Before describing the "use of one angle in curved channels," it may be well to say that the principle is a very old one. It has been applied in different ways, and is used in the "danger angle," mentioned in Sailors' Horn Book and Harrington's Navigation, and is well known to all navigators. The principle used in navigating narrow and curved channels is the same as the danger angle, but applied under slightly different circumstances. It is the danger-angle idea somewhat amplified. It had been used in the C. S. Steamer Hassler and in the U.S.S. Saratoga for several years of occasionally difficult navigation and piloting, when it occurred to me that its use was not general in the Navy; and finding, upon inquiry and discussion, that it was but little known or used for curved channels, I described to the Department the convenience I had found in employing it, and suggested further trials of it at various entrances on our coast. A Board appointed in the Navy Department to examine the subject reported favorably as to its probable value in practice.
This method is applicable in entering many of our coast ports. Among these may be named: Portland, Salem, New Bedford, Oyster Bay, Sandy Hook, Patuxent River, Key West, and others. At Sandy Hook, where the ranges are, most of them, a long way from the channels they mark, slight mists are sufficient to cause them to be obscured, and at the same time to cause confusion as to the buoys; while a curve passing through Highland Light and Scotland Light Ship may be found useful to carry a ship safely from the Scotland around the Hook, and into the anchorage inside the Hook. And if this method should find favor, greater security and convenience could be reached by the erection of one or two beacons at suitable points of a good curve. The reef at Key West offers several examples of curved entrances of much safety and convenience.
The principal objection to the general use of this method is the ignorance of the use of the sextant and of the measurement of horizontal angles among a majority of seamen and officers in the coasting trade and merchant service. Here, again, if this method proved useful, a simple and cheap instrument could be made, without a movable arm, and registering permanently one angle—namely, the angle of two known objects in the vicinity—which, being kept at the proper number of degrees, would ensure a ship being on a safe curve. The objects and their proper angle being carefully determined practically for each port, these simple instruments would be constructed bearing the names of port and of objects used, and the number of degrees of angle.
All these matters are consequent upon the method being found useful; and I recommend the use of this method to officers, not as being certainly valuable, but as worthy of being thoroughly tested. I have had occasional incomplete trials of the method at San Juan de Porto Rico, Key West, Oyster Bay, Sandy Hook, and on the Pacific Coast, but have been at those times engrossed with survey work or the training of apprentices, and unable to give sufficient attention to the method. It should be understood that no new principle is claimed, and the only point specially made is that its application to curved channels may be found, in certain ports, very useful and convenient.
Upon approaching a harbor or channel where piloting becomes necessary, and where this method promises to be of use, identify on the chart some prominent points or objects in the vicinity of the curved channels to be followed. Then note what general curve the ship's course will have to follow in the channels, and describe roughly a circumference, of which this curve shall approximately be an arc, and which circumference shall pass through two of the prominent points or objects recognized on the coast. A headland, or simply a marked bend in the land, may be used in default of better-defined objects, the angle being taken to the tangent of the point, if the bends or profiles are sufficiently salient to prevent large errors by the change in the point of tangency as we advance. It is rare, of course, to find the exact curve desired, but by trying different known points on shore, and different lengths of radius, a convenient curve can be frequently found which will answer all the purposes of safety. This being done, draw lines from any one point of the circumference to the objects through which the circumference has been passed. The angle made by these lines will be constant for all points of the curve which lie in that arc of the circumference, as all angles in a circumference subtended by the same arc are equal, and as this angle will in all cases be subtended by the opposite arc connecting the two points.
Thus, if a ship so direct her course as to make this angle (between the two objects) the number of degrees required, and keep it unchanged, or nearly so, she will be constantly on, or nearly on, the circumference referred to; and, as the angle becomes less, she will know that she is passing outside of that curve, and, as it becomes greater, that she is passing inside of it. If we have to round shoals in entering a harbor, B, we make, first, satisfactory curves for the ship to describe in clearing them, such as M; then seek for a circle whose arc shall approximate to this curve and which passes through two prominent points, or any objects readily recognized, such as H and P; such a circle would be M'. At any point on the arc between H and P, lines drawn from H and P to meet in the circumference will make a certain angle—103° in this case. Hence, by approaching these two objects on a safe bearing until their angle, as measured from the ship, becomes 103°, we will find ourselves upon this safe and convenient curve, which we may follow by edging out when we increase our angle above 103°, and by edging in as it becomes too small. The same way with the next curve, and so on throughout.
There are many cases where the shoal does not discover itself by breakers or discolored water, and when distances from the shore must, without this aid, be judged by the eye—a dangerous plan for strangers unaccustomed to the appearance of the shores, heights of cliffs, and such details. In such cases, if recognizable ranges back of the anchorage B, or of the point C, are not to be found, the convenience of this one-angle method becomes apparent; while, if to these circumstances we add the existence of a shoal D, or of rocks, as shown on the side of the channel, this method becomes more than convenient, being a valuable guarantee of safety. This is especially true when, in narrow waters and sharp bends of channels, time will not permit of bearings of objects being taken and plotted (the ship might ground while waiting for a position); and a principal virtue of this method is that the chart-work proper is done beforehand, and the officer is left free to handle his vessel with this check and guide always at hand. The sextant, set to the angle required, may be used by the officer himself who is conning, or by his assistant, and the ship may thus with ease and confidence be steered upon a safe and convenient curve or succession of curves.
The principle already mentioned can be extended by the further use of other objects on the same side, defining other curves and making a continuous safe course throughout. Also, if the proper course becomes of reverse curvature, objects on the other side of the channel may be used for defining by their angle a reverse curve for continuing the course; or such reverse curve may be used as a help to the first curve in a difficult passage.
The centre and radius of the required circumference are best found by inspection. Let the eye determine roughly the kind of curve needed to pass comfortably through the dangers; then sweep the arc most like that curve, using the centre and radius which seem needed for it; then search in the vicinity of that portion of this circumference which passes over land and among known objects for two suitable points. Having found these, endeavor so to adjust the centre and radius that the circumference, while fulfilling its office as a safe curve through the dangers, shall also pass through these two points. There will be found, as a rule, but little difficulty in doing this in cases where this method is useful. The angle made by lines from the two objects to a point in the circumference should be between 40° and 140°. It is not so reliable between 20° and 140°, and between 140° and 160°, and it had better not be used when less than 20° or more than 160°.
Should this method, in practice, find favor among officers, and be approved by the Department, the labor of inspecting the charts, describing the most convenient and useful curves, and providing, rules for following out these methods, would naturally fall upon the officers who superintend the preparation and issuing of charts, and would simply be an addition to the sailing directions of certain ports where this method promises usefulness. It should be tested practically at the place before directions are written. The work of inspection of the chart beforehand, and of preparing the curve, would not be required of the navigating officer of the vessel, who would only need to accustom himself to the measurement of horizontal sextant-angles. It is also probable, in the case of this method being favorably considered, that beacons or other marks for day or night would be erected in such localities as do not offer at the proper vicinities prominent and distinctive characteristics for use in defining by their angle convenient curves for piloting through a channel.
This method is productive of much satisfaction in the advantage it gives of being able to take the sextant or similar instrument with which one's position or curve is to be determined, to all parts of the ship and use it aloft or on deck with equal ease and accuracy. This advantage of the sextant over the compass is very marked when distant lights or other objects are shut out by mangrove swamps or scrub growth on flat lands, making them invisible from deck, but in sight from tops of an ordinary vessel. Such ports as Key West and Charleston, S. C. are instances of the above.
It may be well to state that this plan cannot be of service in piloting through straight channels, in which ranges and bearings are alone of service. It is useful only where the course to be steered is curved nor is it of use when this curve is very slight, as in such cases the angle of the objects would be too great or too small, or their distance too great for accuracy.
Many harbors do not need curves of this method, being already well supplied with range lights, day marks, etc.; and it is not intended to be understood that this method should supplant other methods of running on ranges, bearings, etc., but only that it may be a valuable auxiliary to those methods on some charts, and an invaluable substitute for other methods on charts which do not possess the proper lights and ranges, and where curved channels have to be followed.
The writer of these notes is, however, disposed to believe, if the method be found worthy of adoption, that, in many already well-lighted and marked harbors, economy in the number of marks will be obtained by substituting this method in certain cases. An example of this is to be seen in the main ship-channel near Sandy, Hook, where by using this method one lighted beacon at the "Dry Romer" would make unnecessary the following—viz.: West Beacon, Bayside Beacon, and Wilson's Beacon. But the writer wishes to disclaim any intent to propose any changes in existing methods, and brings forward this notice only with reference to its auxiliary character in most ports, and to its own intrinsic value in other cases of ports not marked or lighted properly, or perhaps not at all —such, for instance, as San Juan de Porto Rico, where the writer has found the method very valuable at moments quite critical from a piloting point
Application of the One-Angle Method to the Chart of Sandy Hook.
The chart of Sandy Hook entrance shows (see plate opposite) a curve marked A, defined by preserving the angle of 46° between Highland Lights and Scotland Light Ship. This curve carries 23 feet through South and Main channels.
Another curve marked B is defined by an angle of 86° between Hook Beacon and Scotland Light Ship, and carries 24 to 25 fee through the Gedney channel.
Another marked Cis defined by an angle of 73° between Scotland Light Ship and Sandy Hook Light, and carries the same drafts through the Gedney.
Many other convenient curves suggest themselves here, by the use of the lights, light ships, and beacons already in place, and the erection of one or two more beacons in suitable places at slight cost.
The distance of the range beacons from the vessels using them causes them, in most weathers, to be of little value, and it would be a satisfaction to the navigator to have close at hand, upon Sandy Hook, large, easily seen guide beacons by day, and bright guide lights at night. For instance, the curve marked C through Gedney's channel could be followed with ease and exactness by erecting a beacon at a point on the southern part of the Hook, which I have roughly marked X, and keeping the angle between it and Sandy Hook Light 32° (about).
Entering by Gedney and Main channels, when we consider the search for entering buoys at night, the compass courses, influenced by currents of which we are ignorant, and the ranges of far distant lights, usually confused by mists, such an accurate and convenient method as here described will seem preferable to many, especially to those to whom the rough measurement of angles is not a mystery.