- The mooring and maneuvering board diagram was brought into existence because of the need of some method of plotting and keeping track of the bearing and distance between ships. Its use in anchoring is simple, as for "this purpose it is nothing more or less than a big compass card. The ship at anchor on which another ship is going to anchor, or moor, is simply a fixed point from which one is to anchor at a prescribed distance on a prescribed bearing.
- When two ships are steaming in the presence of each other and one is ordered to take a certain prescribed position from the other, the problem becomes a very different one from that stated in the preceding paragraph. The moving ship from which the bearing and distance are to be taken (called the guide) is underway, and the problem for the second ship becomes one of obtaining a certain prescribed position relative to a moving object and holding that prescribed position while the other object (the guide) continues to move steadily on her course at her speed.
- As these two ships proceed, they open out, (or close in), forge ahead, (or drop back), and the second ship moves with reference to the first ship on a definite line, which line gives the relative movement path of one ship with reference to the other.
- In all studies of the mooring and maneuvering board, and course and speed triangles, as prescribed for the mooring board, the full significance and use of this relative movement line have not been properly accentuated. As a matter of fact, it is the most vital element of all, because it is the line on which you must place yourself in order to attain the position from the guide to which you have been ordered.
Only by taking into consideration the relative movement resulting from the speeds of the guide and yourself and the angle between the course of the guide and your own course, is it possible to take promptly a certain position with reference to the moving ship—the guide.
- Suppose in Figure 1 two ships, A and B, start at the same instant from O with speeds Oa and Ob knots per hour and with courses differing by ?°. At the end of the first hour their positions will be at a and b respectively; and at the end of the fourth hour will, be at A and B, respectively. As A and B start to travel along their respective courses from O, they will start to separate along a line as ab, and this line represents their relative movement. Study of Figure 1 shows that as long as A and B maintain their initial speeds and courses, this relative move
ment line always moves parallel to itself, and its direction, as stated before, is the same so long as the speeds and difference of courses are not changed.
The triangle OAB, Figure 2, is called the speed triangle and represents or contains the following elements:
- The speed of the guide.
- The course of the guide.
- The speed of own ship.
- The course of your own ship.
- The line of relative movement of the ships.
6. This triangle is the basis of all work that is done on the mooring board while underway. The relation of its sides, angles and resulting direction of the relative movement line for changes in the sides and angles must be at the finger tips of the mooring board operator. Without this, it is impossible either to use the mooring board properly, rapidly and efficiently, or to intelligently understand articles, texts, or publications based upon mooring board principles.
With a complete and thorough understanding of the relations of these parts and the speed triangles as outlined above, the field in which they can be usefully and practically applied as governing the regulations of ships underway is almost infinite.
Knowing certain of these elements, it is possible to determine the others. For example : Knowing the speed of the guide and the relative movement required, it is desired to find the speed and the course of B. In Figure 2 draw OA to scale to represent A’s
speed and in the direction of A’s course. Through A draw AB in direction of relative movement desired and lay off AB equal to the distance from the guide it is desired to reach in the same time that A steamed from O to A. Then draw BO. Thus on the same scale that AO equals A’s speed, OB equals B’s required speed, and the angle AOB thus determined gives the difference between the course steered by A and the course that B should take.
- In Figure 3, suppose B, at the end of an interval of time, had reached a position x hundred yards from A on AB and was to maintain that position resuming A’s course and speed. Then at this moment the relative movement of the ship would be zero, but still B would be steaming along x hundred yards from A on the bearing AB, as in Figure 3. The time it takes B to reach this position will depend not only upon the distance of the new position from A, but B’s relative rate of speed along AB. The method of calculating this time will be given later on.
A study of Figure 4 will show the rate of separation, i.e., the speed of relative movement, along AB may be varied by changing B’s course and speed. For example, if B takes either speeds O4, O5, or 06, with their corresponding courses O4, O5, 06, the relative movement along AB will be the same as to direction, but it will take different times on each course to reach B at a prescribed distance and bearing from A.
As a matter of similar interest if B maintains a constant speed, but steers any one of the courses O2, O1, or O3 at this speed, the relative movement will correspondingly be along the lines A2, A1 or A3.
- In Figure 5, suppose that with given speeds and courses, A and B have left O at the same instant, B having orders to take station ? ° on A’s bow and distant y hundred yards. Plotting the speed triangle OAB, the relative movement is on AB inclined ? ° to A’s course.
At the end of a certain interval of time A will have moved from O to A, and B from O to B, and they will be distant AB yards. At a later interval A will have arrived at a and B at b, still on the same relative bear
ing but distant from A x hundred yards., Finally A will arrive at a2 and B at b2 on the proper relative bearing, and at the required distance of y hundred yards. At this point B takes A’s course and speed to maintain station. In reaching this position B would have steamed a distance Ob2. The time required to get in the new position would be the distance steamed by each ship divided by its speed. A much simpler procedure for ascertaining how long it would take B to reach a given station will be given later on in paragraph 17.
- For the particular problem given we could have found B’s course as follows: Lay off OA=speed of guide. Plot O and D as the present and new position of B. Through A draw AB parallel to OD. With O as a center and a radius OB=B’s speed strike an are cutting AB at B. Join BO. The required course for the speed OB is ? = AOB. Had it been desired to use other speeds for B, arcs with radii Of2 or Of1 corresponding to these speeds would cut AB at f2 and f1 respectively, giving corresponding courses AOf2 and AOf1. In both cases the direction of the relative movement would be the same, i.e., along AB. With speed Of2, however, B would take longer to arrive in position, and in the other case less time, than if speed OB had been used. Study the Figure.
Hence the mooring board rule: Lay off from the center a line representing the course and speed of the guide. From the extremity of this line draw a second line parallel to a line connecting your present position with the new position you are to attain, relative to the guide. The intersection of this line with any speed circle with O as a center will show the course which must be steered to reach the desired position, or station, at that particular speed.
- In Figure 6, the speed and course triangle OAB has been reproduced. It will become at once apparent that for convenience and accuracy of solution of various triangles, a series of concentric speed circles can be drawn on which any speed in use can be laid down and rapidly measured either for the guide or for your own ship. It will also suggest itself that facility in determining compass course will be increased by adding a protractor or compass rose circle, such as COC, on the outer edge of the diagram—hence the mooring board diagram. (See Fig. 8).
In Figure 6, from what has already been explained, the triangle on the right hand side of the circle will give the direction of the relative movement of any ship in relation to the guide when going from O to the position B2; or from B3, to O; or from B3 to B2, when such ship uses the course-angle ? and the speed OB. Similarly, the speed triangle OAB, on the left hand side of the circle (Figure 6), shows the relative movement line of a ship going from B2 to B3, or from O to B3, relative to the guide.
A change of your course, or a change of your speed, or a change of both your course and speed, all relative to the guide, will produce changes in the direction and length of the sides and angles of this triangle, and for the same base line OA (which is the speed of the guide and which in this study is maintained constant, whatever its value may be in knots per hour) will produce innumerable variations in the slope of the relative bearing
line and the courses and speeds which may be combined to attain a required position.
Repeating, this speed triangle contains:
- The guide’s speed laid down on any arbitrarily assumed scale.
- The guide’s course.
- Your own speed measured on the same scale as that on which the guide’s speed is measured.
- Your own course relative to the guide’s course.
- The line of relative movement of your ship to or from the guide.
Attention is called to the fact that items 1 and 2 above are always fixed by the problem in each and every case, for the simple reason that if you do not know the guide’s speed and the guide’s course, you cannot accurately maneuver on her; and, if the guide does not maintain a steady speed on her course, you cannot accurately maneuver on her. In the former condition, you would have two entirely unknown quantities; in the latter condition, you would have two entirely fluctuating quantities. Neither of these sets of unknown conditions for a guide renders it practical for another ship to coordinate herself to the guide’s movements.
- Studying the triangle further, and this is particularly important, because it is the basis of the entire use of the maneuvering board, we find in these five elements that:
- Guide’s speed are known and fixed
- Guide’s course
- Your speed may each be varied, but of these three items you must assume
- Your course two to produce the third one
- Line of relative movement
Or, to put it another way:
(1) and (2) are fixed by the problem in all cases.
Any combination of an assumed (3) and
- will produce a resulting (5).
Any combination of an assumed (4) and
- will produce a resulting (3).
Any combination of an assumed (3) and (5) will produce a resulting (4).
The resultant in each case being that of the particular set of conditions assumed.
- It is the ability to understand these combinations and to mentally picture them rapidly which will enable you to use the mooring board successfully. Practically every maneuver is governed or guided or a position obtained by having two of these elements given and assuming two others in such combination that the resultant fifth element (a relative movement line, or a new course, or a speed, as the case may be) will put your ship in the required position relative to the guide. Familiarity with the rapid combination of these elements on the maneuvering board is necessary before the board can be used successfully, and a thorough knowledge of the relations of these various parts of this triangle will enable you to rapidly select combinations at your command which will give you not only practical information, but, if properly used, the best information.
In the first study of this diagram the two ships A and B were started from the same point, but this was done only as a matter of convenience in developing the principles involved which are applicable to any original positions of the two ships whether together or separated at the start of the maneuver.
A Further Study of the Principles of Relative Movement
- In Figure 7 the guide is at O, steaming on course 20° (true) at 12 knots speed. P is a ship 2,000 yards from the guide on line of bearing 40° on the guide’s bow (i.e., P bears 60° true from O). They are steaming steadily along at 12 knots in this position. In this situation the relative movement of P with reference to O is zero. Assume now that P changes courses 60° to the right of the guide’s course (to course 80° true) and maintains her original speed of 12 knots. Constructing the speed triangle OAB we see that as soon as P turns, a relative movement with reference to O will take place and P will begin to travel along the line Pa, successive plotted positions relative to the guide being shown at 1, 2, 3, 4, etc., on the line Pa. As long as P holds this course-angle of 60° relative to the guide’s course, she will continue to travel on the line Pa, and will reach some indefinite position along that line depending upon how long she holds her course and speed. The direction of the line Pa from P is determined from the speed triangle as generally explained in Figure 6, and as applied to the specific problem in Figure 7. By the selection of combinations of speed and course-angle as referred to in paragraph 11, it is apparent that we can go out from P on a predetermined line (in other words, control the direction of Pa from P if we select the proper combination of elements as referred to in paragraph 11).
- Suppose “b” a ship at any position with reference to the guide, steaming the same course at the same speed of the guide. Suppose “b”, using standard speed, changes course 30° to the left of the guide’s course, in this case to course 350°, (true) the construction of the speed triangle OAB1 will show that for these conditions the relative movement line of “b” with reference to the guide O will plot at positions 6, 7, 8 and 9 on the line “bd”. If “b” holds her course of 30° to the left of the guide’s course and continues to steam at standard speed, she will eventually arrive at some position P1 on the line “bd.” Suppose the position P1 is a new position that you are ordered to take with reference to the guide. It is apparent from the study of the speed triangles that we can reach the position P1 on a predetermined line by the assumption of the proper elements as noted above in paragraph 11.
A very important principle is established right here with reference to the study of these two movements. The study with reference to the point P has developed the fact that we can move out from the position P on any predetermined line of relative movement by selecting the proper combination of elements with reference to the guide.
The study of the movement from b to P, has brought out the fact that we can approach any given position on a predetermined line by selecting the proper elements in accordance with the principles of paragraph 11.
If P, while traveling along Pa, has decided that she wanted to go to the position Pt on a course 30° relative to the guide, all that would be necessary for her to do would be to construct through P, the relative move-
ment line P1b for the 30° course, and where Pa crossed P1b at c, change course 30° to the left of the base course, finally arriving at P1.
- The studies preceding this are merely the analysis of the various phases of dropping back from a position P, 40° on the bow of the guide to another position P1, 40° abaft the beam of the guide. A slight study of the figure will make it self-evident
that in order to go directly from P to P1, P would have to change course through something over 180°, a condition which is undesirable and impractical in changing line of bearing in the fleet. Instead of making, therefore, the violent movement between P and P1, it is broken up into two movements of a first change from base course away from the guide, and another change from base course toward the guide. Such a maneuver is termed a “two-course maneuver” and is the basis on which the two-course angle card is developed.
- The foregoing are merely my own personal notes on this subject.
Summarized, the ship at P can, within reasonable limits, select any course she
pleases to go out on, and can select a predetermined line to come back on. The time to change back through the base course to the second course is given at the intermediate position “c”, and this intermediate position is determined by the intersection of the relative movement lines Pa and P1b.
- The particular study of Figure 7 is based on a dropping back problem in which the ship dropping back maintains standard speed. Any speed could be selected to go out on or come back on, and the lines Pa and P1b adjusted accordingly from the speed triangles constructed with the data selected. The principle of approaching such a position as P! on a predetermined line, that is, with a predetermined course relative to the guide’s course, is very useful and important, as is also the significance and meaning of the intermediate position “c”.
Figure 7 contains the principles on which the course-angle cards are constructed, and what is more important, gives a mooring board process for determining a two-course maneuver to drop back in case course-angle cards are not available. The course-angle cards have the advantage of having the time required to perform the maneuver etched on them, an element which the mooring board process does not give directly.
Finding the Time Required to go from One Position to Another Position Relative to a Moving Guide
- In maneuvering to change from one position to another relative to the guide, there is constantly being asked on the bridge the question “How long will it take us to get into our new position?” The maneuvering board gives a quick answer to the question when used in conjunction with the thumb rule—“knots per hour equals hundreds of yards in three minutes.” This expression simply means that the same numerical figure which represents a speed in knots per hour represents also the number of hundreds of yards at that speed which are traversed in three minutes.
For illustration:
15 knots per hour = 1500 yds. In 3 minutes.
9 knots per hour = 900 yds. in 3 minutes.
7.5 knots per hour = 750 yds. in 3 minutes.
2.7 knots per hour = 270 yds. in 3 minutes.
from whence the yards per minute are rapidly obtained by mental arithmetic.
So, to find how long it will take you to go from one position on the guide to another position, measure on the distance scale the distance in yards between your present and new position, divide this by your relative speed in yards per minute and the result is the number of minutes it will take you to go from your present position to your new position relative to the guide.
For example, in Figure 8, let one division on the scale represent 500 yards for distance and two knots for speed. Let the guide O and the ship P1 be steaming in column at 12 knots on course 330, P1 being 2,000 yards astern of the guide.
The guide now signals P1 to take position 30° abaft the guide beam at distance 1,700 yards. How long will it take Pt to get to her new position P2 assuming P1 goes out to her new station at 15 knots speed?
Solution: To scale, complete the relative movement triangle OAB. The relative speed at which P1 travels toward her new position is AB. With a pair of dividers AB on the scale measures 4.4 knots, so that P1 is attaining the new position at the rate of 4.4 knots per hour.
4.4 knots per hour = 440 yds in three minutes = 146 2/3 yds per minute.
The distance to be traveled is P1 P2 which measured on the scale by dividers is 1,900 yards.
Hence time to reach new position = 1900/146 ¾ minutes.
In practice we would say roughly that we were approaching our new position at about 150 yards per minute and reach there in 1900/150 thirteen minutes.
The foregoing method of finding the relative speed in yards per minute and mentally dividing it into the yards to be travelled to reach the new position is invaluable as a quick means of finding how many minutes it takes to go from one position to another.
P1’s course to her new position would be, as shown by the diagram Figure 8, 342 ½° at 15 knots speed.