former force, A more darigei'ous, '”thoughiimprobable, case in 'which a gust of wind strikes theship just as'she'has'completed'a roll to windward' can similarl 'be investigated; it is fou'nd 'that the safe angle of steady heel under this condition is considerablyfless than that represented -by OM'. It"thus appears that it is'of the-greatest im¢ portance that' sailing vessels should possess large dynamical stability in order to provide against the'risk of capsizing due to Htlctuatidns in the wind-pressure. Althoughtheméglect of the windand water resistances in the above investigation' materially 'modifies ~ the quantitative results, the general conclusions point to the necessity for sufficient range and free board however large the righting levers may be at small inclinations. ' ~ "
M The centres of effort and of lateral resistance have not the same longitudinal position, consequently horizontal éouple is produced which turns the vessel either into the wind 'orf away from it. In the former condition the vessel is said to'bef“'ardent, " and in the latter to be “ slack.” In order- that a-vessel maybe quick inggoing about and etnot require-too large a helm angleon a straight course, she shoulld be slightly' “ ardent, " -i'.e. the true centre of'efTort should' be slightly abaft the true centre of 'lateral resistance; ' The assumed and true positions of these centres difier to some extent, and on making allowance for this'it'is found that in the, -'ma, j ority of vessels possessing slight ardency the assum*ed'C.E. lies slightly before instead of abarft the assumed C.L.R.f 'In' small sailing boats the points are usual y very near togetherfbut in a large number of sallingships, including H.M. sloops, their distance apart islabout -05' L, and in yachts' about -02'L, where L is the length. ' - ', ~
It may be noted in this connexion that the area of sail spread and thesize of the ship are 'often connected 'by the coefficient%%~knoWn as the Driving Power, The, value forrsmall sailing 'boats rand for yachts is about zoo, and for- full-rigged sailing ships from.8o to -loo (including plain sailonly). ~ ~; ., » i . v - The method of estimating the: righting moment of-a ship when Lough:inclined from al posi tion of equilibrium through a small mdk", angle-in the longitudinal plane is exactly analogous to that smbuny used in the- case of small transverse mclination, and t similar propositions are true in both cases, Vllsi* ~ € I. .Consecutive water-lines-inuersecta-bout an axis passing through the centre of flotation., . . - l - . » ~ » 2. The height of the longitudinal meta centre M above the centre of buoyancyiis equal to the moment of inertia about this axis divided by the volume of displacement of the ship.-3.1 The righting moment at any small angle of inclination 0~(circular measure) is equal to . ~ Iw
c;M a. T
In fig. 21 'let'WL be the water-line corresponding to the positions G and B, and conceive a longitudinal movement of a portion of M .
yd 8.-. J -ll.», ~, |,
FIG.21. = ~,
the weights in the ship causing G to move horizontally to G'. If Gf be abaft G the ship will alter trim by the stern until B moves to B' vertically beneath G' and the water-line changes to W'L', intersecting WL at the centre of' flotation F. If L be the length of the ship between the draught marks, the change of trim (WW'=-l-l5L') is equal to L.0, and the moment changing trim is W.GG' or W.GM 10: the change of trim in inches (other linear dimensions being in feetlis-therefore' 1 ' V < WXGG, +WXGM, ,
The change of trim due to any horizontal movement of weights is therefore equal to the moment of the shift of weight divided by the quantity ',
I2 X L
which is the moment required to change trim one inch. Since the longitudinal moment of ineritia of the Water=pl'ane' includes the cube of the length as a factor, the longitudinal 'BM is usually large compared with BG, and the moment to change trim I in. in foot-tons is nearly equal to ',
" W><BM W><L -I2><'E><V*'42Ol:" L
which is approximately constant for moderate variations of draught. If a weight of moderate amount 'w tons be placed at a distance of a feet abaft the gentre of jiqtqtion F, the bodily sinkage in inches is ¥, the moment changing trim by the stern is 'wa foot-tons, and the change of trim is therefore 1% where 'l' is the “ tons per inch ” and M the moment to change trimfl in, If b be the distance of Fiabaft the middleof length, the draughts forward and aft are increased respectively by l.'i L+2b
and “f T*M "'2L, -
L QL-2b. h,
2 W Tfilvl 21. '“° es; ~ ».
A ship" provided'§ }'ith' waterl'tight'compartn'ients is liabletp have water admitted into any of them on account lof damage Stibmt received, or may require to carry water orothei' 'fluidyih E 'Y bulk as ballast or cargo. The effect of this addition on the LY en d draught and the stability is therefore of interest. “There amaze ° are t ree casesz- ';-
1. When the water completely .fills a compartment; 2. When the water partially fills a compartment up to the level of the water-line, remaining in free communication with the sea; and 3. When a compartment is partially filled with water without any communication with the sea.
In the first case the water is regarded as a weight added to the ship; the mean sinkage is obtained from the displacement curve, t 'e change of trim from the “ moment to change trim, ” and the angle of heel from themetacentric diagram, or (for large angles) the cross curves. In general, if thecompartrnent filled is low in the ship, the stability is increased; if high, it is diminished. In'the second case, assume in the first place the compartment to be amidships, so that no heel or change of trimyoccurs, and to be moderate in siie, so that the sinkage is moderate in amount. ' T A Let ABCD (fig. 22) be such a compartment bounded by; watertight bulkheads sufficiently high to prevent water'reaching adjoining A 9
W- s in
- -'—'-f'°~-'~°~— ' / °°f' ”—“ fm?—7 .
W F '- .
~B G' » ~~
" ' FIG.22. ' ' T
compartments. Let the water-lines be WEFL, W'GHL', ' before and after bilging; let A, u. be the area of the whole water-plane»WEFL and of the portion EF within the compartment respectively, in square feet; and let v be the volume contained in EBCF diminished by the volume of any solid cargo in the compartment;, The buoyancy is reduced by ans amount v by bilging, and the amount added through sinking must be equal to the amount so-lost. » If x be the sinkage in feet, then . ' ». '-A
~ w=x(A-a), .'»
so that the mean sinkage is equal to the buoyancy lost 'divideclby the area of the intact water-plane. In the event of the compartment being so situated as to cause heel andthange of trim, the mean sinkage is first determined as above, and the effectof heel and change of trim super osed. ' - T ' ' ' ' ', To obtain the heel produced? the position of the centre of flotation for the intact'po'rtion of the water-plane is, found, and thence the vertical and horizontal positions of the new centre of buoyancy. are deduced by takingateount of the buoyancy lost through bilging, and then regained by the layer between the two water-planes. The moment of inertia of the intact water-plane is found about an axis through the new centre of flotation and thence the height of .theinéw meta centre M' determined. The heel 6 (assumed small) is found by equating the horizontal shift of B to sin 0X the vertical distance of M' above G, both bein equal to the moment causing heel divided by the displacement.” Tn a similar manner the change of trim is obtained. If the compartment bilged is largeso that considerable changes in its area and that of the ship at the Water-line result, the sink age and alteration in 'stability arefound by a tentative process, closer approximations to the nnal 'water-line' being successively made. '
An investigation of the stability when bilged at or near the' waterline is, of“special importance in warships owing to their liability 'to damageby gunfire in action, with the consequent opening up' of'a large number of compartments to the sea. 'Calculations are made 'oi the sinkage and stability when the unarmoured or lightly farinoured parts of the 'ship are completely riddledythe stability should be sufficient to provide for this contingency. The third case, where the ship is intact but has compartments partially filled with water or other liquid, is of frequent occurrence.
Practical illustrations 'occur in connexion with' the filling and