CHAPTER VII. METHODS OF OBSERVING THE ROLLING AND PITCHING MOTIONS OF SHIPS. ENOUGH has been said in previous pages to show how variable, and how liable to mislead an observer, are the conditions surrounding the behaviour of a ship at sea. The ship, herself in motion, is surrounded by water also in motion; and it is extremely difficult, by means of unaided personal observation, to determine even so apparently simple a matter as the position of the true vertical at any instant. To estimate correctly the angles through which a ship may be rolling or pitching, it is therefore necessary to bring apparatus of some kind into action; and in the use of such apparatus there are many sources of possible error which must be prevented from coming into operation. Upon the correctness of these observations we are greatly dependent, since deductions from theory are thus checked, and the extent to which they can be made a safe guide for the naval architect in designing new ships is ascertained. Numerous examples illustrating the substantial agreement of observation with the chief deductions from theory have been given in the previous chapter; but up to the present time the comparison has been mainly of a qualitative character, and before more exact results are obtained, it will be necessary to have compiled and collated much more exact and extensive records than are at present accessible. The chief problem to be solved is this. What are the conditions of wave motion that will produce the maximum oscillation in a ship, of which the still-water period of oscillation as well as the coefficients of resistance are known; and what will be the range of that maximum oscillation? Or, it may be desirable to ascertain generally what extent of motion will be impressed upon a ship by a series of waves of certain assumed dimensions. Pure theory will not be likely to supply correct answers to these questions; but the conclusions of theory, being correct as to the character of the motion established, may be modified as to the extent of the motion by recorded observations of the behaviour of ships amongst waves of which the particulars have also been observed. To do this in a satisfactory manner, many observations will, as was said, be required; and the freer individual observations are from errors, the more certain will be the process of modification. Methods of observing correctly the lengths, heights, and periods of waves have been described in detail in Chapter V.; and it is now proposed to sketch the methods which have been adopted at various times for observing the rolling and pitching oscillations of ships. Of these methods, the following are the most important:(1) The use of pendulums, with various forms of clinometers; these pendulums having periods of oscillation which are very short as compared with the periods of the ships. (2) The use of gyroscopic apparatus. (3) The use of "batten" instruments. (4) The use of automatic apparatus, such as that employed by Mr. Froude on board the Devastation. Taking these in the order they have been named, it may be well to glance at their chief features, and to indicate the probable correctness or otherwise of their records. Pendulums, or clinometers, are the simplest instruments, but they are not trustworthy indicators of the angles of inclination attained by a ship when rolling in still water, and much less of those moved through by a ship rolling or pitching at sea. When a ship is held at a steady angle of heel (for example, as shown by Fig. 30, page 64), a pendulum suspended in her will hang vertically, no matter where its point of suspension may be placed, and will indicate the angle of heel correctly. The only force then acting upon the pendulum is its weight, i.e. the directive force of gravity, the line of action being vertical. But when, instead of being steadily inclined, the ship is made to oscillate in still water, she will turn about an axis, passing through or very near to the centre of gravity; hence every point not lying in the axis of rotation will be subjected to angular accelerations, similar to those which were described at page 107 for a simple pendulum. Supposing the point of suspension of the clinometer to be either above or below the axis of rotation, it will be subjected to these accelerating forces, as well as to the directive force of gravity, and at each instant, instead of placing itself vertically, the clinometer, or pendulum, will tend to assume a position determined by the resultant of gravity and the accelerating force. As the period of the pendulums used is short as compared with the period of the ship, the position towards which it tends to move will probably be reached very nearly at each instant. The case is, in fact, similar to that represented in Fig. 71, page 203. If the length of the upper pendulum (AB) is supposed to represent the distance from the axis of rotation of the ship to the point of suspension of the pendulum which is intended to denote her inclinations, the clinometer pendulum may be represented by BC. As AB sways from side to side, the point B is subjected to angular accelerations, and these must be compounded with gravity in order to determine the position which BC will assume; for obviously BC will no longer hang vertically. · The angular accelerating force reaches its maximum when the extremity of an oscillation is reached, consequently it is at that position that the clinometer will depart furthest from the vertical position. In Fig. 71, suppose VAB to mark the extreme angle of inclination reached by the ship, See page 111, Chapter IV. and let AB be produced to D: then, to an observer on board, the angle CBD will represent the excess of the apparent inclination of the ship to the vertical above the true inclination. It will be seen that the linear acceleration of the point of suspension B depends upon its distance from the axis of rotation A in Fig. 71. If B coincides with the axis of rotation, it is subjected to no accelerating forces, and a quickmoving pendulum hung very near to the height of the centre of gravity of a ship rolling in still water will, therefore, hang vertically, or nearly so, during the motion, indicating with very close approximation the true angles of inclination. Hence this valuable practical rule: when a ship is rolling in still water, if a pendulum is used to note the angles of inclination, it should be hung at the height of the centre of gravity of the ship; for if hung above or below that position, it will indicate greater angles than are really rolled through, the error of the indications increasing with the distance of the point of suspension from the axis of rotation and the rapidity of the rolling motion of the ship. The errors of the pendulum indications for still-water oscillations may be approximately estimated from the following formula, which was proposed by Mr. Froude :Let a true angle of inclination reached by the ship; B = apparent angle of inclination indicated by the pendulum; T = period of oscillation (in seconds) for the ship; Then = If, instead of 3.27, we write 33, this takes the approximate form, a = 10 T2 x B, which will be sufficiently near for practical purposes. Take one or two simple illustrative examples. For the Prince Consort T5 seconds; and h may be taken as 20 feet, if the pendulum were placed on the bridge. and the pendulum increases the true angle of heel by no less than 20 per cent. In the Devastation a pendulum placed on the flying deck may be taken as 25 feet above water; also T = 63 seconds. a Then = 10 × (63)2 2 450 = 450 6 B ̄10 × (63)2+3 × 25-450+75 525 = 7; α= 6 Here the pendulum indications exaggerate the true angles of inclination by about 16 per cent.; notwithstanding the greater height of the point of suspension above the centre of gravity, the slower motion of the Devastation makes the error smaller than in the Prince Consort. So much for the simple case of still-water oscillations. When we turn to the more complicated case of a ship oscillating amongst waves, there are good reasons for supposing that the errors of pendulum observations will be exaggerated. The centre of gravity of the ship is then, as explained in the preceding chapter, subjected to the action of horizontal and vertical accelerating forces. If the pendulum were hung at the centre of gravity (G) of the ship shown on a wave in Fig. 62, page 153, it would, therefore, no longer maintain a truly vertical position during the oscillations, but would assume at each instant a position determined by the resultant of the accelerating forces impressed upon it and of gravity. The direction of this resultant has been shown to coincide with that of the corresponding normal to the effective wave slope.* Hence * See the remarks on page 151 and Fig. 60. |