Tides Handbook

Tides / Astro Package

Table of Contents Table of Contents....................................................................... Contents................ ................................................................................................ ......................................... 2 Tides...................................................... ........................................................ .............................................................................. ...................... 4 Introduction..................... Introduction............................................................................ ................................................................................................ ......................................... 4 Tide and and Tidal Current Relationship............................................... Relationship............................................................................... ................................ 4 Causes of Tides .................................................... ........................................................................................................... ........................................................... .... 4 Causes of Tidal Streams..................................................................................... ............. 8 Types of Tides........................................................................ ......................................... 8 Canadian Reference Diagram ................................................ ....................................................................................... ....................................... 10 American Reference Diagram............................................................................ ........... 11 Aide-Mémoire Aide-Mémoire for Using Tide Tables........................................................................... 12 Canadian Reference Ports .................................................. ......................................................................................... ....................................... 12 Canadian Secondary Ports ................................................. ........................................................................................ ....................................... 12 American Reference Stations................................................................ .................... 14 American Subordinate Subordinate Stations................................................................................. 14 Tidal Stream Calculations............. Calculations..................................................................... ............................................................................ .................... 14 Tidal Stream Stream and Tides Tides Graphs................................................................. Graphs................................................................. .................... 14 Tides Graph...................................................... Graph............................................................................................................. ......................................................... .. 15 Tidal Stream Graph................................ Graph........................................................................................ ................................................................... ........... 16 Questions on Canadian Tide Tables ................................................... ................................................................................. .............................. 17 Part I. Standard Ports .................................................... .................................................................................................... ................................................ 17 A. Times and Heights Heights of of High and Low Water ...................................................... ........................................................ .. 17 B. Times the Tide Tide Reaches a Specific Specific Height......................................................... Height......................................................... .. 17 C. Height Height of Tide at a Specific Specific Time.................................................... Time ........................................................................ .................... 17 Part II. Secondary Ports ................................................ ................................................................................................ ................................................ 18 Questions on American Tide Tables................................. Tables................................................................................. ................................................ 19 Part I. American Standard Ports................................................................................. .. 19 Part II. American East Coast........................................ Coast........................................................................................ ................................................ 19 A. Time the Tide Reaches a Specific Height........................... Height......................................................... .............................. 19 B. Height of Tide at a Specific Time................................................................... Time........... .......................................................... .. 19 Astronomics Astronomics ................................................... ........................................................................................................... ................................................................... ........... 21 Introduction.................... Introduction............................................................................ ............................................................................................... ....................................... 21 Rising and Setting......................................................... Setting. ........................................................................................................ ................................................ 21 Finding the Zone Times of Sunrise, Sunset, and and Twilight Twilight ....................................... 21 QUESTIONS FOR ASTRONOMICS......................................................... ASTRONOMICS.. ............................................................................ ..................... 23 RISING AND SETTING CALCULATIONS ................................................... .............................................................. ........... 23 ANNEX A.................................................................................. A.......................... ............................................................................................... ....................................... 24 Answers for Canadian Canadian Tide Tables..................... Tables............................................................................. .......................................................... .. 24 Part 1 Standard Standard Ports......................................................... ....................................... 24 Answers for American Tide Tables ................................................ .............................................................................. .............................. 32 ASTRONOMICS – RISING AND SETTING CALCULATIONS ................................. 37 PART I ....................................................... ............................................................................................................... ................................................................... ........... 37 Question 1. ...................................................... .............................................................................................................. .......................................................... .. 37 Question 2 ....................................................... ............................................................................................................... .......................................................... .. 39 Question 3 ....................................................... ............................................................................................................... .......................................................... .. 41

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Question 4 ........................................................ ............................................................................................................... ......................................................... .. 43 Question 5 ........................................................ ............................................................................................................... ......................................................... .. 46 Question 6 ........................................................ ............................................................................................................... ......................................................... .. 47 PART II...................................................... II.............................................................................................................. ................................................................... ........... 49 Question 1 ........................................................ ............................................................................................................... ......................................................... .. 49 Question 2 ....................................................... ............................................................................................................... .......................................................... .. 53 Question 3 ....................................................... ............................................................................................................... .......................................................... .. 57 Question 4 ....................................................... ............................................................................................................... .......................................................... .. 61 PART III .................................................... ............................................................................................................ ................................................................... ........... 65 Question 1 ....................................................... ............................................................................................................... .......................................................... .. 65 ANNEX B – Canadian Tide Tables................................ Tables................................................................................. ................................................. 68 ANNEX C – American Tide Tables .................................................. ................................................................................ .............................. 87 ANNEX D – Astro Tables ........................................................ ............................................................................................... ....................................... 98 ANNEX E – Miscellaneous Miscellaneous Tables ................................................... ............................................................................... ............................ 117

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Tides Introduction This chapter discusses the theory behind tides and tidal streams and then details instructions on calculating tides for Canadian and American ports. The last section details the application of the tidal triangle in conducting passages. Tides are the periodic motion of the waters of the sea due to changes in the attractive forces of the moon and sun upon the rotating earth. Tides can either help or hinder a mariner. A high tide may provide enough depth to clear a bar, while a low tide may prevent entering or leaving a harbour. Tidal streams or currents are the horizontal motion of water due to changes in the tide. Tidal streams may hinder the mariner by setting the ship towards dangers or slow his progress. It can also aid the mariner by adding to the speed made good. By understanding tides and making timely use of predictions published in tide and tidal current tables, the navigator can plan an expeditious and safe passage.

Tide and Tidal Current Relationship It is necessary to distinguish clearly between tide and tidal current, for the relation between them is complex and variable. For the sake of clarity mariners have adopted the following definitions: Tide is the vertical rise and fall of the water, and tidal stream is the horizontal flow. The tide rises and falls, while the tidal stream ebbs and floods.

Causes of Tides The principal tide force is the differential forces generated through the gravitational attraction of the bodies (earth-sun and earth-moon). The moon is the main tide generating body and the effect of the sun is only about half that of the moon. When the earth, moon and the sun are lying approximately on the same horizontal axis in space, the tractive forces of the moon and sun are pulling in the same direction. The resultant ranges in tides are greater than average and are referred to as spring tides (see Figure 7-1). If the moon is between the earth and the sun (new moon) it is called conjunction and if the moon is on the opposite side of the sun (full moon) it is opposition .

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Conjunction (not to scale)

Opposition (not to scale) Figure 7-1: Spring Tides

When the moon and sun are almost at right angles to each other the tractive forces are the weakest. This alignment is referred to as quadrature and the resultant tides are called neap tides (see Figure 7-2), whose ranges are less than average.

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Quadrature (not to scale) Figure 7-2: Neap Tides The centrifugal forces on the earth produced by the earth's orbit around the sun and the moon's orbit around the earth also influences tides. The moon completes its orbit around the earth once every 29.2 days (a lunar month). During that period its distance from the earth varies. It can be readily understood that the closer the moon is to the earth, the greater will be its attraction on the earth's surface. Perigee is the term used when the moon is closest to the earth and hence the effect on tidal forces the strongest. Apogee is the term used when the moon is furthest from the earth and hence the effect on tidal forces the weakest. (See Figure 7-3.)

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Apogee 257,000 Miles

Perigee 225,000 Miles

Figure 7-3: Apogee and Perigee Since the Earth completes an elliptical orbit around the sun once every 365 days (a solar year), it follows that its distance will vary. When the earth is nearest the sun (in January) and the tidal forces are the strongest, it is said to be perihelion. When the earth is furthest away from the sun (in July) and the tidal forces are the weakest, it is said to be aphelion. (See Figure 7-4.)

Perihelion (January)

Aphelion (July)

Figure 7-4: Aphelion and Perihelion

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Causes of Tidal Streams The change in the tidal stream from flood to ebb, or vice versa, does not always coincide with the high and low water. In certain channels and inlets, the change may not take place until about half tide, because the land has a great effect on the direction and strength of the tidal streams. Considerable research must, in most cases, be carried out before accurate predictions of the set and rate of tidal streams can be predicted. Streams may also be considerably affected in direction, duration and velocity by the wind. No rule can be given for wind effects, but generally speaking, when the wind and stream are in the same direction, the duration and velocity will be increased and when opposing directions, the duration and velocity will be decreased. The rate of tidal stream is generally given for spring tides; for neaps, the rate can be taken as approximately one half the spring rate.

Types of Tides There are three types of tides. They are classified according to the characteristics of the tidal pattern: a.

Semi-diurnal. There are two high and two low waters each tidal day, with relatively small inequality in the high and low water heights.

b.

Diurnal. A single high and a single low water occur each tidal day.

c.

Mixed. The diurnal and semi-diurnal oscillations are both important factors and the tide is characterized by a large inequality in the high water heights, low water heights, or in both. There are usually two high and two low waters each day (occasionally the tide may become diurnal).

Definitions (to be used in conjunction with Figure 7-5 where applicable) d.

Tides. The periodical vertical oscillations of the sea in response to the tide-raising forces of the moon and the sun;

e.

Tidal streams. The periodical horizontal oscillations of the sea in response to the tide-raising forces of the sun and moon;

f.

High water . The highest level reached by the sea during one tidal oscillation;

g.

Low water. The lowest level reached by the sea during tidal oscillation;

h.

Maximum rate. The greatest rate reached in each of the two, more or less opposing, directions by the tidal stream in one oscillation;

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i.

Slack water. The periods, preceding and succeeding maximum rate, when the tidal streams are at their weakest; j.

Chart datum. The low water plane to which the depths of features permanently covered by the sea, and the height of features periodically covered and uncovered by the sea, are referred. The tidal levels and predicted high and low water heights of the tide are also referred to this plane. By international agreement, CHART DATUM SHOULD BE THE PLANE SO LOW THAT THE TIDE WILL NOT FREQUENTLY FALL BELOW IT;

k.

Height of tide. The vertical distance between the level of the sea and chart datum;

l.

Range of tide. The difference between the level of successive high and low waters;

m.

Mean water level. Average of all hourly water levels over the available period of record;

n.

Springs. the range of the semi-diurnal tides varies mainly with the phases of the moon, from new to full moon and vice versa. Springs are those semi-diurnal tides of greatest range, which occur in each of these periods;

o.

Neaps. Those semi-diurnal tides of least range which occur in each period from first quarter to last quarter and vice-versa;

p.

Higher Highwater Large Tide (HHWLT) and Lower Low Water Large Tide (LLWLT). Average of highest high waters and lowest low waters, respectively, from 19 years of prediction;

q.

Higher High Water Mean Tide (HHWMT) and Lower Low Water Mean Tide (LLWMT). average of all the higher high waters and lower low waters, respectively, from 19 years of predictions;

r.

Current. The horizontal movement of the water due to causes mainly meteorological and geographical, other than the tide raising forces of the moon and sun. It may be a progressive or fluctuating movement;

s.

Flow. The combination at any instant of tidal streams and currents;

t.

Reference Ports . Those ports for which predictions of the standard times and heights of HW and LW are published; and

u.

Secondary Ports . Those ports for which tidal differences and ratios on a standard port are published.

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Canadian Reference Diagram

Figures 7-5 A and B

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American Reference Diagram

RELATION BETWEEN TIDAL SURFACES, CHARTING DATUM S AND PHYSICAL FEATURES

Canadian Tide Tables

The Canadian Tide Tables predict the time and height of tides for Canadian and some U.S. Reference Ports. Secondary Ports are listed with time differences and ratios on Standard Ports. The current tables list the times and rates of maximum water velocity in both the ebb and flood direction. Additionally, the times of slack water, when the tidal stream reverses direction, are tabulated. This information is tabulated for all current stations. American Tide and Tidal Stream Tables

U.S. tables are published as two different publications, each consisting of separate volumes. Tide Tables

These tables are published in four volumes as follows: a. b. c. c.

Europe and West Coast of Africa (including Mediterranean); East Coast, North and South America (including Greenland); West Coast, North and South America (including Hawaii); and Central and Western Pacific Ocean and Indian Ocean.

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Tidal Stream/Current Tables

These tables are published in two volumes as follows: a. b.

Pacific Coast; and Atlantic Coast.

Both sets of tables follow much the same format as the Canadian tables use, Standard (Reference) and Secondary ports/stations. The tide tables also contain a section for calculating the local mean time of sunrise/sunset.

Aide-Mémoire for Using Tide Tables Canadian Reference Ports

a. b. c. d. e.

Extract the appropriate information from the question; Draw a diagram if necessary; Consider time zone, if DST is applicable, apply it by adding one hour to the tabular times; Extract the information from the tables; Determine: (1) (2) (3)

f. g. h.

range; duration; and ∆ of time/ ∆ of height, where ∆ = difference;

Enter the table and interpolate to get the reference column; Enter the second table and interpolate to get ∆ of time/ ∆ of height; and Apply the correction to the appropriate height or time.

Canadian Secondary Ports

a. b. c. d.

Extract the appropriate information from the question; Draw a diagram if necessary; Find the secondary port in the index (look it up in the table of secondary ports); Extract the following information:   HHW Time Mean Large

e. f.

Standard Port

LLW Time Mean Large

HW Mean Large

LW_____ Mean Large

Extract the appropriate information from the required day on the reference port; Consider time zone, if DST is applicable, apply by adding one hour to the tabular times; and

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g.

Interpolate/extrapolate to find the required correction. The following formula may help: x=a y b, where x = difference in tabulated height from nearest standard y = difference between mean and large for HW or LW of standard b = difference between mean and large correction for HW or LW, and a = difference between correction for mean or large and new correction. Standard Port

HHW Time Mean Large +30 +5.0 +3.0

LLW Time Mean Large -020 -1.0 +2.0

HW Mean Large 10.0 12.6

LW______ Mean Large 4.4 2.0

Secondary Port: Bumpkin Bay Standard Port: Baggywrinkle Harbour Times for Standard Port: 0200 11.2 0830 1.6 High water corrections: x = 11.2 -10.0 = 1.2 y = 12.6 -10.0 = 2.6

b = 5.0 - 3.0 = 2.0

Therefore, x = a, a = x * b = 1.2 * 2.0 = 0.92 - 0.9 y b y 2.6 Hence, correction = 5.0 - 0.9 = 4.1 Low water corrections: x = 2.0 - 1.6 = 0.4 y = 4.4 - 2.0 = 2.4 b = 2.0 - (-1.0) = 2.0 + 1.0 = 3.0 Therefore, a = x * b = 0.4 * 3.0 = 0.5 y 2.4 Hence, correction = 2.0 + 0.5 = 2.5 Corrected tides for Bumpkin Bay are: 0230 15.3 0810 4.1

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American Reference Stations

a.

Follow steps a. through e. as per Canadian Reference Ports;

b.

Enter the appropriate section of Table 3 and extract the differences in time or height as required. No interpolation is required although it is permissible to do so; and

c.

Apply the corrections to the appropriate height or time.

American Subordinate Stations

a. b.

Follow steps a. through c. as per Canadian Secondary Ports; Extract the following information: (1) the times and heights of tide for the appropriate day for the reference station, and (2) DIFFERENCES: Time High Water

c.

Height Low Water

High Water

Low Water

Correct the times and heights as required.

Tidal Stream Calculations

The calculations for tidal streams are very similar to that of the tides. Examples are found in the tide and tables publications and you will have ample opportunity to practice in class. In addition, you will be responsible for these calculations while ashore, at sea in YAGs and while in the simulator.

Tidal Stream and Tides Graphs Examples of tide graphs and tidal stream graphs can be found in Figure 7-6 and Figure 7-7. It can be seen from the tide graph graph for Port Neville, Johnstone Strait (Figure 7-6) that the height of tide (HOT) at 1600 is 8.8 feet. Similarly, Similarl y, the tidal stream in Porlier Pass (Figure 7-6) at 1000 is ebbing at a rate of 4 knots in the direction of 211 degrees True.

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Tides Graph

Figure7-6TidalGraph

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Tidal Stream Graph

Figure 7-7 Tidal Stream Graph

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Questions on Canadian Tide Tables Part I. Standard Ports A. Times and Heights of High and Low Water

1.

What are the times and heights of high and low water at Fulford Harbour, BC on 14 January 03?

2..

What are the times and heights of high and low water at Vancouver, BC on 2 August 03.

3.

a.

What is the highest recorded extreme of tide at Alert Bay,BC?

b. Which of the following reference ports has the largest large tide range: Point Atkinson, Bella Bella, or Prince Rupert? B. Times the Tide Reaches a Specific Height

4.

What is the first time during the forenoon of 20 April 03 in Vancouver BC that the tide will fall to 8.7 feet?

5.

On 24 March 03 you are preparing to depart from the government wharf at Campbell River BC. Alongside the wharf the depth of the water at chart datum is 7 ft and your draught is 12 ft. What is the first time in the afternoon that you can depart the jetty ensuring a 2 ft clearance?

6.

Between what times will there be less than 8.5 feet of tide at Fulford Harbour BC on 28 May 03?

7.

On 6 May 03 in Prince Rupert BC the ship’s divers are attempting to clear the ship’s anchor which is fouled on a submarine cable. If the charted depth at the anchorage position is 38 ft, when must diving cease on the anchor if your divers are restricted to depths of 50 ft or less? The divers enter the water at 0700(+7).

8.

What is the last time after 1600(+7) on 28 June 03 that your ship with a masthead height of 64 ft could proceed under the Second Narrows Lift Bridge in Vancouver? The Bridge is undergoing repairs and is locked at a charted elevation of 59 ft. You require 2 ft clearance for safety.

C. Height of Tide at a Specific Time

9.

What is the height of tide at 0215(+8) on 25 Mar 03 at Pt Atkinson, BC?

10.

How much water above chart datum is there at the time of your departure 0730(+7) from alongside in Prince Rupert, BC on 20 June 03?

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11.

What is the vertical clearance under the First Narrows Bridge, Vancouver(charted elevation 61m) at 1700Z on 20 October 03?

12.

What is the height of tide at 1300(+8) on 9 December 03 in Sooke, BC?

13.

How much water lies over a rock marked as “dries 2 ft” at 0530(+7) on 6 May 03 in Port Alberni, BC?

Part II. Secondary Ports 14.

What are the times and heights of high and low water on 9 May 03 at Khyex Point in northwestern BC?

15.

What is your clearance on a Shoal (charted depth 4 ft) at Sooke Basin at 0700(+7) on 19 April 03? Your draught is 6 ft.

16.

What depth is the minimum amount of water that will be over Romulus Reef (charted depth 6.8 ft), Porlier Pass during the PM of 6 Dec 03?

For answers see Annex A.

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Questions on American Tide Tables Part I. American Standard Ports 1.

What are the times and heights of high and low water at Breakwater harbour, Delaware on 7 Dec 03?

2.

a.

What are the times and heights of high and low water in Tampico Harbour on 2 Mar 03?

b.

What is the range and duration?

c.

What time zone are you in?

a.

What are the times and heights of high and low water on the Savannah River Entrance on 22 Aug 03?

b.

What time zone are you in?

3.

Part II. American East Coast A.

Time the Tide Reaches a Specific Height

4.

You are scheduled to arrive in Boston mass, on 22 Aug 03. There is a sand bar in the harbour approached with a charted depth of 24 ft. What is the earliest time that you may cross the bar in the afternoon if you CO insists on 6 ft of safe water underneath the ship at all times? Your draught is 23ft.

5.

You are required to enter Savannah, GA in the afternoon of the 28 June 03 to load supplies. The Charted depth at the berth is 5 fathoms 1 foot. In order for the crane to clear your mast the tide must be no higher than 8 ft 6 in. Your draught is 32 ft and the CO insists on 3 ft of water between your keel and the bottom. When, up until 2359, can you load supplies?

B.

Height of Tide at a Specific Time

6.

What is the height of tide at 1100 on the 17 May 03 Bridgeport, Conn?

7.

The sill of a drydock in Hampton Roads is 17 ft below charted datum. You draught is 18 ft. How much clearance will you have if you enter the dock at 1700 2 Apr 03?

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8.

9.

10.

A jetty in Savannah, Georgia has an alongside depth of 20 ft. You are required to remain alongside from 161600 until 212359 Nov 03. Your draught is 18 ft. a.

What is the expected minimum clearance under your vessel?

b.

What is the clearance on departure?

a.

What is the height of tide at 2300 on 16 Nov 03 in Comodoro Rivadavia, Argentina?

b.

What time zone are they in?

What are the times and heights of high and low water at Roosevelt Roads, P.R. on 3 Apr 03?

For answers to these questions see ANNEX A.

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Astronomics Introduction Rising and Setting Finding the Zone Times of Sunrise, Sunset, and Twilight

On the daily pages of the Almanac the Local Mean Time of Civil and Nautical Twilight, both morning, evening, sunrise, and sunset are tabulated. It will be noticed that these times are tabulated for the three-day period and apply to the center day specifically. For many purposes this accuracy is all that is necessary and interpolation for the day is not required. However, if accuracy is required, interpolation for the day is necessary. The examples and problems in this book have been calculated for the specific day. EXAMPLE Find the zone times of Morning Civil Twilight, Sunrise, Evening Nautical Twilight and Sunset in Lat 41 °40’N 62°18’W on 01 July 89. Morning Civil Twilight

LMT 0402

From Almanac for the nearest tabular latitude which is less that the true latitude (40 °N), in the upper Civil Twilight column. Enter the table on p.xxxii at the back of the Almanac (Table I). Go down the tabular interval headed 5° (the interval between 40 °N and 41°40’N being 1 °40’N). Now go horizontally across to the right until you reach the columns headed 20m and 25m (the difference between the times tabulated for 40 °N and 45°N is actually 23m). A four way interpolation now gives a correction of 7m which is subtracted because civil twilight at 45 °N is earlier than at 40 °N. Now apply your longitude in time 62 °18’W = 4h09m (to the nearest minute) taken from the conversion table page (i) in the back of the Almanac.

Corr - 07 LMT 0355 Long East: subtract +0409 Long West: add GMT 0804 This gives GMT. Now apply your Zone to GMT to obtain zone time. In Corr -0400 this case we are in Zone +4 L time 0404

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Now work out Sunrise, Evening Nautical Twilight, and Sunrise in the same way.

LMT for 40°N Correction LMT Long W GMT Zone Zone Time

Sunrise 0435 - 6 min 4h29 +4h09 0838 - 4h00 0438 (+4)

E.N.T. 2047 + 9 min 20h56 +4h09 0105 2 July - 4h00 2105 (+4)

Sunset 1933 + 5min 19h38 +4h09 2347 - 4h00 1947 (+4)

It is customary to use the time of civil twilight for pre-computing star sights, but nautical twilight for total darkness problems.

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QUESTIONS FOR ASTRONOMICS RISING AND SETTING CALCULATIONS Part I

Calculate the sunrise, sunset, morning nautical twilight, and evening nautical twilight for the following dates. 1. 2. 3. 4. 5. 6.

02 Jan 03 10 Jan 03 14 Jan 03 09 May 03 14 Jul 03 11 Aug 03

Lat: 43˚32’N Lat: 44˚35’N Lat: 28˚30’N Lat: 36˚50’S Lat: 58˚38’N Lat: 69˚20’N

Long: 62˚20’W (+3) Long: 63˚30’W (+4) Long: 71˚15’W (+5) Long: 174˚52’E (+11) Long: 154˚00’W (+9) Long: 40˚30’W (+2)

Part II

Calculate the sunrise, sunset, morning nautical twilight, evening nautical twilight, moonrise and moonset for the following dates. 1. 2. 3. 4.

15 Apr 03 30 Jul 03 30 Sep 03 12 Oct 03

Lat: 42˚30’S Lat: 40˚21’N Lat: 41˚20’N Lat: 58°21’S

Long: 169˚41’W Long: 07˚32’W (Z) Long: 63˚47’E (-4) Long: 46°00’E (-4)

Part III

Calculate the moonrise and moonset for the following date. 1.

23 Jan 03

Lat: 28 °30’N Long: 71°15’W

For answers to these questions see ANNEX A.

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ANNEX A Answers for Canadian Tide Tables Part 1 Standard Ports

1.

Fulford Harbour, BC 14 January 03 DST? - No

2.

0450 0755 1210 2030

10.2 ft 9.8 ft 10.5 ft 2.3 ft

3.11 m 2.99 m 3.20 m 0.70 m

1210 2030

10.5 ft 2.3 ft

3.20 m 0.70 m

Vancouver, BC

Highest Lowest

2 August 03

DST? – Yes

3.

0350 0750 1420 2110

8.5 ft 12.5 ft 4.3 ft 15.1 ft

2.59 m 3.81 m 1.31 m 4.60 m

1420 2110

4.3 ft 15.1 ft

1.31 m 4.60 m

a.

b.

4.

Recorded Extremes For Alert Bay Highest High Water 19.3 ft Lowest Low Water -0.7 ft

Lowest Highest

5.9 m -0.2 m

Prince Rupert Large Tide Range – Largest

Vancouver, BC

20 April 03 (+3)

DST? – Yes 0200 0705 1430

10.2 ft 14.1 ft 1.3 ft

3.11 m 4.30 m 0.40 m

24

2155

15.1 ft

4.60 m

0300 0805 1530 2255

10.2 ft 14.1 ft 1.3 ft 15.1 ft

3.11 m 4.30 m 0.40 m 4.60 m

0805 X 1530

14.1 ft 8.7 ft 1.3 ft

14.1 -1.3 R= 12.8

1530 -0805 D = 7h25

14.1 -8.7 HD = 5.4

= 0805 + 3h21 = 11h26 Column 8.5 5.

Campbell River, BC 24 March 03 DST? = No Charted Depth = 7 ft Draught = 12 ft Clearance = 2ft Clearance + Draught = Charted Depth + HOT 2 ft + 12 ft = 7ft + HOT 7 ft = HOT 0335 0815 1620

11.5 ft 12.8 ft 3.6 ft

3.51 m 3.90 m 1.10 m

0815 X 1620

12.8 ft 7 ft 3.6 ft

1620 12.8 7 -0815 -3.6 -3.6 D = 8h05 R= 9.2 ft HD = 3.4 ∆ = 1159 X = 1620 - ∆D = 1620 – 3h26 = 12h54 is last time in forenoon Column 7.5 ∆ = 1159 6.

Fulford Harbour, BC 28 May 03 (+7) DST? – Yes

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0210 0930 1715 2125

9.8 ft 3.0 ft 9.2 ft 8.2 ft

9.8 ft 0210 3.0 ft 0930 R = 6.8 ft D = 7h20

7.

2.99 m 0.91 m 2.80 m 2.50 m 9.8 ft 8.5 ft HD= 1.3 ft

0310 2h 0510

9.2 ft 3.0 ft R= 6.2 ft

1715 0930 D= 7h 45

9.2 ft 1815 8.5 ft 1h10 HD= 0.7 ft 1705

9.2 ft 8.2 ft R= 1.0 ft

2125 1715 D= 4h10

8.5 ft 8.2 ft HD 0.3 ft

2225 1h23 2302

Prince Rupert, BC 6 May 03 (+8) DST? – Yes 0335 1030 1650 2215

19.0 ft 4.9 ft 16.7 ft 9.8 ft

5.79 m 1.49 m 5.09 m 2.99 m

0435 1130 1750 2315

19.0 ft 4.9 ft 16.7 ft 9.8 ft

5.79 m 1.49 m 5.09 m 2.99 m

Depth + HOT = X 38 + HOT = 50 50 - 38 = 12 ft HOT = 12 ft 0435 X 1130

19.0 ft 12.0 ft 4.9 ft

19.0 -4.9 R= 14.1

0435 -1130 D= 6h55

2h47 - ∆D

19.0 -12.0 HD= 7.0

0435 + 3h27 = 0802 (+7)

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Column 10 8.

Vancouver, BC 28 June 03 (+8) DST ? – Yes Last time after 1600 (+7) CH Elevation + HHWLT = Mast Ht + Clearance + HOT 59 ft 16.5 64 ft 2 ft 75 – 66 = HOT 95 ft 0300 1055 1835 2330

13.1 ft 2.3 ft 14.4 11.8

3.99 m 0.70 m 4.39 m 3.60 m

0400 1155 1935 0030

13.1 ft 2.3 ft 14.4 11.8

3.99 m 0.70 m 4.39 m 3.60 m

1155 X 1935

2.3 ft 9.5 14.4

14.4 -2.3 R= 12.1

14.4 -9.5 HD= 4.9

1155 -1935 D= 7h40

Column 8.3 3h21 1935 – 3h21 = 1614 (+7) 9.

Point Atkinson (+8) 25 March 03 0215 DST? – No 0030 0550 0940 1735

14.1 ft 11.5 ft 12.5 ft 3.4 ft

4.30 m 3.51 m 3.81 m 1.04 m

0030 0215 0550 14.1

14.1 ft X 11.5 ft 0030

0030

27

-11.5 R = 2.6

-0550 D= 5h20

-0215 TD= 1h45

Column 5 = .8 ∆D – 14.1 14.1 - .8 = 13.3 ft (+8) 10.

Prince Rupert 20 June 03 (+7) DST? – Yes 0530 1200 1840

18.0 ft 5.2 ft 17.7 ft

5.49 m 1.58 m 5.39 m

0630 1300 1940

18.0 ft 5.2 ft 17.7 ft

5.49 m 1.58 m 5.39 m

0630 0730 1300

18.0 ft X 5.2 ft

18.0 -5.2 R = 12.8

0630 -1300 D=6h30

0630 -0730 TD=1hr

Column = 1.5 = 1.0 18.0 –1.0 = 17.0 ft (+7) 11.

First Narrows Bridge, Vancouver BC (+7) 20 October 03 DST? – Yes 0635 1425 2050 0055

5.2 ft 14.4 ft 9.5 ft 11.2 ft

1.58 m 4.39 m 2.89 m 3.41 m

0735 1525 2150 0155

5.2 ft 14.4 ft 9.5 ft 11.2 ft

1.58 m 4.39 m 2.89 m 3.41 m

0735

5.2 ft

28

1000 1525

X 14.4

14.4 -5.2 R = 9.2

0735 -1525 D=7h50

0735 -0900 TD=2h35

5.2 + 2.3 = 7.5 ft CH Elevation + HHWLT = Mast HT + Clearance + HOT 200ft + 16.5= 7.5 216.5 – 7.5 = 209 12.

Sooke 9 Dec 03 HOT at 1300 (+8) DST? – No 1210 2110

10.2 ft 2.0 ft

1210 1300 2110

10.2 ft X 2.0

10.2 -2.0 R = 8.2 ft

1210 -2110 D=9hrs

3.11 m 0.61 m

1300 -1210 TD= 50 min

Column .5 10.2 - .2 = 10.0 ft (8+) 13.

Port Alberni BC 6 May 03

0530 (+7)

DST? – Yes 0225 0930 1610 2105

9.8 ft 1.6 ft 7.9 ft 5.6 ft

2.99 m 0.49 m 2.41 m 1.71 m

0325 1030 1710

9.8 ft 1.6 ft 7.9 ft

2.99 m 0.49 m 2.41 m

2205

5.6 ft

1.71 m

29

0325 0530 1030

9.8 ft X 1.6 ft

1030 -0325 D= 0705

9.8 -1.6 R= 8.2 ft

0530 -0325 TD= 0205

HOT – DH = Clearance X - 2 = Clearance 8.2 - 2 = 6.2 Column 4 = 1.6 X = 9.8 -1.6 8.2 14.

Khyex Point 9 May 03 (+7) DST? – Yes

On Prince Rupert

0030 0630 1325 2010

10.8 ft 16.7 ft 6.2 ft 16.4 ft

3.29 m 5.09 m 1.89 m 5.00 m

0130 0730 1425 2110

10.8 ft 16.7 ft 6.2 ft 16.4 ft

3.29 m 5.09 m 1.89 m 5.00 m

Khyex Pt = LHW = + 49 min + 1h54 min 0324 0819 1619 2159 15.

8.3 ft 13.6 ft 3.7 ft 13.3 ft

- 3.1 - 2.5 2.53 m 4.15 m 1.13 m 4.05 m

Sooke Basin 19 April 03 (+7) DST? – Yes Charted depth 4ft Draught 6ft Draught + Clearance = Depth + HOT 6ft + 2ft = 4ft + HOT 8ft = 4ft + HOT

30

HOT = 4ft 0215 1055 1840 1950

10.2 ft 0.7 ft 7.5 ft 7.2 ft

3.11 m 0.21 m 2.29 m 2.19 m

0315 1155 1940 2050

10.2 ft 0.7 ft 7.5 ft 7.2 ft

3.11 m 0.21 m 2.29 m 2.19 m

1248 -0325 D = 9h23

9.3 -1.4 R= 7.9

0700 0325 TD= 3h35

HHW +10 min - .9 ft

LLW +53 min + .7 ft

0325 0700 1248

9.3 X 1.4

X = 9.3 - ∆H = 9.3 – 2.6 X = 6.7 6 ft Clearance = 4 + 6.7 Clearance = 4.7 ft 16.

Romulus Reef – Porlier Pass 6 Dec 03 (+8) On Fulford Harbour DST? – No 0515 0920 1400 2140

10.2 ft 9.2 ft 10.2 ft 2.3 ft

HHW Time – 05 Mean + 1.6 0510 0953 1355 2213 2213@ 9.4 ft 11.8 -6.8 ft 5 ft @ 1400

3.11 m 2.80 m 3.11 m 0.70 m LLW Time + 33 Mean + 03

11.8 ft 9.5 ft 11.8 ft 2.6 ft

3.60 m 2.89 m 3.60 m 0.79 m Charted depth 6.8 ft

31

Answers for American Tide Tables 1) Breakwater Harbour, Delaware, 7th Dec, 03 DST? – NO 0057 0728 1350 1948

0.2 4.7 0.2 3.5

0728 1948

4.7 3.5 High water

0057 1350

0.2 0.2 Low water

2) Tampico Harbour, 2nd March 03 DST? – NO 0011 0828 1621 2042

1.1 -0.3 1.0 0.8

0011 1621

1.1 1.0 High Water

0828 2042

-0.3 0.8 Low Water

B) 1.1 -0.3 1.4

1.0 -0.3 1.3

1.0 -0.8 1.2 = daily ranges

0011 0828 1621 -0828 -1621 -2042 8h17 7h53 4h21 = daily durations C) 90° ÷ 15 = + 6

32

3) Savannah River Entrance, GA, 22 August 03 DST? – YES 0318 0928 1545 2220

5.9 1.2 +DST 7.0 1.7

0418 1028 1645 2320

0418 1645

5.9 7.0

High Water

1028 2320

1.2 1.7

Low Water

5.9 1.2 7.0 1.7

B) 75° ÷ 15 = + 5

4) Boston, Mass, 22 August 03 DST? – YES 0029 0643 1238 1855

1.7 7.3 + DST 2.3 9.1

0129 0743 1338 1955

1.7 7.3 2.3 9.1

DRAUGHT + CLEARANCE = CHARTED DEPTH + HOT 23 + 6 = 24 + HOT 29 = 24 + HOT HOT = 5 FT 0743 X 1338

7.3 5.0 2.3

1338 -0743 D= 5h21

1338 X 1955

2.3 5.0 9.1

1955 -1338 D=5h33

7.3 -2.3 R= 5.0 9.1 - 2.3 R= 6.8

7.3 -5.0 TD= 2.3 5.0 -2.3 TD= 2.7

2h19 + 0743 = 0902

2h24 + 1338 = 1602

1602 is the earliest time in the afternoon we may cross the bar.

5) Savannah, GA, 28th June 03

33

0147 0730 1346 1945

DST? – YES 0.8 7.1 0.3 +DST 8.6

0247 0830 1446 2045

0.8 7.1 0.3 8.6

0231

0.6

0331

0.6

DRAUGHT + CLEARANCE = CHARTED DEPTH + HOT 32 + 3 = 31 + HOT 35 = 31 + HOT HOT = 4 0830 7.1 X 4.0 1446 0.3

1446 -0830 D= 5h16

1446 X 2045

0.3 4.0 8.6

2045 -1446 D= 5h31

2045 X 0331

8.6 4.0 0.6

2045 -0331 D= 4h16

7.1 7.1 -0.3 -4.0 R= 6.8 HD= 3.1 8.6 -0.3 R= 8.3

8.6 -0.6 R= 8.0

4.0 -0.3 HD= 3.7

4.0 -0.6 HD= 3.4

2h57 + 0830 = 1127

3h02 + 1446 = 1748

1h46 – 0331 = 0145

We can load supplies between 1748 and 2045 6) Bridgeport Connecticut, 17th May 03 DST? – YES 0556 1200 1805

-1.0 7.4 -0.2

0656 +DST 1300 1905

0656 1100 1300

-1.0 1300 X -0656 7.4 D=6h 04

-1.0 7.4 -0.2

-1.0 (-)7.4 R=8.4

1300 -1100 TD= 2h

7.4 – 2.1 = 5.3 @ 1100

7) Hampton Roads, 2nd April 2003 DST? – NO

34

0327 0933 1532 2143

0.0 2.6 0.1 2.8

2143 -1532 D= 7h15

1532 1700 2143

0.1 X 2.8

2.8 1700 -0.1 -1532 R=2.7 TD=3h42

1.5 + 0.1 = 1.6 @ 1700 You will have .6ft of Clearance

8)

Savannah Georgia, 16th-21st November 2003

Alongside depth - Draught + Hot = Minimum Clearance 20 ft – 18 ft + Hot = Minimum Clearance 2 ft + 0.1 ft = 2.1 ft minimum clearance 2.1ft minimum clearance @ 2351, 20th Nov 03 1232, 21st Nov 03 B) Departure time: 2359, 21st Nov 03 DST? – NO 0549 1232 1806 0045

8.9 0.1 8.6 -0.3

1806 -0045 D=6h38

1806 2359 0045

8.6 -0.3 R=8.3

8.6 X -0.3

2359 -0045 TD= 46 min

0.3 subtract 0.3 = -0.6 @ 2359

9) 16th November 03, Comodoro Rivadavia, Argentina DST? - NO 0331 0939

3.2 16.1

2126 2300

15.6 X

35

1539 2126

5.3 15.6

0408

3.6 (17th Nov)

15.6 -3.6 R=12.0 2126

0408

2126 -0408 D=6h42

3.6

2126 -2300 TD=1h34

15.6 -1.5 14.1 @ 2300

B) Time Meridian 45 ° West. 45 ÷ 15= 9 Time Zone + 9

10. 3rd April 2003, Roosevelt Roads, Puerto Rico On San Juan, Puerto Rico DST? - NO TIME HW +0 02

HEIGHT LW +0 20

0429 1000 1554 2241

0.2 ft 1.0 ft + Corrections 0.1 ft 1.4 ft

0449 1614

0.65 0.64 Low Water

1002 2243

1.63 1.67 High Water

HW *0.63 0449 1002 1614 2243

LW *0.63

0.65 1.63 0.64 1.67

36

ASTRONOMICS – RISING AND SETTING CALCULATIONS PART I Question 1.

02 Jan 03

Lat : 43°32’N Long : 62° 20’W

(+3)

SUNRISE

Step 1: 45° 43°32’ 40°

02 Jan 0738 ____ 0722

Step 2: 0738 - 0722 16 minutes

Step 3: Tabular interval = 5 ° 43°32’ - 40° = 3°32’ Using a tabular interval of 5 °, 3°32’ and 16 min, you find 11 minutes Step 4: Add this value (11 min) to the time closest to the Equator. 0722 45° 0738 + 11 minutes 43°32’ 0733 0733 40° 0722 Step 5: Conversion of arc to time 62° 4:08 20’W 0:01::20 4:09::20

Step 6: 0733 +0409 1142 - 0300 0842 (+3)

SUNSET

Step 1: 45° 43°32’ 40°

02 Jan 1630 ____ 1646

Step 2: 1646 - 1630 16 minutes

Step 3: Tabular interval = 5 ° 43°32’ - 40° = 3°32’ Using a tabular interval of 5 °, 3°32’ and 16 min, you find 11 minutes Step 4: Subtract this value (11 min) to the time closest to the Equator. 1646 45° 1630 - 11 minutes 43 °32’ 1635 1635 40° 1646

37

Step 5: Conversion of arc to time 62° 4:08 20’W 0:01::20 4:09::20

Step 6: 1635 +0409 2044 - 0300 1744 (+3)

MORNING NAUTICAL TWILIGHT

Step 1: 45° 43°32’ 40°

02 Jan 0628 ____ 0618

Step 2:

0628 - 0618 10 minutes

Step 3: Tabular interval = 5 ° 43°32’ - 40° = 3°32’ Using a tabular interval of 5 °, 3°32’ and 10 min, you find 8 minutes Step 4: Add this value (8 min) to the time closest to the Equator. 0618 45° 0628 + 8 minutes 43°32’ 0626 0626 40° 0618 Step 5: Conversion of arc to time 62° 4:08 20’W 0:01::20 4:09::20

Step 6: 0626 +0409 1035 - 0300 735 (+3)

EVENING NAUTICAL TWILIGHT

Step 1: 45° 43°32’ 40°

02 Jan 1740 ____ 1750

Step 2: 1750 - 1740 10 minutes

Step 3: Tabular interval = 5 ° 43°32’ - 40° = 3°32’ Using a tabular interval of 5 °, 3°32’ and 10 min, you find 7 minutes Step 4: Subtract this value (7 min) to the time closest to the Equator. 1750 - 7 minutes 1743

45° 43°32’ 40°

1740 1743 1750

38

Step 5: Conversion of arc to time 62° 4:08 20’W 0:01::20 4:09::20

Step 6: 1743 +0409 2152 - 0300 1852 (+3)

Question 2

10 Jan 03

Lat : 44°35’N Long : 63° 30’W

(+4)

SUNRISE

Step 1: 45° 44°35’ 40° Step 2:

8 Jan 0738 _____ 0722 0738 - 0722 16 minutes

10 Jan _____

11 Jan 0737 _____ 0721 0737 - 0721 16 minutes

Step 3: Tabular interval = 5 ° 44°35’ - 40 ° = 4°35’ Using a tabular interval of 5 °, 4°35’ and 16 min, you find 15 minutes Using a tabular interval of 5 °, 4°35’ and 16 min, you find 15 minutes Step 4: Add this value (15 min) to the time closest to the Equator. 0722 0721 45 ° 0738 + 15 min 15 min 44°35’ 0737 0736 0737 0736 40 ° 0722 Step 5: Conversion of arc to time 63° 4:12 30’W 0:02 4:14 (Add when West)

0737 0736 0721

Step 6: 0736 + 0414 1150 GMT - 0400 0750 (+4)

39

SUNSET

Step 1: 45° 44°35’ 40° Step 2:

8 Jan 1636 _____ 1651

10 Jan _____

1651 - 1636 15 minutes

11 Jan 1639 _____ 1654 1654 - 1639 15 minutes

Step 3: Tabular interval = 5 ° 44°35’ - 40 ° = 4°35’ Using a tabular interval of 5 °, 4°35’ and 15 min, you find 13 minutes Using a tabular interval of 5 °, 4°35’ and 15 min, you find 13 minutes Step 4: Subtract this value (15 min) to the time closest to the Equator. 1651 1654 45 ° 1636 1639 - 13 min - 13 min 44°35’ 1638 1640 1641 1638 1641 40 ° 1651 1654 Step 5: Conversion of arc to time 63° 4:12 30’W 0:02 4:14 (Add when West)

Step 6: 1640 + 0414 2054 GMT - 0400 1654 (+4)


Step 1: 45° 44°35’ 40° Step 2:

8 Jan 0628 _____ 0618 0628 - 0618 10 minutes

10 Jan _____

11 Jan 0627 _____ 0618 0627 - 0618 9 minutes

Step 3: Tabular interval = 5 ° 44°35’ - 40 ° = 4°35’ Using a tabular interval of 5 °, 4°35’ and 10 min, you find 9 minutes Using a tabular interval of 5 °, 4°35’ and 9 min, you find 8 minutes Step 4: Add this value (9 & 8 min) to the time closest to the Equator. 0618 0618 45 ° 0628 0627 + 9 min + 8 min 44°35’ 0627 0626 0626 0627 0626 40 ° 0618 0618

40

Step 5: Conversion of arc to time 63° 4:12 30’W 0:02 4:14 (Add when West)

Step 6: 0626 + 0414 1040 GMT - 0400 0640 (+4)


Step 1: 45° 44°35’ 40° Step 2:

8 Jan 1746 _____ 1755

10 Jan

11 Jan 1749 _____ 1758

_____

1755 - 1746 9 minutes

1758 - 1749 9 minutes

Step 3: Tabular interval = 5 ° 44°35’ - 40 ° = 4°35’ Using a tabular interval of 5 °, 4°35’ and 9 min, you find 8 minutes Using a tabular interval of 5 °, 4°35’ and 9 min, you find 8 minutes Step 4: Subtract this value (9 & 8 min) to the time closest to the Equator. 1755 1758 45 ° 1746 1749 - 8 min - 8 min 44°35’ 1747 1748 1750 1747 1750 40 ° 1755 1758 Step 5: Conversion of arc to time 63° 4:12 30’W 0:02 4:14 (Add when West)

Step 6: 1748 + 0414 2202 GMT - 0400 1802 (+4)

Question 3

14 Jan 03

Lat : 28°30’N Long : 71° 15’W

(+5)

SUNRISE

Step 1: 30° 28°30’ 20°

14 Jan 0657 ____ 0638

Step 3: Tabular interval = 10 °

Step 2: 0657 - 0638 19 minutes

28°30’ - 20° = 8°30’

41

Using a tab interval of 10 °, 8°30’ and 19 min, you find 17 min. in Table I Step 4: Add this value (17 min) to the time closest to the Equator which is 0638. 0638 30° 0657 + 17 minutes 28°30’ 0655 0655 20° 0638


Step 6: 0655 +0445 1140 GMT -0500 0640 (+5)

SUNSET

Step 1: 30° 28°30’ 20°

14 Jan 1722 ____ 1741

Step 2: 1741 - 1722 19 minutes

Step 3: Tabular interval = 10 ° 28°30’ - 20° = 8°30’ Using a tabular interval of 10 °, 8°30’ and 19 min, you find 16 minutes in Table I Step 4: Subtract this value (16 min) to the time closest to the Equator. 1741 30° 1722 - 16 minutes 28 °30’ 1725 1725 20° 1741 Step 5: Conversion of arc to time 71° 4:44 15’W 0:01 4:45 (Add when West)

Step 6: 1725 +0445 2210 GMT -0500 1710 (+5)


Step 1: 30° 28°30’ 20°

14 Jan 0602 ____ 0547

Step 2: 0602 - 0547 15 minutes

42

Step 3: Tabular interval = 10 ° 28°30’ - 20° = 8°30’ Using a tabular interval of 10 °, 8°30’ and 15 min, you find 13 minutes in Table I Step 4: Add this value (13 min) to the time closest to the Equator which is 0547. 0547 30° 0602 + 13 minutes 28°30’ 0600 0600 20° 0547

Step 5: Conversion of arc to time 71° 4:44 15’W 0:01 4:45

Step 6: 0600 +0445 1045 -0500 545 (+5)


Step 1: 30° 28°30’ 20°

14 Jan 1817 ____ 1831

Step 2: 1831 - 1817 14 minutes

Step 3: Tabular interval = 10 ° 28°30’ - 20° = 8°30’ Using a tabular interval of 10 °, 8°30’ and 14 min, you find 12 minutes in Table I Step 4: Subtract this value (14 min) to the time closest to the Equator. 1831 30° 1817 - 12 minutes 28 °30’ 1819 1819 20° 1831 Step 5: Conversion of arc to time 71° 4:44 15’W 0:01 4:45 (Add when West)

Step 6: 1819 +0445 2304 GMT -0500 1804 (+5)

Question 4

9 May 03

Lat : 36°50’S Long : 174 ° 52’E

(-11)

43

SUNRISE

Step 1: 35° 36°50’ 40° Step 2:

8 May 0642 _____ 0651

9 May _____

0652 - 0642 9 minutes

11 May 0644 _____ 0654 0654 - 0644 10 minutes

Step 3: Tabular interval = 5 ° 36°50’ - 35 ° = 1°50’ Using a tabular interval of 5 °, 1°50’ and 9 min, you find 3 minutes Using a tabular interval of 5 °, 1°50’ and 10 min, you find 3 minutes Step 4: Add this value (3 min) to the time closest to the Equator. 0642 0644 35 ° 0642 + 3 min + 3 min 36°50’ 0645 0646 0645 0647 40 ° 0651 Step 5: Conversion of arc to time 174° 11:36 52’E 0:03::28 11:39::28 (Subtract when East)

0644 0647 0654

Step 6: 0646 -1139 1907 GMT +1100 0607 (-11)

SUNSET

Step 1: 35° 36°50’ 40° Step 2:

8 May 1711 _____ 1701 1711 - 1701 10 minutes

9 May _____

11 May 1708 _____ 1658 1708 - 1658 10 minutes

Step 3: Tabular interval = 5 ° 36°50’ - 35 ° = 1°50’ Using a tabular interval of 5 °, 1°50’ and 10 min, you find 3 minutes Using a tabular interval of 5 °, 1°50’ and 10 min, you find 3 minutes Step 4: Subtract this value (3 min) to the time closest to the Equator. 1711 1708 35 ° 1711 1708 - 3 min - 3 min 36°50’ 1708 1707 1705 1708 1705 40 ° 1701 1658

44

Step 5: Conversion of arc to time 174° 11:36 52’E 0:03::28 11:39::28 (Subtract when East)

Step 6: 1707 -1139 0528 GMT +1100 1628 (-11)


Step 1: 35° 36°50’ 40° Step 2:

8 May 0545 _____ 0550

9 May _____

0550 - 0545 5 minutes

11 May 0547 _____ 0553 0553 - 0547 6 minutes

Step 3: Tabular interval = 5 ° 36°50’ - 35 ° = 1°50’ Using a tabular interval of 5 °, 1°50’ and 6 min, you find 2 minutes Using a tabular interval of 5 °, 1°50’ and 6 min, you find 2 minutes Step 4: Add this value (2 min) to the time closest to the Equator. 0545 0547 35 ° 0545 + 2 min + 2 min 36°50’ 0547 0548 0547 0549 40 ° 0550 Step 5: Conversion of arc to time 174° 11:36 52’E 0:03::28 11:39::28 (Subtract when East)

0547 0549 0553

Step 6: 0548 -1139 1807 GMT +1100 0507 (-11)


Step 1: 35° 36°50’ 40° Step 2:

8 May 1808 _____ 1802 1808 - 1802 6 minutes

Step 3: Tabular interval = 5 °

9 May _____

11 May 1806 _____ 1800 1806 - 1800 6 minutes

36°50’ - 35 ° = 1°50’

45

Using a tabular interval of 5 °, 1°50’ and 6 min, you find 2 minutes Using a tabular interval of 5 °, 1°50’ and 6 min, you find 2 minutes Step 4: Subtract this value (2 min) to the time closest to the Equator. 1808 1806 35 ° 1808 1806 - 2 min - 2 min 36°50’ 1806 1805 1804 1806 1804 40 ° 1802 1800 Step 5: Conversion of arc to time 174° 11:36 52’E 0:03::28 11:39::28 (Subtract when East)

Step 6: 1805 -1139 0626 GMT +1100 1726 (-11)

Question 5

14 July 03

Lat : 58 °38’N Long : 154° 00’W

(+9)

SUNRISE

Step 1: 60° 58°38’ 58° 00’W 0:00 10:16

13 July 0259 _____ 0316

14 July _____

16 July 0305 _____ 0321 0311 -1016 1327 GMT 0427 (+9)

(Add when West)

SUNSET

Step 1: 60° 58°38’ 58° Step 2:

13 July 2111 _____ 2054 2111 - 2054 17 minutes

14 July _____

16 July 2106 _____ 2049 2106 - 2049 17 minutes

Step 3: Tabular interval = 2 ° 58°38’ - 58 ° = 0°38’ Using a tabular interval of 2 °, 0°38’ and 17 min, you find 7 minutes Using a tabular interval of 2 °, 0°38’ and 17 min, you find 7 minutes

46

Step 4: Add this value (7 & 7 min) to the time closest to the Equator. 2054 2049 60 ° 2111 2106 + 7 min + 7 min 58°38’ 2101 2059 2056 2101 2056 58 ° 2054 2049 Step 5: Conversion of arc to time 154° 10:16 00’W 0:00 10:16 (Add when West)

Step 6: 2059 + 1016 0715 GMT - 0900 2215 (+9)


Nil


Nil

Question 6

11 Aug 03 Lat : 69°20’N Long : 40° 30’W

(+2)

SUNRISE

Step 1: 70° 69°20’ 68° Step 2:

9 Aug 0220 _____ 0251 0251 - 0220 31 minutes

11 Aug _____

12 Aug 0238 _____ 0305 0305 - 0238 27 minutes

Step 3: Tabular interval = 2 ° 69°20’ - 68 ° = 1°20’ Using a tabular interval of 2 °, 1°20’ and 31 min, you find 19 minutes Using a tabular interval of 2 °, 1°20’ and 27 min, you find 17 minutes Step 4: Subtract this value (19 & 16 min) to the time closest to the Equator. 0251 0305 70 ° 0220 0238 - 19 min - 17 min 69°20’ 0232 0242 0248 0232 0248 68 ° 0251 0305

47


Step 6: 0242 + 0242 0524 GMT - 0200 0324 (+2) 0224 DST

SUNSET

Step 1: 70° 69°20’ 68° Step 2:

9 Aug 2146 _____ 2116

11 Aug

12 Aug 2128 _____ 2102

_____

2146 - 2116 30 minutes

2128 - 2102 26 minutes


Step 4: Add this value (19 & 16 min) to the time closest to the Equator. 2116 2102 70 ° 2146 2128 + 19 min + 16 min 69°20’ 2135 2124 2118 2135 2118 68 ° 2116 2102 Step 5: Conversion of arc to time 07° 2:40 32’W 0:02 2:42 (Add when West)

Step 6: 2124 + 0242 0006 GMT - 0200 2206 (+2) 2106 DST


Nil


Nil

48

PART II Question 1

15 Apr 03

Lat : 42°30’S Long : 169 ° 41’W

SUNRISE

Step 1: 40° 42°30’ 45° Step 2:

14 Apr 0628 _____ 0633

15 Apr

17 Apr

_____ N/A

0633 - 0628 5 minutes

Step 3: Tabular interval = 5 ° 42°30’ - 40 ° = 2°30’ Using a tabular interval of 5 °, 2°30’ and 5 min, you find 2 minutes Step 4: Add this value (2 min ) to the time closest to the Equator. 0628 ? 40° 0628 + 2 min + ? min 42°30’ 0630 0630 0630 ? 45° 0633 Step 5: Conversion of arc to time 169° 11:17 42’W 0:02::44 13:61 (Add when West)

Step 6: 0630 + 1400 2030 GMT - 1000 0630 (+10)

SUNSET

Step 1: 40° 42°30’ 45° Step 2:

14 Apr 1733 _____ 1727 1733 - 1727 6 minutes

15 Apr _____

17 Apr 1728 _____ 1722 1728 - 1722 6 minutes


49

Step 4: Subtract this value (2 min ) to the time closest to the Equator. 1733 1728 40 ° 1733 1728 - 2 min - 2 min 42°30’ 1731 1729 1726 1731 1726 45 ° 1726 1722 Step 5: Conversion of arc to time 169° 11:16 41’W 0:02::48 11:18::48 (Add when West)

Step 6: 1729 + 1118 0447 GMT - 1000 1847 (+10)


Step 1: 40° 42°30’ 45° Step 2:

14 Apr 0529 _____ 0529

15 Apr _____

0530 - 0529 0 minute

17 Apr 0531 _____ 0533 0533 - 0531 2 minute

Step 3: Tabular interval = 5 ° 42°30’ - 40 ° = 2°30’ Using a tabular interval of 5 °, 2°30’ and 0 min, you find 0 minute Using a tabular interval of 5 °, 2°30’ and 2 min, you find 1 minute Step 4: Add this value (1 min) to the time closest to the Equator. 0529 0531 40 ° 0529 + 1 min + 1 min 42°30’ 0529 0530 0530 0532 45 ° 0529 Step 5: Conversion of arc to time 169° 11:16 41’W 0:03::04 11:19::04 (Add when West)

0531 0532 0533

Step 6: 0530 + 1119 1649 GMT - 1000 0649 (+10)


Step 1: 40° 42°30’ 45°

14 Apr 1831 _____ 1831

15 Apr _____

17 Apr 1827 _____ 1826

50

Step 2:

1831 - 1831 0 minute

1827 - 1826 1 minute

Step 3: Tabular interval = 5 ° 42°30’ - 40 ° = 2°30’ Using a tabular interval of 5 °, 2°30’ and 0 min, you find 0 minute Using a tabular interval of 5 °, 2°30’ and 1 min, you find 1 minute Step 4: Subtract this value (1 min) to the time closest to the Equator. 1831 1827 40 ° 1831 1827 - 0 min - 1 min 42°30’ 1831 1829 1826 1831 1826 45 ° 1831 1826 Step 5: Conversion of arc to time 169° 11:16 41’W 0:02::48 11:18::48 (Add when West)

Step 6: 1829 + 1119 0548 GMT - 1000 1948 (+10)

MOONRISE

Step 1: 40° 42°30’ 45° Step 2:

15 Apr 1708 _____ 1708 1708 - 1708 0 minutes

16 Apr 1737 _____ 1733

(*use following date in west longitudes)

1733 - 1737 4 minutes

Step 3: Tabular interval = 5 ° 42°30’ - 40 ° = 2°30’ Using a tabular interval of 5 °, 2°30’ and 0 min, you find 0 min in Table I. Using a tabular interval of 5 °, 2°30’ and 4 min, you find 2 min in Table I. Step 4: Add this value (0& 2 min) to the time closest to the Equator. 1708 1737 40 ° 1708 1737 + 0 min - 2 min 42°30’ 1708 1739 1708 1735 45 ° 1708 1733

51

Step 5: 1735 – 1708 = 27 minutes Using Table II (p.xxxii), a longitude of 169 °41’W and a time of 27 min, you find a time of 13 minutes (west = add this number (13 min) to the time obtained in step 6) Step 6: Conversion of arc to time 169° 11:16 41’W 0:02::44 11:18::44 +0:13 11:31::44 (Add when West)

Step 7: 1708 + 1131 0839 GMT - 1000 1639 (+10)

MOONSET

Step 1: 40° 42°30’ 45° Step 2:

15 Apr 0430 _____ 0427 0430 - 0427 3 minutes

16 Apr 0546 _____ 0548


0546 - 0548 2 minutes

Step 3: Tabular interval = 5 ° 42°30’ - 40 ° = 2°30’ Using a tabular interval of 5 °, 2°30’ and 3 min, you find 2 min in Table I. Using a tabular interval of 5 °, 2°30’ and 2 min, you find 2 min in Table I. Step 4: Subtract this value (6 & 4 min) to the time closest to the Equator. 0430 00546 40 ° 0430 0546 - 2 min + 2 min 42°30’ 0428 0548 0428 0548 45 ° 0427 0548

Step 5: 0548 – 0428 = 01 hr 20 minutes Using Table II (p.xxxii), a longitude of 169 °41’W and a time of 01 hr 20 min, you find a time of 39 minutes (west = add this number (39 min) to the time obtained in step 6)

52

Step 6: Conversion of arc to time 169° 11:16 41’W 0:02::44 11:18::44 +0:39

Step 7: 0428 + 1157 1625 GMT - 1000 0525 (+10)

Question 2

30 July 03

Lat : 40°21’N Long : 07° 32’W

(Z)

SUNRISE

Step 1: 45° 40°21’ 40° Step 2:

28 July 0440 _____ 0454

30 July _____

0454 - 0440 14 minutes

31 July 0444 _____ 0457 0457 - 0444 13 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 14 min, you find 1 minute Using a tabular interval of 5 °, 0°21’ and 13 min, you find 1 minute Step 4: Subtract this value (1 min) to the time closest to the Equator. 0454 0457 45 ° 0440 0444 - 1 min - 1 min 40°21’ 0453 0456 0456 0453 0456 40 ° 0454 0457 Step 5: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08 (Add when West)

Step 6: 0456 + 0030 0526 GMT

SUNSET

Step 1: 45° 40°21’ 40°

28 July 1932 _____ 1918

30 July _____

31 July 1929 _____ 1915

53

Step 2:

1932 - 1918 14 minutes

1929 - 1915 14 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 14 min, you find 1 minute Using a tabular interval of 5 °, 0°21’ and 14 min, you find 1 minute Step 4: Add this value (1 min) to the time closest to the Equator. 1918 1915 45 ° 1932 + 1 min + 1 min 40°21’ 1919 1916 1919 1916 40 ° 1918 Step 5: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08 (Add when West)

1929 1916 1915

Step 6: 1916 + 0030 1946 GMT


Step 1: 45° 40°21’ 40° Step 2:

28 July 0322 _____ 0345 0345 - 0322 23 minutes

30 July _____

31 July 0327 _____ 0349 0349 - 0327 22 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 23 min, you find 1 minute Using a tabular interval of 5 °, 0°21’ and 22 min, you find 1 minute Step 4: Subtract this value (1 min) to the time closest to the Equator. 0345 0349 45 ° 0322 0327 - 1 min - 1 min 40°21’ 0344 0347 0348 0344 0348 40 ° 0345 0349 Step 5: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08

Step 6: 0347 + 0030 0417 GMT (Add when West)

54


Step 1: 45° 40°21’ 40° Step 2:

28 July 2050 _____ 2027 2050 - 2027 23 minutes

30 July _____

31 July 2045 _____ 2023 2045 - 2023 22 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 23 min, you find 1 minute Using a tabular interval of 5 °, 0°21’ and 22 min, you find 1 minute Step 4: Add this value (1 min) to the time closest to the Equator. 2027 2023 45 ° 2050 + 1 min + 1 min 40°21’ 2028 2024 2028 2024 40 ° 2027 Step 5: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08 (Add when West) MOONRISE Step 1: 45° 40°21’ 40°

Step 2:

30 Jul 0550 _____ 0535 0535 - 0550 15 minutes

2045 2024 2023

Step 6: 2024 + 0030 2054 GMT

31 Jul (*use following date 0700 in west longitudes) _____ 0649 0649 -0700 11 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 15 min, you find 1 min in Table I. Using a tabular interval of 5 °, 0°21’ and 11 min, you find 1 min in Table I. Step 4: Subtract this value (1 min) to the time closest to the Equator. 0535 0649 30 ° 0550 0700 + 1 min + 1 min 28°30’ 0536 0546 0650 0536 0650 20 ° 0535 0649

55

Step 5: 0650 – 0536 = 01 hr 14 minutes Using Table II (p.xxxii), a longitude of 07 ° 32’W and a time of 01 hr 14 minutes, you find a time of 2 minutes (west = add this number ( 2 min) to the time obtained in step 6) Step 6: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08 +0:02::00 0: 32::08

Step 7: 0546 + 0032 0618

GMT

MOONSET

Step 1: 45° 40°21’ 40° Step 2:

30 Jul 2043 _____ 2031 2043 - 2031 12 minutes

31 Jul (*use following date 2108 in west longitudes) _____ 2100 2108 -2100 8 minutes

Step 3: Tabular interval = 5 ° 40°21’ - 40 ° = 0°21’ Using a tabular interval of 5 °, 0°21’ and 12 min, you find 1 min in Table I. Using a tabular interval of 5 °, 0°21’ and 8 min, you find 0 min in Table I. Step 4: Add this value (1 min) to the time closest to the Equator. 2031 2100 30 ° 2043 + 1 min + 0 min 28°30’ 2032 2032 2100 20 ° 2031

2108 2100 2100

Step 5: 2108 – 2032 = 36 minutes Using Table II (p.xxxii), a longitude of 07 ° 32’W and a time of 36 minutes, you find a time of 1 minute (west = add this number (1 min) to the time obtained in step 6) Step 6: Conversion of arc to time 07° 0:28 32’W 0:02::08 0:30::08 +0:01 0:31::08

Step 7: 2048 + 0031 2119 GMT -0100 2019

56

Question 3

30 Sep 03

Lat: 41˚20’N Long: 63˚47’E

(-4)

SUNRISE

Step 1: 45° 41°20’ 40° Step 2:

29 Sept 0555 _____ 0554

30 Sept _____

0555 - 0554 1 minute

2 Oct 0559 _____ 0557 0559 - 0557 2 minutes

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 1 min, you find 0 minutes Using a tabular interval of 5 °, 1°20’ and 2 min, you find 0 minutes Step 4: Subtract this value (0 min) to the time closest to the Equator. 0554 0557 45 ° 0555 0559 - 0 min - 0 min 41°20’ 0554 0555 0557 0554 0557 40 ° 0554 0557 Interpolate between 0554 and 0557 to give you the time for 30 Sept 03 This gives you a time of 0555. Step 5: Conversion of arc to time 63° 4:12 47’E 0:03::08 4:15::08 (Subtract when East)

Step 6: 0555 - 0415 0140 GMT +0400 0540 (-4)

SUNSET

Step 1: 45° 41°20’ 40° Step 2:

29 Sept 1745 _____ 1746 1746 - 1745 1 minute

30 Sept _____

2 Oct 1739 _____ 1741 1741 - 1739 2 minutes

57

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 1 min, you find 0 min. in Table I Using a tabular interval of 5 °, 1°20’ and 2 min, you find 0 min. in Table I Step 4: Subtract this value (0 min) to the time closest to the Equator. 1746 1741 45 ° 1745 1739 - 0 min - 0 min 41°20’ 1746 1741 1746 1741 40 ° 1746 1744 1741 Interpolate between 1746 and 1741 to give you the time for 30 Sept 03. This gives you a time of 1744. Step 5: Conversion of arc to time 63° 4:12 47’E 0:03::08 4:15::08 (Subtract when East)

Step 6: 1744 - 0415 1329 GMT +0400 1729 (-4)


Step 1: 45° 41°20’ 40° Step 2:

29 Sept 0451 _____ 0455 0455 - 0451 4 minutes

30 Sept _____

2 Oct 0455 _____ 0458 0458 - 0455 3 minutes

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 4 min, you find 1 min. in Table I Using a tabular interval of 5 °, 1°20’ and 3 min, you find 1 min. in Table I Step 4: Subtract this value (1 min) to the time closest to the Equator. 0455 0458 45 ° 0451 0455 - 1 min - 1 min 41°20’ 0455 0455 0455 0454 0457 40 ° 0455 0458 Interpolate between 0454 and 0457 to give you the time for 30 Sept 03. This gives you a time of 0455.

58

Step 5: Conversion of arc to time 63° 4:12 47’E 0:03::08 4:15::08 (Subtract when East)

Step 6: 0455 - 0415 0040 GMT +0400 0440 (-4)


Step 1: 45° 41°20’ 40° Step 2:

29 Sept 1849 _____ 1845 1849 - 1845 4 minutes

30 Sept _____

2 Oct 1843 _____ 1840 1843 - 1840 3 minutes

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 4 min, you find 1 minute in Table I Using a tabular interval of 5 °, 1°20’ and 3 min, you find 0 minutes in Table I Step 4: Subtract this value (0 & 1 min) to the time closest to the Equator. 1845 1840 45 ° 1849 1843 - 1 min - 0 min 41°20’ 1845 1842 1840 1844 1840 40 ° 1845 1840 Interpolate between 1845 and 1840 to give you the time for 30 Sept 03. This gives you a time of 1845. Step 5: Conversion of arc to time 63° 4:12 47’E 0:03::08 4:15::08 (Subtract when East)

Step 6: 1845 - 0415 1430 GMT +0400 1830 (-4)

MOONRISE

Step 1: 45° 41°20’ 40°

29 Sept 1000 _____ 0946

30 Sept 1121 _____ 1104

(*use previous date in east longitudes)

59

Step 2:

1000 - 0946 14 minutes

1121 - 1104 17 minutes

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 14 mins, you find 4 mins. in Table I Using a tabular interval of 5 °, 1°20’ and 17 mins, you find 4mins. In Table I Step 4: Add this value (4 & 4 min) to the time closest to the Equator. 0946 1104 45 ° 1000 1121 + 4 min + 4 min 41°20’ 0950 0959 1108 0950 1108 40 ° 0946 1104 Step 5: 1108 – 0950 = 1 h 18 mins. Using Table II (p.xxxii), a longitude of 63 ° 47’E and a time of 1 h 18 minutes, you find a time of 13 minutes (east = subtract this number (13 min) to the time obtained in step 6) Step 6: Conversion of arc to time 63° 4:12 47’E 0:03::08 - 4:14::08 - 0:13 4:01::08 (Subtract when East)

Step 7: 0959 - 0401 0558 GMT + 0500 1058 (-5)

MOONSET

Step 1: 45° 41°20’ 40° Step 2:

29 Sept 1953 _____ 1939 1953 -1939 14 minutes

30 Sept 2035 _____ 2016


2035 - 2016 19 minutes

Step 3: Tabular interval = 5 ° 41°20’ - 40 ° = 1°20’ Using a tabular interval of 5 °, 1°20’ and 14 min, you find 4 min in Table I. Using a tabular interval of 5 °, 1°20’ and 19 min, you find 5 min in Table I.

60

Step 4: Subtract this value (1 min) to the time closest to the Equator. 1953 2035 45 ° 1939 2016 - 4 min - 5 min 41°20’ 1949 2015 2030 1949 2030 40 ° 1953 2035 Step 5: 2030 – 1949 = 41 minutes Using Table II (p.xxxii), a longitude of 63 ° 47’E and a time of 41 minutes, you find a time of 7 minutes (east = subtract this number (7 min) to the time obtained in step 6) Step 6: Conversion of arc to time 63° 4:12 47’E 0:03::08 - 4:14::08 - 0:41 3:27 (Subtract when East)

Step 7: 2015 - 0327 1712 GMT + 0500 2212 (-5)

Question 4

12 Oct 03

Lat : 58°21’S Long : 46 ° 00’E

SUNRISE Step 1: 58˚ 58°21’ 60°

Step 2:

11 Oct 0456 _____ 0452 0456 - 0452 4 minutes

(-4)

12 Oct _____

14 Oct 0448 _____ 0443 0448 - 0443 5 minutes

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 4 min, you find 1 minute Using a tabular interval of 2 °, 0°21’ and 5 min, you find 1 minute Step 4: Subtract this value (1 min) to the time closest to the Equator. 0456 0448 58 ° 0456 0448 - 1 min - 1 min 58°21’ 0455 0452 0447 0455 0447 60 ° 0452 0443

61

Step 5: Conversion of arc to time 46° 3:04 00’E 0:00 3:04 (Subtract when East)

Step 6: 0452 -0304 0148 GMT +0400 0548 (-4)

SUNSET

Step 1: 58° 58°21’ 60°

Step 2:

11 Oct 1839 _____ 1843

12 Oct _____

1843 - 1839 4 minutes

14 Oct 1846 _____ 1851

1851 - 1846 5 minutes

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 4 min, you find 1 minute Using a tabular interval of 2 °, 0°21’ and 5 min, you find 1 minute Step 4: Add this value (1 min) to the time closest to the Equator. 1839 1846 58 ° 1839 + 1 min + 1 min 58°21’ 1840 1843 1840 1847 60 ° 1843 Step 5: Conversion of arc to time 46° 3:04 00’E 0:00 3:04 (Subtract when East)

1846 1847 1851

Step 6: 1843 -0304 1539 GMT +0400 1939 (-4)


Step 1: 58° 58°21’ 60° Step 2:

11 Oct 0323 _____ 0312 0323 - 0312 11 minutes

12 Oct _____

14 Oct 0313 _____ 0300 0313 - 0300 13 minutes

62

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 11 min, you find 2 minutes Using a tabular interval of 2 °, 0°21’ and 13 min, you find 3minutes Step 4: Subtract this value (2 & 3 min ) to the time closest to the Equator. 0323 0313 58 ° 0323 0313 - 2 min - 3 min 58°21’ 0321 0317 0310 0321 0310 60 ° 0312 0300 Step 5: Conversion of arc to time 46° 3:04 00’E 0:00 3:04 (Subtract when East)

Step 6: 0317 -0304 0013 GMT +0400 0413 (-4)


Step 1: 58° 58°21’ 60° Step 2:

11 Oct 2013 _____ 2024 2024 - 2013 11 minutes

12 Oct _____

14 Oct 2022 _____ 2034 2034 - 2022 12 minutes

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 11 min, you find 2 minute Using a tabular interval of 2 °, 0°21’ and 12 min, you find 2 minute Step 4: Add this value (2 min) to the time closest to the Equator. 2013 2022 58 ° 2013 + 2 min + 2 min 58°21’ 2015 2018 2015 2024 60 ° 2024 Step 5: Conversion of arc to time 46° 3:04 00’E 0:00 3:04 (Subtract when East)

2022 2024 2034

Step 6: 2018 -0304 1714 GMT +0400 2114 (-4)

63

MOONRISE

Step 1: 58° 58°21’ 60° Step 2:

11 Oct 2012 _____ 2020 2012 - 2020 8 minutes

12 Oct 2133 _____ 2145


2133 - 2145 12 minute

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 8 min, you find 1 min in Table I. Using a tabular interval of 2 °, 0°21’ and 12 min, you find 1 min in Table I. Step 4: Add this value (1 & 1 min) to the time closest to the Equator. 2012 2133 58 ° 2012 2133 + 1 min + 1 min 58°21’ 2013 2134 2013 2134 60 ° 2020 2145 Step 5: 2134 – 2013 = 01 hr 21 min Using Table II (p.xxxii), a longitude of 46 ° 00’E and a time of 01 hr 21 min, you find a time of 10 minutes (east = subtract this number (10 min) to the time obtained in step 6) Step 6: Conversion of arc to time 46° 3:04 00’E 0:00 - 3:04 - 0:10 2:54 (Subtract when East)

Step 7: 2134 - 0254 1824 +0400 22245(-4)

MOONSET

Step 1: 58° 58°21’ 60° Step 2:

11 Oct 0530 _____ 0526 0530 -0526 4 minutes

12 Oct 0536 _____ 0528


0536 - 0528 8 minutes

64

Step 3: Tabular interval = 2 ° 58°21’ - 58 ° = 0°21’ Using a tabular interval of 2 °, 0°21’ and 4 min, you find 1 min in Table I. Using a tabular interval of 2 °, 0°21’ and 8 min, you find 1 min in Table I. Step 4: Add this value (1 min) to the time closest to the Equator. 0530 0536 58 ° 0530 + 1 min + 1 min 58°21’ 0531 0531 0537 60 ° 0536

0536 0537 0528

Step 5: 0537 – 0531 = 6 minutes Using Table II (p.xxxii), a longitude of 46 ° 00’E and a time of 6 minutes, you find a time of 1 minutes (east = subtract this number (1 min) to the time obtained in step 6) Step 6: Conversion of arc to time Step 7: 0535 46° 3:04 - 0303 00’E 0:00 0232 GMT - 3:04 +0400 - 0:01 0632 (-4) 3:03 (Subtract when East) PART III Question 1

23 Jan 03

Lat : 28°30’N Long : 71° 15’W

MOONRISE

Step 1: 30° 28°30’ 20° Step 2:

23 Jan 0006 _____ 0051 0051 - 0006 45 minutes

24 Jan 0013 _____ 0051


0051 - 0013 38 minutes

Step 3: Tabular interval = 10 ° 28°30’ - 20 ° = 8°30’ Using a tabular interval of 10 °, 8°30’ and 45 min, you find 36 minutes in Table I. Using a tabular interval of 10 °, 8°30’ and 38 min, you find 31 minutes in Table I.

65

Step 4: Subtract this value (11 & 6 min) to the time closest to the Equator. 0051 0051 30 ° 0006 0013 - 36 min - 31 min 28°30’ 0015 0020 0015 0020 20 ° 0051 0051 Step 5: 0020 – 0015 = 5 minutes Using Table II (p.xxxii), a longitude of 71 ° 15’W and a time of 5 minutes, you find a time of 1 minutes (west = add this number (1 min) to the time

Step 6: Conversion of arc to time 71° 4:44 15’W 0:01 4:45 +0:01 4:46 (Add when West)

Step 7: 0015 + 0446 0502 GMT - 0500 0002 (+5)

MOONSET

Step 1: 30° 28°30’ 20° Step 2:

23 Jan 1027 _____ 1027 1027 - 1027 0 minutes

24 Jan (*use following date 1101 in west longitudes) _____ 1106 1101 - 1106 5 minutes

Step 3: Tabular interval = 10 ° 28°30’ - 20 ° = 8°30’ Using a tabular interval of 10 °, 8°30’ and 0 min, you find 0 minutes in Table I. Using a tabular interval of 10 °, 8°30’ and 5 min, you find 4 minutes in Table I. Step 4: Add this value (0 & 4 min) to the time closest to the Equator. 1027 1106 30 ° 1027 1101 + 0 min + 4 min 28°30’ 1027 1102 1027 1102 20 ° 1027 1106 Step 5: 1102 – 1027 = 35 minutes Using Table II (p.xxxii), a longitude of 71 ° 15’W and a time of 35 minutes, you find a time of 7 minutes (west = add this number (7 min) to the time obtained in step 6)

66

Step 6: Conversion of arc to time 71° 4:44 15’W 0:01 4:45 +0:07 4:52 (Add when West)

Step 7: 1027 + 0452 1519 GMT -0500 1019 (+5)

67

ANNEX B – Canadian Tide Tables

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

ANNEX C – American Tide Tables

87

88

89

90

91

92

93

94

95

96

97

ANNEX D – Astro Tables

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

ANNEX E – Miscellaneous Tables

117

118

119

120

121

Tides Handbook

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