Tuesday, March 31, 2009

Azimuths Circles

When taking an azimuth of a celestial body, the azimuth circle is used. An azimuth circle is a nonmagnetic metal ring sized to fit on a 7 inch compass bowl or on a gyro repeater. The inner lip is graduated in degrees from 000° to 360° in a counterclockwise direction for the purpose of taking relative bearings. Two sighting vanes the forward or far van containing a vertical wire, and the after or near vane containing a peep sight will help when making observations of bearings and azimuths. Two finger lugs are used to position the instrument while aligning the vanes. A hinged reflector vane mounted at the base and beyond the forward vane is used for reflecting stars and planets when observing azimuths. Below the forward vane there is a reflecting mirror and a extended vertical wire are mounted, this helps the navigator to read the bearing or azimuth from the reflected portion of the compass card.

For observing azimuths of the Sun, an additional reflecting mirror and housing are mounted on the ring, each midway between the forward and after vanes. The Sun's rays are reflected by the mirror to the housing where a vertical slit admits a line of light. This admitted light passes through a 45° reflecting prism and is projected on the compass card from which the azimuth is directly read. In observing both bearings and azimuths there are two spirit levels, which are attached must be used to level the instrument. Azimuth and bearing are the same in meaning, the horizontal angle that a line drawn from your position to the object sighted makes with a line drawn from your position to true north. The word azimuth applies only to bearings of heavenly bodies. Lets say for example, it is not the bearing, but the azimuth of the Sun, and not the azimuth, but the bearing of a lighthouse. A bearing circle is a nonmagnetic metal ring equipped with sighting devices that is fitted over a gyro repeater or magnetic compass. The bearing circle is used to take bearings of objects on earth's surface. The azimuth circle is a bearing circle equipped with additional attachments for measuring azimuths of celestial bodies. You can either take bearings or azimuths with a azimuth circle.

When taking a bearing lets say that you are getting a bearing on a lighthouse. Install either a bearing or azimuth circle on the gyro repeater, and make sure that the circle rotates freely. Train the vanes on the lighthouse so the lighthouse appears behind the vertical wire in the far vane. Drop your gaze to the prism at the base of the far vane, then read the bearing indicated by a hairline in the prism.

Taking a Azimuth
The azimuth circle can be used in two ways to measure the azimuth of a celestial body. The first method is used with a brilliant body such as the Sun. At the upper center you will see a concave mirror, and at the lower center, a prism attachment. Sight with the mirror nearest you, and the prism toward the observed body. Light from that body is reflected from the concave mirror into the prism. The prism, in turn throws a thin beam on the compass card. This beam strikes the graduation that indicates the azimuth. The second method is used for azimuths of bodies whose brightness is insufficient to throw such a distinct beam. Behind the far vane on the azimuth circle is a dark glass that can be pivoted so as to pick up celestial bodies at various altitudes. When a body is sighted, its reflection appears behind the vertical wire in the far vane, and its azimuth may be read under the hairline in the prism.

The inner lip of the azimuth circle is graduated counterclockwise in degrees making it possible, to obtain relative bearings of objects by training the vanes on an object, then reading the graduation on the inner circle alongside the lubber’s line on the pelorus or repeater. Each of the far vanes contains a spirit level to indicate when the circle is level. Bearings taken when the azimuth or bearing circle is not on an even keel are inaccurate.

Telescopic Alidades
Another means of taking bearings is by using an alidade, which, like the bearing circle, is mounted on a repeater. The telescopic alidade is a bearing circle with a small telescope attached to it. The image is magnified, making distant objects appear larger to the observer. A series of prisms inside the low power telescope enables the bearing taker to read the bearing directly from the compass card without removing the eye from the eye piece. Bearings and azimuths can be true, per gyrocompass (PGC), magnetic, or per steering compass

Thursday, March 26, 2009

Piloting and Currents

One of the problems in small boat piloting has to do with currents, and how they effect your boats speed and the courses that you steer make good a desired track, and the time required to reach a destination. Sometimes this is called current sailing. As your boat is moved and steered through the water, it moves with respect to it. At the same time the water might be moving with respect to the bottom and the shore beause of the current. The direction and speed of your boat is the effect of these two motions combined. The actual course you make good over the bottom will not be the same as your DR track, in terms of course or speed.

Tidal currents are important and should not be underestimated. Unexpected current is always a threat to a vessel because it can carry your vessel off course and into dangerous water. The risk is even more with slower boat speeds and conditions of low visibility.

Leeway is the leeward (away from the wind) motion of a vessel due to the wind. While sailboats are most affected by it, larger vessel's are not immune to its action. The wind's effect need not be considered separately from current, but the two may be lumped together, with such factors as wave action on the boat, and the total off setting influence termed "current."

Definitions of Current Sailing Terms
The terms "Course" and "Speed" are used in DR plots for the motion of the boat through the water without regard to current. The intended track is the expected path a vessel, as plotted on a chart, after consideration has been given to the effect of current.

Track is the direction (True) of the intended track line.

Speed of Advance (SOA), is the intended rate of travel along the intended track line. The intended will not always be your actual track.

Course over Ground (COG), is the direction of the actual path of your boat, the track made good is sometimes called "Course made good."

Speed over Ground (SOG), is your actual speed of travel along this track, this is sometimes called "Speed made good."

Currents have two basic situations:
1. When the set of the current is in the same direction as the boats motion, or if it's in exactly the opposite direction.
2. When the direction of the current is at an angle to the boats course, either right or an oblique angle. The first is the simplest and is easy to solve. The speed of the current (Drift) is added or subtracted from the speed through the water to get the speed over ground. When the boat's motion and the set of the current form an angle with each other, the solution is not difficult. Their are several methods that you can use, one of which is a current diagram.

Basically, a current diagram represents the two component motions separately, as if they occurred independently and which, of course, they do not. These diagrams can be drawn in terms of velocities or distances. Distances are easier and usually used. If distances are plotted, be sure to use the same period of time for each component motion, one hour is commonly used since the units of distance will then be the same numerically as the units of speed.

The accuracy which the course and speed can be found depends on the accuracy with which the current has been determined. Values of the current usually must be taken from tidal current tables or charts, or estimated by the operator from visual observations.

Current diagrams are also called "vector triangles of velocity". The term "vector" in mathematics means quantity that has both magnitude and direction. In current sailing, the directed quantities are the motions of your boat and the water (the current).

A vector can be represented graphically by an arrow or a straight line with an indicating the direction, and the length of the line scaled to the speed of your boat. When two motions are not in line with each other they form two sides of a triangle. Completing the triangle will give you the third side which will be the course or speed of your boat.

If your set and drift can be estimated, a better position is found by applying the correction to the DR position. This is called an estimated position. If a current is setting in the same direction as your course or its reciprocal, the course made good is the same, only the speed changes. If course and set are in the same direction, the speeds are added. If in opposite directions, the smaller speed is subtracted from the larger. For boats crossing a current, three current vector diagrams can be made giving the information needed to determine speed and courses to be steered. These diagrams can be made on scrap paper or on a plotting.

Example 1: Find your course and speed made good through a current with your boats speed at 10 knots, course 080°, current set 140°, and drift 2 knots.
Step 1: From point A draw the line AB. This is your boats course and speed (080° at 10 knots) in length.
Step 2: From B draw in BC, the set and drift of the current, 140° at 2 knots. The direction and length of AC are the estimated course made good (089° ) and speed made good (11.2 knots).

Example 2: Find the course to steer at a given speed to make good a desired course, your boats speed is 12 knots, the desired course 095°, the current is 170°, and the drift 2.5 knots.
Step 1: From point A draw in your course line AB in the direction of 095° (indefinite length).
Step 2: From point A draw in the current line AC for the set 170° and drift 2.5 knots. Using C as a center, take your dividers, swing an arc of radius (boats speed 12 knots) CD, intersecting the line AB at D. Measure the direction of line CD (083.5°). This is your course to steer. Measure the length of the line AD, 12.4 knots is your speed made good.

Example 3: Determine what course and speed you must do in order to make a desired course and a desired speed good. Desired course 265°, desired speed to be made good 15 knots, current set of 185° , and a drift of 3 knots.
Step 1: From A draw line AB in the direction to be made good (265° ) and for a length equal to the speed to be made good (15 knots).
Step 2: From A draw AC, the set and drift of the current 185° and 3 knots.
Step 3: Draw a line from C to B. The direction of this line is 276°, this is your course to be steered. The length of the line equals the speed required (14.8 knots).

These current vectors can be made to any convenient scale and at any convenient place such as the center of the compass rose, unused area of the plotting sheet, a separate sheet of paper, or directly on the plot. Leeway is the leeward motion of a vessel due to wind. It can be expressed as distance, speed, or angular difference between the course steered and the course made good through the water. The amount of leeway depends on the speed and relative direction of the wind, type of vessel, exposed freeboard, trim, state of the sea, and depth of water. Leeway is applied by adding its effect to that of the current and other elements introducing geographical error in the dead reckoning.

Wednesday, March 25, 2009

Celestial Navigation Glossary

Altitude - the arc of a vertical circle between the horizon and a point or body on the celestial sphere. Altitude as measured by a sextant is called sextant altitude (hs). Sextant altitude corrected only for inaccuracies in the reading (instrument, index, and personal errors) and inaccuracies in the reference level (principally dip) is called apparent altitude (ha). After all corrections are applied, it is called corrected sextant altitude or observed altitude (Ho). An altitude taken directly from a table is called a tabular or tabulated altitude (ht). Tabular altitude as interpolated for declination, latitude, and LHA increments as required are called computed altitude (Hc).

Altitude Difference (d) - the first difference between successive tabulations of altitude in a latitude column of these tables.

Argument - one of the values used for entering a table or diagram.

Assumed Latitude (aL), Assumed Longitude (aLo) - geographical coordinates assumed to facilitate sight reduction.

Assumed Position (AP) - a point at which an observer is assumed to be located.

Azimuth (Zn) - the horizontal direction of a celestial body or point from a terrestrial point, the arc of the horizon, or the angle at the zenith, between the north part of the celestial meridian or principal vertical circle and a vertical circle through the body or point, measured from 000° at the north part of the principal vertical circle clockwise through 360°.

Azimuth Angle (Z) - the arc of the horizon, or the angle at the zenith, between the north part or south part of the celestial meridian, according to the elevated pole, and a vertical circle through the body or point, measured from 0° at the north or south reference eastward or westward through 180° according to whether the body is east or west of the local meridian. It is prefixed N or S to agree with the latitude and suffixed E or W to agree with the meridian angle.
Celestial Equator - the primary great circle of the celestial sphere, everywhere 90° from the celestial poles, the intersection of the extended plane of the equator and the celestial sphere. Also called Equinoctial.

Celestial Horizon - that circle of the celestial sphere formed by the intersection of the celestial sphere and a plane through the center of the Earth and perpendicular to zenith-nadir line.
Celestial Meridian - on the celestial sphere, a great circle through the celestial poles and the zenith. The expression usually refers to the upper branch, that half from pole to pole which passes through the zenith.

Course Angle - course measured from 0° at the reference direction clockwise or counterclockwise through 180°, It is labeled with the reference direction as a prefix and the direction of measurement from the reference direction as a suffix. Such as course angle S21° E is 21° East of South, or true course 159°.

Course Line - the graphic representation of a ship's course.

Declination (Dec.) - angular distance north or south of the celestial equator, the arc of an hour circle between the celestial equator and a point on the celestial sphere, measured northward or southward from the celestial equator through 90°, and labeled N or S (+ or -) to indicate the direction of measurement.

Declination Increment (Dec. Inc.) - in sight reduction, the excess of the actual declination of a celestial body over the integral declination argument.

Double-Second Difference (DSD) - the sum of successive second differences. Because second differences are not tabulated in these tables, the DSD can be formed most by subtracting, algebraically, the first difference immediately above the tabular altitude difference (d) corresponding to the entering arguments from the first difference below. The result will always be a negative value.

Ecliptic - the apparent annual path of the Sun among the stars, the intersection of the plane of the Earth's orbit with the celestial sphere. This is a great circle of the celestial sphere inclined at an angle of about 23° 27' to the celestial equator.

Elevated Pole (Pn or Ps) - the celestial pole above the observer's horizon, agreeing in name with the observer's latitude.

First Difference - the difference between successive tabulations of a quantity.

First Point of Aries (Y) - that point of intersection of the ecliptic and the celestial equator occupied by the Sun as it changes from south to north declination on or about March 21. Also called Vernal Equinox.

Geographical Position (GP) - the point where a line drawn from a celestial body to the Earth's center passes through the Earth's surface.

Great Circle - the intersection of a sphere and a plane through its center.

Great Circle Course - the direction of the great circle through the point of departure and the destination, expressed as angular distance from a reference direction, usually north, to the direction of the great circle. The angle varies from point to point along the great circle. At the point of departure it is called Initial Great Circle Course.

Greenwich Hour Angle (GHA) - angular distance west of the Greenwich celestial meridian, the arc of the celestial equator, or the angle at the celestial pole, between the upper branch of the Greenwich celestial meridian and the hour circle of a point on the celestial sphere, measured westward from the Greenwich celestial meridian through 360°.

Hour Circle - on the celestial sphere, a great circle through the celestial poles and a celestial body or the vernal equinox. Hour circles are perpendicular to the celestial equator.

Intercept (a) - the difference in minutes of arc between the computed and observed altitudes (corrected sextant altitudes). It is labeled T (toward) or A (away) as the observed altitude is greater or smaller than the computed altitude, Hc greater than Ho, intercept is away (A), Ho greater than Hc, intercept is toward (T ).

Line of Position (LOP) - a line indicating a series of possible positions of a craft, determined by observation or measurement.

Local Hour Angle (LHA) - angular distance west of the local celestial meridian, the arc of the celestial equator, or the angle at the celestial pole, between the upper branch of the local celestial meridian and the hour circle of a celestial body or point on the celestial sphere, measured westward from the local celestial meridian through 360°.

Meridian Angle (t) - angular distance east or west of the local celestial meridian, the arc of the celestial equator, or the angle at the celestial pole, between the upper branch of the local celestial meridian and the hour circle of a celestial body, measured eastward or westward from the local celestial meridian through 180°, and labeled E or W to indicate the direction of measurement.
Nadir (Na) - that point on the celestial sphere 180° from the observer's zenith.

Name - the labels N and S which are attached to latitude and declination are said to be of the same name when they are both N or S and contrary name when one is N and the other is S.

Navigational Triangle - the spherical triangle solved in computing altitude and azimuth and great circle sailing problems. The celestial triangle is formed on the celestial sphere by the great circles connecting the elevated pole, zenith of the assumed position of the observer, and a celestial body. The terrestrial triangle is formed on the Earth by the great circles connecting the pole and two places on the Earth, the assumed position of the observer and geographical position of the body for celestial observations, and the point of departure and destination for great circle sailing problems. The term astronomical triangle applies to either the celestial or terrestrial triangle used for solving celestial observations.

Polar Distance (p) - angular distance from a celestial pole, the arc of an hour circle between a celestial pole, usually the elevated pole, and a point on the celestial sphere, measured from the celestial pole through 180°.

Prime Meridian - the meridian of longitude 0°, used as the origin for measurement of longitude.

Prime Vertical - the vertical circle through the east and west points of the horizon.

Principal Vertical Circle - the vertical circle through the north and south points of the horizon, coinciding with the celestial meridian.

Respondent - the value in a table or diagram corresponding to the entering arguments.

Second Difference - the difference between successive first differences.

Sidereal Hour Angle (SHA) - angular distance west of the vernal equinox, the arc of the celestial equator, or the angle at the celestial pole, between the hour circle of the vernal equinox and the hour circle of a point on the celestial sphere, measured westward from the hour circle of the vernal equinox through 360°.

Sight Reduction - the process of deriving from a sight (observation of the altitude, and sometimes also the azimuth, of a celestial body) the information needed for establishing a line of position.

Small Circle - the intersection of a sphere and a plane which does not pass through its center.
Vertical Circle - on the celestial sphere, a great circle through the zenith and nadir. Vertical circles are perpendicular to the horizon.

Zenith (Z) - that point on the celestial sphere vertically overhead.

Zenith Distance (z) - angular distance from the zenith, the arc of a vertical circle between the zenith and a point on the celestial sphere.

Tuesday, March 24, 2009

Navigation General Nautical Astronomy

These are just some of the questions on the Coast Guard exam for Navigation General. This is just one of subjects required for a merchant marine license.

1. The GHA of a star ?
A. Increases at a rate of approximately 15° per hour
B. Increases at a rate of approximately 4° per hour
C. Decreases at a rate of approximately 15° per hour
D. Decreases at a rate of approximately 4° per hour

2. In the celestial equator system of coordinates what is equivalent to the longitude of the Earth system of coordinates?
A. Zenith distance
B. Azimuth angle
C. Declination
D. Greenwich hour angle

3. In the celestial equator system of coordinates what is the equivalent to the meridians of the Earth system of coordinates?
A. Horizon
B. Hour circles
C. Vertical circles
D. Parallel of declination

4. In the celestial equator system of coordinates what is equivalent to the colatitude of the Earth system of coordinates?
A. Coaltitude
B. Zenith distance
C. Polar distance
D. Declination

5. If the right ascension of a body is 9 hours, it also?
A. Is 135°
B. Corresponds to an SHA for the body of 45°
C. Means that the GP of the body is in the western hemisphere
D. All of the above

6. The GHA of the first point of Aries is 315° and the GHA of a planet is 150°. What is the right ascension of the planet?
A. 7 hours
B. 11 hours
C. 19 hours
D. 23 hours

7. The angle measured eastward from the vernal equinox along the celestial equator often expressed in time units?
A. Greenwich sidereal time
B. Right ascension
C. Local sideral time
D. Sideral hour angle

8. Right ascension is primarily used by the navigator for?
A. Calculating amplitudes
B. Calculating great circle sailing by the Agiton method
C. Entering the Air Navigation Tables (Selected Stars) Pub. 249
D. Plotting on star finders

9. The ecliptic is?
A. The path the Sun appears to take among the stars
B. The path the Earth appears to take among the stars
C. a diagram of the zodiac
D. a great circle on a gnomonic chart

10. The navigator is concerned with three systems of coordinates. Which system is not of major concern?
A. Terrestrial
B. Ecliptic
C. Celestial horizon
D. Celestial equator

11. The equator is?
A. The primary great circle of the Earth perpendicular to the axis
B. The line to which all celestial observations are reduced
C. The line from which a celestial body's altitude is measured
D. All of the above

12. The angle at the pole measured through 180° from the prime meridian to the meridian of a point is known as?
A. The departure
B. The polar arc
C. Longitude
D. Greenwich hour angle

13. A plane perpendicular to the polar axis will never form what line on the Earth's surface?
A. Great circle
B. Equator
C. Small circle
D. Meridian

14. A plane that cuts the Earth's surface at any angle and passes through the center will always form?
A. the equator
B. a great circle
C. a small circle
D. a meridian

15. A plane that cuts the Earth's surface and passes through the poles will always form?
A. the equator
B. a loxodromic curve
C. a small circle
D. a meridian

16. When correcting apparent altitude to observed altitude, you do NOT apply a correction for?
A. The equivalent reading to the center of the body
B. The equivalent reading from the center of the Earth
C. The bending of the rays of light from the body
D. Inaccuracies in the reference level

17. When applying a dip correction to the sighted sextant angle (hs), you always subtract the dip because you are correcting?
A. hs to the visible horizon
B. hs to the sensible horizon
C. hs to the celestial horizon
D. Ho to the celestial horizon

18.The height of eye correction is smaller than geometrical dip because of?
A. The angle between the horizontal and the line of sight to the visible horizon
B. Index error
C. Parallax
D. Terrestrial refraction

19. A semidiameter correction is applied to observations of ?
A. Mars
B. The Moon
C. Jupiter
D. All of the above

20.The diameter of the Sun and Moon as seen from the Earth varies slightly but averages about?
A. 1'
B. 52'
C. 32'
D. 15.5'

Sunday, March 22, 2009

Basic Chart Plotting

Plotting Directions
Once you have determined a direction by compass, pelorus, or some other means, you have to plot it on your chart. There are several ways and instruments for doing this, and they are the same tools used for determining direction from a chart.

Course Plotters
These are clear plastic, usually rectangular, that have one or more semi-circular angular scales marked on them. The center of the scales is at or near the center of one of the longer sides of the plotter and usually has a small circle or bull's eye. Plotters normally have two main scales, one from 000° to 180° and the other from 180° to 360° each calibrated in degrees. There can also be smaller auxiliary scales that are offset 90 degrees from the main scales. Lines are marked on the plotter parallel to the longer sides.

How to use Course Plotters
To determine the direction of a course or bearing from a given point. Place the plotter on the chart so that one of its longer sides is along your course or bearing line, and slide the plotter until the bull's eye is over a meridian (longitude lines running north / south). Read the true direction on the scale where it is intersected by the meridian. Easterly courses are read on the scale that reads from 000° to 180° and westerly courses on the other main scale. If it is more convenient you, find your plotted course or bearing with one of the plotter's marked parallel lines rather than its edge. It is not a must that you actually draw in the line connecting the two points, the plotter can be aligned using only the two points concerned but you will usually find it easier and safer to draw in the connecting line.

When the direction to be measured is within 20 degrees or so of due north or south, it might be harder to reach a meridian by sliding the course plotter across the chart. The small inner auxiliary scales have been included on the plotter for these cases. Slide the plotter until the bull's eye intersects a parallel of latitude (east / west) line. The intersection of this line using the proper auxiliary scale indicates the direction of the course or bearings. To plot a specified direction course or bearing from a given point. Put a pencil on your starting point, keep one of the longer edges of the course plotter snug against your pencil, and slide the plotter around until the center bull's eye and the desired mark on the appropriate main scale both lie along the same meridian. With the plotter positioned draw your direction from your starting point.

You can also first position the plotter using the bull's eye and scale markings without using the origin point, then slide the plotter up or down the meridian until one of the longer edges is over your starting point and then draw in your direction line. For directions near north or south, use one of the small auxiliary scales on a parallel of latitude. To extend a line that will be longer than the length of the course plotter. Place your dividers, opened to three or four inches, tightly against the edge of the plotter and then slide the plotter along using the divider points as guides. Draw in the extension of the course or bearing line after the plotter has been advanced. To draw a new line parallel to an existing course or bearing line. Use the parallel lines marked on the course plotter as guides.

Course Protractors
Some people like to use a course protractor as their main plotting tool. This instrument is not as easy to use as the course plotter, but you can get the same results. To measure the direction of a course or bearing. Place the center of the course protractor on the chart exactly over the your starting point, such as your boat's position or an aid to navigation. Then swing the protractor's arm around to the nearest compass rose on the chart, making the upper edge of the arm, which is in line with the center of the compass part of the course protractor pass directly over the center of the compass rose. Holding the course protractor arm in this position, turn the compass part of the protractor around until the arm's upper edge cuts across the same degree marking of the protractor compass as it does at the compass rose. The compass and the rose are now parallel. Holding the protractor compass tight against the chart, move the protractor arm around until its edge cuts across the second point of your course or bearing. You can now read the direction in degrees directly from the protractor compass scale. To lay off a line in a given direction from the given point. Line up the protractor rose with the chart's compass rose. Then rotate the arm until the desired direction is shown on the compass scale, and draw in the line, extend the line back to the starting point.

Parallel Rulers
One of the traditional instrument for measuring and plotting directions on charts is a set of parallel rulers. Parallel rulers can be made of black clear transparent plastic. The two rulers are connected by linkages that keep their edges parallel. To measure the direction of a line, line up one ruler with the desired objects on the chart and then walk the pair across the chart to the nearest compass rose by alternately holding one ruler and moving the other. To plot a line of direction, reverse the process, start at the compass rose and walk to the desired origin point. Make sure you push down slightly so the rulers do not slip.

Drawing Triangles
You can also use a pair of ordinary plastic drawing triangels for transferring a direction from one part of a chart to another, but only for short distances. The two triangles need not be similar in size or shape. Place the two longest sides together, and line up one of the other sides of one triangle with the course or bearing line, or with your desired direction at the compass rose. Hold the other triangle firmly in place as a base, and slide the first one along its edge carrying the specified line to a new position while maintaining its direction. If you have to, alternately slide and hold the triangles for moving longer distances.

Distance is measured on a chart with a pair of dividers. Open the two arms and the friction at the pivot is good enough to hold the separation between the points. Most dividers have some means for adjusting this friction, it should be enough to hold the arms in place, but not so much as to make opening or closing hard. A special type of dividers has a center cross piece which can be rotated by a knurled knob to set and maintain the opening between the arms, the distance between the points cannot accidentally change. These type of dividers are useful if kept set to some standard distance, such as one mile to the scale of the chart you are using.

To measure distance with dividers, first open them to the distance between two points on the chart, then transfer them without change to the chart's latitude scale. Note that the zero point on this scale is not at the left-hand end, but is one basic unit up the scale. This unit to the left of zero is more finely divided than are the remaining basic units. To measure any distance, set the right hand point of the dividers on the basic unit mark so that the left hand point falls somewhere on the divided unit.

If the distance on the chart cannot be spanned with the dividers opened wide, 60 degrees is the maximum practical opening, set them at a convenient opening for a whole number of units on the scale or latitude subdivisions, step this off the number of times, then measure the odd remainder. The total distance is then the sum of the parts stepped off and measured separately. To mark off a desired distance on the chart, set the right point of the dividers on the nearest lower whole number of units, and the left point on the remaining fractional part of a unit measured leftward from zero on the scale. The dividers are now properly set for the specified distance at the scale of the chart being used and can be applied to the chart. If the distance is too great for one setting of the dividers, step it off in increments.

Nautical Charts

To travel safely in a boat, you must have knowledge of water depths, shoals, and channels. You should also know the location of aids to navigation and landmarks, and where ports and harbors can be found. At any near shore position, you can measure the depth of water and see some landmarks, but for true safety you should know the depth ahead, the actual location of the aids to navigation you can see, and where more navigational aids will be on the course you follow. To plan the best route you should know the dangers to navigation along the way. This information can be found by updating your charts from notice to mariners (NTM) or by purchasing print on demand nautical charts.

A nautical chart is a representation on a plane surface of a portion of the earth's surface showing the water, natural and man-made features of interest to a navigator. A map is a similar but used on land in which shows roads, and cities. A chart's basic purpose is to give you information that lets you make the right decision in time to avoid danger. Your charts should be accurate. Even a small error in charting the position of a submerged obstruction can be a danger to your vessel.

Geographic Coordinates
Charts show a grid of intersecting lines to aid in describing a specific position on the water. These lines are charted representations of a system of geographic coordinates that exist on the earth's surface.

Meridians and Parallels
Geographic coordinates are defined by two sets of great and small circles. One is a set of great circles each of which passes through the north and south geographic poles, these are the Meridians of Longitude. The other set is a series of circles each established by a plane cutting through the earth perpendicular to the polar axis. The largest of these is midway between the poles and passes through the center of the earth, becoming a great circle, this is the Equator. Other parallel planes form small circles known as the Parallels of Latitude.

Geographic coordinates are measured in terms of Degrees. The meridian that passes through Greenwich, England, is the reference for all measurements of longitude and is designated as the Prime Meridian, or 0 degrees. The longitude of any position on earth is described as East or West of Greenwich, to a maximum in either direction of 180°. Parallels of latitude are measured in degrees north or south from the equator, from 0° at the equator to 90° at each pole. For greater precision in position, degrees are subdivided into Minutes (60 minutes = 1 degree) and Seconds (60 seconds = 1 minute). In some cases, minutes are divided decimally in tenths. One degree of latitude is equal to 60 nautical miles, one minute of latitude is approximately one nautical mile.

Direction is defined as the angle between a line connecting one point with another point and a base or reference line extending from the original point toward the True or Magnetic North Pole. This angle is measured in degrees clockwise. Direction on charts can be described as so many degrees True (T) or so many degrees Magnetic (M). The difference between these directions is Variation and must be allowed for.

Measurement of Direction
To facilitate the measurement of direction, as in plotting bearings and laying out courses, charts have a Compass Rose printed on them. A compass rose has two or three concentric circles, several inches in diameter and accurately subdivided. The outer circle has its zero at true north, this is emphasized with a star. The inner circle or circles are oriented to magnetic north. The middle circle, if there are three, is magnetic direction expressed in degrees, with an arrow printed over the zero point to indicate magnetic north. The inner most circle is also magnetic direction, but in terms of Points, and half and quarter points, (One point = 11 1/4 degrees.)

The difference between the two sets of circles is magnetic variation at that location on the compass rose. The amount of the variation and its direction (Easterly or Westerly) is given in words and figures in the center of the rose, together with a statement of the year that such variation existed and the annual rate of change. Each chart has several compass roses printed on it in locations where they do not conflict with navigational information. For large area charts, the magnetic variation can differ for various portions of the chart. Check each chart when you first start to use it, and make sure, you use the compass rose nearest the area for which you are plotting. Depending on a chart's type and scale, graduations on its compass rose circles may be for intervals of 1 degree, 2 degrees, or 5 degrees.

Distances on charts are measured in statute or in nautical miles. The Statute (Land) Mile is 5,280 feet. The Nautical Mile is 6,076.1 feet (1,852 m) is used on ocean and coastal waters. You might have to convert from one unit to the other. This is not hard to do, 1 nautical mile = 1.15 statute miles, or roughly 7 nautical miles. One kilometer = 0.62 statute or 0.54 nautical miles. In navigation, distances of up to a mile or so usually expressed in Yards, a unit that is the same no matter which mile is used on the chart. Meter can also come in use for short distances, 1 meter = 1.094 yards.

Because a chart is a representation of navigable water area, actual distances must be scaled down to much shorter dimensions on paper. This reduction is the Scale of the chart, and it can be expressed as a ratio, 1:80,000 meaning that 1 unit on the chart represents 80,000 units on the actual land or water surface. The ratio of chart to actual distance can also be expressed as a Numerical or Equivalent Scale, such as "1 inch = 1.1 miles, another way of expressing a 1:80,000 scale. Try and fix in your mind the scale of the chart you are using.

Friday, March 20, 2009

Navigational Fixes

A fix is defined as the point of intersection of two or more simultaneously obtained lines of position. The symbol for a fix is a small circle around the point of intersection. For better identification, it is labeled with time expressed in four digits. Fixes can be obtained by means of the following combinations of lines of position.
(a) A line of bearing and a distance arc.
(b) Two or more lines of bearing.
(c) Two or more distance arcs.
(d) Two or more ranges.
(e) A range and a line of bearing.
(f) A range and a distance arc.

Because two circles may intersect at two points, two distance arcs used to obtain a fix are are not the best to use. When making your choice between two points of intersection you have to consider an approximate bearing, a sounding, or your DR position. When a distance arc of one landmark is used with a bearing of a different landmark you have the problem of choosing between the two points of intersection.

Selecting Landmarks
When selecting landmarks for use in obtaining lines of position (LOPS), two considerations enter the problem, angle of intersection and the number of objects. Two lines of position crossing at nearly right angles will result in a fix with a small amount of error as compared to two lines of position separated by less than a 30° spread. If a small unknown compass error exists, or if a slight error is made in reading the bearings, the result will be less in a fix produced by widely separated lines of position than when a fix is obtained from lines of position separated by only a few degrees. If only two landmarks are used, an error in observation or identification might not be apparent. By obtaining three or more lines of position, each LOP acts as a check. If all LOPs cross in a pinpoint or form a small triangle, the fix can be considered good. Where three lines of position are used, a spread of 120° is the best for accuracy.

Sometimes you don't have a choice in landmarks, their number, or spread. You then have to use whatever reference marks are available, no matter how undesirable. When evaluating your fix, the number of landmarks and their spread should be considered. When three lines of position cross forming a triangle, it is hard to know whether the triangle is the result of a compass error or an erroneous LOP. Intersection of four lines of position usually indicates which LOP is in error.

Compass Error in a Plotted Fix
When your lines of position cross to form a small triangle, the fix is considered to be the center of the triangle, at a point determined visually. If the size of the triangle looks large, then it is possible that the compass has an error and the ship's actual position might be outside the triangle. To eliminate the compass error from the fixes, assume an error, then by successive trials, and assumptions, determine the actual error. If the assumed error is labeled wrong (east or west), the triangle will plot larger. If the error is labeled properly but the triangle still exists, but reduced in size, the second trial should assume a larger error in the same direction.

Horizontal Sextant Angles
In piloting, the most accurate fixes can be found by measuring the horizontal angles between three fixed objects whose exact positions are known. By using a sextant, horizontal angles are measured between the object in the middle and the one on either side. Something to keep in mind is that this method should not be used when the three objects are on a circle whose arc passes through the observer. These situations are known as "swingers" or "revolvers." To avoid swingers or revolvers, objects selected should be in a straight line. When this selection is impracticable, the object in the middle should be nearer the observer than the other two, or the angle between the middle object and the two end ones should be 180° or more.

Horizontal sextant angles should be taken as nearly simultaneously as possible, preferably by two people on a predetermined signal. The angles are then set on a three arm protractor. The protractor arms are then aligned to the objects on the chart, and the observer's location is the focal point of the three arms. The three arm protractor is a device of metal or rigid plastic, and has one fixed and two movable arms.The fixed center arm is secured to or is part of a graduated circle. The other two arms, fitted with clamping devices, pivot around this circle. The left and right arms can be set to form any angle with the middle arm. All arms have a common vertex. To determine an observer's exact location, the three arm protractor can be aligned, such as lighthouses on a chart.

Running Fix
A running fix is what you might call a dead-reckoning fix, because the location of one of the lines of position determined by dead-reckoning calculation of the ship's direction and distance traveled during an interval. The most common example of running fix is a situation where a line of position obtained at a certain time is advanced. Example, at 1500 the ship took a bearing of 245° on light "A". If you have run for 20 minutes at 12 knots on course 012°. Twenty minutes at 12 knots means that you have run 4 nautical miles. This distance is measured to scale along the course line in the direction traveled, and the new line of position is drawn at this point parallel to the old one. The new line of position is labeled 1500-1520 to show that it is a line of position advanced the amount of the run in that interval. At 1500 the ship was somewhere along the 1500 line of position. At 1520 you are somewhere near a point on the 1500-1520 line. The exact spot depends on how accurately the direction and distance traveled are represented by the measured distance along the course line.

You might ask why a ship would advance a line of position in the way described above. Suppose that another object is farther up the coast from light "A". The object is shown on the chart but cannot be seen from the ship until you arrive at a point somewhere on the 1500-1520 line of position. Intersection of a line of position obtained from a bearing on this object with the 1500-1520 line locates a running fix (a running fix, remember not a fix). The running fix is labeled "1520 R. fix."

Bow and Beam
It is the distance a ship runs on the same course to double the angle of bearing of an object on her bow equals her distance away from the object at the time of the second bearing. You don't really need to know why this is true, but a knowledge of trigonometry will help give you the answer. The most common of this is with bow and beam bearings. A ship starts to determine her run from the time the fixed object bears 315° relative which is 45° on her port bow. By the time the object is 270° relative (90° from the bow, or abeam), you have run 1.0 nautical mile. At the time of the second bearing the object is also 1.0 nautical mile distant on the beam. Now you will able to locate a running fix by bearing and distance of a single object. Why is it called a running fix? It is a running fix because you have to calculate by DR methods the direction and distance run between bearings.

Piloting by Soundings
A position obtained by soundings usually is approximate. Accuracy of this type of position depends on (1) how completely and accurately depths are indicated on the chart and (2) the irregularity of the depths. It is impossible to obtain a position by soundings if the ship is located in an area where depth is uniform throughout. In practice, position by soundings ordinarily serves as a check on a fix taken by some other means. Suppose you have only one spot on or near your DR track where water depth is 6 fathoms, and the depth over the rest of the area for miles around is 20 fathoms. If you heave the lead line and record 6 fathoms, you can be sure you are located at the one point where a 6-fathom depth was shown on the chart.

Piloting by soundings is not as simple as that of course, but it gives you an idea of the whats involved. What you really do is get a contour of the bottom you are passing over, and try to match it up with a similar contour shown by depth figures on the chart. One of the best methods is to draw a straight line on a piece of transparent paper or plastic. Calculate how far apart your soundings will be in other words, the length of the ship's run between soundings, and mark off distances on the line to the scale of the chart. Alongside the mark representing each sounding, record the depth obtained at that sounding. The line obtained represents ship's course. The line of soundings recorded on the overlay should fit the depth marks on the chart somewhere near you DR track. If it makes an accurate fit, it probably is a close approximation of the course the ship actually is making good.

Wednesday, March 18, 2009

Navigation and Dead Reckoning

Dead reckoning is the method of navigation by which your position is determined by means of the direction and distance traveled from a known point of departure. A vessel underway is moving through the water, which is always changing. The vessel might leave point A, steer an exact course according to the true bearing between point A and point B, and still wind up a long distance from B, depending on how much leeway your vessel makes. Estimating the distance traveled seldom gives you a exact fix.

The dead reckoning (DR) position is only an estimated position. A fix is a exact position from the intersection of two or more lines of position. A DR position is not a fix, but is calculated from the last fix obtained. In piloting, a fix is obtained by bearings taken on objects whose locations are charted. In celestial navigation, position (fix) is determined by observations of the heavenly bodies. When a ship out of sight of land is prevented by bad weather from taking celestial observations, she must navigate by other means. Normally, electronic navigation is used when the ship is located in an area where it is available. If nothing else can be used, the ship must navigate by dead reckoning.

Plotting a DR Track
In early sailing days, "dead log" was one of the methods used to measure ship's speed. The means of measuring speed consisted merely of timing the interval between which a piece of wood tossed overboard at the bow was off the stern. The length of the ship being known, it was a simple calculation to estimate the vessels speed. The dead log is considered by some as one source of the word "dead" in dead reckoning. Another theory is that dead reckoning originally was "deduced" reckoning. Shortened in the logbooks to "ded" and "a" somehow crept in, making it "dead." Whatever the source, nothing is really dead about dead reckoning.

Following a ship's DR track from one fix to the next is a continous process while underway. A constant check on your approximate position is needed by the navigator for many reasons. In celestial observations, it lets you locate your assumed position reasonably close to the ship's actual position. How is the DR track plotted? Suppose that a fix , determined at 0900 by celestial observation, piloting, or electronic navigation, located your ship in latitude 44° 36.5' N, longitude 124° 03.5' W. It is your last fix, and your DR track begins at this position, along the line of the true course steered. Assume that your course is 220° T. You set your parallel rulers or triangles on 220° and shift them to the fix, then draw a line from the fix bearing 220° T. As long as you stay on that course, your DR track will advance along this line. Let's say you're steaming at 20 knots. In 1 hour, or at 1000, your DR position will be 20 nautical miles from the 0900 fix, along the 220° T course line. The line bearing 220° from the fix is the course line or rhumb line. Label it "C 220° " above the line, and "S 20" for a 20 knot speed below the line. Label the fix 0900 and the DR position at 1000.

The 1000 DR represents where you will be if you travel exactly 20 nautical miles on C 220°, that is, if you are not set to either side of your DR track. If you have a strong headwind or a head sea against the bow, chances are that you won't quite make 20 nautical miles. Although the helmsman may keep the vessel on exactly 220°T for every second of the hour, it is probable that a wind, current, or a combination of the two elements will work to set the vessel to one side of the course. For this reason, it's unlikely for the DR position to match with your actual position, even after steaming only 1 hour.

Lines of Position
Piloting is the use of 2 or more lines of position, the intersection marks the ship's position. A line of position is determined with reference to a landmark. For this purpose, a landmark must be identified easily, and its position must be shown on the chart that you are using. Lines of position are of three general types: ranges, bearings, and distance arcs. Two instruments used in taking bearings are the bearing circle and alidade. A bearing circle is a nonmagnetic metal ring equipped with sighting devices. It is fitted over a gyro repeater or a magnetic compass. Let's say you want to take a bearing on a lighthouse. First, put the bearing circle on the gyro repeater or magnetic compass, and make sure the vanes rotate freely. Next, line up the vanes in a way that when you look through the opening in the near vane, you see the lighthouse directly behind the vertical wire in the vane. You then read the lighthouse bearing on the prism at the base of the far vane.
A alidade is a telescope equipped with crosshair, level vial, polarizing light filter, and internal focusing. The telescope is mounted on a ring that fits on a gyro repeater or magnetic compass. The optical system simultaneously projects an image of approximately 25° of the compass card, together with a view of the level vial, onto the optical axis of the telescope. By doing this, both the object and its bearing can be viewed at the same time through the alidade eyepiece.

A ship is on a range when two landmarks are observed in line. This range is represented on a chart by means of a straight line through two known chart symbols. The line is labeled with the time expressed in four digits above the line.

It is preferable to plot true bearings, but either true or magnetic bearings can be plotted. If a relative bearing of a landmark is observed, it should be converted to true bearing by adding ship's true heading. In plotting because bearing indicates the direction of a terrestrial object from the observer, a line of position is drawn from the landmark in a reciprocal direction. If a lighthouse bears 040°, then the ship bears 220° from the lighthouse. A bearing line of position is labeled with the time expressed in four digits above the line.

A special type of bearing is the tangent. When a bearing is observed of the right edge of a projection of land, the bearing is a right tangent. If a bearing on the left edge of a projection of land, as viewed by the observer, it is a left tangent. A tangent gives an accurate line of position if the point of land is sufficiently abrupt to provide a definite point for measurement, it is inaccurate when the slope is so gradual that the point for measurement moves horizontally with the rise and fall of the tide. A distance arc is a circular line of position. When the distance from an observer to a landmark is known, the observer's position is on the circle, with the landmark as center, having a radius equal to the measured distance. The entire circle need not be drawn because in practice the navigator normally knows his position near enough that drawing an arc of a circle suffices. The arc is labeled with the time above expressed in four digits. The distance to a landmark can be measured by using radar, stadimeter, or sextant, in along with Table 9 (Green Book) of the American Practical Navigator (Bowditch).

The stadimeter is used most frequently to measure distances from your ship to others in a formation. In piloting, it also is used as a navigational instrument to ascertain distance to some navigational aid as for example, when a ship's position is being determined by bearing and distance of a fixed object of known height.

Stadimeters are of two types, the Fisk type and the Brandon sextant type. In using either type, the height of the object whose distance is desired must be known, and that height must be between 50 and 200 feet. (Usually, when measuring distances to ships the height used is from the boot topping to the top of the mast or the highest radar. Distances are measured with reasonable accuracy up to 2000 yards. Beyond that range the accuracy of the stadimeter decreases. Say you want to get the range to a 120-foot light structure. Move the carriage containing the index drum to the 120-foot mark on the index arm. Sight through the telescope at the light structure. As with the sextant, you will see a direct and a reflected image. Turning the drum causes the reflected image to move up or down relative to the direct image. When the top of the reflected image is in line with the bottom of the direct image, distance in yards can be read directly from the drum.

Sunday, March 15, 2009

Celestial Navigation and Time Diagrams

Figure 1

Figure 2

Figure 3
Sometimes the various angles on the celestial sphere are interrelated and can be easier to understand by drawing a time diagram. Time diagrams are used to understand the relationships between the values of the various hour angles.
In a time diagram you are viewing the celestial sphere from the celestial south pole. The center represents the celestial south pole, "Ps", the outer circumference represents the celestial equator, and a line drawn from the center to the edge represents a celestial meridian or an hour circle containing a body. Most of the time, the line drawn from the center to the 12 o'clock position represent either the Greenwich celestial meridian, labeled "G", or the local celestial meridian, labeled "M". Small "g" and "m" represent the lower branches of their meridians.
In figure 1 this is a time diagram where GHA of the sun is. The upper branch of the sun’s hour circle is shown as a solid line. The angle or arc of the celestial equator between the Greenwich meridian and the sun’s hour circle is 90°. The GHA of the sun at this instant is 90°. GHA is always measured westward from G. Local hour angle (LHA) is the name given to the angle of arc (expressed in degrees, minutes, and tenths of minutes) of the celestial equator between the celestial meridian of a point on the celestial sphere and the hour circle of a heavenly body. It is always measured westward from the local meridian through 360°.
Let’s try an example problem of LHA on a time diagram. Say you are at longitude 135° from M toward Greenwich which means that Greenwich will be shown east of M. Think about this for a minute, you are to the west of Greenwich, which means Greenwich is to the east of you. Now that you know where Greenwich is and where you are, let’s figure the LHA of the sun as it is shown above in figure 1.
Figure 2 shows you that the sun is 90° west of Greenwich. We know that the LHA is always measured westward from your location meridian (M) to the hour circle of the body (in this example, the sun). The LHA here is the whole 360° around minus the 45° between the sun’s hour circle and M. This 45° can be found by looking at figure 2 or by subtracting 90° from 135°. Let’s think this over, you are 135°W of Greenwich, G is135° clockwise from you. The sun is 90° W or counterclockwise from G, the difference is 45°. Subtract this 45° from 360° and you will get 315°, the LHA. Look at figure 2. You can see, the sun is east (clockwise on the diagram) of your local meridian (M). Now suppose that you are at the same longitude (135° W), but the GHA of the sun is 225° instead of 90°.
The time diagram will appear as shown in figure 3. The sun is now west of your meridian (M). The LHA is always measured westward from the local celestial meridian to the hour circle of the body. Now the LHA is the 90° from M to the sun’s hour circle. Here are two general rules that will help you in finding the LHA when the GHA and longitude are known:
1. LHA = GHA - W (used when longitude is west)
2. LHA = GHA + E (used when longitude is east)
When in west longitude you might have to add 360° to the GHA before the subtraction can be made. In east longitude, 360° is subtracted from the LHA if it exceeds this amount. You can check your work by referring to a time diagram. It gives you a graphic means of obtaining the data you need.
The GHA of a star is measured in the same direction from Greenwich to the star but because the SHA enters the picture here, your method of locating a star on the time diagram is a little bit different. First, you have to locate the vernal equinox by its tabulated GHA. Let’s say the GHA of the vernal equinox for the time of your observation is 45°. You locate the vernal equinox 45° W from Greenwich. From the Nautical Almanac you find the SHA of the star in your looking for. You already know that the SHA is measured to the west from the vernal equinox (first point of Aries). All you have to do here is find the SHA of this star and measure the SHA westward from the vernal equinox, you then have the star located on your time diagram.
Note: Meridian angle "t", this value is measured either eastward or westward from the local meridian to the hour circle of the body. Its value cannot exceed 180 degrees. If LHA exceeds 180 degrees "t" will be equal to 360 degrees minus LHA.
Try this example problem:
You are in longitude 104° east. The Greenwich hour angle of a star is 211°. The meridian angle "t" of the star is?
A. 45 degrees east
B. 45 degrees west
C. 315 degrees east
D. 315 degrees west
Step 1: Draw a basic time diagram as with the local celestial meridian "M" up. The solid part of the line is the upper branch of your meridian (the part you are on), and the dotted line represents the lower branch. Next put in the known values. Place "G," the meridian of Greenwich, 104 degrees west of "M" because you are east of Greenwich.
Step 2: Next measure westward from Greenwich (counterclockwise) the 211 degrees of GHA and draw in the hour circle of the star.
Note: You do not have to use exact measuring methods, a close approximation will be good enough.
Step 3: LHA is the measurement westward between the local celestial meridian and the hour circle of the body, from 0 degrees to 360 degrees. Draw the LHA on your time diagram. Look at the angles you have drawn, you should see that the LHA of the star is equal to the longitude plus the GHA of the star (104 + 211 = 315).
Step 4: Remember the note above about the definition of meridian angle, "t". The meridian angle is the measurement between the local celestial meridian and the hour circle of the body, its value cannot exceed 180 degrees, and it is labeled east or west. In short, "t" is the shortest angular distance between "M" and the body's hour circle. In this problem you can see that meridian angle, "t", is equal to 360 degrees minus the LHA determined above and is east (360 - 315 = 45° East).

Nautical Astronomy Questions

These are Coast Guard exam question that you may find on the Navigation General exam.

1. The spinning motion of a body around its axis is called?
A. revolution
B. rotation
C. orbit
D. space motion

2. The precession of the equinoxes occurs in a?
A. easterly direction
B. westerly direction
C. northerly direction
D. southerly direction

3. The ecliptic is?
A. the path the sun appears to take among the stars
B. the path the earth appears to take among the stars
C. a diagram of the zodiac
D. a great circle on a nomadic chart

4. Which condition exist during summer solstice in the northern hemisphere?
A. The north polar regions are in continual darkness
B. The northern hemisphere is having short days and long nights
C. The southern hemisphere is having winter
D. The sun shines equally on both hemispheres

5. A first magnitude star is?
A. 2.5 times as bright as a second magnitude star
B 3 times as bright as a second magnitude star
C. 5 times as bright as a second magnitude star
D. 10 times as bright as a second magnitude star

6. What is the length of the lunar day?
A. 24h 50m 00s
B. 24h 00m 00s
C. 23h 56m 04s
D. 23h 03m 56s

7. After Venus passes the point of greatest elongation east in its orbit, the first position at which elongation will be zero is?
A. superior conjunction
B. inferior conjunction
C. opposition
D. none of the above

8. The planet Mars will have its greatest magnitude when at?
A. conjunction
B. opposition
C. east quadrature
D. west quadrature

9. Inferior conjunction is possible for?
A. Mars
B. Venus
C. Saturn
D. Jupiter

10. In low latitudes first quarter moon will always rise at about?
A. sunrise
B. 1200 local time
C. sunset
D. 2400 local mean time

11. The sun is closest to the earth in what month?
A. October
B. July
C. April
D. January

12. The dimmest stars that could reasonably be used for navigational purposes are of what madnitude?
A. First
B. Third
C. Sixth
D. Tenth

13. Aphelion is the point where the sun?
A. moon , and earth form a right angle
B. moon, and earth are in line
C. crosses the celestial equator
D. is farthest from the earth

14. When a superior planet is at 90 degrees elongation, it is also at?
A. conjunction
B. opposition
C. quadrature
D. transit

15. The moon is nearest the earth at?
A. perigee
B. the vernal equinox
C. the new moon
D. the full moon

Saturday, March 14, 2009

Nautical Astronomy, The Celestial Sphere

The Earth and the Moon
The earth's major satellite the moon, has motions similar to those of the earth. With respect to the sun, the moon rotates on its axis once in a period of about. 29.5 days, and revolves in its orbit around the earth in exactly the same period of time. Like the earth, the moon's orbit is not a perfect circle. The point of the orbit where the moon is closest to earth is called perigee, and when it is at its greatest distance it is at apogee.

The orbit of the moon is inclined about 5° to the ecliptic, and its axis of rotation is inclined 6.5 degrees to the plane of its orbit. Like the earth, the moon's axis is moving due to precession. As the moon goes through one orbit around the earth, completing one lunar month, its appearance changes. And as it does so, the moon is said to go through a series of phases. Since the moons orbit is only inclined a small amount from the ecliptic it appears to follow the sun through the sky, but falls further behind each day.

At the start of the lunar month (new moon), the moon is between the earth and sun. Each day thereafter the moon appears to have moved about 12 degrees to the east of the sun due to movement in its orbit. This causes the moon to rise about 50 minutes later each day relative to the sun. After about three days, a crescent moon is visible from earth with the points or cusps pointed away from the sun. Because the visible moon is in the process of getting bigger, it is called a waxing crescent. The line dividing the illuminated side from the shadow is called the terminator. When the lunar month is a week old, half of the moon is visible (first quarter). The next phase is called gibbous which is followed by full moon.

At full moon the moon is again in line with earth and sun, but this time the earth lies in the middle. After full moon, the visible moon begins to shrink, or wane, going through gibbous, last quarter, and waning crescent phases back to new moon. Because the moon's orbit is inclined to the ecliptic, the earth, moon, and sun rarely line up perfectly to cause either the moon or earth to pass through the shadow of the other. When they do an eclipse occurs.

The Celestial Sphere and Apparent Motion
Use of heavenly bodies for celestial navigation requires the idea that was accepted as the truth hundreds of years ago and later proved totally false. To use celestial navigation's mathematical principles, you must assume the following to be true.

1. The center of the earth is the center of a great celestial sphere.
2. This sphere has a radius (distance from the center of the earth to the surface of the celestial sphere) of infinite length.
3. All the celestial bodies used in navigation are located on the surface of the celestial sphere at the same distance from the earth.
4. The earth is stationary and the surface of the celestial sphere rotates around the earth, causing the celestial bodies to appear to move across the sky.

What you see from earth, and use in your navigation calculations, is the apparent motion of these bodies on the sphere. It appears to observers on earth that the bodies rise in the east, move in a westerly direction across the sky, and set in the west each day. It also appears that the sun, moon and planets move north, then south, and then north again on the celestial sphere. All of this motion described above is called apparent motion.

Apparent motion is the result of the real motions of the earth, which in some cases are combined with the real motions of the other body. Actual motions effect each celestial bodies apparent motion on the celestial sphere follows:

Sun - The apparent motion of rising and setting results from the earth's rotation. Movement of the sun north and south in the sky with the seasons results from revolution and the inclination of earths axis.

Stars - Rising and setting results from earths rotation, other motions of the stars happen very slowly as a result of precession of the earth's axis.

Planets - Rising and setting and other apparent motions of the planets result from a combination of the earth's rotation and revolution, and the revolutions of the planets.

Moon - The apparent rising and setting and the movement of the moon north or south results from a combination of earth's rotation and revolution, taken together with the moon's rotation, revolution, and precession.

Astronomy and Celestial Navigation

This is about the the celestial sphere and apparent motion as it applies to celestial navigation.
The earth has several separate motions in space including three major motions and some minor motions. The terms "major" and "minor" refer to their effect in celestial navigation and the calculations used to solve navigation related problems.

The major motions are rotation, revolution, and precession. Rotation refers to the earth's rotation on its axis once each day relative to the sun and other celestial bodies. The rising and setting of the sun and the passage of the stars, planets, and moon across the sky during the hours of darkness are results from rotation.

The second major motion, revolution, refers to the motion of the earth around the sun once each year. The earth's path or orbit along with the orbits of the other planets in the solar system is an ellipse. The sun is not at the center of the ellipse. If the earth's orbit is used to define a plane, the orbits of all the other planets, except Pluto would lie in the same plane. This plane in which all the planets revolve is called the Ecliptic. The earth's axis of rotation is inclined at an angle of 23.5° to the ecliptic, which also is the plane of the equator being inclined 23.5° to the ecliptic. This inclination causes the changes in the seasons on earth. As the earth revolves the light rays of the sun changes, being greatest in the northern hemisphere in June, when the northern hemisphere is titled toward the sun, and in the southern hemisphere in December when the southern hemisphere is titled toward the sun.

The points in the orbit where the angle of is greatest are called the summer and winter solstices. The points in the orbit when the sun's light shines equally over both hemispheres occurs in March and September of each year. These points are called the vernal equinox in March, and the autumnal equinox in September. With the sun off center, the earth reaches its closest point to the sun in January, after the winter solstice. This point is called Perihelion. The furthest point in the orbit from the sun is reached in July, after the summer solstice, and this is called Aphelion.

The third major motion, precession of the equinoxes, is caused by the gravitational force of the sun, moon and the other heavenly bodies acting together to deflect the axis of the rotating earth. This force causes the earth to act like a spinning top. The axis slowly traces a circle while remaining inclined at the same angle to the plane of the ecliptic. The earth's axis will travel through a circle over a period of 25,800 years. In time, precession will cause the axis to move away from the star Polaris, which we call the pole star.

The earth is located in a system which circles a mid sized star, our sun. The sun is located between the center and the edge of cluster of millions of stars circling the center of what is called a galaxy. This formation is one of other galaxies in the universe. The nearest other star in our galaxy is 4.3 light years away. Considering that light travels 186,000 miles in one second, the distance it would travel in 4.3 years is a long way. The light from the sun reaches earth in about 8.33 minutes. The distances are so great to the stars that the light rays which radiate from them are parallel lines when they reach our solar system. Over these distances the stars appear in the same place relative to the other stars from any point on the earth's orbit around the sun.

The stars are categorized by their brightness, or magnitude, with the brightest called first magnitude and the dimmest which can be seen with the unaided eye categorized as sixth magnitude. A first magnitude star is 2.5 times brighter than a second magnitude, and 6.3 (2.5 x 2.5) times brighter than a third magnitude. Each star is given a magnitude number by astronomers, with the first magnitude stars having numbers of 1.5 or less. Some of the brightest stars are so bright they have been given minus numbers. Examples are stars like Sirius (-1.6) and Canopus (- 0.9). The planets are also given numbers which vary with their positions in their orbits. Sometimes the planet Venus is so bright that it can be seen by the unaided eye in the daytime. As an interesting note, the sun's magnitude number is - 26.7.

Stars appear in different colors in the sky, and this color difference is caused by differences in their internal temperature. Astronomers group stars as red, white, or yellow giants, dwarfs, or mid-size stars depending on their stage of evolution. Only a small number of stars are used for navigational purposes. These are stars with magnitudes of 3 or brighter. There are 57 navigation stars listed in the daily pages of the Nautical Almanac.

Solar System
The sun is the central body of a system of nine principal planets including the earth. Satellites (moons) of the planets, and thousands of minor planets, comets and meteors are included in this system. All of these bodies, encircling the sun, are in motion relative to the stars. This motion is called space motion. The other planets like the earth, revolve around the sun in their orbits. Planets whose orbit lies outside the earth's orbit are called superior planets. The two planets with orbits smaller than the earth, Venus and Mercury, are called inferior planets. Because they are closest to earth, the planets used for navigation are Venus, Mars, Jupiter, and Saturn.
The orbits of all the planets except Pluto, lie in the same plane of the ecliptic as the earth's orbit. This makes it appear that the planets are either preceding or following the sun in its path through the sky as seen from earth. Whether a planet is preceding or following the sun depends on where the planet and earth are in their own orbits. Where a planet is located relative to the sun, when seen from earth at a given time, is known as planetary configuration.

When the sun lies directly between the earth and an inferior planet, the planet is at superior conjunction. When the inferior planet is directly between the earth and sun it is at inferior conjunction. When an inferior planet, while moving in its orbit from superior toward inferior conjunction reaches the point where the angle between the planet and sun as seen from the earth reaches its greatest value, it is said to be at greatest elongation east. After passing inferior conjunction, the inferior planet, continuing in its orbit, will appear west of the sun. When at its greatest angle west of the sun it is at greatest elongation west.

Superior planets are at conjunction when they are at the point in their orbits where the earth, sun and the planet are directly in line with the sun between the earth and planet. When a superior planet is aligned with the earth and sun with the earth in the middle, the planet is at opposition. The points in a superior planet's orbit where the difference in bearing between the planet and the sun, as seen from the earth, is 90 degrees is called quadrature. It is at east quadrature when the planet is east of or following the sun in the sky, and west quadrature when west of or preceding the sun.

Time Zones and Longitude

The standard for time measurement is the apparent movement of the sun from east to west across the sky. The sun moves westward about 15 degrees of longitude each hour, or 360 degrees in 24 hours. Based on this, each time zone is 15 degrees of longitude in width. The same time is kept at all locations within a time zone. Each time zone is given a number from zero to plus twelve, if the zone is in west longitude, or from zero to minus twelve its in east longitude. These numbers are called zone descriptions (ZD).

The central meridian of each time zone is a multiple of 15. For example, 60 degrees west is the central meridian of the + 4 time zone: 60 ÷ 15 = 4. Each time zone then extends 7.5 degrees east and west of the central meridian. The + 4 time zone is from 52.5° W to 67.5° W of longitude.

The upper branch of the Greenwich meridian is the central meridian of the zero time zone, which extends from 7.5 degrees east to 7.5 degrees west longitude. The lower branch of the Greenwich meridian, or 180th meridian, is the central meridian of the + / - 12 time zone. Longitudes from 172.5° west to 180° E / W are in the +12 time zone, and longitudes from 172.5° east to 180° E / W are in the -12 zone. The International Date Line follows the 180th meridian for most of its length. The date line zig-zags in places to keep all islands of a group on the same date. The date on the west side of the date line in ZD -12 (Long. 172.5° E - 180°) is one day later than in ZD + 12 (172.5° W - 180°).

When a ship crosses the date line heading west it becomes the same zone time 24 hours or one day later. When heading east over the date line it becomes one day earlier when the ship enters the + 12 time zone. This seems confusing now but it will become clear once the rules are understood. Determination of the time zone of a particular position is found by dividing its longitude by 15.

Example: Find the zone description of a ship at longitude 141° 30.0' East.

1. Convert the longitude to degrees and tenths of degrees by converting the minutes to the nearest 1/10 of a degree. 141°30.0' = 141.5 degrees.

2. Divide 141.5 by 15 = 9.43, now the zone description is - 9. (It is minus because it is East Longitude).

Note: If the longitude divided by 15 above had been more than 9.5 the zone description would have been rounded to -10. In the example above the central meridian of the time zone is - 9 x 15 = 135 East Longitude.

You should try and memorize the central meridians of the time zones: 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, and 180 east and west. Remember, the central meridians are always even multiples of 15. The time zone boundaries for a given locality can be found by remembering the limits of each zone extend 7.5 degrees of longitude east and west of the standard or central meridians.

A variation to the normal practice of keeping zone time is daylight savings time. When daylight time is in effect the entire time zone keeps the time normally kept by the time zone adjacent to the east. They set their clocks ahead one hour. Knowing the longitude and zone time at one location allows you to determine the zone time at a second location provided you know the longitude of the location.

Example: When it is 1635 zone time on 1 July 1981, for a ship at 43° 22.0' West Longitude, what is the zone time and date at Greenwich? What is the zone time and date for a ship at 108° 42.0' East Longitude?

There are two rules you should know:
Rule 1: When converting from local zone time (ZT) to Greenwich mean time (GMT), the zone description of the local time zone is added or subtracted from the local zone time as indicated by its sign (+ or -).

Rule 2: When converting from Greenwich mean time (GMT) to zone time (ZT) the sign of the local time zone description is reversed before applying it to GMT.

Example: Step 1. Find the zone description of the first ship. The first ship is in the +3 time zone (43° 22.0' or 43.4° divided by 15 = 2.89, which would be rounded up to 3. Since the longitude is west the sign of ZD is a plus.)

Step 2. To convert from zone time (ZT) at the first ship to Greenwich mean time, the zone description at the first ship is applied to the zone time. 1635 ZT +3 = 1935 GMT 1 July 1981.

Step 3. Find the zone description of the second ship. Longitude 108° 42.0' E (108.7°) divided by 15 = 7.25 which is rounded to 7. Since the longitude is east, zone description is -7. To find local zone time you follow Rule 2.

GMT was determined to be 1935, now you have to reverse the sign of zone description 7, which becomes +7, and apply it to GMT. 1935 GMT +7 = 0235 ZT, on 2 July 1981 at the second ship. Knowing the rules for conversion of zone time to GMT and the reverse is very important in solving most of these types of problems found in the celestial portion of the USCG license exams.

Friday, March 13, 2009

Fundamental Terrestrial Navigation

The earth is an Oblate Spheroid which means it is a sphere which is slightly flattened at the poles and slightly bulged at the equator. For navigation purposes it is considered a perfect sphere with some important features which form the foundation for the coordinate system used for determining positions. A basic knowledge of the earth coordinate system is a fundamental to understanding the earths coordinate system.

The first, is the axis of the earth's rotation. If you imagine the axis as a straight line passing through the center of the earth, the two points where it passes through the surface are called the North and South terrestrial poles.

Another fundamental reference is established by passing a plane through the center of the earth, perpendicular to the axis of rotation. This action is similar to cutting a grapefruit in half with a knife, and will be a line on the surface of the earth exactly halfway between the poles. This line is called the equator. The equator cuts the earth into two equal halves called the Northern and Southern Hemispheres. The equator is an example of a great circle. A great circle is formed by any plane which passes through the center of the earth and divides it into equal hemispheres. Distance can be measured along great circles because each degree of arc along these circles equals 60 nautical miles. Since each degree contains 60 minutes, each minute of arc along a great circle equals one nautical mile. Planes which pass through the earth's surface, but not through the center of the earth, are circles on the surface which are called small circles.

Planes which pass through the earth's surface, but not through the center, parallel to the plane of the equator, are small circles called parallels. Parallels are the top and bottom borders and horizontal lines printed on charts used in piloting. A parallel is located in terms of the number of degrees, minutes, and tenths of minutes of arc measured between the equator and the parallel.
Parallel is another name for latitude, and is termed north if measured from the equator toward the North Pole, and south if measured toward the South Pole. Latitude is zero at the equator and 90 degrees North or South at the poles. The pole of the hemisphere in which an observer is located is called the elevated pole. The elevated pole is always the pole which is nearer to the observer which means the North Pole for an observer in north latitude, and the South Pole for an observer in the Southern Hemisphere. Latitude provides one of the coordinates needed for locating positions on the earth's surface, but a second coordinate is needed so you can pinpoint a spot on a parallel of latitude. To do this a universally accepted starting point for measurement similar to the equator in measuring latitude had to be established. It was agreed that the great circle described on the earth's surface by passing a plane through the center, both poles, and the Royal Observatory at Greenwich, England would be the starting point for a measurement called longitude.

All great circles passing through both poles are called meridians. Meridians are represented by the side borders and the vertical solid lines printed on charts used in piloting. Since these meridians are also great circles, you can measure distance using the latitude scale which is printed along the side border. The meridian of zero degrees longitude is called the Greenwich or prime meridian. The Greenwich meridian is actually the upper branch of the Greenwich meridian because it is the half of the meridian which has the poles as end points and passes through Greenwich. The other half of the Greenwich meridian, called the lower branch, is called the 180th meridian. Another way of describing this is that the upper branch of a meridian is that half which extends from the North Pole to the South Pole on the same side of the earth as the observer is located. The lower branch of any meridian is at the longitude which is 180 degrees from the meridian on which an observer is located.

Longitude is measured eastward or westward from the upper branch of the Greenwich meridian to the meridian passing through a given point. It is equal to the angle between the the Greenwich meridian and the meridian of the place measured at the pole. This angle cannot exceed 180 degrees and is called "west" if the point in question is located between Greenwich and 180 degrees west. If the point lies east of Greenwich, but less than 180 degrees east, it is in east longitude. The180th meridian is called both180 east and west.

Each degree of latitude or longitude is divided into sixty minutes. But only minutes of latitude equal 1 nautical mile, because latitude is measured along a meridian which is a great circle. Each minute is divided into sixty seconds or tenths of minutes. Division of minutes into tenths is the most common practice. Positions are given with latitude first followed by longitude such as Lat. 44°36.8' N, Long. 124°06.3' W.