ON A PARTICULAR ACTION OF THE JIB.

BY HENRY RAPER, LIEUT. R.N., V.P.R.A.S.

Ir is generally taken for granted by seamen, as a self-evident proposition, that the jib has the effect of lifting the ship's head, and they accordingly attribute the increased violence with which the ship plunges, as the wind freshens and the sea gets up, merely to the effort exerted by this powerful sail in dragging the ship through the seas. But it is evident that every force acting horizontally upon the ship, and applied above the surface of the water, must necessarily tend to cause her to decline towards the opposite side from that to which it is applied; every sail, therefore, must, in some degree, tend to depress the head, and thereby aggravate the plunging of the ship; and if at the same time the tendency of any sail, from the manner in which it is set, be such as to produce an opposite or raising effect, the final or total effect upon the ship can be due but to the difference of two contending efforts.

In the present paper it is not proposed to enter upon the general effect of the jib, but merely to consider the circumstances under which it acts either to raise or depress the ship's head.

It is not necessary, in order to understand the nature of the action in question, to refer at all to mathematical investigation, though this is indispensable in obtaining the measures of the effects produced. Accordingly, the treatment of the problem itself is deferred altogether to the end of this paper, where will be found the manner of reducing questions of this kind to calculation, with an example.

Suppose, in order to fix the attention, the jib to be a flat board, instead of a curved and flexible surface, which supposition does not affect the argument, and that the clue is fast amidships. Now, when the wind blows upon a sail, the effect produced by the pressures upon all parts is the same as if they took place at the centre of effort, or centre of gravity of the surface, which is two-thirds down the middle of this sail from the head; and the direction in which the total pressure takes effect is perpendicular to the surface. Hence, when the sail is thus hanging vertically, the total pressure or resultant springs from the centre of effort, and extends in a horizontal line directly to leeward, or eight points from the ship's head. This horizontal effort of the sail, which is the same in direction, though not in intensity, whatever may be the direction of the wind, has therefore no tendency to raise or depress the ship's head. But if the sheet be eased off and the sail revolve round the stay through two points and a half, the resultant will be found, in most ships, to lead two points above the horizontal plane, and two points before the beam; and this, as before, holds good without any regard to the direction of the wind-the sail of course being supposed to be trimmed full and not aback. In this position, therefore, there is an effort to draw the ship a-head, and at the same time to elevate her bow. If now we suppose the ship to be heeled over by the wind or other cause, it is evident that the resultant of the sail will itself be carried downwards, though a corresponding angle: in most ships an inclination of a point and a half will cause the resultant of the jib (trimmed as above) to point below the horizontal plane; thus, therefore, there will now be a force to draw the ship a-head, as before the ship was inclined, and an effort to depress her bow.

In this last case there can arise no question of the final effect of the sail in depressing the bow, because it is the sum of the two efforts into

which the total action is resolved-namely, the direct effort or pull of the sail acting at a great elevation above the water, and the downward pressure of the sail acting at a point considerably before the centre of gravity; but in any other case-namely, in which the resultant of the sail tends upwards, the final effect being the difference of two efforts must be determined by finding, by calculation, which of the two preponderates.

In all vessels the jib tends to lift the head while the vessel is upright, or but slightly heeled over; and also when the wind is aft, or upon the quarter, unless she is heeled over in a very extraordinary degree.

The elements necessary in calculating the following results are taken from Mr. Edye's Tables of Displacement;' and from these data it appears that, if the jib move through an angle of 25° round the jib-stay from its first position, the angle of inclination in different ships, at which this sail begins to tend altogether to depress the bow, is as follows:In the 80-gun ship, 130; in the 46-gun frigate, 124°; in the 18-gun brig, 11°; in the schooner, 16°; and in the cutter, 14°. It appears also that, while the jib and fore-sail of the cutter are nearly equal in direct effort, the fore-sail tends to aggravate the plunge more than the jib, in the proportion of 17 to 10, at an inclination of 20°.

When the jib is eased in, the stay becomes more vertical, while the centre of effort is both lowered and brought further aft. Its depressing effort will be found, accordingly, to be nearly the same, except that the leading of the sheet is somewhat changed.

When the jib-stay is slack, the sheet requires to be hauled farther aft, to make the sail stand. This diminishes the direct or drawing effort of the sail, and, at the same time, by flattening the foot, increases the downward effort.

In concluding the present brief notice, it may be observed that, though we cannot determine the absolute force of any sail, yet we can assign its several effects upon the ship in their true relative proportions, and thus obtain useful conclusions. Thus, for example, we can infer, by help of the annexed formulæ, that the effect of the foretop-gallantsail in an 18-gun brig, close hauled, and heeled over 25°, in causing her to plunge, is to that of the main-top-gallant sail (a sail of equal size, and set in the same manner) as 8 to 7.

As figures to exhibit the mechanical conditions of these questions would be very complicated, and as, besides, they are not necessary for those who are acquainted with theoretical mechanics, they are omitted.

Let the length of the vessel be considered as the axis of x, her breadth that of y, and z vertical, the centre of gravity being the origin. Let R be the resultant or total pressure of the sail; this may be resolved into a horizontal force, X, to draw the ship a-head; also into Y, to press her to leeward; and into Z, a force acting directly upwards or downwards; then the effort f, or moment of force of the sail to cause rotation round the axis of y, that is, to elevate or depress the bow, is

f=Z x—X z.............(l.)

If Z x be the greater of these two, f is positive, or the effect is to raise the bow; if it is the lesser, the effect is depressing.

*The effect of a force acting in a vertical line, to raise either end of the vessel, is altogether independent of the height above the centre of gravity (i. e. of the place in the vertical line, where it acts), and would be the same whether it acted higher or lower. So again, the effort of a horizontal force, or direct pull, in raising or depressing either end of the vessel, is independent of the horizontal distance from the centre of gravity (i.e. of the place in the horizontal line, where it acts), and would be the same whether it acted before or abaft the centre of gravity.

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If be the angle of elevation which R makes with the horizontal plane, and the angle, or difference of azimuth, between the ship's head and the horizontal projection of R, then, if R is the pressure on the sail, Z = R sin. , X= R cos. cos. ; hence

Rz cos. cos p....(2).

f = Rx sin. The angles and depend entirely, in any case, upon the manner in which the sail is set, and x and z upon the place of its centre of effort with respect to the centre of gravity of the ship. We have now, therefore, to express and in terms of the angle which the jib-stay makes with the horizon, and y, the angle made by the plane of the sail, when set, with the plane of the masts, the plane of the sail revolving round the jibstay as an axis. The following equations are easily deduced, sin. cos. z sin. (3). Whence cos. & = 6

√ 1 − cos.2 × sin.2 4............(4),

cos.2 x sin.2 4.

....

f = R (x cos. x sin. This equation, like (2), is general. as nearly square as such a sail can shortness, and x = 45° for ex., then

-

.(5).

z sin. x sin. 4)....(6).
When the wind is aft, and the jib
is large. Suppose it 90° for

be,

f = 0·7 P(x 2) nearly.

Hence, since is always greater than z, the jib has always a powerful lifting effort when the wind is aft or on the quarter.

We have now to consider the case in which the ship is heeled through an angle. We may suppose R to be constant, though, in fact, the increasing force of the wind to heel the ship will increase R more than the inclination diminishes it; resuming, therefore, (2), and accenting the other quantities,

f' R (x' sin.

=

2' cos.

cos. ')

now x = x, 2 = z cos. ; sin. = sin. cos. cos. sin. sin.....' (7), and cos. cos. ' = cos. cos. ; whence we obtain, after substituting as before, and 4,

f' R [x (cos. x sin. cos. — cos. sin. 4) z sin. x sin cos ]....(8). This expression, which is complete for all values of the elements concerned, exhibits the effect of a sail set on a mast or stay, and anywhere situated, in elevating or depressing the bow of the vessel, under any inclination. By changing the sign of x, the case is that of a sail abaft the centre of gravity; when the sign of cos. z is changed, the mast rakes forward; when that of sin. 4 is changed, the sail is taken aback, and when that of sin. is changed, the ship heels to windward.

The equation (7) affords the angle to which a vessel must heel, so that the resultant of a sail trimmed to any proposed angle with the plane of the masts, may be horizontal, or sin. '=0, whence tan. =cos. x tan.....(9) When the jib is eased in, a and z diminish, while increases. The direct effort of the sail is

R sin. x sin. cos.....(10) The value of 4, at which the jib is by making (8)

neutral as regards plunging, is formed 0, whence tan 4 = tan (cos. x

sin. x)....(11)

x

Ex. In the 46-gun frigate x = 103 feet, ≈ 48 feet, x = 3940, assume

=25°, then tan. = 0'4663 (*7716

48
103

2964), which gives ◊ = 1210.

The force R is an unknown function of the area of the sail, the force and direction of the wind. In two sails similarly set, R is supposed to be as the area.

It is not worth while to introduce the pitching of the ship, or motion in the plane az, as this would complicate the expressions without corresponding utility, since the pitching is confined to much narrower limits than the heeling, and is besides an alternating motion.

NARRATIVE OF THE EXPEDITION TO COORG IN 1834.

PART III.

HEAD-QUARTER DIVISION-COL. P. LINDSAY.

On the morning of the 3rd of April Colonel P. Lindsay, with the head-quarter division of the Coorg field force, broke up from his encamping-ground at Hebhauly, and advanced on Ramasamy Curnaweye. The pagoda here was occupied by the enemy, but was hastily abandoned; and the force effected the passage of the Ghaut. The enemy again made a stand, at a difficult barrier situated in a thick jungle, the approach to which was much obstructed; but the troops speedily dislodged and drove them off. The enemy were reported to have lost eight or ten people killed, and one gun and twelve prisoners were taken. The loss on our side was but slight: three men wounded, and a horse shot under Lieutenant Hicks, D.Ă.A.G.

EASTERN COLUMN-LIEUT.-COL. STEWART.

In consequence of the commissariat supplies not having been brought over the river the evening before, Lieut.-Colonel Stewart was detained on his encamping-ground until after mid-day. The passage of rivers in India, with troops, is always interesting, and sometimes, owing to the freshes, dangerous-particularly when having to cross them before daylight. To prevent confusion in these cases, a couple of officers are generally sent on in advance for the purpose of providing lighted torches for both banks; of ascertaining whether there are, or are not, fords; and of procuring a sufficient number of villagers to carry the baggage and ammunition in and out of the boats. The detachment under Captain (now Major) Willat's command had to cross many rivers and backwaters between Cannanore and Coombla. They had with them five elephants, and 80 or 100 bullocks; and nothing could have been more beautiful than the scene they presented on the banks of a deep and rapid river, overhung with forest-trees and the feathery bamboo: a hundred torches flashing amongst the foliage on either bank, occasionally revealing red coats, glittering bayonets, or a huge elephant lying down to be unloaded, whilst another, just rising with his mahoot on his neck, was walking sedately to where he was to attempt the passage. One splash is heard, and another, and the elephants are struggling through the waters: they swim with ease, but their motions are tremendous-at one moment exposing to full view the mahoot patting his charge's head to keep him in good humour, and the next nearly burying him in the stream. Nearly at the same time the bullocks are swimming in a drove the palankeens or doolies are arriving with the sick-and part of the troops, with torches in every boat, and each man with his firelock in his hand, are distinctly seen crossing nearly in a line--whilst empty boats, returning with but one torch each, appear like little stars on the dark surface of the deep: mirth and good humour abound amongst the officers and men-the joke goes round— and it is only the strictness with which the men are examined and numbered off when getting into the boats which shows, in truth, that in essentials everything is under the rule of discipline.

The means of transport are of two sorts: round wicker boats, the same as used in the days of Porus and Alexander, covered with horse

or bullock skins, and, though leaky, are very safe; and two canoes joined stem and stem, and stern and stern, with boards, sometimes nearly forming a raft; add to these the single flat-bottomed canoe-the most dangerous of all, and always used at night, and in a strong tideway, with great reluctance.

But to return to Colonel Stewart. His guides having made off the day before he quitted his encampment, he was much perplexed; but, nevertheless, continued to advance. Having marched about two miles, a fire was opened on the advanced guard from a high stockade, but at a great distance, only a few spent balls reaching the head of the column. A gun was immediately brought up, whilst a party was detached to each flank to carry the breastwork and barriers. The success of this manœuvre was complete; the enemy evacuating their post as our men reached the crest of their immense barriers, rising one above another to the height of fifty feet, overgrown with thorns, and so steep as to be very difficult of access. They here lost seven or eight men; amongst them a Mogul or Patan named Kurreem Khan, who had reinforced the place the evening before with a detachment of 300 men, in consequence, as we have understood, of our having forced the passage of the Cauvery -and on whose desperate valour there is reason to suppose the Rajah placed the utmost confidence for the defence of this important post, which would appear to be the key of the country between Ramasamy Curnaweye and Seedapoor; having in its rear a high road in excellent order leading direct to Mercara.

On account of an accident happening to one of the gun-carriages, and only originally possessing two, Lieut.-Colonel Stewart encamped a little beyond the stockade, which was a large square place measuring nearly half a mile across. He first, however, destroyed some of the defences on the Mercara road-at first from ignorance of its being the wrong road, and afterwards from a desire to delude the enemy as to the route he intended to pursue.

NORTHERN COLUMN-COL. WAUGH.

At daylight on the morning of the 3rd the force under Colonel Waugh moved off its ground; and, although there was a general feeling throughout the brigade that difficulties were that day to be overcome, and hard fighting to be expected, a confidence was entertained that before nightfall a junction would be effected with the force under the command of Colonel Lindsay, C.B. The advanced guard consisted of 80 Europeans, 160 Native Infantry, and 80 Pioneers, under the command of Major Bird, 31st N.I.

After the first two miles the road almost entirely disappeared, and became so bad that the pioneers were busily employed for two hours in bringing the guns half a mile. Between seven and eight a distant cannonade was heard: it was Colonel Lindsay attacking the pagoda at Ramasamy Curnaweye. About half-past nine the column had arrived at the margin of a dense jungle, in which it was evident the enemy was posted. Colonel Waugh, perceiving this, directed the head of the column to diverge off the road and to the left, and then resume its course in a line parallel to the road-avoiding a fire from a breastwork, which was thus placed at too great a distance to do any injury. The advance here halted to allow the guns to come up. From the nature U. S. JOURN, No. 114, MAY, 1838.

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