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.
