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Originally appearing in Volume V24, Page 957 of the 1911 Encyclopedia Britannica.
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SCALE OF FEET 0 100 200 300 400 500 800 700 800 900 1070 1 ~I I I The curve given is that described by the pivoting point. The first time round is shown in a drawn line, the second time round in a dotted line. h. m. s. A, Position of ship's centre of gravity when helm is half over . 12 B, Position of ship's centre of gravity after she had turned through the first 18o° . 12 C, Position of ship's centre of gravity after she had turned through the second 18o° . 12 D, Position of ship's centre of gravity after she had turned through the third 18o° . 12 E, Position of ship's centre of gravity after she had turned through the fourth 18o° I2 Speed on final circle, 7.14 knots. Diameter of final circle, 1240 ft. Tactical diameter, 1315 ft. Time of turning through 18o°, 2 min. 31 sec. 32 52 35 23.4 38 4 40 46 43 28 been verified in a few cases, the value adopted for E, being that for a riveted structure or about 1o,000 tons per-square inch. In some model experiments made in air and in water, the frequency in the latter case was found to be reduced, and owing to the rapid damping of the free vibrations and to a virtual increase in the mass-inertia caused by the concomitant motion of the surrounding water, which occurs in the ship and not in the model when vibrated in air, there must be a difference in the results. A second difference is due to the ratio of depth to length in a ship being sufficient to make the term for rotational inertia appreciable, which factor is neglected in the formulae fors thin bar and the dynamic model. The extent to which such results require modification cannot be determined until further experiments have been made. Finally it appears that vibration in a ship can generally be avoided only by removing its cause; the addition of further stiffening to the structure with the object of reducing vibration has not infrequently had the opposite effect, the natural frequency being brought more nearly into synchronism with that of the disturbing force. The adoption of the steam turbine obviates many of the causes producing vibration referred to above, leaving only those due to the forces resulting from inequalities in the working or position of the propellers. Steering. The information available on the steering and manceuvring qualities of ships is largely due tq the. results' of the methodic trialsmade with H.M. ships. These include observations of the paths when turning under different angles of helm, at various speeds, with and without assistance from the propellers, and with variation in certain features of the hull.which influence the steering, Such as the addition of bilge keels, change of draught or trim, and the omission of the after deadwood. One of,the first attempts at plotting the curve traversed by a ship under the action of her rudder, and the position of the ship at any instant .with reference to that curve, was made by the writer in 1877 with H.M.S. "Thunderer " (see Appendix XIII. to Report of Inflexible's " Committee).' The position of the ship was fixed at numerous intervals with reference to the line of advance by observing simultaneously (a) the direction of her head and (b) the angles of the base of a triangle, whose apex was a floating object within the approximate circle in which she turned, and whose base was the line between two observers at fixed points on the deck, one forward and the other aft; these angles in conjunction with the base fixing the distance of the middle line plane of the ship from the floating object. The data were observed for different speeds and with different angles of rudder, and with and without the turning effect of the screws. Fig. 61 gives the plotted positions of the ship continued for two complete turns with 31° of helm-when going ahead initially at Io•5 knots. The straight line which becomes curved at the point A is the initial course of the ship. The short lines give the positions of the ship when turning at intervals of a minute; and the curve drawn touches the positions successively occupied by the middle line of the ship. It will be seen that the bow of .the ship is nearer the centre of the circle, or curve in which she turns, than the stern. The vessel may be regarded as going ahead and turning or pivoting about a point well forward in her middle line; this is termed the " pivoting point," the middle line being, at this point, a tangent to the curve concentric with and similar to that described by her centre of gravity. In the " Thunderer " the pivoting point was situated about 5o ft. abaft the stem. Similar information for a more modern ship is given in fig. 62 for the Japanese battleship .'.Yashima" when turning tinder 32° of helm with an initial speed of 17-5 knots.' AAA-is the,loeus:,.gf the pivoting point O,"and BBB that of the' ship's centre of gravity. The bow of the ship is directed inwards with reference to the latter curve; the angle between the middle line plane and the tangent to the curve BBB is termed the " drift angle." The distance between the pivoting point and the ship's centre of gravity is equal to p sin ¢, where p is radius of curvature of BBB and ¢ is the drift angle. The value of d is about 23° in the" Yashima," and about Io° in the " Thunderer"; and the pivoting point 0 of the former ship is situated very near the fore end of the vessel. CCC is the path of the outer edge of the stern and represents the clear space required when turning. In both ships the path is spiral in form until about 16 points (18o°) have been turned through, and it then becomes approximately a circle. The maximum distance that the ship's centre of gravity travels in her original direction after the helm is put over is termed the "advance," and the " tactical diameter " is the perpendicular distance between the original line of advance and the ship's position after turning through 16 points. For an approximate investigation of the forces in operation during the turning of.a ship, the ,motion may be divided into three stages: (a) when the rudder is first put over and the pressures Nature of on the hull are those necessary to produce angular accelera- forces tion; (b) when the accelerative forces are combined with when those caused by the resistance of the ship to rotation; and when (c) when finally turning uniformly in a circular path. The turning. characters of the forces acting during the states (a) and (c) can be ascertained, and the type of motion under the complex conditions represented by (b) will consist of a gradual replacement of the motion at (a) by.that at (c). Initially, on putting the helm over, the change in the stream line mbtioii at the stern produces a pressure upon the rudder normal to its plane. If the rudder is unbalanced, there is generally an additional pressure upon the after deadwood caused by the widening of the stream lines approaching the rudder. The resultant of these pressures on rudder and deadwood is a force P at the stern which may be resolved longitudinally and transversely into R and Q, where R tends to reduce the speed of the ship and Q to move the stern outwards (fig. 63). The proportion of the force P due to the deadwood is unknown, but it is small in recent warships in which the after deadwood is considerably cut away; the portion due to the ~P rudder pressure can be calculated from the results of experiments on plates moving obliquely through water. If A is the area of the rudder in square feet, 0 the angle of helm and V the relative velocity in knots with which the water impinges on the rudder (assumed equal to the speed of the ship increased by the slip of the screw), then P (in tons) = k. AV'sinO, approximately where the mean value of k for small inclinations isz for a square rudder and about -A-'b for a rectangular rudder. of breadth twice its depth (k also varies with the angle of incidence.; when the latter is greater than about 35°, the above formula becomes inapplicable). The convergence of the stream lines at the stern due to the angle of run, and the oblique and variable motion-of the water caused by the screw propellers, modify the value of k..as applied to the determination of the rudder pressure; but it is evident that with ships of fairly similar types the force causing initial turning varies with the shape of the rudder and approximately as its area, the angle of helm and the square of the speed. The initial angular motion of the ship is due to the action of the component Q of the pressure on the rudder and deadwood, which is equivalent to a force Q at the centre of gravity tending to produce a lateral translation of the ship as a whole and a couple Q. BG tending to rotate the ship about the centre of gravity. Both the lateral and angular movements of the ship are accompanied by the motion of a mass of water, which may be regarded as virtually increasing the mass. and moment of inertia of the ship. Denoting these quantities, thus increased, by W and 1 respectively, the initial lateral acceleration of the ship is equal to , and its lateral speed at the end of ai short interval of time At, during which Q and W may be supposed to have remained constant is At At the same instant and under similar hypotheses the angular velocity about the centre of gravity is . At. Hence a point 0 forward in the middle line of the ship taken so that GO. Q' B G .At= w. At or GO = W BG is, at the in- stant considered, at rest except for the motion of the ship ahead, which is due to the original speed of the ship before putting the rudder over, somewhat reduced by the action of the component R of the rudder pressure during the time At. The instantaneous centre of the motion of the ship must therefore be somewhere in the perpendicular at 0 to the middle line of the ship, the point 0 thus corresponding to the " pivoting point " as 'previously defined for the steady motion of the ship in a circle. The actual position .of 0 cannot be calculated, as it depends on the values of I and W, which are different from, and not expressible in terms of, 'the moment of inertia I' and mass W' of the ship itself; but from the method by which it is determined it is clearly forward of " the centre of gravity; and so far the investigation is confirmed by observation, which shows that the first effect of putting the rudder over is to cause the stern of the ship to swing towards the side to which the helm is moved to a much greater extent than the bow moves towards the opposite side. If the time At be supposed to become infinitesimal, and the effect ' Similar experiments had been made by M. Risbec on the " Elorn " (Revue maritime et coloniale, 1876). ' See " The Steering Qualities of the `Yashima,' " Trans. Inst. Nay. Archs., 1898. 63. of putting over the rudder be regarded as an impulse (measured by the finite product P. dt), delivered at the stern of the ship normal to the rudder, the resistance of the water to the rotation of the ship may be neglected, and the instantaneous centre of the turning motion (as distinguished from the motion ahead) is the point 0 on a straight line GB perpendicular to the direction of the impulse, and such that GO. GB =wan expression for the position of 0 of the same form as obtained before. In this case w,=10, where k is the radius of gyration of the ship about a vertical axis through the centre of gravity, and the point 0 is obtained by the geometrical construction shown in fig. 64, given by Professor W. M. Rankine, where 9 GL = k and is perpendicular to GB, and the angle BLO is a right angle. The value of I is dependent on (1) the. distribution of weight in the ship, being large when heavy weights are situated near bow and stern, (2) the length of the ship, and (3) the underwater form near the ends, being relatively large in fine ended vessels with large areas of deadwood. W is also dependent on the shape of the ship under-water. The handiness of a ship or her readiness to respond to slight alterations in helm is mainly dependent on the relation between Q XBG the moment of rudder pressure for a given angle, and I the virtual moment of inertia. If I is-comparatively large, the vessel will turn slowly under helm until, gathering way, the rapidity of its angular motion becomes so large that reverse helm may be required to limit the change of course to that desired. Unhandiness is usually experienced at low speeds (Q being then small) and also hi shallow water when I is increased by the restriction in the flow of water from one side of the ship to the other. Improvement in the handiness in these circumstances has been obtained in certain ships with unbalanced rudders by filling in the after deadwood, the loss from the increased inertia being more than compensated by the greater turning moment due to the pressure on the after dead-wood. When the ship is turning steadily in a circle, if C (fig. 63) is' the centre of rotation, and CO. perpendicular to the middle line of ship, the motion is equivalent to a progression ahead with speed V (which is considerably less than the initial speed), combined with a rotation about the " pivoting point " 0, which is generally situated slightly abaft the bow; the drift angle 4, is given by the relation OG=OC tan O. The time of turning through 18o° is where r is the radius OC. The forces acting upon the ship are now—the pressure P on rudder and deadwood (if any), the centrifugal force W%y°S , the thrust of the propellers, and the pressures on the hull. The last named consist of forces PI outwards before 0, and P2 inwards abaft 0; of these PI is usually negligible in amount; P2 cannot be directly estimated, but since work is done against it by the trans-verse motion of the after part of the ships a reduction of speed results whose amount is largely dependent on the obliquity of motion at the centre of gravity, that is on the drift angle O. Under full helm the ratio of the steady speed when turning to the initial speed is often about 6o or 70%; but in some quickly turning ships it is less than 5o%. Of the remaining forces, the transverse com- ponent WVgr s24, of the centrifugal force is known since the final diameter of turning 2r is approximately the same as the tactical diameter. To obtain P, it is to be observed that the water impinges on the rudder in a direction BF intermediate between BE (perpendicular to BC) due to the ship's motion and BD due to the form at the stern; if BF is assumed to bisect the angle DBE, the effective rudder angle is approximately 0-0. The pressure on the rudder is therefore less than when helm is first put over and is further reduced on account of the diminution in the speed of the ship. From experiments made with the object of measuring P when turning steadily, it is found that the pressure recorded was about one-fourth of the value calculated on the assumption of the ship retaining her original speed and effective rudder angle; when helm had just been put hard over, from one-half to one-third of the theoretical pressure was obtained. ' (See Bulletin de l'Association Technique Maritime, 1897; American Institution of Naval Archs. and Mar. Eng., 1893.) The transverse forces calculated on this basis for a battleship of 15,000 tons displacement when turning steadily under full helm are approximately–centrifugal force 200 tons, pressure on rudder 40 tons, and Q2, the transverse component of P2, 240 tons passing through a point on the middle line about 40 ft. abaft the centre of gravity. The following equations applicable to the state of steady rotationcan be obtained from the above considerations, neglecting Pr and the small, couple due to R: WVicosI 4 Q2=Q T gr (i.) Q2XGM=GBXQ' . (ii.) From (i.) it is seen that a small tactical diameter will be obtained when Q2 is large compared with Q; from (ii.) it follows that the point M (fig. 63) should then be near G. These conditions are realised in a ship whose resistance to leeway is considerable but concentrated about the middle of the length, such, for example, as a yacht having a deep web keel, or a boat with centre board and drop keel. In these instances •the vessel may be regarded as virtually anchored by its keel, and the pivoting point brought to a position in close proximity to the centre of gravity. Similarly tactical diameters of vessels of ordinary type are reduced by diminishing the resistance to lateral motion at the after end and by increasing it amidships or forward. During the turning trials made with H.M.S. " Thunderer," observations were made of the heel caused by the transverse forces brought into play when turning. On first putting the Heelwhea helm over a small inward 'heel caused by the pressure, eeir of the rudder was observed; as the rotational speed of the ship increased this inclination was succeeded by a steady out-ward heel, amounting to about 10 at 7 knots speed. The latter is caused by the couple formed by the centrifugal force and'thela 'eral resistance diminished by the (usually) small couple due' to' the rudder pressure. During some more recent trials carried out on the " Yashima" the angle of heel was 8° at full speed. Similar large inclinations are generally found with modern warships having small turning circles and high speeds and whose centres of gravity are also situated high up; at moderate speeds, however, the heel is of small amount. On putting the helm quickly amidships when turning, the opposing couple. due to the rudder pressure is removed or reversed and the angle of heel momentarily increased; instances have occurred of ships with small stability and comparatively large " rudder couples" capsizing through this cause. "` The rudders used in ships are of two types:—(1) . Unbalanced, shown in figs. 65, 67,.68; and (2) balanced, shown in'f gs 66, 67 (at bow) and 69 to 74. An unbalanced rudder is in stable equi- librium Types of when amidships and force has to be applied to the Tde tiller; in order to place it at any angle to the tniddlh. line. f3' . It is supported at its forward edge by means of pintles working, in gudgeons on the sternpost; and owing to its simplicity of construction. and to its property of returning quickly to, the middle line when the tiller is released through any cause, this type is preferred when the force required to put the rudder hard over is sufficiently moderate to enable steering to be performed' by hand or by an engine and gear of moderate size'when steam steering is admissible. With high speeds and large manoeuvring powers, the unbalanced type is generally unsuitable; and balanced rudders are adopted sr, H.M.S. ` Duncan " similar. Edward VII." in order to reduce the force required and the work done: to obtain large angles of helm. , A balanced rudder is unstable amidships, and, if left free comes to rest at a moderate angle on either side of the middle line. Slightly less than one-third of the area is usually placed before the axis; in some ships in which a greater proportion has been put forward, difficulty has been experienced in bringing back the rudder to ar1iidships. As shown in the figures, the method of support has varied in different ships; in many cases a steadying pintle has been placed at the heel or mid-depth, but in the latest warships the support has necessarily been taken entirely inboard. In the merchant service, unbalanced rudders of the form shown in fig. 65 are generally fitted ; the rudder extends"up to, or above, the water-line, and is comparatively narrow longitudinally. Some-what greater efficiency when using small or moderate angles of helm is obtained with rudders of this shape; as, for a given pressure AP on rudder, the turning moment on the rudder head, and the power required for working the rudder are also less. A type of balanced rudder devised by Professor Biles and adopted in some large Atlantic liners is shown in fig. 66. Broader and shallower rudders are adopted in warships owing to the necessity of keeping the whole of the steering gear below the water-line for protection.(fig. 74), which had, in addition to the usual rudder at the stern, a double-balanced rudder in the bow, which could be drawn up into recesses in the hull; the two rudders were about 3 ft. apart and when in use worked together. The results of the turning trials of some of the Experimental principal classes of warships are given in the following results. table: Ship or Class. Displacement Length Area of Speed in Advance Tactical Tactical in in Immersed Knots at in Diameter Diameter Longitudinal Plane Tons. Feet. divided by Commencement yards. in divided Area of of Turn. Yards. by Length. Rudder. Dreadnought 17,900 490 37.5 19 490 440 2.7 Lord Nelson 16,500 410 40'5 17 400 370 2.7 King Edward VII. 16,350 425 44.8 161 450 440 3.1 Formidable . 15,000 400 45.2 141 440 500 3'7 Majestic 14,900 390 47'8 16 450 500 3.9 Minotaur . 14,600 490 48.4 19 480 600 3.7 Monmouth . 9,800 440 44'4 231 590 790 5.4 Drake 14,100 500 46.8 23; 700 810 4'9 Diadem 11,000 435 44'5 201 650 920 6.3 Powerful 14,200 500 50.3 22 800 1.120 6.7 Minerva 5,600 350 48.3 18 540 770 6.6 Arrogant. . 5,750 320 33'5 17 350 380 3.6 Helm angle about 35° in all cases. The unbalanced type was mainly used in British battleships up to H.M.S. " Formidable " (19o') and " Duncan " (1903) (fig. 67). In the " King Edward VII." class (1905) (fig. 68) the rudder was balanced, about one-fourth of its area being placed before the axis; balanced rudders supported at about mid-depth were fitted in the "Yashima " (1897) and the FIG. 69.—H.M.S." Lord Nelson." " Lord Nelson " class (1905) "Yashima" and H.M.Ss. "Swift- (fig. 69). In H.M.S. "Dread-sure," "Warrior" and'` Minotaur" nought " (1906) and recent similar. battleships, twin-balanced rudders are fitted immediately behind the inner propellers (fig. 70), to obtain additional steering effect from the propeller race, and to enable the ship to be steered from rest in getting under way. Owing to the higher speeds of first-class cruisers, balanced rudders were used; those fitted in " Diadem " as Section at A.P. FIG. 7o.—H.M.S. " Dreadnought." and " Powerful " classes (1897–1900) are shown in fig. 71, and for " Cressy," " Monmouth " and " Devonshire " classes (1901–1905) • in fig. 72. In " Warrior " and " Minotaur " classes (1907 1908) the rudders are as shown in fig. 69. The older second-class cruisers had rudders and sterns of the type shown for H.M.S. " Powerful" in fig. H.M.S. " Diadem " similar. p, Arrogant " class (1898), in which two rudders were fitted in conjunction with a considerable cut-up at the stern in order to obtain increased manoeuvring capacity (fig. 73). Recent second-class cruisers have rudders of the type shown in fig. 69. Auxiliary rudders have been fitted in H.M. ships in a few in-stances. An interesting example was that of H.M.S. " Polyphemus " In the last column the tactical diameter is expressed in terms of the length of the ship; this ratio enables a rough comparison between the steering capacities of different ships to be expressed. The improvement in turning in modern warships has been due largely to the increase of rudder area in relation to the area of the immersed middle-line plane, which has been made possible by the adoption of balanced rudders. Considerable improvement has also been effected by cutting away the after deadwood; this will be seen on comparing the performances of H.M.Ss. "Monmouth " and " Diadem," and " Drake " and " Powerful "; the former ship of each pair has her after deadwood partially cut away and has a smaller tactical diameter. In the " Yashima " the whole of the deadwood is removed and a very large rudder fitted; her tactical diameter is twice her length. The rudder area is relatively much less in merchant vessels, where the necessity for a small tactical diameter does not arise. Experiments have been made to ascertain separate effects of angle of helm, time of putting helm over, and draught and trim of ship. The effect of variation of helm angle is shown in table below: Tactical Diameter in Yards at about 12 knots speed. Ship. Battleship. First- 1 Second- Torpedo- Class Class Boat Cruiser. Cruiser. Destroyer. Io° helm 750 1400 1600 700 20° helm 55o low Iwo 500 35° helm 450 750 800 300 In ships having unbalanced rudders and fitted with hand-steering gear considerable time is required to put the helm hard over at full speed; and consequently the tactical diameter and the advance are greater at high speeds than at low speeds. When steam-steering gear is provided the helm can usually be put hard over in from to to 20 seconds at any speed; and in modern warships the speed is found to have little influence on the path described when turning. In the case of torpedo-boat destroyers marked increases in the tactical diameter and in the advance occur at high speeds, the cause of which is not fully known. In such vessels of length 270 ft. and displacement 900 tons, the tactical diameter is about 55o yds. at 30 knots and 300 yds. at 15 knots. A moderate variation in the mean draught has little effect on the course, but additional trim by the stern results in a greater space being required for turning. By working one propeller ahead and the other astern the space required for turning may be shortened, but the time of turning is frequently increased. The character of the path described depends on the relation between the revolutions of the screws. In a single-screw ship, with the propeller well immersed, the upper blades experience greater resistance to rotation than the lower blades, since the forward velocity of the frictional wake is greatest at the surface; hence a right-handed screw tends to turn the ship's head to starboard, and requires starboard helm. The reverse is occasionally experienced when the upper portion of the screw is incompletely immersed. When a ship is going astern manoeuvring is performed with some uncertainty, as the rudder is near the pivoting point. ' Arrogant."
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