrees. 32 49 46 N 14 46 W 33 50 07N 07 21 W 34 All we do is to move the first (morning) position line by the distance and direction that the boat has moved and cross it with the noon sight. We could then transfer both lines to the afternoon sight's position line to give a three position line fix. In practice we can mix and match position lines so that a depth sounding or a single bearing of land or the position lines from any other astro sight can all be used to establish a position.

35 Meridian Passage sight to calculate a latitude.

sun sights and plotting

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