Celestial Navigation - Ynot Sailingynotsailing.com/Celestial/Part3.pdf · 12.1.4. Almanac –...

Celestial Navigation

1-1

Rev 5 © Ynot Sailing 2011

11. Plotting

11.1. Objective In this section you will learn how to set up and use universal plotting sheets

11.2. Plotting Sheets There are commercially available Universal Plotting Sheets that are 13 by 14 inches, double sided, and come in packs of 50. However on the next page you will find a smaller version (8 ½ x 11) that is perfectly adequate. There are also 2 pdf files on the course CD that will allow you to print as many as you like at 8 ½ x 11 and also 11 x 17 inches.

11.3. Preparing the Plotting Sheet Before you can start any plotting you must customize the plotting sheet to be useful for your latitude and longitude. Here are step by step directions.

1. Select the middle horizontal line to be the latitude of the AP. Label the lines at 1º intervals.

2. To add the longitude lines to your plotting sheet use the scale on the top right hand quadrant of the compass rose. For example, when working at latitude 36° draw a vertical line though 36º on this scale. Now draw another line on the opposite side as shown. Label the middle line as the whole degree of longitude nearest to your AP.

3. The marks on the central vertical line are minutes of latitude which of course are equal to nautical miles. Measurements anywhere on the plotting sheet may be made by using dividers to transfer distances to this scale.

4. The scale in the corner is used to measure minutes of longitude. To use it, find your working latitude on the scale on the right edge and draw a horizontal line through the scale. Now, minutes of longitude may be measured along this horizontal line.


Page 11-2



Page 11-3


11.4. Plotting an Intercept (NAO and H.O.249) So to plot our LOP we must first plot the AP. The latitude of the AP will always be a round number of degrees. It is the latitude that was used to enter the tables. In the example this was 36ºN. The AP longitude will be the number that was used to get a round number for the LHA. In the example this was 009º 13.7’W. Having plotted the AP draw a line at the azimuth angle through the AP. Measure along this line the distance equivalent to the difference between Ho and Hc, towards or away from the AP depending on which is greater, and draw a short line at 90º to the azimuth line. This straight line is the LOP; you will remember that it is in fact a small segment of a COP.

To determine whether to draw the LOP toward or away use the name of a well-known Japanese navigator, Captain Homoto, as a memory aid;

HoMoTo = Ho More Towards.

Another memory aid is Coast Guard Academy = Calculated Greater Away.

Use the plotting sheet on the previous page to plot the intercept from the example.

Do not fall into the trap of assuming that the intersection of these two lines is your position. The last line you drew is only a segment of a Circle of Position. You could be anywhere on that circle! You can consider it to be a LOP and as you will remember from Coastal Navigation you need at least two, preferably three, LOPs to get a fix.

There will be exercises later that will demonstrate this.


Page 11-4



Page 12-1


12. Sight Reduction – Stars, Moon, Planets A lot of what you learned when reducing the Sun sight will also apply to the stars, the moon, and the planets. In this section we will focus on the differences. So pull out a sight reduction form and follow along as we work through each section of the form.

12.1.1. Sight Data Section This section is used in exactly the same way no matter which type of body is being used. When using the Sun and the Moon remember to identify which limb is used.

12.1.2. Time Section This section is used in exactly the same way no matter which type of body is being used.

12.1.3. Almanac –LHA When working with stars the SHA is used in conjunction with GHA Aries to determine the LHA of the star. Refer back to sections 6.6, 6.7, & 6.8 if you need a refresher.

When working with the planets and the moon the v value and corresponding correction from the increments pages must be included.

12.1.4. Almanac – Declination When working with the Sun, the planets, and the moon the d value and corresponding correction from the increments pages must be included.

Look at the GHA and Dec columns to decide the polarity of the v and d values respectively. Don’t try to remember when the d and v factors need to be applied. Just look at the data on the Nautical Almanac daily page. If the body you are using has either (both in the case of the Moon) then the correction needs to be applied.

12.2. Sextant This section is used in exactly the same way no matter which type of body is being used.

12.3. Altitude Corrections

12.3.1. Sun, Stars and Planets The altitude corrections are found on Tables A2 and, for low altitude sights, A3. Please note that the individual planets have an additional correction that is date sensitive.


Page 12-2


12.3.3. Moon All the altitude corrections for the moon are found on pages xxxiv and xxxv towards the back of the Nautical Almanac. For convenience the Dip table has been repeated on page xxxiv. In addition to the altitude correction there are two additional corrections to be applied.

a) When using the upper limb 30’ must be subtracted and,

b) a correction for Horizontal Parallax (HP) must also be applied.

The instructions on page xxxiv are very clear but here is an example.

Date: May 8th 2007 Time: 08-37-42 GMT

Ha is 27º 47.2’.

Moon Lower limb.

HP from the almanac daily page at 08 hours is 56.6

To determine the altitude correction use the top part of the table.

Ha is the argument and gives a correction of 59.8.

To determine the HP correction use the bottom part of the table in the same column as used for the altitude correction with the HP value from the daily page as the entry argument. In this case the HP correction is 3.8.

Both corrections are added.

Ho = 27º 47.2’ + 59.8’ + 3.8’ = 28º 50.8’


Page 12-3


12.4. Sight Reduction Exercise - 3 Stars In all of the following exercises the difference between Hc and Ho will never be more than 10’.

The date is 23 Feb 2007. Your DR position is 45º 45.0’N 045º 45’W. The magnetic variation is 10º E.

The table below is your sight data sheet from your dawn session.

WT Hs Body Brg IE Ht Eye Watch Error

06-33-22 49º 13.8’ Deneb 055º 1.9 on 10 ft 7 Secs slow

06-33-52 17º 43.0’ Antares 165º 1.9 on 10 ft 7 Secs slow

06-34-48 41º 41.1’ Dubhe 310º 1.9 on 10 ft 7 Secs slow

What is your position and how far are from your DR position?

12.5. Sight Reduction Exercise - 3 Unidentified Stars The date is 7 May 2007. You are just north of Corsica in the Mediterranean; your DR position is 43º 40.7’N 008º 37.6’E. The variation is 12º W.

The table below is your sight data sheet from your dawn session. The bearings were taken with a hand bearing compass.

WT Hs Body Brg IE Ht Eye Watch Error

04-44-17 23º 31.6’ ??? 290ºM 1.5 on 10 ft 1-12 slow

04-45-22 31º 53.4’ ??? 093ºM 1.5 on 10 ft 1-12 slow

04-46-39 54º 44.7’ ??? 182ºM 1.5 on 10 ft 1-12 slow

1. Identify each of the stars. 2. Which is the brightest of these? 3. Which is the dimmest of these? 4. What is your position? 5. How far are you from your DR position?


Page 12-4


12.6. Sight Reduction Exercise – Moon The year is 2007 and all sights were of the Moon lower limb.

Use the sight reduction forms that you will find in the appendix.

For all the examples the height of eye is 9 feet and the index error is 4.3’ off. Ignore daylight saving time.

DR L DR Lo Date Time Watch Error Hs

1 45° 34.9’N 073°37.1W 9 May 05-55-38 25 sec slow 22° 09.7’

2 35º 09.2’N 075° 18.8’W 13 Jun 04-35-32 14 sec fast 16º 32.7’

3 35° 15.4’N 005° 19.6’W 22 Jun 14-37-37 19 sec fast 24° 44.7’

4 45º 34.9’S 018° 47.7’W 18 Jul 15-50-18 38 sec slow 38° 17.9’


Page 13-1


13 Latitude from the Sun

From the diagram we can deduce that:

Zenith Distance = 90º - Altitude ZD = 90º - Ho

Latitude = Zenith Distance + Declination L = ZD + Dec

Substituting for ZD L = 90º - Ho + Dec

The altitude (Ho) we get with the sextant. The Declination we look up in the Nautical Almanac. Remember to use the declination for noon at your longitude not noon at Greenwich! If we make sure we measure the angle when the Sun is at its highest point in the sky it must be local noon. We do not need accurate time because the Sun’s altitude changes very little either side of noon - it seems to hang in the sky for a few minutes. Determining Latitude is then just some simple math.


Page 13-2


13.1 Noon Sight Scenarios

There are three possible scenarios involving taking a noon sight of the Sun.

In the list of scenarios below scenario 1 is covered by the previous explanation.

Your homework task is to develop formulae for scenarios 2 and 3. Draw some sketches similar to the diagram on the previous page to help you visualise the interactions of the various angles.

1. The latitude of the observer and the declination of the Sun both have the same name with the latitude numerically greater.

2. As above but the latitude of the observer is the opposite name to the declination of the Sun.

3. The latitude of the observer and the declination of the Sun both have the same name with the latitude numerically less.

Now all of the foregoing apply to any body at its meridian passage. For bodies other than the Sun there is a fourth scenario. If you want to torture your mind further go ahead and identify the scenario and develop a formula for it.

This is a situation that only extreme sailors will encounter. This is definitely not required for the CYA exam!


Page 14-1


14 Latitude from Polaris The distance from the Earth to Polaris is

so large we can consider that the light rays are parallel anywhere on Earth.

From the diagram we can deduce that:

Ho + 90º - Lat = 90º

Rearranging the equation we get:

Ho = Lat

Unfortunately it’s not quite that simple because, contrary to what you may have been led to believe, Polaris is not exactly in line with the Earth’s North Pole; however it is never more than 1⁰ away. Consequently there are three simple corrections to be applied.

Here’s the Polaris sight reduction process:

Make all the usual corrections to Hs to get Ho

Determine LHA Aries (rounded to the nearest degree)

Turn to the Polaris table towards the back of the Nautical Almanac and look up ao from the top part of the table using LHA Aries as the entry argument.

Using your approximate latitude look up a1 from the next part of the table staying in the same column as the LHA.

Look up the a2 value for the appropriate month from the next part of the table again staying in the same column as the LHA.

The formula for latitude is:

Lat = Ho -1º+a0+a1+a2

Don’t bother trying to remember this formula. It is given at the bottom of the first page of the Polaris tables.

A sight reduction form specifically for Polaris is included in the appendices.


Page 14-2


14.1. Latitude from Polaris Exercise Determine the latitude for each of the following.

Dates are 2007; Watch error is 1 min 34 sec fast.

Use the Polaris sight reduction forms in the appendix.

DR L DR Lo Date Time Hs IE Ht (ft) Lat

1 48°34.9’N 062°21.8’W 18 Jul 15:48:12 48° 20.0’ 2.0’ on 6 2 51° 56’N 001° 51’E 13 Jun 12:56:29 52° 24.1’ 2.3’ off 9.5 3 45° 37’N 044° 26’W 9 May 11:16:38 46° 18.5’ 2.3 on 10 4 36° 42’N 045° 57’W 22 Feb 14:17:42 37° 24.2’ 2.1 off 8 5 10° 37’N 060° 18’E 21 Jun 16:14:22 10° 31.4’ 0 10 6 25° 37’N 060° 18’E 20 Sep 13:14:22 25° 07.2’ 1.2 on 8

15. Compass checking

When completing any sight reduction azimuth, the true bearing, to the body’s GP is obtained. If the body is low enough for its bearing to be measured using the steering compass it gives an ideal way to check the deviation. For example the Zn of a star is 197º, the variation 13ºE and the compass reads 188º. Fill in what you know.

T V M D C 197º 13ºE 188º

The magnetic can be calculated

T V M D C 197º 13ºE 184º 188º

The Deviation can be calculated

T V M D C 197º 13ºE 184º 4ºW 188º

This deviation of course relates to the boat’s heading at the time the bearing was taken. Exercise 15-1 Compass Checking

1. On 22nd June 2007 while taking sights at evening twilight you notice that Venus is almost dead ahead and low enough to get a good bearing. Watch error is 6 seconds fast, your index error is 4’ on the arc and your height of eye is 10. Your DR position is 47° 14.0’N 067° 18.0’W. Your course is 265°T and your speed 4.0 knots. The boat’s heading is altered at 20-36-42 to point at Venus and the steering compass reads 296º. Variation is 8ºW. What is the deviation?


Page 16-1


16. Compass checking When completing any sight reduction azimuth, the true bearing, to the body’s GP is obtained. If the body is low enough for its bearing to be measured using the steering compass it gives an ideal way to check the deviation.

For example the Zn of a star is 197º, the variation 13ºE and the compass reads 188º.

Insert what you know T V M D C

197º 13ºE 188º

The magnetic can be calculated

T V M D C 197º 13ºE 184º 188º

The Deviation can be calculated

T V M D C 197º 13ºE 184º 4ºW 188º

This deviation of course relates to the boat’s heading at the time the bearing was taken.

16.1. Compass Checking Exercise 1. On 22nd June 2007 while taking sights at evening twilight you notice that Venus is

almost dead ahead and low enough to get a good bearing. Watch error is 6 seconds fast, your index error is 4’ on the arc and your height of eye is 10. Your DR position is 47° 14.0’N 067° 18.0’W. Your course is 265°T and your speed 4.0 knots. The boat’s heading is altered at 20-36-42 to point at Venus and the steering compass reads 296º. Variation is 8ºW. What is the deviation?


Page 17-1


17. Great Circles

17.1. Objective

To be able to calculate the great circle distance between any two point s on the Earth’s surface.

17.2. Introduction

The shortest distance between any two points on the Earth’s surface is part of a great circle. When planning ocean voyages of several hundreds of miles it is typically a great circle route that is chosen providing of course it does not cross any land masses or dangerous areas.

Gnonomic chart projections can be used but the method of determining distance is not easy or intuitive. Using the exact same process that you have learned to perform sight reductions you will be able to calculate the distance between any two points and the initial course to steer.

The sight reduction tables provide solutions to spherical triangles and therefore can be used to determine the great circle distances by using the .

17.3. Method

The entry arguments to the tables are Lat, LHA, Dec.

Lat = Latitude of point of departure.

LHA = Difference in Longitude between departure and destination.

Dec = Latitude of point of destination.

Great Circle Distance (nm) = (90⁰-Hc) x 60

Zn = Initial course to steer.

17.4. Exercise

Calculate the great circle distance and the initial course to steer from Halifax to Gibraltar.

Halifax 44° 40’ N, 63° 37’W Gibraltar 36°7’N, 5 20’W

The answer is 2651nm and 80.1⁰.

Your answer should be close but not exactly the same. Explain why.

Celestial Navigation - Ynot Sailingynotsailing.com/Celestial/Part3.pdf · 12.1.4. Almanac –...

Documents

Transcript of Celestial Navigation - Ynot Sailingynotsailing.com/Celestial/Part3.pdf · 12.1.4. Almanac –...