of reference points can also be expedited by using bearings on these reference points taken from the calculated position of the ship on the chart. Once having determined the position, the calculated position at the moment of observation must be plotted on the chart, and the error of closure indicated. The moment in time and the log reading are recorded (with a fraction) beside the observed point. If the error of closure is great, i.e., if it exceeds the value calculated from Eq. (95) two- or threefold, the accuracy of all observations and calculations must be checked. If no error is observed, observation must be repeated using another method, or some other combination of reference points. In order to control the accuracy of observations, a comparison must be made between distances between them and the distance calculated from the log and from the speed of the vessel. A test sounding is also taken. The only basis for transferring the calculation is an observation known to be more accurate than the calculated position. An observed position is designated by a point enclosed in a small circle, whereas a calculated-observed position (from the mizzen topmast, bearings taken on two reference points at various times, etc.) is designated by a triangle. Observations made with radio equipment are indicated by an arrow, while those made with sonar gear are designated by a wavy line and astronomical observations are enclosed with a second circle (Table 9). 3. Determining a Ship's Position from Two Angles Having prepared the sextant for observations (see Section 42) and having identified three prominent landmarks, measure and record the horizontal angles between the left and center, and the center and right landmarks. Note and record the time and log reading. If the speed of the ship is high, and the angles are measured slowly, measure the first angle twice (before and after measuring the second) and determine its mean value. If the sextant index correction exceeds 2-3', correct the sextant readings: Set the measured angles a and ẞ on the protractor: left-right, right-left (in the absence of a protractor, plot them on a sheet of tracing paper). Place the protractor on the chart so that the tapered sections of the rulers (lines drawn on the tracing paper) pass through the centers of the representations of the landmarks (Fig. 70). Make a pinhole in the center of the protractor (common vertex of the angles on the tracing paper), and designate the point obtained as the fix. В Fig. 70. Determining position from two angles. If the ship is close to a circle passing through the three landmarks selected for observation (Fig. 71), then determination of her position will be inaccurate B Ᏸ Fig. 71. Case of indeterminacy. (a case of indeterminacy). In order to avoid this, in selecting landmarks with the eye draw a circle passing through the landmarks. If the DR position of the ship is close to this circle, select other landmarks. The mean quadratic error in determining position is approximately: M≈ 0.25 D2ma dm sin 0 [cables], (100) where Dm dm ma - - mean distance to the landmarks, nm; mean distance between the center and outermost landmarks, nm; mean quadratic error in measuring and plotting the angles, in degrees (it can be assumed as 0°.2); - angle of intersection of the lines of position (it can be obtained from the chart, drawing with the eye the circles enclosing angles a and ẞ, as shown in Fig. 70). 4. Determining a Ship's Position from Simultaneous Bearings on Several Landmarks It is preferable to determine a ship's position from bearings on three or four landmarks, since in determining position from two bearings on two landmarks there is no control over accuracy of bearings and plots. Determination of position from two bearings can be considered justified only in cases in which there is no possibility of determination using more reliable methods (for example, if only two landmarks are visible to the ship and it is impossible to measure the distances to them). Having selected and identified the landmarks, we must in quick succession take and record their bearings, and note and record the time and log reading. The first on which bearings are taken are landmarks the angles on the bow of which are closer to 0° (180°); at night the less observable landmarks (flashing lights). If the speed of the ship is considerable, and the bearings are taken slowly, they must be related to a single moment: take bearings on the first, second and third landmarks, then the second and first again; calculate the mean values of the bearings on the first and second landmarks. After adjusting the compass bearings with a compass correction (see Section 37), construct lines of bearings on the map from landmarks on which bearings have been taken. At their point of intersection note the observed position of the ship. If in determining a ship's position from three (four) landmarks the lines of bearings do not intersect at one point, forming a triangle of error the sides of which are less than 5 mm on the chart, then the observed point is considered its center. If the sides of the triangle of error exceed 5 mm, the correctness of identification of the landmarks, bearings and calculations must be ascertained; repeat the observation, using other landmarks. Retention of the orientation and dimensions of the triangle of error in several successive observations, with no errors in identification of landmarks, correction and plotting of bearings usually indicates an error in calculating the compass correction. In this case, in order to determine the ship's position all bearings must be taken in one direction and at the same angle (2-3°) and plotted again (Fig. 72). Connecting the corresponding apexes of the old and new triangles of error with straight lines, we obtain, at their point of intersection, the observed position, which is not affected by the error in compass correction. Plotting bearings from this point to the landmarks, and assuming they are true bearings, compass correction can be obtained from Eq. (81). The correctness of the result must be verified through subsequent observations. M Fig. 72. Eliminating systematic error in compass cor- The mean quadratic error in determining position from two bearings is approximately Dm M(2) ≈ 0.25 sin 0 my [cables] (101) where Dm ть mean distance to the landmarks, nm; mean quadratic error in taking a bearing, in degrees (in using a gyro compass, it can be assumed as 1°.0); 0 - difference in bearings on the landmarks. The third bearing only slightly (usually not more than 15-20%) increases the accuracy of determination of a ship's position, but on the other hand makes it possible to control the correctness of bearings and plotting observations on the chart. 5. Determining a Ship's Position from If there is only one landmark within sight of a ship, her position can be determined using the cross bearing method (Fig. 73). After taking a bearing the first time, record the bearing, time and log reading. When the bearing changes by an angle of not less than 30°, it is taken again. The time and log reading are noted and recorded. Bearings corrected by the compass correction are plotted on the chart. From random point C on the line of the first bearing an auxiliary straight line is constructed, parallel to the course steered (or parallel to the course line when navigating in a current). Distance S, run by the ship during the time interval between bearings (taking current into account when navigating in a current), is plotted along this line. From the auxiliary point E obtained, a straight line is constructed, parallel to the line of the first bearing, until it intersects the line of the second bearing. The observed point is designated with a triangle. S Fig. 73. Determining position using the cross These constructions are made in determining position from simultaneous bearings on two landmarks (Fig. 74). Line I is the first line of position, drawn to the point from which the second bearing is taken. |