Coast Guard Bridge Navigation Refresher Guidebook (August 2011 Edition)

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B r i d g e N a v i g a t i o n & S e a m a n s h i p

R e f r e s h e r G u i d e b o o k

August 2011 Edition



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Table of Contents

Introduction .................................................................................................................... 5Maneuvering Boards....................................................................................................... 6

Maneuvering Boards: Wind Calculations .................................................................... 7True Wind Determination........................................................................................ 8

Desired Wind Determination................................................................................. 12Maneuvering Boards: Contact Calculations............................................................... 16

Single contact calculations .................................................................................... 17Avoidance/Intercept .............................................................................................. 21

Celestial Navigation...................................................................................................... 26Time of Phenomenon ................................................................................................ 31

Sunrise/Sunset....................................................................................................... 31Moonrise/Moonset ................................................................................................ 34

Meridian Passage (Time of LAN for the Sun)........................................................ 37Sextant Fundamentals ............................................................................................... 40

Sextant Nomenclature ........................................................................................... 40

Sextant Usage: Standard Corrections..................................................................... 41Local Apparent Noon................................................................................................ 44Celestial Sight Reduction .......................................................................................... 47

Compasses .................................................................................................................... 52Gyro Error................................................................................................................. 52

Amplitude of the Sun ............................................................................................ 53Azimuth of the Sun ............................................................................................... 56

Deviation/Variation Calculations............................................................................... 59Piloting Techniques....................................................................................................... 62

3 Minute Rule ........................................................................................................... 626 Minute Rule ........................................................................................................... 62

Doubling the Angle on the Bow................................................................................ 62Six Rules of Dead Reckoning.................................................................................... 63

Radian Rule .............................................................................................................. 63Interpolation.............................................................................................................. 63

Set and Drift.............................................................................................................. 64Anchoring: Swing and Drag Circles .......................................................................... 65

Universal Plotting Sheet Construction ....................................................................... 67Visibility of Lights.................................................................................................... 69Common Conversion Factors .................................................................................... 71

Tides and Currents ........................................................................................................ 72Calculating Tides Manually....................................................................................... 72

Calculating Currents Manually.................................................................................. 76Tides and Currents Tricks ......................................................................................... 78

Weather ........................................................................................................................ 79Beaufort Forces......................................................................................................... 79

Useful Tricks and Sayings......................................................................................... 79Rules of the Road.......................................................................................................... 81

Notes ............................................................................................................................ 82An Excerpt from "Cruise of the Snark" by Jack London................................................ 84



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I n t r o d u c t i o n

This guidebook is designed for bridge personnel aboard Coast Guard cutters who have

mastered navigation fundamentals at one point in their careers, but due to longevity,rotation, or lack of practice may have “forgotten” some skills. The basic navigational

mathematics and techniques described in this guidebook are meant as refresher trainingand not an introductory course. The prudent navigator will utilize every opportunity to

practice and pass on their skills to the next generation of navigators.

There are several refresher training videos on YouTube on the "USCG KnowledgeChannel" at "Chris87306." They work through some of the same problems in the text.

Feedback: If you find errors or have suggestions for other topics, please email the author

at [email protected]. Thanks and safe voyages!



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M a n e u v e r in g B o a r d s

Maneuvering Boards are useful for a number of quick calculations during a normal

bridge watch. In a matter of minutes, the navigator can determine the true course andspeed of a contact, determine the course or speed to steer to avoid or intercept the contact,

and determine the true or desired wind for operations or log-keeping.

It takes constant practice on maneuvering boards to become and stay proficient.



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M a n e u v e r in g B o a r d s : W i n d C a l c u l at io n s



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True Wind Determination

The Basic Idea: Use vectors to determine the true speed and direction of the wind basedon your ship’s course/speed and the relative wind read from the anemometer.

Definitions:

Vector: A line/arrow that represents direction and intensity (speed).Relative Wind: The wind read from the anemometer or weather log.

Apparent Wind: The compass direction from which the wind appears to be blowing,taking into account your ship’s course and speed.

Scales: The maneuvering board has multiple scales available for use depending on thespeeds and distances required.

Procedure: The vector for your ship’s course and speed is plotted and called “E-R.” The

relative wind is converted into an apparent wind and plotted as “R-W.” The remaining

vector, “E-W,” represents the true direction and speed of the wind.

Common Pitfalls:

1. You must convert the relative wind into the apparent wind before plotting a solution.2. The vector “E-W” is read from E to W. The wind blows from a given direction.

3. Use the same scale for all vectors. It reduces the chance of errors when using differentscales for distance or speed.

Example:

Your ship is on heading 090T at 8 knots. The wind read from the anemometer is 030Relative at 12 knots. Calculate the true direction and intensity of the wind.

Step One: Plot Your Course and Speed (E-R Vector):



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Step Two: Convert the Relative Wind into an Apparent Wind:

The apparent wind is equal to the ship’s heading plus the bearing of the relative wind. In

this case the ship’s head is 090T and the relative wind is 030R. The apparent wind is

120T. (090T+030R=120T) Place a small arrow on the outer ring of the maneuvering board indicating that the apparent wind is from 120T.

Sidebar: If the ship’s heading plus the relative wind direction total is more than 360degrees, subtract 360 from the total. For example: if the ship’s head is 270T and the

relative wind is 130R, then the total equals 400 degrees. 400-360 = 040T. The apparent wind would be 040T.

E R

ApparentWind



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Step Three: Draw the Apparent Wind Vector:

Beginning at point “R” draw a vector parallel to the apparent wind direction (120T –

300T) and as long as the intensity of the relative wind (12 knots). Label it “R-W.”

E R

ApparentWind

W 12 kts



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Step Four: Plot the True Wind Solution:

The remaining vector “E-W” represents the true wind direction and intensity. The

solution is read from E to W. The true wind is from 160T at 6.5 knots. It helps to circle

the solution to avoid confusion.

Check your work: on a ship moving forward, the true wind is always on the same side

and aft of the apparent wind. In this example, the relative wind was 30 degrees off the starboard bow, while the true wind solution was 160T or 70 degrees off the starboard

bow.

E

R

ApparentWind

W

TrueWind

6.5 kts



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Desired Wind Determination

The Basic Idea: Determine the course and speed to steer in order to obtain a desired

relative wind across the deck.

Definitions:Vector: A line/arrow that represents direction and intensity (speed).

Relative Wind: The wind read from the anemometer or weather log.Apparent Wind: The compass direction from which the wind appears to be blowing,

taking into account your ship’s course and speed.Desired Relative Wind: A desired wind across the deck for operational planning (flight

operations, firefighting, boat launches, etc).True Wind: The true compass direction and speed from which the wind is blowing,

regardless of the observer’s motion through the water.

Scales: The maneuvering board has multiple scales available for use depending on thespeeds and distances required. It is generally best to stick to the same scale to avoidconfusion.

Procedure: Use the maneuvering board in “relative” mode by indicating the ship’s head

as 000R. Plot the desired relative wind direction and speed as a vector from point “A” tothe origin. Determine ship’s required speed by swinging an arc from point “A” towards

the ship’s relative head and label the intersecting point as “B.” Indicate a representationof the true wind by creating a line parallel to “A-B” from the origin. The required ship’s

course will have the same angular relationship between the 000R heading and therepresentation of the desired wind.

Common Pitfalls:

1. Use the same scale throughout if possible.2. When plotting the relative heading, extend the line from the origin all the way to the

outer ring of the maneuvering board. This line does not represent the ship’s course andspeed.

3. When plotting the representation of the true wind, do not confuse this line with theactual true wind. It is only a representation used to determine the angular measurement

between the true wind and the required ships heading.

Example:

The true wind is blowing from 160T at 6.5 knots.Calculate the course and speed your ship must steer to obtain a desired relative wind of 12 knots from a direction 30 degrees off the port bow.



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Step One: Plot the Desired Relative Wind

Consider the maneuvering board to be in “relative” mode by plotting the ship’s head as000R. Plot the desired relative wind along the 330R line from a point 12 nm (or 12 kts)

away. Label this point “A.” Use any convenient scale but be sure to label the scale in

use. This example uses the 2:1 scale.

2:1 scalein use

DesiredRelativeWind(330R)

RelativeShip’s Head(000R)

A



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Step Two: Use the True Wind Speed to Determine Required Ship’s Speed:

Set a pair of dividers to the true wind speed of 6.5 knots and swing an arc from point “A”

until it intersects your relative ship’s head line (000R). There will generally be two

intersection points. Pick the intersection point closer to the origin and label it point “B.”Connect the line “A-B.”

Sidebar: It is usually preferable to use the intersection point closest to the origin becauseit results in a slower ship speed. However, for some operations a higher ship speed may

be desired. Either solution will produce the same desired wind speed and direction.

2:1 scalein use



A

6.5 kts = TrueWind Speed

B



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Step Three: Determine the Angular Relationship Between the True Wind and the

Desired Ship’s Head to Determine the Solution:

Draw a dashed parallel line to “A-B” which begins at the origin and extends outward to

the edge of the maneuvering board. The angle between this line and the 000R line (66degrees) indicates the angular relationship between the true wind (160T) and the ship’shead required to obtain the desired relative wind.

The required course is 66R+160T = 226T. The required speed is given by the length of

the line from the origin to point “B,” or 8 knots.

2:1 scalein use



A

B

Representationof True Wind

160T at 6.5knots

Angular DistanceBetween RequiredShip’s Head and TrueWind (66 degrees)

Required Ship’sSpeed (8 knots)

Solution: Point the

ship 66 degrees tothe right of the TrueWind (226T) andtransit at 8 knots.



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M a n e u v e r i n g B o a r d s : C o n t a ct

C a l c u l a t i o n s



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Single contact calculations

The Basic Idea: Use vectors to determine the closest point of approach, true course andtrue speed of a radar contact.

Definitions:

Vector: A line/arrow that represents direction and intensity (speed).CPA: Closest Point of Approach; indicates a contacts bearing, range and time at which it

will be closest to “own-ship.”

Procedure: The vector for your ship’s course and speed is plotted and called “E-R.” Therelative motion of the radar contact is plotted using consecutive bearings and ranges to

the contact and is used to construct a vector “R-M”. The closest point of approach(bearing, range and time) is determined. The radar contact’s speed and direction of

relative motion are determined and used to calculate the contact’s true course and speed

by completing the triangle with the “E-M” vector.

Common Pitfalls:

1. Be mindful of which scales you are using.2. Use the logarithmic nomogram correctly: read the instructions on the maneuvering

board. The nomogram at the bottom of the maneuvering board can solve for any value of speed, distance, or time if you know the other two.

Example:

Your ship is on heading 330T at 7 knots.You plot a radar contact with the following bearings/ranges/times

Time: 1412

Bearing: 000 TRange: 9.0 nm

Time: 1415

Bearing: 001 TRange: 8.3 nm

Time: 1418

Bearing: 002 T

Range: 7.7 nm

Calculate the contact’s CPA (bearing, range and time).

Calculate the contact’s speed and direction of relative motion.Calculate the contact’s true course and speed.



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Step One: Plot Ownship Course and Speed and Contact Bearing/Ranges:

Label ownship vector “E-R.” Use any convenient scale, but be mindful of which scale is

in use at all times.

Plot the contact’s bearing and range for each given time.

E

R

1412

1415

1418



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Step Two: Draw the Relative Motion Line to Determine Closest Point of Approach

(CPA) Details and Speed/Direction of Relative Motion (SRM/DRM):

1. CPA bearing/distance is located at the closest point that the relative motion line gets

to the origin (077T at 2.0 nm). Orange Text and Hash Marks on the Diagram 2. DRM is determined by rolling the relative motion line to the origin and reading the bearing (167T). Red Arrows in example.

3. SRM is determined by using the logarithmic nomogram at the bottom of themaneuvering board. (11 knots). Blue Letters/Numbers/Dividers in example.

4. CPA time is determined by using the logarithmic nomogram at the bottom of themaneuvering board (41 minutes from 1418 = 1459) Green Letters/Numbers/Dividers in

example .

E

R

14121415

1418

Direction of Relative Motion =167 T

CPA Bearing: 077 T CPA Range: 2.0 nm

2300 yards 6 minutes

6 minutes

2300 yards

SRM=11kts

7.4 nm

7.4 nm

41 minutes

CPA Time - 41 minutesfrom 1418 = 1459



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Step Three: Determine the Contact’s True Course and Speed:

Draw a vector parallel to the direction of relative motion line (167T), beginning at point

“R” and ending at point “M.” Draw the vector equivalent to the length of the speed of

relative motion (11kts).

The remaining vector “E-M” is equivalent to the true course and speed of the radar

contact, 192T at 4.7 kts.

Sometimes it helps to draw a picture of the two vessels to consider various rules of theroad scenarios.

E

R

1412

1415

1418

6 minutes

2300 yards

SRM=11kts

M

True Courseand Speedof Contact

11 kts

192T



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Avoidance/Intercept

The Basic Idea: After determining the course and speed of a contact using vectors,manipulate the situation to pass as close or as far from the contact as you desire.

Definitions:

Vector: A line/arrow that represents direction and intensity (speed).CPA: Closest Point of Approach; indicates a contacts bearing, range and time at which it

will be closest to “ownship.”

Procedure: After determining the direction and speed of relative motion, true course andspeed of a contact, change the “R-M” vector to bring the contact as close or as far from

the origin as desired. Then compute a new “E-R” vector to indicate the course and speedyour ship must steer to cause the desired situation to occur.

Common Pitfalls:1. Be mindful of which scales you are using.2. Use the logarithmic nomogram correctly: read the instructions on the maneuvering

board.

Example: Your ship is on heading 330T at 7 knots.

You detect a radar contact with the following bearings/ranges/times

Time: 1412Bearing: 000 T

Range: 9.0 nm


Range: 8.3 nm


Range: 7.7 nm

After you have determined the contact’s CPA, speed/direction of relative motion, and

true course/speed, alter course at 1423 to open the target to a 4.0 nm CPA.



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Step One: Determine the Contact’s SRM/DRM, CPA, True Course/Speed:

See the previous section to determine this information. Below is a diagram/summary of

the pertinent information from the last example.

Direction/Speed of Relative Motion: 167T at 11 ktsCPA: Bearing 077T Distance: 2.0nm Time: 1459

True Course/Speed: 192T at 4.7kts

E

R

1412

1415

1418

6 minutes

2300 yards

SRM=11kts

M


11 kts



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Step Two: Determine the Maneuvering Time:

In order to create a new relative motion line, the time of maneuver must be calculated and

plotted. The desired time of movement is 1423. This is an arbitrary figure and simply

allows 5 minutes after the last contact position data before maneuvering the ship.

Use the calculated Speed of Relative Motion (11 kts) on the logarithmic nomogram to

calculate the distance the contact will travel in the allotted time (5 minutes1900 yards). Plot an estimated position for the contact at 1423 on the maneuvering board.

E

R

1412

1415

1418

SRM=11kts

M


1900 yards

5 minutes

1900 Yards

1423



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Step Three: Calculate a New Relative Motion Line:

From the 1423 location, draw a new relative motion line which has the contact behaving

as you’d like it to. In this case, the relative motion line will be moved out to have a CPA

of 4.0 nm. If you desired to intercept the contact, the relative motion line would beturned into a CBDR (constant bearing, decreasing range) situation.

E

R

1412

1415

1418

SRM=11kts

M


1900 yards

5 minutes

1900 Yards

1423

NewRelativeMotion Line



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Step Four: Determine Own-Ship’s Course and Speed to Steer:

Since the contact’s true course and speed vector will not change, and you have artificially

manipulated the relative motion line, then the own-ship’s course and speed must be

changed to make the desired maneuvering situation take place.

Parallel the new relative motion line to the maneuvering triangle and determine a new

course/speed to steer. The own-ship’s course and speed could be any line that interceptsthe new relative motion line, but in practice the own-ship generally keeps it’s speed the

same and avoids/intercepts by maneuver alone. You must maneuver to course 329T and

maintain speed to avoid the contact by 4.0 nm.

E

1412

1415

1418

SRM=11kts

M

True Courseand Speedof Contact(Does NotChange)

1900 yards

5 minutes

1423

New RelativeMotion Line

R (new)

R (old)



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C e l e s t i a l N a v i g a t i o n

Use the following pages from the Nautical Almanac for the

Celestial Navigation section examples.



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The daily page from the Nautical Almanac for February 4th, 2009.



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The Conversion of Arc to Time page from the Nautical Almanac.



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Table 1 and Table 2 from the Nautical Almanac



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The Altitude Correction Tables from the Nautical Almanac (Standard Corrections).



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T i m e o f P h e n o m e n o n

Calculating the time of a celestial phenomenon can be useful when mission planning for

SAR cases, flight operations, boat operations, and law enforcement evolutions. It isgenerally faster to calculate sunrise and sunset manually than to log on to a workstation

and look the answer up on the internet. It also tends to be more accurate because “fatfinger” mistakes on the computer are easy.

Sunrise/Sunset

The procedures for calculating sunrise and sunset are identical.

The Basic Idea: Determine the time of sunrise or sunset by calculating the time at aknown point and comparing it to the ship’s position.

Definitions:

Interpolate: to estimate the value of a figure based on known tabulated data (see sectionon interpolation).

Standard Meridian: Longitude lines beginning at zero and proceeding every 15 degreesaround the planet (15, 30, 45, 60 75, etc). These correspond to the standard time zones

around the world.Standard Latitude: The latitudes for which time values are calculated in the Nautical

Almanac.

Procedure: Obtain the ship’s position at the approximate time of desired phenomenon.

Use the daily pages in the Nautical Almanac to interpolate the sunrise/sunset time for theship’s latitude compared to a pair of standard latitudes. Adjust this time based on theship’s distance from a standard meridian (longitude line). Adjust for daylight savings

time if necessary.

Common Pitfalls:1. Account for daylight savings time either by picking the actual time zone being

observed or by adding 1 hour to answer.

Example:

Calculate the time of sunset on February 4

th

, 2009 in position 42-30N, 078-22W.

Step One: Interpolate for Latitude Correction:

Locate the daily pages for 04 February 2009. Locate the column for “sunset.” Find theclosest latitude values which bracket the ship’s actual longitude. Interpolate for the

difference or utilize Table 1 on page xxxii near the back of the Nautical Almanac.



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To interpolate:

Value for Latitude 45: 1712Value for Latitude 40: 1723

Time difference: 11 minutes.

Therefore in this part of the world, there is a difference in sunset times of 11 minutes for

every 5 degrees of latitude.

Since the ship’s latitude is 42-30N, the ship is 2 degrees and 30 minutes north of thetabulated latitude of 40 degrees. This is also exactly halfway between 40N and 45N, so

the time difference should be exactly half of 11 minutes, or 5 minutes, 30 seconds.

Sidebar: if the ship’s latitude was not exactly halfway between Standard Latitudes, a slightly more difficult but manageable interpolation is necessary.

The latitude-corrected time of sunset is 5 minutes and 30 seconds before 1723, or

17:17:30 (rounded to 1718). This “mental interpolation” procedure can be used withfairly good accuracy, even for values which are more difficult than this example problem.

However, an alternative method, (or the only method when the time difference betweensuccessive latitudes is more than 20 minutes), is to use Table 1 in the Nautical Almanac.

Step Two: Determine the Distance from the Nearest “Standard Meridian:”

As defined, the standard meridians are located every 15 degrees west of Greenwich

around the planet. In this case, the closest standard meridian is 075W.

This means that if the ship were at exactly 075W, the sunset would occur at 1718 (asdetermined by the latitude correction).

However, the ship is not at 075W, it is at 078-22W, or 3 degrees and 22 minutes west of

the standard meridian.

Sidebar: A key point to remember is that as far as celestial navigation, longitude is time.The celestial bodies move at a known rate around the sky. For instance the sun moves 1

degree of longitude every 4 minutes. It moves 15 degrees of longitude in 1 hour (hencethe reason for standard meridians every 15 degrees).

Step Three: Correct for Longitude:

To correct for the ship’s longitude, you must account for 3 degrees and 22 minutes of sun

movement. Using the “conversion of arc to time” table on page i in the NauticalAlmanac (located on the first of the cream colored pages), determine the value for 3

degrees and 22 seconds.



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Value for 3 degrees: 12 minutesValue for 22 minutes: 1 minute 28 seconds

Total difference: 13 minutes 28 seconds.

Step Four: Determine the Total Correction:

Add the longitude difference to the latitude-corrected time to obtain the totally corrected

time of sunset:

Latitude corrected time: 17:17:30Longitude correction: 13 minutes, 28 seconds

Corrected sunset time for ship’s position: 17:30:58, or 1731.

The sun will set at 1731 at the ship’s position.

Sidebar: Daylight savings time: During daylight savings time, people generally think they

“spring” their clocks ahead one hour. In fact, they actually observe the time zone to theeast of their correct standard meridian.

For example, in the winter, a ship in Boston (longitude 071) observes the 075 standard

meridian. 075W is 5 time zones to the west of Greenwich. Therefore, their time zonedesignator is +5R. During the summer months, the same ship in the same position will

adjust their clocks ahead one hour and observe +4Q.

In order to account for daylight savings time, you can complete the time of phenomenon

calculations for the nearest standard meridian and then adjust by adding 1 hour. Alternatively, you can account for daylight savings time earlier by selecting the actual standard meridian the ship is observing and determining a slightly larger longitude

correction.



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Moonrise/Moonset

The procedures for calculating moonrise and moonset are identical.

The Basic Idea: Determine the time of moonrise or moonset by calculating the time at a

known point and comparing it to the ship’s position.

Definitions:



around the world.Standard Latitude: The latitudes for which time values are calculated in the Nautical

Almanac.

Procedure: Obtain the ship’s position at the approximate time of desired phenomenon.Use the daily pages in the Nautical Almanac to interpolate the moonrise/moonset time for

the ship’s latitude compared to a standard latitude for the current date and also for the preceding or following date. Utilize Table II in the Nautical Almanac to correct for

longitude. Adjust for daylight savings time if necessary.

Common Pitfalls:1. Account for daylight savings time either by picking the actual time zone being

observed or by adding 1 hour to answer.2. Utilize Table II in the Nautical Almanac to correct for longitude instead of the

“conversion of arc to time.”

Example:

Calculate the time of moonrise on February 4th, 2009 in position 42-30N, 078-22W.

Step One: Interpolate for Latitude Correction:

Locate the daily page for 04 February 2009. On the right hand page, locate the columnfor “moonrise.” Find the closest latitude values which bracket the ship’s actual

longitude. Interpolate for the difference or utilize Table 1 on page xxxii near the back of the Nautical Almanac.

To interpolate:

Value for Latitude 45: 1116





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Therefore in this part of the world, there is a difference in moonrise times of 21 minutesfor every 5 degrees of latitude.

Since the ship’s latitude is 42-30N, the ship is 2 degrees and 30 minutes north of the

tabulated latitude of 40 degrees. This is also exactly halfway between 40N and 45N, so

the time difference should be exactly half of 21 minutes, or 10 minutes, 30 seconds.

The latitude-corrected time of moonrise is 10 minutes and 30 seconds before 1137, or

11:26:30. This can be rounded to 1127. This “mental interpolation” procedure can beused with fairly good accuracy, even for values which are more difficult than this

example problem. Alternatively, you can use Table 1 in the Nautical Almanac to obtainthe same result.

Step Two: Determine Latitude-Corrected time for the Following Day**:

**For the following day in West Longitudes, and for the preceding day in East

Longitudes.

Use the same process as “step one” to determine the Latitude corrected time of moonrisefor February 5

th, since the ship is in the Western Hemisphere.




Latitude-Corrected Time: 1223

Step Three: Utilize Table II in the Nautical Almanac to Correct for Longitude:

Table II is located on page xxxii near the back of the Nautical Almanac. In order to usethis table, you calculated the latitude-corrected time of moonrise for February 4

thand for

February 5th. The time difference for these two consecutive days is:

February 4th

: 1127February 5

th: 1223

Difference: 56 minutes

Enter the table and locate the nearest values for “Longitude” (80 degrees) and

“Difference Between the Times…” (60 minutes) to determine a longitude correction of

13 minutes.



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Step Four: Apply the Longitude Correction and Correct for Daylight Savings Time

if Necessary:

Add 13 minutes to the Latitude-Corrected time for February 4th

(1127) to obtain a

moonrise time of 1140.

A daylight savings time correction is not necessary in this case.



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Meridian Passage (Time of LAN for the Sun)

Meridian Passage is the time that a celestial body passes due north or south of the

observer. For the sun this is called “LAN” or Local Apparent Noon.

The Basic Idea: Determine the time of meridian passage by calculating the time at aknown point and comparing it to the ship’s position.

Definitions:



around the world.

Standard Latitude: The latitudes for which time values are calculated in the NauticalAlmanac.

Procedure: Obtain the ship’s position at the approximate time of desired phenomenon.Calculate the ship’s longitude difference from the nearest “standard meridian” and apply

a correction to the meridian passage time based on this distance. Adjust for daylightsavings time if necessary.

Why is Meridian Passage important?

Particularly for the sun, this is the time when the observer can determine their latitude

with minimal calculations. Determining the time of meridian passage allows you toknow when to “shoot LAN.”

Common Pitfalls:

1. Account for daylight savings time either by picking the actual time zone beingobserved or by adding 1 hour to answer.

2. No Latitude correction is required.

Example:

Calculate the time of the sun’s meridian passage (LAN) on February 4th

, 2009 in position

for the longitude 078-22W.

Step One: Obtain Meridian Passage Time from the Nautical Almanac:

The meridian passage time is located on the bottom right hand page of the daily pages in

the Nautical Almanac. For 4 February 2009, the time of the sun’s meridian passage is1214.



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Step Two: Determine the Distance from the Nearest “Standard Meridian:”

As defined above, the standard meridians are located every 15 degrees west of Greenwicharound the planet. In this case, the closest standard meridian is 075W.

This means that if the ship were at exactly 075W, meridian passage would occur at 1214(straight from the Nautical Almanac).

However, the ship is not at 075W, it is at 078-22W, or 3 degrees and 22 minutes west of the standard meridian.

Sidebar: A key point to remember is that as far as celestial navigation, longitude is time.

The celestial bodies move at a known rate around the sky. For instance the sun moves 1degree of longitude every 4 minutes. It moves 15 degrees of longitude in 1 hour (hence

the reason for standard meridians every 15 degrees).

Step Three: Correct for Longitude:

To correct for the ship’s longitude, you must account for 3 degrees and 22 minutes of sunmovement. Using the “conversion of arc to time” table on page i in the Nautical

Almanac (located on the first of the cream colored pages), determine the value for 3degrees and 22 seconds.

Value for 3 degrees: 12 minutes

Value for 22 minutes: 1 minute 28 seconds

Total difference: 13 minutes 28 seconds.

Step Four: Determine the Total Correction:

Add the longitude difference to the latitude-corrected time to obtain the totally correctedtime of meridian passage:

Time of Meridian Passage at Standard Meridian: 1214

Longitude correction: 13 minutes, 28 seconds

Corrected meridian passage time for ship’s position: 1227

The sun will pass the observer’s meridian at 1227 and will be at its highest point in thesky.

Sidebar: Daylight savings time: During daylight savings time, people generally think they

“spring” their clocks ahead one hour. In fact, they actually observe the time zone to theeast of their correct standard meridian.



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For example, in the winter, a ship in Boston (longitude 071) observes the 075 standard meridian. 075W is 5 time zones to the west of Greenwich. Therefore, their time zone

designator is +5R. During the summer months, the same ship in the same position will adjust their clocks ahead one hour and observe +4Q.

In order to account for daylight savings time, the navigator can complete the time of phenomenon calculations for the nearest standard meridian and then adjust by adding 1hour. Alternatively, you can account for daylight savings time earlier by selecting the

actual standard meridian the ship is observing and determining a slightly larger longitude correction.



40

S e x t a n t F u n d a m e n t a ls

Sextant Nomenclature

Here is a diagram of a sextant and its parts:



41

Sextant Usage: Standard Corrections

The Basic Idea: When using a sextant, there are several errors that must almost always

be corrected, including the error inherent in the device, a correction for height above thesurface of the earth, and a correction for the atmosphere’s refraction of the celestial body.

These corrections are called “standard corrections” since they are completed for nearlyevery observation.

Definitions:

Index Error: the error in the sextant itself from faulty manufacturing, mirror mis-alignment, humidity, etc.

Index Correction, or IC: the correction due to index error.Height of Eye: the observer’s height above the surface of the earth.

Procedure: Before making any observation, determine the index correction of the sextant by using the horizon. Next, correct for the height of observation above the horizon byusing the Nautical Almanac’s inside front cover. Finally, depending on the body being

observed, apply a “main” correction for the atmospheric refraction.

Common Pitfalls:1. Arithmetic errors.

2. Not accounting for the observer’s physical height above the deck of the ship.3. Using the wrong time period for the “main” correction.

4. Reading the value from the sextant incorrectly.

Step One: Determine Index Correction:

Set the sextant to zero and look at the horizon. There should be an unbroken line acrossthe field of vision. If there is not, adjust the micrometer drum until the horizon is

straight.

Read the value off the sextant and note it as “IC.” If the correction moves the micrometer drum to the negative side of zero (for example: 57.5’), then the IC is called “off” the arc.

If the correction moves the micrometer drum to the positive side of zero (for example02.5’), then the IC is called “on” the arc.

A correction must be made to all observations to account for the Index Error. If the error is “off” the arc, you must add back the appropriate number of minutes to the observedaltitude. If the error is “on” the arc, you must subtract the appropriate number of minutes

to the observed altitude.

Alternatively, you can mentally determine what must happen to bring the sextant “back into alignment,” and apply that correction.



42

Here are a few examples of IC’s to drive home the point of “on the arc” versus “off thearc:”

Micrometer Drum Reading Index Error Necessary Correction

58.5’ 1.5’ off +1.5

56.0’ 4.0’ off +4.002.4’ 2.4’ on -2.403.9’ 3.9’ on -3.9

Step Two: Determine Height of Eye: See the Nautical Almanac for a description of

how to use these tables.

When making celestial calculations, 1.0’ minute of arc on the sextant translates to 1.0nautical mile on the surface of the earth. Therefore even seemingly small errors can have

a large difference on the final result of the calculation. All figures in the NauticalAlmanac and associated

calculations assume theobserver is at sea level, in

other words the observer’seyeballs are at sea level.

This is almost always not the

case, and the observer’sheight of eye above the

horizon must be accountedfor.

After determining how highthe observer’s eye is abovethe horizon, use the “Dip”

table on the front page of the Nautical Almanac to

determine the correction thatmust be applied (note the

“Dip” tables for the moon areon the last page of the

Nautical Almanac).

The “Dip” correction isalmost always negative, since

the observer is almost alwaysabove sea level when using a

sextant. Interpolation isusually not necessary.



43

Step Three: Determine the “Main” Correction, using the Altitude Correction Table:

This step is not always completed for all celestial sights. However, for any sun sights,this correction accounts for the sun’s refraction through the atmosphere and also for the

“thickness” of the sun.

Refraction: Consider the sun when it is high in the sky versus when it is on the horizonand how different it looks. Depending on the amount of atmosphere that you are looking

through, the sun will appear altered. The “Main” correction accounts for this.

“Thickness” of the Sun: The sun covers approximately 30’ of arc in the sky. The valuesin the Nautical Almanac are given for the exact center of the sun. Since this is

impractical to use, you generally shoot the Upper or Lower “limb” of the sun. The“Main” correction also accounts for this “semi-diameter” of the sun.

This table is also located on the very first page of the Nautical Almanac, but the observer

must ensure they enter the appropriate column based on the time of year.

Sidebar: Parallax - The tables assume the trigonometry of the spherical triangle isbeing measured from the center of the earth, not its surface. Parallax is the correction

for this assumption, since we are measuring at the surface. It applies to the sun, moonand planets, but not the stars. Therefore, the table for the sun must be entered for the

proper 6-month period of the year and the upper or lower limb of the sun.



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L o c a l A p p a r e n t N o o n

Meridian Passage is the time that a celestial body passes due north or south of the

observer. For the sun this is called “LAN” or Local Apparent Noon.

The Basic Idea: When the sun passes due north or south of the observer (or directlyover), the “navigational triangle” collapses into a line, and the navigator can easily

determine the ship’s latitude with minor arithmetic.

Definitions:Altitude: the height of a body above the horizon measured with a sextant.

Zenith Distance: the angular distance of a body from the point directly above theobserver’s head.

Declination: the latitude of the point on the earth directly beneath a celestial body at any

moment. Navigational Triangle: A triangle constructed by a navigator in order to solve a sphericaltrigonometry problem as a means to determining a line of position from a celestial body.

At meridian passage, this spherical triangle “collapses” into a line and makes themathematics extremely simple.

Procedure: Calculate the time of meridian passage (see meridian passage section).

Observe the altitude of the sun when it reaches its highest point and convert it into azenith distance. Determine the declination of the sun via the Nautical Almanac.

Determine the ship’s latitude by calculation.

Discussion:

When you measure the angle from the horizon to the celestial body, you are actuallyreally interested in the angle from the celestial body to the point directly above your head.

This measurement is called Zenith Distance, and is a measurement that is equivalent to areal amount of nautical miles on the Earth’s surface by multiplying the measurement by

60.

For example, if you measure the angle to the sun as 35 degrees, the zenith distance is 55degrees (90-35=55), or 3,300 (55x60) nautical miles. Therefore the distance from you to

the point on the earth directly beneath the sun is 3,300 nautical miles.

When calculating latitude by meridian passage of the sun, the ship’s latitude is equivalentto one of four possible equations:

Situation One: If the ship is in the same hemisphere as the body but has a higher latitude

than the body (June in Boston):Latitude = Zenith Distance + Body’s Declination.



45

Situation Two: If the ship is in the same hemisphere as the body but has a lower latitudethan the body (June in Panama):

Latitude = Body’s Declination – Zenith Distance.

Situation Three: If the ship is in the opposite hemisphere from the body:

Latitude = Zenith Distance - Body’s Declination.

Situation Four: If the ship is directly beneath the sun:

Latitude = Body’s Declination.

Common Pitfalls:1. Ensure the calculations are carried out for the correct “situation.”

2. Ensure the proper “standard” corrections are made to the sextant reading.

Example:

On February 4

th

2009, the ship’s DR position is 34-50N and 065-00W. LAN has beencalculated to be 1234 at the DR position.

You observe the sun’s lower limb as 38-55.0 degrees per sextant. The sextant reading

was taken at a point 20 feet above sea level. Index error was determined to be 2.0’ on thearc.

Step One: Apply the “Standard Corrections:”

Per the Nautical Almanac:

The dip correction is -4.3’ (for a height of eye of 20 feet)The index correction is -2.0’ (determined by looking at the horizon)The altitude correction is +15.1 (determined from the Almanac for the month/body).

Sextant Reading 38-55.0

Dip -00-04.3Index Correction -00-02.0

Altitude (Main) Correction +00-15.1

Height Observed: 39-03.8

Step Two: Calculate the Zenith Distance:

Zenith Distance is equal to 90 degrees minus the height observed. This is equal to theangle from celestial body to the point directly above your head (zenith).

Zenith Distance: 90-00.0 - 39-03.8 Note: it's often easier to use 89.60.0

in place of 90.00.0 to make mental arithmetic easier.Zenith Distance: 50-56.2



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Step Three: Determine the Ship’s Latitude:

Since the sun’s declination is southerly, and the ship is in the northern hemisphere, theship’s latitude is equal to the Zenith Distance – the Body’s Declination (Situation Three).

Per the Nautical Almanac, the sun’s declination is S 16-05.5 (interpolated for the actualtime of LAN)

Latitude = Zenith Distance – DeclinationLatitude = 50-56.2 – 16-05.5

Latitude = 34-50.7N



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C e l e s t ia l S i g h t R e d u c t i o n

It is beyond the scope of this guidebook to provide sight reduction training and explain

the intricacies of celestial theory, the navigational triangle, or spherical trigonometry,refer to Bowditch or Dutton's for excellent explanations of these topics.

However, as a refresher guidebook, below are some tips, explanations, and examples of

sight reductions in the hopes that if you can either refresh yourself on long lost celestialnavigation abilities or get a start on teaching yourself.

I highly recommend reading the passage from Jack London at the end of this guidebook

for an idea of how you should approach celestial navigation.

Key Point One: How accurate do you have to be? Typical celestial navigation trainingfocuses on lots of corrections and fine math to be able to get to within a quarter mile of accuracy. However, the one aspect of celestial sight reduction that is most subject to

variability is the sighting process itself. Most human eyeballs can't accurately distinguishobjects through a sextant on a dim evening or morning to more than about 3nm. That,

combined with the fact that celestial navigation is used in the open ocean in the absenceof terrestrial navigation aids, means that as long as your answers are within 3-5nm, you

are doing well. By all means, strive for more accuracy and always work to develop your techniques, but keep the big picture in mind!

Key Point Two: The actual sight measurement is the most critical step! The ability to

accurately measure an angle makes the biggest difference in the successful outcome of the math. Whether you are manually reducing the sight or using a program like STELLA,

remember that garbage in equals garbage out.1. Always remember to adjust shades appropriately for the conditions for daytime

observations or be on deck in adequate time to know the sky and still have a horizon for night observations.

2. Always bring the object to a point just below the horizon, and then bring the object back up to the horizon from below.

3. Always rock the sextant to ensure that you are measuring the object at the lowest point(to ensure that you are not getting false results due to the motion of the ship or your

inherent crookedness).

4. Always allow the sextant to come to ambient temperature before shooting.

Key Point Three: Ditch the strip form as soon as you can. The strip forms help you, and

arguably help you learn the theory, but in the end they inhibit a true understanding of what is actually going on in the sky and in the math. Keep the big picture, learn the

basics, and you will be fine without the forms.



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Examples: Below are a few examples of sights right from my log. The data from thenautical almanac and HO229 are not present due to space constraints. These examples

are designed to remind you of the parts of the problem...not to teach celestial sightreduction! They are refreshers only, not full problems with explanations.

Problem One: Latitude By Polaris March 8, 2011Watch time: 18:25:28

Watch correction: add 1:50 for error and 5 hours for GMTCorrected watch time: 23:27:18

Observation: 42:42.6

Standard corrections:-2.0 for index error

-3.3 for height of eye (dip)-1.1 for main correction

Corrected height: 42:36.2

GHA of Aries for the given watch time (whole hours): 151:18.0additional time for watch time minutes/seconds: 6:23.0

Total GHA of Aries: 157:41.0Subtract estimated longitude: -070:26

Local hour angle of Aries: 087:15

Using Pole Star tables and formula from Nautical Almanac:Latitude = Hc -1 +a0 +a1+ a2

= 42:36.2 -1 +30.6+0.6+0.9

Latitude = 42:08.3N

Problem Two: Sun Line of Position

July 9, 2009Sun, Lower Limb

Watch time: 17:35:18Correct to GMT: 21:35:18 (no watch error).

Observation: 31:03.0

Combined standard corrections for IC, Dip, MC: +8.2Corrected height: 31:11.2

GHA of the sun for 2100 hours: 133:57.6

GHA of the sun for 35:18 minutes: 8:49.5Total GHA of the sun: 142:47.1

Declination (from nautical almanac, includes both hours and minutes of dec): N22:58.4



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Assumed position: 34N (closest whole Lat), and 075:47.1 (pick long with same

increments as GHA to make the math easier).Therefore the LHA of the sun for our assumed position: 67.

Data used for going into HO229:LHA 67Dec: N22 (increments used later)

Latitude: 34N

Data taken from HO229:Z: 87.8, therefore Zn=360-Z = 277.2

HC: 30:39.1d:27.5, which is used in combination with Dec increments at the front or back of the book

to determine that 28.0 must be added to the HC to obtain the true calculated height.

Height calculated: 31:07.1Height observed: 31:11.2

Difference: 4.1 miles towards 277.2

Plot: On a chart, plot the assumed position. Plot a line from the assumed position in adirection of 277.2, for a distance of 4.1 miles. Plot a perpendicular line at this point; that

represents the sun line of position.

Problem Three: Mars Line of Position 16 July 2009

Watch time: 04:31:17

Corrected time: 07:31:18 (corrected from Nova Scotia to Greenwich and watch error)

Height observed: 21:40.8

Apply standard corrections for IC, Dip, MC: -8.1Corrected height: 21:31.7

Declination of Mars: N20:15.4 (planets don't change declination quickly).

GHA of Mars for 0700 hours: 338:16.5GHA of Mars for 31:18 minutes: 7:49.5

Total GHA of Mars: 346:06.3

Assumed position: 43N, 65:06.3 W (assumed longitude to make LHA math easier).Therefore the LHA for the assumed position is 281

Data used to enter HO229:

LHA 281Latitude: 43N

Declination: N20 (increments used later)



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Data from HO229:Z:082.1=Zn (see note at the top of page of HO229)

HC:21:22.2d:38.1 which is used in combination with the declination increment and the front/back of

HO229 to determine that 9.0 must be added to the HC.

Height Calculated: 21:31.2Height Observed: 21:31.7

Difference: 0.5 towards 082.1

Plot: On a chart plot the assumed position, then plot a line in the direction of 082.1 for adistance of 0.5nm. Plot a perpendicular line, which represents the line of position from

Mars.

Example Four: Dubhe (star) Line of Position:

5 June 2009

Watch time: 0016:47, corrected to GMT of 0116:47Height observed: 41:03.8

Standard corrections for IC, Dip, MC: -7.8Corrected height observed: 40:56.0

Declination of Dubhe: N61:42.2

GHA of Aries for 0100 hours: 268:35.8GHA of Aries for 16:47 minutes: 004:14.9

Total GHA of Aries: 272:50.7SHA of Dubhe: 193:55.1

LHA of Dubhe: 466:45.8, corrected to 106:45.8 (subtract 360)

Assumed position: 35N, 39:45.8W (assumed longitude to make math easier, thereforeLHA is 67

Data used to enter HO229:

LHA: 67Declination: N61 (increments used later)

Latitude: 35N

Data obtained from HO229:Z: 36.3, therefore Zn=360-Z = 323.7

HC: 41:03.5d: -.6, which is used with the front/back cover of HO229 to determine that the HC

correction is negligible.

Height calculated: 41:03.5Height observed: 40:56.0

Difference: 7.5 away from 323.7



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Plot: on a chart plot the assumed position, plot a line away from 323.7 for 7.5 miles anddraw the perpendicular as the line of position.

General Notes:

To remember if you need to plot towards or away from the assumed position, remember Ho Mo To (if the "height observed" is "more" plot "towards"). Also you can do a thoughtexperiment: If the height observed is more than the height calculated, you are clearly

closer to the object in question (since it is higher in the sky), and need to plot towards it.

The Zn and Z issue is explained in HO229, it depends on whether LHA is greater or lessthan 180. As a check, the Zn should be roughly in the compass direction of the object.

For instance if you are plotting the sun in the morning, Zn should be to the east. If theseare wrong, it saves you the trouble of plotting until you figure out the error.



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C o m p a s s e s

G y r o E r r o r

Determining gyro error at sea is no longer as critical as it once was before the advent of

GPS and the course over ground display. However it is still extremely important todetermine gyro error prior to entering piloting waters, otherwise all visual bearings will

be off by a substantial margin.

There are several ways of determining gyro error while in piloting waters (terrestrialrange, triangulation), but while in the open ocean, only celestial bodies can be used. The

two main ways to determine gyro error in the open ocean are by amplitude of the sun and by the azimuth (bearing) of the sun or Polaris.



53

Amplitude of the Sun

Calculating gyro error by amplitude of the sun is the simplest way to determine gyro

error celestially. It is necessary to have a clear horizon for sunrise or sunset.

The Basic Idea: Compare a measured gyro bearing to the sun to a computed bearing todetermine gyro error.

Definitions:

Amplitude: The angular distance of a celestial body north or south of the “prime vertical”or the equator. Over the course of the year, every daily sunrise/sunset moves north and

south in a regular pattern. On the equinox (spring and fall), the sun rises at 090 and setsat 270. If viewed from the equator at the solstice, the sun rises and sets about 23.5

degrees north or south of 090 and 270.

Declination: Any celestial body can be defined by the spot on the surface of the earth(Geographic Position) that is directly beneath the body. This position is defined by the body's latitude, or declination and body's longitude, or Greenwich Hour Angle.

Declination is the latitude of the body’s Geographic Position at a given moment. Naming Scheme: When using amplitudes, they have their own naming scheme.

Bearings are defined in terms of due east and west. If the sun was observed rising at100T, you would define it as E 10 S. In essence this means “10 degrees south of east.”

This naming scheme makes it easier to use Table 22 in Bowditch.

Sidebar: Here are a few more examples to drive home the point of naming schemes:

Date Time Tabulated Amplitude Value April 8 Sunrise 2.1 E 2.1 N, or 087.9

June 15 Sunrise 20.4 E 20.4 N, or 069.6 August 12 Sunset 17.4 W17.4 N, or 287.4

September 21 Sunset 0.0 W0.0N, or 270October 31 Sunrise 12.5 E 12.5 S, or 102.5

December 19 Sunset 21.0 W 21.0 S or 249.0

Procedure: When the sun’s lower limb is 2/3 of its diameter above the horizon (atsunrise or sunset), measure a bearing using an alidade. Using Table 22 in Bowditch,

calculate the bearing the sun should be at. Compare the two bearings using the memory

aid “Gyro best, error west. Gyro least, error east.”

Common Pitfalls:

1. Using Table 22 incorrectly.2. Interpolation errors.

3. Mislabeling the gyro error (East versus West).



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Example:

On February 4th, 2009, at 0900Z the ship is in position 45N and 122W. When the sun’s

lower limb was 2/3 of it’s diameter above the horizon, you observed the sun’s bearing

(per gyrocompass) to be 102T. Calculate the gyro error.

Step One: Use Table 22 (Bowditch) to determine the “Amplitude”:

On February 4th, 2009, at 0900Z the sun’s declination is S16-08.1 per the Nautical

Almanac. This means that the sun’s latitude at that moment is 16 degrees and 08.1

minutes south of the equator.

Enter Table 22 in Bowditch with the sun’s declination (S16-08.1) and the ship’s latitude(45N).

Note that there is no entry for

exactly S16-08.1; interpolation isnecessary. Depending on the

accuracy required, one can either “mentally interpolate” or use math

to determine the exact amount.Since ships only log gyro error to

the nearest ½ degree, it is generallyacceptable to “mentally interpolate”

these values. Also note that there is an entry for exactly 45N latitude. If

the ship were at a different location,

interpolation for the latitude would be necessary as well.

In this example, the actualdeclination is 16-08.1, or 16.135.

(08.1/60 = .135)

Note that 16.135 is roughly20% of the way from 16.0

to 16.5 (the table enteringarguments).

Therefore, the value we are

interested in should be20% of the way from 22.9

to 23.7 (the table values).

This comes out to be a value of

23.1.



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Step Two: Use the “Amplitude” from Table 22 to Calculate a Computed Bearing:

The value from Table 22 is 23.1. What this means is you must add or subtract this value

from 090 or 270, depending on the season and the day. In this example, the observation

took place at sunrise, and it is winter, so the sun’s computed amplitude is 23.1 degrees“south of east,” or E 23.1 S, or 103.1 per gyro compass.

Step Three: Determine Gyro Error:

To determine gyro error, compare the computed bearing to the observed bearing andapply the correct sign.

The memory aid is: “Gyro Best, Error West. Gyro Least, Error East.” If the gyro value is

higher than the computed value, the error is West. Conversely, if the gyro value is lessthan the computed value, the error is East.

Computed Value: 103.1

Observed Value: 102.0

Difference: 1.1 degree. Round this to the nearest ½ degree, or 1 degree.

The gyro value is less than the computed value, so the final answer is 1E gyro error.

Sidebar: Here are a few more examples to drive home the point of determining the signof the calculated error:

Computed Value Observed Value Gyro Error 270 271 1W 256 254 2E

092 093 1W 103 102.3 0.5E

264.3 265 0.5W



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Azimuth of the Sun

Calculating gyro error by azimuth of a celestial body requires a bit of math, but is a

reliable way to determine gyro error when no other means are available.

The Basic Idea: Compare a measured gyro bearing to a body to the computed bearing todetermine gyro error.

Definitions:

Declination: Any celestial body can be defined by the spot on the surface of the earth(Geographic Position) that is directly beneath the body. This position is defined by the

body's latitude, or declination and the body's longitude, or Greenwich Hour Angle. Declination is the latitude of the body’s Geographic Position at a given moment.

Local Hour Angle (LHA): The longitude difference between the observer’s position and

the longitude of the position directly beneath the celestial body. LHA is alwaysmeasured westward from the observer to the body's GHA.Azimuth: the bearing to a celestial body.

Procedure: Determine the Local Hour Angle, declination, and DR latitude. Determine

the base azimuth (bearing) argument from HO 229. Perform a triple interpolation todetermine the total correction required. Compare the computed azimuth to the observed

azimuth to determine gyro error.

Common Pitfalls:1. Interpolation errors and arithmetic errors.

Example:

At 1430R, you sight the sun at 211T per gyro compass. Compute the gyro error. The

ship’s GPS position is 41-30N and 080-00W.

Step One: Obtain the Base Arguments and Increments for Declination, Latitude,

and Local Hour Angle Data:

The initial goal is to obtain whole amounts of latitude, declination, and LHA to enter into

HO 229. Convert 1430R to GMT 1930Z.

At 1930Z, the interpolated declination from the Nautical Almanac is S16-00.2 Therefore the base argument is 16 degrees.

The ship’s GPS latitude was given as 41-30N. Therefore the base argument is 41

degrees. Note that the latitude is “contrary” to the declination of the sun. This means thetwo are in opposite hemispheres.



57

The local hour angle is defined as the distance (in longitude) from the observer’s positionto the geographic position of the body; or the longitude of the point on the earth directly

beneath the body. This longitude is also called the Greenwich Hour Angle.

The ship’s position is given as 080-00W. At 1930Z, the interpolated Greenwich Hour

Angle (GHA) of the sun is 109-00.5.

The Local Hour Angle is 109-00.5 – 080-00 = 29-00.5 degrees. Therefore, the base

argument is 29 degrees.

The base arguments are therefore:

Latitude: 41 degrees.

LHA: 29 degrees.

Declination: 16 degrees.

The increments are therefore:

Latitude: 30 minutes.

LHA: 00.5 minutes.

Declination: 00.2 minutes.

Step Two: Construct a Triple Interpolation Table:

Since HO 229 does not have the exact values we are looking for, but only has the basearguments, it is necessary to interpolate for all values. The azimuth from HO 229 for

these three base argument values is 148.5 degrees. Constructing a table for the values

simplifies things:

Enter the base arguments, then enter HO 229 and take turns increasing the LHA,

Declination, and Latitude by 1 whole amount while keeping the others constant, notingthe differences in the table under the “Azimuth Difference” heading.

Category Whole Amount Increment Azimuth Difference

LHA 29 Degrees 00.5 minutes 147.5 (-1.0)

Latitude (Contrary) 41 Degrees 30 minutes 148.7 (+0.2)

Declination 16 Degrees 00.2 minutes 148.9 (+0.4)



58

Step Three: Multiply the Azimuth Differences by the LHA, Lat, and Dec Increments

to Obtain a Total Correction:

In order to interpolate for the exact values of Latitude, Declination, and LHA that we are

looking for, it is necessary to multiply the azimuth differences by the increments for Lat,

Dec, and LHA and divide by 60 (to properly interpolate) to obtain a total correction.

LHA Increment: 00.5 minutes x (-1.0) = 0.5 / 60 = -0.001

Latitude Increment: 30 minutes x (+0.2) = 6 / 60 = +0.1 Declination Increment: 00.2 minutes x (+0.4) = 0.08 / 60 = +0.001

Total Correction: +0.1

Step Four: Apply the Correction to the Base Azimuth to Obtain a True Azimuth:

148.5 degrees +0.1 = 148.6 degrees.

Note the naming scheme for the azimuth (angle) just obtained is to call the prefix N/S

depending on the observers latitude, and the suffix E/W depending on if the body is eastor west of the observer. There is also a formula in HO229 to describe the situation...if the

LHA is less than 180, than Zn = 360-Z.

In this case, the LHA is 29, which is less than 180, so the Zn (True Azimuth) is 360 – Z,or 360 – 148.6 = 211.4T

Step Five: Compare the Calculated Azimuth to the Observed Azimuth to Obtain

Gyro Error:

Computed Azimuth: 211.4TObserved Azimuth: 211.0T

Gyro Error: 0.4 degrees East (Gyro Best, Error West. Gyro Least, Error East)



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D e v i a t i o n / V a r i a t i o n C a l c u l a t i o n s

Compasses often do not indicate the actual course the ship is following and must be

corrected due to a variety of factors.

The Basic Idea: Given certain values for variation, deviation, magnetic compass, gyrocompass and heading, determine the values for the rest of the unknown categories.

Definitions:Variation: The difference between True north and Magnetic north. This changes based

on the ship’s position on the earth.Deviation: The accumulation of errors in the magnetic compass due to configuration of

the ship (metal, magnets, etc). This changes based on the heading of the ship, not the position of the ship.

Compass Error: Variation added to Deviation.

PSC: Stands for “Per Steering Compass,” or the magnetic compass heading.Heading: The course being steered.Bearing: A compass direction to an object, regardless of the course being steered.

Can Dead Men Vote Twice At Elections:Can: Compass – the value read from the magnetic compass

Dead: Deviation – the deviation according to the deviation table for a heading.Vote: Variation – as determined by the nearest compass rose on the chart.

Twice: True – the True, corrected heading.At Elections – a memory aid to assist the mariner in remembering that corrections

are “added east” when proceeding from “Compass” to “True.” The values are “addedwest” when moving the other direction.

Procedure: Remember the memory aid: “Can Dead Men Vote Twice At Elections?”

Construct a grid to assist in determining values.

Common Pitfalls:1. Don’t skip steps: construct the table every time to be sure of the calculation.

2. Deviation is based on the ship’s heading, not the position.

Examples:

1. A ship is steering 090PSC (by magnetic compass). The deviation table indicates 4E for

this heading. The nearest compass rose on the chart indicates 12W Variation. Determinethe true heading.

Solution: Utilize the memory aid and chart. Can Dead Men Vote Twice (at elections)?

Moving in this direction, easterly values are added.



60

Moving in this direction () and adding east

2. From a chart, the bearing between two points is 221T. The local variation is 9E and

the deviation table says 2W for this heading. What is the magnetic compass course tosteer?

Solution: Either use the same chart backwards, but remember to “add west” when moving

“backwards” or remember a different aid when moving “backwards:” True Vampires

Make Dull Companions (at wakes). One can easily understand what the letters stand for,

but the navigator must remember to “add west” in this case. These two charts show both

ways of solving the problem.

Same Chart, just moving the opposite direction () and adding west

Different Chart, moving the same way () and adding west

Using the gyro compass does not make things much more difficult, just add two morecategories into the chart: one for Gyro Error, and one for Gyro Compass Heading.

3. A ship is steering 180PSC (by magnetic compass). From the chart, the variation is

10E. The deviation table indicates 4W deviation on this heading. Gyro error wascalculated to be 1W by azimuth of the sun. What is the Gyro Heading to steer?

Solution: construct a similar table. Moving in this direction (correcting), remember to

“add east.”

Can

Compass

Dead

Deviation

Men

Magnetic

Vote

Variation

Twice (at elections

True (add east )

090PSC (given) 4E (deviation table) Unknown 12W (chart) Wanted

094M (090+4) 082T (094-12)

Can

Compass

Dead

Deviation

Men

Magnetic

Vote

Variation

Twice (at electio

True (add east

Wanted 2W (deviation table) Unknown 9E (chart) 221T (given)

214PSC (212+2) 212M (221-9)

True

True

Vampires

Variation

Make

Magnetic

Dull

Deviations

Companions (a

wakes)Compass (add we

221T (given) 9E (chart) Unknown 2W (deviation table) Wanted

212M (221-9) 214PSC (212+2



61

Moving in this direction () adding east

4. A ship is steering 270PGC (per gyro compass). The charted variation is 13W. Thedeviation table indicates the deviation is 3E on this heading. Gyro error was determined

to be 2E by Amplitude of the Sun. What is the course to steer per magnetic compass(PSC)?

Solution: Again, either use the same chart but remember to “add west” when “un-

correcting” or moving backwards, or construct a new chart.

Moving in this direction () and adding west

Moving in this direction () and adding west

Compass Deviation Magnetic Variation True Gyro Error Gyro He

180PSC(given) 4W (deviationtable) Unknown 10E (chart) Unknown 1W (given) Want

176M (180-4) 186 (176+10) 185 (18

Compass

Can

Deviation

Dead

Magnetic

Men

Variation

Vote

True

Twice

Gyro Error Gyro He

Wanted 3E (deviation

table)

Unknown 13W (chart) Unknown 2E (given) 270PG

(give

278PSC

(281-3)281M

(268+13)

268T (270-2)

Gyro Heading Gyro Error True

True

Variation

Vampires

Magnetic

Make

Deviation

Dull

Comp

Compan

270PGC(given)

2E (given) Unknown 13W (chart) Unknown 3E (deviationtable)

Want

268T (270-2) 281M (268+13) 278P(281-



62

P i l o t in g T e c h n i q u e s

The following section contains a collection of piloting techniques or "tricks" which can be helpful to the navigator.

3 M i n u t e R u l e

The distance traveled (in yards) in three minutes equals ship speed (in knots) times 100.

Speed Distance Traveled (Yards) in Three Minutes5 kts 500 yards in three minutes

10 kts 1000 yards in three minutes15 kts 1500 yards in three minutes

20 kts 2000 yards in three minutes

6 M i n u t e R u l e

The distance traveled (in nautical miles) in 6 minutes equals ship speed (in knots) divided by 10.

Speed Distance Traveled (Nautical Miles) in Six Minutes

5 kts ½ Nautical Mile10 kts 1 Nautical Mile

15 kts 1.5 Nautical Miles20 kts 2 Nautical Miles

D o u b l i n g t h e A n g l e o n t h e B o w

Note the bearing to a fixed object. When the bearing to the fixed object has doubled, the

ship has traveled an equal distance to the current distance to the fixed object.

For example, a ship is proceedingnorthbound and sights a

lighthouse at 045R. When theship sights the same lighthouse at

090R, the current distance to thelighthouse (2 nm) is equal to the

distance run since the originalsight (2 nm).

2 nm

90 Deg

2 nm

45 Deg



63

S i x R u l e s o f D e a d R e c k o n i n g

1. Plot a new DR for every course change.

2. Plot a new DR at every speed change.3. Plot a new DR at any new fix.

4. Plot a new DR at any new running fix.5. Plot a new DR on the hour, every hour.6. Plot a new DR any time a new Line of Position is obtained.

R a d i a n R u l e

The radian rule is useful to quickly determine the closest point of approach of a fixed

object. Measure the angle off the bow to an object, divide the angle by 60, and multiplythe result by the range (in yards) to obtain the horizontal separation at closest point of approach.

For example: A buoy bears 003R at a range of 3 miles.

3/60 = 0.05

0.05 x 6000 = 300 yards

The ship will pass 300 yards from the buoy at closest point of approach

I n t e r p o l a t i o n

Interpolation is a critical skill for performing celestial navigation calculations using tablessuch as the Nautical Almanac or HO229.

Basically, interpolation means finding a desired value given two tabulated values. Here

are a few examples:

Example One:

Tabulated Values: Desired Value Answer 25N 1520 30N 1525

35N 1530

Explanation: Since the desired value (30N) was halfway between the tabulated values(25N and 30N, the answer is halfway between the two tabulated answers (1520 and 1530)



64

Example Two:

Tabulated Values: Desired Value Answer 25N 1520 28N 1523

35N 1530

Explanation: In this case, the desired value (28N) is not exactly halfway between thetabulated values, but rather 3/10ths of the way between the tabulated values (25N and

30N). Therefore, the answer is 3/10ths (30%) of the way between the tabulated answers(1520 and 1530), or 1523.

The mathematics:

1530-1520 (the difference in answers for tabulated values) = 10.

28N is 30% of the way from 25N to 35N (the tabulated values).

30% of 10 is 3.

1520 +3 = 1523, the answer.

S e t a n d D r i f t

When a ship is steering a course and speed, a DR is calculated per the rules in the “SixRules of Dead Reckoning” section. However, it is very rare that the ship actually ends up

at the DR position. The reason the ship is off course is “current.”

“Current” refers to the total accumulation of factors that cause a ship to be off course.These factors include wind, current (water movement), propeller deficiencies, helmsman

error, hull growth, list/trim or any number of other causes.

“Current” is quantified or measured by the terms “set” and “drift.” “Set” defines thedirection of the current. “Drift” defines the speed of the current.

To calculate set and drift, plot a new fix on the same chart, UPS, or maneuvering board as

the previous DR. Set is the bearing from the DR to the new fix. Drift is the distancefrom the DR to the new fix (divided by the amount of time since the last fix).

0300

0330 FIX

0330

Dr

300T

Set



65

After calculating set and drift, two new terms can be defined: “Course Made Good” and

“Speed Made Good” are defined by the bearing and range from the previous fix to thenew fix.

A n c h o r i n g : S w i n g a n d D r a g C i r c l es

Once anchored, the Navigator should plot "swing" and "drag" circles for the designatedanchorage.

A swing circle is a circle on a chart centered on the position of the anchor, with a radius

equal to the length of chain/line let out plus the length of the ship. For example, if theship is 110 feet long, and the OOD lets out 2 shots (180 feet) of line, the swing circle

would be plotted as: 110' + 180' = 290' (96.5yds). A swing circle is plotted to ensure thatno matter how the ship lies based on wind and current, she will not fall upon any

obstructions.

A drag circle is a slightly smaller circle on a chart centered on the position of the anchor,with a radius equal to the length of chain/line let out plus the distance from the hawsepipe

(where the anchor exits the ship) to the pelorus (the spot from which you measure bearings, usually the gyrocompass repeater and alidade). For example, if the ship is 295

feet long, the distance from the hawsepipe to the bridge alidade is 210 feet, and the OOD

lets out 3 shots (270 feet) of chain, the drag circle would be plotted as: 210' + 270' = 480'(160yds). A drag circle is plotted at the theoretically largest radius a ship could be atwithout dragging anchor.

Key to both of these is determining where the anchor actually is. Upon letting go the

anchor, the bridge watch should immediately record a position, using a GPS or visual bearings. This provides a good start, and 99% of the time provides the actual anchor

position. However, often the OOD will back down on the anchor to ensure it is set,

0300

0330 FIX

0330

Speed Made Good

Course Made Good



66

which sometimes drags the anchor a bit. Upon hearing that the anchor is "brought to andholding," under moderate strain, a new position should be plotted equal to the current

ship's position plus the amount of chain let out. This will give the actual anchor position,and then swing and drag circles can be plotted from there.

A swing and drag circle plotted based on the anchor's position. The inner circle is the swing circle, equal

to the length of chain (green arrow) plus the distance from the hawsepipe to the pelorus (orange circle).

The outer circle is the drag circle, equal to the length of chain (green arrow) plus the length of the ship

(red arrow).



67

U n i v e r s a l P l o t ti n g S h e e t C o n s t r u c t i o n

The Universal Plotting Sheet (UPS) is used to present a more clear and spacious

representation than the bridge chart. It follows that the scale selected should be two or more times greater than that of the chart. A key factor is the ship’s speed—the slower the

speed, the greater the need to increase scale so that fixes are not crowded together. If thechart represents 2”=60 nm, the UPS should be scaled to 2”= 30nm, or 2”=12nm. Scalesfor 20 nm, 15 nm and 10 nm do not translate as easily to the pre-printed numbers on the

UPS, so are not used. It is possible to do so, but requires more care in measuring thescales.

Larger scale means a smaller area is represented on the chart or UPS (“Large Scale, smallarea. Small Scale, large area”). For the UPS, the standard scale is 60 miles between

Latitude lines (this is pre-printed on the UPS), and 60 degrees (but not 60 miles) betweenLongitude lines. Below is a selection of other convenient scales which can be used in

conjunction with the 60 mile scale pre-printed on the UPS. A “larger” scale means fewer miles are represented between the pre-printed Latitude lines. The box labeled “Nr of fixes

per scaled Latitude/ Long” represents the number of fixes fitting in the space between astandard Latitude or Longitude. Too few and you will be creating too many UPS charts.

Too many and the plot becomes crowded and difficult to read. In all cases, labeling of courses and fixes should be large enough to read easily.

Miles Between Latitude Lines Ship’s speed Nr. Of fixes per Scaled Latitude/

Long. Box 60 NM 8 Kts or greater 4-7 30 NM 7.9---5 Kts. 4-6 12 NM 4.9—2 Kts 3—6 6 NM Under 2 Kts. 3--6

LATITUDE SCALE:

Label the three Latitude lines on the UPS in such a way as to maximize the use of the

UPS. For example, if traveling North-to-South, label the northern most Latitude lineclosest to your current position and then continue southerly.

Select a mid-latitude using the nearest whole degree to your position, and draw that onthe Longitude Scale on the bottom right side of the UPS, from right to left. This becomes

your measure of Longitude, described below.

Number your Latitude lines, all three, in accordance with the scale selected. For example, if your northernmost Latitude is 33°-24’, on a 12 mile scale, the next two

below it would be 33°-12’ and 33°-00’.



68

LONGITUDE SCALE:

Select the mid-latitude scale and draw it in to the Longitude Scale on the lower right side

of the UPS. See above. This scale measures the minutes of Longitude between theLongitude scale lines you have selected. Note that if you selected a Latitude scale of 12

nm, your Longitude scale is 12’ of Longitude. The scales should be kept the same.

Label the minutes at the bottom of the Longitude Scale. Each line should be numbered as

follows.60 mile scale----no change, each line as printed, 10 minute intervals

30 mile scale—renumber from the “zero” going left: 5-10-15-20-2512 mile scale---renumber from the “zero” going left—2-4-6-8-10

6 mile scale---renumber from the “zero” going left---1-2-3-4-5

To label numbers to the right of the “zero” on the Longitude scale:

60 mile scale—2-4-6-8-10 (no change from pre-printed version)30 mile scale---1-2-3-4-512 mile scale---0.4---0.8---1.2---1.6---2.0

6 mile scale---0.2—0.4—0.6—0.8---1.0

To measure Longitude, e.g. 27.5 miles on the 30 mile scale.Place one foot of the divider on the 25 line to the left of zero and the other foot on the 2.5

estimated line (0.5 passed the “2” line) to the right of the zero—the total measured is 25 +2.5= 27.5

Longitude Lines—how to draw:

There is a large circle in the center of the UPS, labeled 0--360°, inside. It is also labeled

10-90° on the outside of this circle. Using the outside, 10-90° place a small tick mark at the selected mid-latitude in the upper right/ lower right quadrants. For Example, if

mid-latitude is 33 degrees, put a tick mark on “33” above and below the 90. Connectthose two ticks from the top to bottom of the page. They represent a Longitude line.

Next, place a tick mark above the “270” line and below using the same number of

degrees as mid-latitude. In this case, you will count 33 degrees above the 270 and tick 303°. Next count 33° below the 270°, and tick 237°. Connect the two tick marks and

you have created a Longitude line a correct distance from the center Longitude line in the

UPS. You would use the Longitude Scale to place minutes and 10ths of minutes.Remember this is the same scale as the Latitude scale.



69

V i s i b i l i t y o f L i g h t s

Computing the visibility of lights is crucial when making landfall from sea.

The Basic Idea: Given a light list, current meteorological conditions, and ship's data,

compute the distance a light should be seen at.

Definitions:

Geographic range: the distance an object can be seen based on height of eye and thecurvature of the earth.

Luminous range: the maximum range at which an observer can see a light under existingmeteorological conditions.

Nominal range: the maximum distance at which a light can be seen in weather conditionswhen the visibility is 10 nautical miles.

Procedure: Compute the geographic range of the light. Compute the theoretical

visibility of the light using the light list and the luminous range diagram from Bowditch.Determine which value is least.

Common Pitfalls:

1. Completing both visibility calculations, but failing to determine which is the limitingdistance.

Example:

A given lighthouse has a nominal range of 15 nautical miles and a height of 150 feet.

Your ship's height of eye is 5 feet. Find the luminous range of the light when thevisibility is 11 nautical miles.

Step One: Use the Luminous Range Diagram to determine the Luminous Range:

Enter the table with a nominal range of 15nm. Find where it intersects the 11nm

visibility line and trace it to find a luminous range result of 16nm.

Step Two: Determine the Geographic Range of the light using Table 12:

Table 12 in Bowditch indicates an object 150 tall has a horizon distance of 14.3nm.Using the same table, the observer has a horizon distance of 2.6nm based on a height of

eye of 5ft. Therefore the theoretical range at which this object can be seen is 14.3+2.6 =16.9nm.

Step Three: Determine the actual range of the light:

The actual range the light can be seen is the lesser of the two calculations. Since the

luminous range is 16nm and the geographic range is 16.9nm, the actual range of the lightis 16nm.



70



71

C o m m o n C o n v e r s io n F a c t o r s

Seconds to decimal conversion table:

Seconds Decimals Seconds Decimals Seconds Decimals

1 .02 21 .35 41 .68

2 .03 22 .37 42 .70

3 .05 23 .38 43 .72

4 .07 24 .40 44 .73

5 .08 25 .42 45 .75

6 .10 26 .43 46 .77

7 .12 27 .45 47 .78

8 .13 28 .47 48 .80

9 .15 29 .48 49 .82

10 .17 30 .50 50 .83

11 .18 31 .52 51 .8512 .20 32 .53 52 .87

13 .22 33 .55 53 .88

14 .23 34 .57 54 .90

15 .25 35 .58 55 .92

16 .27 36 .60 56 .93

17 .28 37 .62 57 .95

18 .30 38 .63 58 .97

19 .32 39 .65 59 .98

20 .33 40 .67 60 1.00

Distance:1 meter 39.37 inches1 meter 3.28 feet

1 meter .55 fathoms1 kilometer .62 statue miles

1 kilometer .54 nautical miles1 fathom 6 feet

1 cable 608 feet1 nm 6076 feet

1 nm 1.15 statue miles1 kt 1.15 mph

Celsius degrees = (F-32) x 5/9Fahrenheit degrees = C x 9/5 +32



72

T i d e s a n d C u r r e n t s

C a l c u l a t i n g T i d e s M a n u a l l yCalculating time of high or low water is fairly easy. Always remember that the tables aretide "predictions." Actual tides can vary significantly due to meteorological or

oceanographic conditions. For example a strong onshore wind will make high tideshigher.

The Basic Idea: Given a set of tidal predictions for a standard station, calculate tidal

offsets and construct a table to determine time of high or low water for a given location.

Procedure: Find the nearest tidal station for your location. Find the nearest referencestation. Calculate offsets to determine tidal height at your location.

Common Pitfalls:

1. Use the correct year.2. Mind your calculations during daylight savings or summer time.

Example:

Calculate the times of high and low water for Boothbay Harbor, Maine on the afternoonof August 4th 2011 in anticipation of anchoring for the evening.

Step One: Find Boothbay Harbor in the index and note offsets. Note the time and depth

offsets for Boothbay Harbor and start constructing a table.

Time (High) Height (High) Time (Low) Height (Low)

Reference Station TBD TBD TBD TBD

Boothbay Offsets -0006 X 0.97 -0008 X 0.97

Boothbay Tides TBD TBD TBD TBD



73

Step Two: Find the indicated reference station and continue filling out the table. Boothbay Harbor uses Portland, Maine as a reference. Continue filling out the table

with the reference station data for the nearest times to your arrival in port.


PORTLAND 1420 10.7ft 2033 -0.5ft


Boothbay Tides TBD TBD TBD TBD



74

Step Three Complete construction of the table by applying the offsets to determine your answer. Be careful of positive/negative signs.


PORTLAND 1420 10.7ft 2033 -0.5ft


Boothbay Tides 1414 10.4ft 2025 -.49ft

Step Four (Optional): Using table 3 from the tide tables can give you the exact state of tide at any time. The table is self explanatory and is located on the next page.



75



76

C a l c u l a t i n g C u r r e n t s M a n u a l l y

The Basic Idea: Given a set of tidal current predictions for a standard station, calculate

tidal offsets and construct a table to determine tidal currents for a given location.

Procedure: Find the nearest tidal current station to your desired location and determineoffsets. Compare offsets to the base station and apply offsets to determine time of slack/current.

Common Pitfalls:

1. Use the correct year.2. Mind your calculations during daylight savings or summer time.

Example:

Calculate the tidal currents for Provincetown Harbor, MA for the evening of February 4,2011 in anticipation of mooring to a buoy for the night.

Step One: Find Provincetown Harbor, MA and note offsets for time, intensity, and speed

ratios. Begin constructing a table with this information.

Slack before

Flood

MaxFlood

Time

Slack before

Ebb

Max EbbTime

MaxFlood

Intensity

Max EbbIntensity

Reference

Station Data

TBD TBD TBD TBD TBD TBD

Provincetown

Offsets

+0004 +0004 +0004 +0004 X0.50 X0.30

ProvincetownHarbor Data




77

Step Two: Find the reference station and continue filling out the table. Provincetown

Harbor uses Boston as a reference station.

Slack

beforeFlood

Max

FloodTime

Slack

beforeEbb

Max Ebb

Time

Max

FloodIntensity

Max Ebb

Intensity

ReferenceStation Data

1807 2126 2358 NA inthis case

1.3kts254True

NA in thiscase

ProvincetownOffsets

+0004 +0004 +0004 +0004 X0.50 X0.30

ProvincetownHarbor Data


Step Three: Apply the offsets to the reference station and complete the problem. Note

that the direction of max flood for Provincetown Harbor comes from the index, not fromthe reference station flood direction.

Slack

beforeFlood

Max

FloodTime

Slack

before Ebb

Max Ebb

Time

Max

FloodIntensity

Max Ebb

Intensity

Reference

Station Data

1807 2126 2358 NA in

this case

1.3kts

254True

NA in

this case

ProvincetownOffsets

+0004 +0004 +0004 +0004 X0.50 X0.30

Provincetown Harbor Data

1811 2130 0002(tomorrow)

NA inthis case

0.65kts315True

NA inthis case



78

T i d e s a n d C u r r e n t s T r i c k s

Rule of 12ths:

During a 6 hour tidal change, the amount of change per hour is roughly:1st hour: 1/12th

2nd hour: 2/12ths3rd hour: 3/12ths

4th hour: 3/12ths5th hour: 2/12ths

6th hour: 1/12th



79

W e a t h e r

B e a u f o r t F o r c e sForce Wind Condition Seas Theoretical Wave Height

0 0-1 kts Calm Mirror 01 1-3 kts Light Air Ripples ¼

2 4-6 kts Light Breeze Wavelets ½ 3 7-10 kts Gentle Breeze Crests 2

4 11-16 kts Moderate Breeze Waves 35 17-21 kts Fresh Breeze Moderate waves 6

6 22-27 kts Strong Breeze Large waves, spray 97 28-33 kts Near Gale Breaking waves 14

8 34-40 kts Gale Breaking waves, foam 189 41-47 kts Strong Gale High breaking waves 23

10 48-55 kts Storm Very high waves 3011 56-63 kts Violent Storm Exceptionally high waves 37

12 64+ kts Hurricane Extreme conditions 45

U s e f u l T r i c k s a n d S a y i n g s

Rain before wind, topsail sheets and halyards mind.

Wind before rain, set sail again.

Rain appearing unaccompanied by wind indicates a front on its way. Wind blowing followed by rain indicates the front has passed and stable weather is ahead.

Red sky at night, sailors delight.

Red sky at morning, sailors take warning.

At night, the setting sun illuminating a red sky indicates clear weather, while in the

morning, a rising sun illuminates a red sky near you which foretells rain.

Mackerel sky and mare's tales

Make tall ships carry small sails.

Altocumulus and long cirrus or cirrostratus clouds indicate the nearest weather front is

to your west and moving in your direction. Clouds get lower to you the closer the weather front is to your location.

Long foretold, long last

Short notice, soon past.

Slow changes in weather take longer to move by, whereas short events are over quickly.

Contrails disappear means dry air.

Plane contrails that disappear indicate dry air aloft, which indicates stable air.



80

First rise after very low, indicates stronger blow.

Once very low pressure moves by, the backside will likely have strong winds from the

west or northwest.

When the wind shifts against the sun,

Trust it not, for back it will run. An easterly shift (veer) usually does not last long.

A ring around the sun or moon means rain or snow coming soon.

The ring is called a halo, and is formed by light refracting off ice crystals in the

atmosphere. The saying comes from the fact that ice crystals are found in cirrostratusclouds, which usually preceded a weather system.

Cold is the night when the stars are bright.

When stars are exceptionally bright it indicates high pressure and clear air. Clear air traps less heat than moist air, so it will likely be colder on a clear night than on a hazy or

overcast night.

Sea gull, sea gull, sit on the sand, it's a sign of rain when you're at hand.

Birds tend to roost more during low pressure. Low pressure indicates foul weather.

Rainbow in the morning gives you fair warning.

Rainbows are formed when you are positioned between the sun and moisture in theatmosphere. In the morning, the sun is to the east, so the moisture is to the west, which

usually means it is moving towards you.

Whether the weather be fine or whether the weather be hot, we'll weather the

weather whatever the weather whether we like it or not. Just deal with it!

Fitzroy's Barometer Rules Wind Direction Pressure Trend Forecast

SW to NW 30.1-30.2 Steady Fair, no change.30.1-30.2 Rising Fair, warmer with rain.

30.2+ Steady Fair, no change.30.2+ Falling Fair, warmer.

S to SW 30.0 Rising Clear, then fair.S to SE 30.2 Falling Wind and rain.

S to E 29.8 Falling NE gale, rain/snow.SE to NE 30.1-30.2 Falling Rain

30.2-30.2 Rapid Fall Wind, Rain.30.0 Falling Rain continuing.

30.0 Rapid Fall Rain, wind, then clearing.E to NE 30.0+ Falling Rain with light wind.

30.1 Rapid Fall Rain/Snow, wind.Shifting W 29.8 Rapid Rise Clearing/Cooler.



81

R u l e s o f t h e R o a dSound Signal Summary for most Power Driven Vessels:

Underway in fog: 1 prolonged every two minutes.Adrift in fog: 2 prolonged every two minutes.

Anchored in fog: 5 second ringing of bell every minuteAltering course to starboard (intent/inland; action/international): 1 short.

Altering course to port (intent/inland; action/international): 2 short.Overtaking on starboard: 2 prolonged, 1 short.

Overtaking on port: 2 prolonged, 2 short.Agreement (inland): Same as proposed signal.

Agreement (international): 1 prolonged, 1 short, 1 prolonged, 1 short. Nearing a bend: 1 prolonged.

Danger signal: 5 short.Getting underway: 1 prolonged.

Operating astern propulsion: 3 short.

Common Dayshapes:

Anchored: BallMotorsailing: Inverted cone.

Towing greater than 200m: Diamond.Fishing/Trawling: Two cones, apex together (hourglass).

Not under command: Two ballsRestricted in Ability to Maneuver: Ball, Diamond, Ball.

Obstructions: Two diamonds mark the safe side; two balls mark the hazard.

"The Rule of the Road"

When all three lights I see ahead,

I turn to starboard and show my red.Green to green, red to red,

Perfect safety, go ahead.

But if to starboard red appear,It is my duty to keep clear.

To act as judgment says is proper,To port or starboard, back or stop her.

And if upon my port is seen

A steamers starboard light of green,I hold my course and watch to see

That green to port keeps clear of me.

Both in safety and in doubtAlways keep a good lookout.

In danger with no room to turn,Ease her, stop her, or go astern.



82

N o t e s



83

N o t e s



84

A n E x c e r p t f ro m " C r u i se o f t h e

S n a r k " b y J a c k L o n d o n

"But," our friends objected, "how dare you go to sea without a navigator on board? You're not a navigator,

are you?"

I had to confess that I was not a navigator, that I had never looked through a sextant in my life, and that I

doubted if I could tell a sextant from a nautical almanac. And when they asked if Roscoe was a navigator, I

shook my head. Roscoe resented this. He had glanced at the "Epitome," bought for our voyage, knew how

to use logarithm tables, had seen a sextant at some time, and, what of this and of his seafaring ancestry, he

concluded that he did know navigation.

But Roscoe was wrong, I still insist. When a young boy he came from Maine to California by way of the

Isthmus of Panama, and that was the only time in his life that he was out of sight of land. He had never

gone to a school of navigation, nor passed an examination in the same; nor had he sailed the deep sea and

learned the art from some other navigator. He was a San Francisco Bay yachtsman, where land is always

only several miles away and the art of navigation is never employed. So the Snark started on her long

voyage without a navigator. The acquisition of the knowledge of navigation has a strange effect on the minds of men. The average

navigator speaks of navigation with deep respect. To the layman navigation is a deed and awful mystery,

which feeling has been generated in him by the deep and awful respect for navigation that the layman has

seen displayed by navigators. I have known frank, ingenuous, and modest young men, open as the day, tolearn navigation and at once betray secretiveness, reserve, and self-importance as if they had achieved some

tremendous intellectual attainment. The average navigator impresses the layman as a priest of some holy

rite. With bated breath, the amateur yachtsman navigator invites one in to look at his chronometer. And so

it was that our friends suffered such apprehension at our sailing without a navigator.

Now this was not Roscoe's fault; he could not help it. He had merely gone the way of all the men who

learned navigation before him. By an understandable and forgivable confusion of values, plus a loss of

orientation, he felt weighted by responsibility, and experienced the possession of power that was like unto

that of a god. All his life Roscoe had lived on land, and therefore in sight of land. Being constantly in

sight of land, with landmarks to guide him, he had managed, with occasional difficulties, to steer his body

around and about the earth. Now he found himself on the sea, wide-stretching, bounded only by the eternal

circle of the sky. This circle looked always the same. There were no landmarks. The sun rose to the eastand set to the west and the stars wheeled through the night. But who may look at the sun or the stars and

say, "My place on the face of the earth at the present moment is four and three-quarter miles to the west of

Jones's Cash Store of Smithersville"? or "I know where I am now, for the Little Dipper informs me that

Boston is three miles away on the second turning to the right"? And yet that was precisely what Roscoe

did.

That he was astounded by the achievement, is putting it mildly. He stood in reverential awe of himself; he

had performed a miraculous feat. The act of finding himself on the face of the waters became a rite, and he

felt himself a superior being to the rest of us who knew not this rite and were dependent on him for being

shepherded across the heaving and limitless waste, the briny highroad that connects the continents andwhereon there are no mile-stones. So, with the sextant he made obeisance to the sun-god, he consultedancient tomes and tables of magic characters, muttered prayers in a strange tongue that sounded like

INDEXERRORPARALLAXREFRACTION, made cabalistic signs on paper, added and carried one, and

then, on a piece of holy script called the Grail--I mean the Chart--he placed his finger on a certain space

conspicuous for its blankness and said, "Here we are."

When we looked at the blank space and asked, "And where is that?" he answered in the cipher-code of the

higher priesthood, "31-15-47 north, 133-5-30 west." And we said "Oh," and felt mighty small.



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So I aver, it was not Roscoe's fault. He was like unto a god, and he carried us in the hollow of his hand

across the blank spaces on the chart. I experienced a great respect for Roscoe; this respect grew so

profound that had he commanded, "Kneel down and worship me," I know that I should have flopped down

on the deck and yammered.

But, one day, there came a still small thought to me that said: "This is not a god; this is Roscoe, a mere manlike myself. What he has done, I can do. Who taught him? Himself. Go you and do likewise--be your

own teacher." And right there Roscoe crashed, and he was high priest of the Snark no longer. I invaded

the sanctuary and demanded the ancient tomes and magic tables, also the prayer- wheel--the sextant, I

mean.

And now, in simple language, I shall describe how I taught myself navigation. One whole afternoon I sat

in the cockpit, steering with one hand and studying logarithms with the other. Two afternoons, two hours

each, I studied the general theory of navigation and the particular process of taking a meridian altitude.

Then I took the sextant, worked out the index error, and shot the sun. The figuring from the data of this

observation was child's play. In the "Epitome" and the "Nautical Almanac" were scores of cunning tables,

all worked out by mathematicians and astronomers. It was like using interest tables and lightning-calculator tables such as you all know. The mystery was mystery no longer. I put my finger on the chart

and announced that that was where we were. I was right too, or at least I was as right as Roscoe, who

selected a spot a quarter of a mile away from mine. Even he was willing to split the distance with me. Ihad exploded the mystery, and yet, such was the miracle of it, I was conscious of new power in me, and I

felt the thrill and tickle of pride. And when Martin asked me, in the same humble and respectful way I had

previously asked Roscoe, as to where we were, it was with exaltation and spiritual chest-throwing that I

answered in the cipher-code of the higher priesthood and heard Martin's self-abasing and worshipful "Oh."

As for Charmian, I felt that in a new way I had proved my right to her; and I was aware of another feeling,

namely, that she was a most fortunate woman to have a man like me.

I couldn't help it. I tell it as a vindication of Roscoe and all the other navigators. The poison of power wasworking in me. I was not as other men--most other men; I knew what they did not know--the mystery of

the heavens--that pointed out the way across the deep. And the taste of power I had received drove me on.

I steered at the wheel long hours with one hand, and studied mystery with the other. By the end of the

week, teaching myself, I was able to do diverse things. For instance, I shot the North Star, at night, of

course; got its altitude, corrected for index error, dip, etc., and found our latitude. And this latitude agreedwith the latitude of the previous noon corrected by dead reckoning up to that moment. Proud? Well, I was

even prouder with my next miracle. I was going to turn in at nine o'clock. I worked out the problem, self-

instructed, and learned what star of the first magnitude would be passing the meridian around half-past

eight. This star proved to be Alpha Crucis. I had never heard of the star before. I looked it up on the star

map. It was one of the stars of the Southern Cross. What! thought I; have we been sailing with the

Southern Cross in the sky of nights and never known it? Dolts that we are! Gudgeons and moles! I

couldn't believe it. I went over the problem again, and verified it. Charmian had the wheel from eight tillten that evening. I told her to keep her eyes open and look due south for the Southern Cross. And when the

stars came out, there shone the Southern Cross low on the horizon. Proud? No medicine man nor high

priest was ever prouder. Furthermore, with the prayer-wheel I shot Alpha Crucis and from its altitude

worked out our latitude. And still furthermore, I shot the North Star, too, and it agreed with what had been

told me by the Southern Cross. Proud? Why, the language of the stars was mine, and I listened and heard

them telling me my way over the deep.

Proud? I was a worker of miracles. I forgot how easily I had taught myself from the printed page. I forgot

that all the work (and a tremendous work, too) had been done by the masterminds before me, the

astronomers and mathematicians, who had discovered and elaborated the whole science of navigation and

made the tables in the "Epitome." I remembered only the everlasting miracle of it-- that I had listened tothe voices of the stars and been told my place upon the highway of the sea. Charmian did not know, Martin

did not know, Tochigi, the cabin-boy, did not know. But I told them. I was God's messenger. I stood

between them and infinity. I translated the high celestial speech into terms of their ordinary understanding.

We were heaven-directed, and it was I who could read the sign-post of the sky!--I! I!



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And now, in a cooler moment, I hasten to blab the whole simplicity of it, to blab on Roscoe and the other

navigators and the rest of the priesthood, all for fear that I may become even as they, secretive, immodest,

and inflated with self-esteem. And I want to say this now: any young fellow with ordinary gray matter,

ordinary education, and with the slightest trace of the student-mind, can get the books, and charts, and

instruments and teach himself navigation. Now I must not be misunderstood. Seamanship is an entirely

different matter. It is not learned in a day, nor in many days; it requires years. Also, navigating by deadreckoning requires long study and practice. But navigating by observations of the sun, moon, and stars,

thanks to the astronomers and mathematicians, is child's play. Any average young fellow can teach himself

in a week. And yet again I must not be misunderstood. I do not mean to say that at the end of a week a

young fellow could take charge of a fifteen-thousand-ton steamer, driving twenty knots an hour through the

brine, racing from land to land, fair weather and foul, clear sky or cloudy, steering by degrees on the

compass card and making landfalls with most amazing precision. But what I do mean is just this: the

average young fellow I have described can get into a staunch sail-boat and put out across the ocean, without

knowing anything about navigation, and at the end of the week he will know enough to know where he is

on the chart. He will be able to take a meridian observation with fair accuracy, and from that observation,

with ten minutes of figuring, work out his latitude and longitude.

And, carrying neither freight nor passengers, being under no press to reach his destination, he can jogcomfortably along, and if at any time he doubts his own navigation and fears an imminent landfall, he can

heave to all night and proceed in the morning.

Joshua Slocum sailed around the world a few years ago in a thirty- seven-foot boat all by himself. I shall

never forget, in his narrative of the voyage, where he heartily indorsed the idea of young men, in similar

small boats, making similar voyage. I promptly indorsed his idea, and so heartily that I took my wife

along. While it certainly makes a Cook's tour look like thirty cents, on top of that, amid on top of the fun

and pleasure, it is a splendid education for a young man--oh, not a mere education in the things of the world

outside, of lands, and peoples, and climates, but an education in the world inside, an education in one's self,

a chance to learn one's own self, to get on speaking terms with one's soul. Then there is the training and the

disciplining of it.

First, naturally, the young fellow will learn his limitations; and next, inevitably, he will proceed to press

back those limitations. And he cannot escape returning from such a voyage a bigger and better man. And

as for sport, it is a king's sport, taking one's self around the world, doing it with one's own hands, depending

on no one but one's self, and at the end, back at the starting-point, contemplating with inner vision the planet rushing through space, and saying:

"I did it; with my own hands I did it. I went clear around that whirling sphere, and I can travel alone,

without any nurse of a sea-captain to guide my steps across the seas. I may not fly to other stars, but of this

star I myself am master."



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Documents

Coast Guard Bridge Navigation Refresher Guidebook (August 2011 Edition)