Greenwich Mean Time (GMT) is a term originally referring to mean solar time at the Royal Observatory in Greenwich, London. It is regularly used to refer to Coordinated Universal Time (UTC) when this is viewed as a time zone. It is also used to refer to Universal Time (UT), which is a standard astronomical concept used in many fields and is sometimes called Zulu time.
Noon Greenwich Mean Time is not necessarily the moment when the noon sun crosses the Greenwich meridian and reaches its highest point in the sky in Greenwich because of Earth's uneven speed in its elliptic orbit and its axial tilt. This event can be up to 16 minutes away from noon GMT (this is called the equation of time). The fictitious mean sun is the annual average motion of the true Sun.
The term GMT has been used with two different conventions for numbering hours. The old astronomical convention before 1925 was to refer to noon as zero hours, whereas the civil convention during the same period was to refer to midnight as zero hours.
As the United Kingdom grew into an advanced maritime nation, British mariners kept at least one chronometer on GMT in order to calculate their longitude from the Greenwich meridian, which was considered to have longitude zero degrees (this convention was internationally adopted in the International Meridian Conference of 1884). The chronometer on GMT did not affect shipboard time itself, which was still solar time. But this practice, combined with mariners from other nations drawing from Nevil Maskelyne's method of lunar distances based on observations at Greenwich, eventually led to GMT being used worldwide as a reference time independent of location. Most time zones were based upon this reference as a number of hours and half-hours "ahead of GMT" or "behind GMT".
The daily rotation of the Earth is somewhat irregular and is slowing down slightly, atomic clocks have a more stable timebase. On 1 January 1972, GMT was replaced as the international time reference by Coordinated Universal Time, maintained by an ensemble of atomic clocks around the world.
Universal Time (UT) is a timescale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time (GMT), the mean solar time on the meridian of Greenwich, and GMT is sometimes used loosely as a synonym for UTC. In fact the expression "Universal Time" is ambiguous, as there are several versions of it, the most commonly used being UTC and UT1. All of these versions of UT are based on sidereal time, but with a scaling factor and other adjustments to make them closer to solar time.
Standard time, divided the world into twenty-four time zones, each one covering exactly 15 degrees of longitude. All clocks within each of these zones is set to the same time as the others, but different by one hour from those in the next zone. The local time at the Royal Greenwich Observatory in Greenwich, England was chosen as standard at the 1884 International Meridian Conference, leading to the use of Greenwich Mean Time in order to set local clocks. This location was chosen because in 1884 two-thirds of all charts and maps already used it as their prime meridian.
In 1928, the term Universal Time was adopted internationally as a more precise term than Greenwich Mean Time, because the GMT could refer to either an astronomical day starting at noon or a civil day starting at midnight. The term Greenwich Mean Time persists in common usage to this day in reference to civil timekeeping.
UTC, Coordinated Universal Time) is an atomic timescale that approximates UT1. It is the international standard on which civil time is based.
UT1, is the principal form of Universal Time. UT1 is the same everywhere on Earth, and is proportional to the true rotation angle of the Earth with respect to a fixed frame of reference. Since the rotational speed of the earth is not uniform, UT1 has an uncertainty of plus or minus 3 milliseconds per day.
Showing posts with label Navigation. Show all posts
Showing posts with label Navigation. Show all posts
Sunday, May 17, 2009
Friday, April 24, 2009
Vessels at Anchor and Aground
Vessel Aground
Vessel less than 50 meters in length
Vessel at anchor with deck illumination
A vessel of less than 7 meters in length, when at anchor not in or near a narrow channel, fairway or where other vessels normally navigate, shall not be required to exhibit the shape prescribed in paragraphs (a) and (b) of this Rule.
A vessel of less than 12 meters in length, when aground, shall not be required to exhibit the lights or shapes prescribed in subparagraphs (d)(i) and (ii) of this Rule.
A vessel of less than 20 meters in length, when at anchor in a special anchorage area designated by the Secretary, shall not be required to exhibit the anchor lights and shapes required by this Rule.
Small craft less than 7 meters in length are not required to show an anchor light or shape if anchored out of the way of all other water traffic. Larger vessels must comply with Rule 30 wherever anchored, this includes the showing of a "anchor ball" dayshape.
Any vessel at anchor may, and vessels of 100 or more meters in length must, show deck or working lights to increase her visibility to other vessels. A vessel made fast to a mooring is "at anchor." A vessel dragging its anchor is not "made fast to the bottom" and, is not a vessel at anchor, but a vessel underway.
The Inland Rules only provide for "special anchorage areas" in which anchor lights and shapes are not required for craft less than 20 meters in length. These are generally established off marinas and yacht clubs where boats are left unmanned on moorings for days at a time and electric power is not available for showing anchor lights. There is no provision in the International Rules for areas where anchor lights and shapes are not required.
International Rule 30(d) requires vessels of 12 meters or more in length when aground to show the three "anchor balls" day signal or two all-round red lights at night, few small craft are equipped to meet this requirement, and most fail to comply. The Inland Rules have the same requirement, but add "if practicable" without defining the limits of practicability. A vessel is not considered "aground" for the purposes of this Rule if she is intentionally placed in contact with the bottom or against the bank to hold her position, in this case, the vessel is underway with no way on.
A vessel of less than 12 meters in length, when aground, shall not be required to exhibit the lights or shapes prescribed in subparagraphs (d)(i) and (ii) of this Rule.
A vessel of less than 20 meters in length, when at anchor in a special anchorage area designated by the Secretary, shall not be required to exhibit the anchor lights and shapes required by this Rule.
Small craft less than 7 meters in length are not required to show an anchor light or shape if anchored out of the way of all other water traffic. Larger vessels must comply with Rule 30 wherever anchored, this includes the showing of a "anchor ball" dayshape.
Any vessel at anchor may, and vessels of 100 or more meters in length must, show deck or working lights to increase her visibility to other vessels. A vessel made fast to a mooring is "at anchor." A vessel dragging its anchor is not "made fast to the bottom" and, is not a vessel at anchor, but a vessel underway.
The Inland Rules only provide for "special anchorage areas" in which anchor lights and shapes are not required for craft less than 20 meters in length. These are generally established off marinas and yacht clubs where boats are left unmanned on moorings for days at a time and electric power is not available for showing anchor lights. There is no provision in the International Rules for areas where anchor lights and shapes are not required.
International Rule 30(d) requires vessels of 12 meters or more in length when aground to show the three "anchor balls" day signal or two all-round red lights at night, few small craft are equipped to meet this requirement, and most fail to comply. The Inland Rules have the same requirement, but add "if practicable" without defining the limits of practicability. A vessel is not considered "aground" for the purposes of this Rule if she is intentionally placed in contact with the bottom or against the bank to hold her position, in this case, the vessel is underway with no way on.
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
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
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).
Vectors
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.
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
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
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).
Vectors
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.
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
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.
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
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
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.
Distance
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.
Scale
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.
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
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.
Distance
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.
Scale
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.
(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.
Ranges
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.
Bearings
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.
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.
Ranges
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.
Bearings
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.
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