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924
[THEORETICAL
SHIPBUILDING


is determined by the disposition of hull material and fittings, machinery, coal and all other movable weights, the position of which is necessarily fixed by other considerations than those of stability; but the height of the meta centre above the centre of buoyancy varies approximately as the cube of the breadth, and any desired value of GM is readily obtained by a suitable modification in the beam. The meta centric height in various typical classes of ships at “ normal load " is as follows 1ciass of ship. (QM in Ft that in which the meta centric height is a minimum. The change in the position of the centre of gravity can be readily determined from an account of the weights removed, added or shifted; and the height of the meta centre is obtained by calculating its position at a number of water lines, and drawing a curve of heights of meta centre above keel on a base of the draught of water. The results are conveniently embodied in the form of a meta centric diagram; the curves of height of meta centres and vertical positions

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First class battleship and cruiser . . Second and third class cruiser and scout Torpedo boat destroyer . First class torpedo boat . Steam picket hual ni launch River gunboat (shallow draught) Large mail and passenger steamer Cargo steamer Sailing ship Tug . K stws 2 to3 1%to2§ 1 8 8 5 1 2 to 1% lol# to2o tO2 to2 to6 Ap roximate 1% to 2% The meta centric height adopted in steamships is governed principally by the following considerations:- (a) It should be sufficiently large to provide such a position of G as will give ample stability at considerable angles of inclination and sufficient range. (b) Where ample stability at large angles is obtained by other means, the stability at small angles, which is entirely due to the meta centric height, should be sufficient to prevent forces due to C ° c .9 C °'. 9 3; o f ga 5. 47 -or . Tw

l. l. ~ 57 ° nun oisvu '91-3 f°E"' 'gg nun us vous? 5 U -I Z 0 o 3o'~6' 2|452 'fa' .evel'Line B' 5/ lf9"7512O730 [Deco CdFBirion , ", | » | '6" |Bl20 | .w..n malCo dirion |25-e' wow Itigm- nditio | FV I / 22»-6 el-1|5 2wv.. ff I 19-6' ||4-so awe, I I / / / f 1 I "re 8429 awe. .', ' » I A r B: I I - . 45' -4 l °'° 5532 "° 5~'l 3§ £l El§ 90° Suu. or: mns in nfcn . ¢, 'f, Q 3 oi 3 g' Ag 3' 8 o ° o 8 o o o 8 2 0 .2 S 9 2 1 9 °' of an SCALE of TONS D§ PLAC£Mi|¢'| FIG. 3.-Metacentric Diagram of a Battleship. wind on upper works, movement of weights athwart ships, turning, &c., causing large and uncomfortable angles of heel. (6) It should be sufficient to allow one or more compartments to become opened to the sea, through accidental damage, without risk of capsizing. (d) It should, if possible, be sufficiently large in the normal condition of the ship to permit the greatest possible freedom in the stowa e of a miscellaneous cargo without producing instability. (e) Dm the other hand an excessive value causes rapid and uncomfortable rolling among waves. A ship having small initial stability is said to be “ crank, ” while one possessed of a large or excessive amount is termed “ stiff.” The former type is generally found to be steadier and easier in rolling among waves; and for this reason when other circumstances permit, the meta centric height is usually chosen as small as possible consistent with safety and comfort. The meta centric height is affected by an alteration in displacement or in position of the centre of gravity caused by loading or unloading cargo, fuel and stores. In consequence the stability has to be investigated for a variety of conditions, particularly

MEAN TO S: » nnnrr Prn|iicH iiixiighis &E:€é'g?. za'—sf 5Of4 issoo g ' ' ' A

B

Q4—3"g fl-9~QV iaueq g 5 -, zu'—2" |1346 |ZD'~~3" 4-9~2 IIOBOOI 5 |l { us—3 4-a~5 8450 l5'~l" 77807 7 I I |2'~-3" 4-7~5 emo 'B D V FIG. 4.-Metacentric Diagram of a Merchant Vessel. of centres of buoyancy being set up from a line intersecting, ” the water lines at 45°. Figs. 3, 4 and 5 are the meta centric diagrams for a battleship, a vessel sharply curved at the bilge typical of a large number of merchant steamers, and a sailing ship of “ Symondite " (or peg top) section; it will be observed that in the first and second the M'curve is slightly concave upwards, and in the third sharply convex. The buoyancy curve in all cases is nearly a straight line whose inclination at a particular water plane to the horizontal is equal to tan"'Ah/V; where A is the water plane area, and h the depth of the centre of buoyancy below the surface. The position of the meta centre at an intermediate water line is obtained from the diagram by drawing a horizontal line at the draught required, and squaring

P Ko gt QE mil E MEAN TONS DISPLT: gp DRAFT PEIHNCH lNTONS L '~-5% l0»49 |017 ue' oi r 906 na'-~'/" B-55 san 9'~~a€ 5-74 295 FIG. 5.-Metacentric Diagram of a Sailing Ship of “ Symondite " section. up from its intersection with the 45° line to meet the curve of metaCentres. With these curves are associated (though usually drawn separately) two others known as the curves of Displacement and of Tons per uwh and expressed' by AA and BB respectively in the above figuresl

These have the mean draught of water as abscissa (vertical), and