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30 arated from the pontoons in all modern types, in order to secure control of pumping, if not for con- siderations affecting stability, all lon- -gitudinals are made water-tight. The problem of loss in_ stability due to free water in a side com- partment is of interest in the special application made to the determina- 'tion of angle of heel for any stage of water contained in compartments. This determination is always made in the case of docks that self-dock their side walls by listing. The cal- culation is only made for the pur- pose of ascertaining the maximum list possible and the corresponding strain on water-tight bulkheads. In actual operations the listing is accom- - plished by dock masters who are usu- ally innocent of any knowledge of the finer tools of the profession, and the procedure in general is the simple one of pumping light on the side to be raised and admitting water to the opposite compartments until the desired degree of heel is attained. Foreseeing such methods the prime aim of the builder should be to so design each member that it may safely bear the maximum load to which it may possibly be subjected. The curves for indicating the depth of contained water for each draught of the dock are especially interesting. In designing a dock the maximum head of water to which skin-plating and water-tight bulkheads will be subjected 'are first calculated, and then the depth of contained water for various draught lines, both with and without ship loads are plotted and curves traced. The practical value of such curves, however, is not great, since the levels of the water in the various compartments are seldom if ever the same at any time throughout the career of a dock. With a ship load it is customary for the intelli- gent .dock master to regulate the pumping by the character of his ship. He will endeavor to carry a certain excess of water in the forward and after compartments when docking a short and heavy ship and will always, even when operating the dock empty, carry excess water in his side-walls to enable him to control trim. This feature of dock operation would justi- fy a doubt as to the wisdom of in- creasing the depth of the watertight compartments of side-walls to give Storage space, As a matter of fact certain types of docks maintain the two center compartments of pontoons watertight and dry in order to de- crease the pumping head. The method proposed for determin- ing stability, while ingenious, does "of buoyancy; their TAE MARINE REVIEW not appear to offer advantages over the customary metl*od of tabulating | calculations for each factor affecting the co-efficient of stability for vary- ing water lines. The customary formula for metacentric height is I+I'--AV--Ei. --------------(1) H= V in which V_ represents volume of displacement; A, difference between metacentric radius and metacentric height; and I, I', and i have the same significance as in the paper. In the same way the expression for co-ef- ficient of stability may be written I+1l'--VA--Ei ------------_(2) C= 35 It will be seen that this expression is equivalent to that used by the auth- or, equation 14 of page 9. In the practical use of these ex- pressions, calculations are made and tabulated in such manner as to give all necessary factors for each water line. The table when completed gives in its columns the height of centers of gravity; heights of centers difference, A; the volumes of displacement, V; the moments of inertia of waterplanes, 1 and 1; the moments of inertia of interior water surfaces, i; the value of Hi from (1); the co-efficient of stability from (2); and the moment to heel 1° from I--I--V A--Ei X.0175----__--__(3) M= ; 35 The water lines generally used are those at the designed freeboard with test ship, at. pontoon deck, at tops of keel blocks, and at such additional draughts as may be necessary to deter- mine the curves. Should there be altars, openings or other peculiarities of the design affecting stability, ad- ditional water lines are placed when such special. features occur. These curves usually. shown are -those for metacentric height, co-effi- Client of stability, and moment to heel 1°, with scales so chosen-as to permit the representation of all neces- sary stability data on one_ sheet. Such sheets are prepared for the dock under each of the following condi- tions: operating as a unit without ship load; operating under a _ long Buip, such as the modern cruiser; under a ship which overhangs bow and stern such as the modern mer- chant steamer whose keel length is not greater than the length of keel blocks; under a short and heavy ship, Such. as the test - battleship: and under such other 'special loads as the future use of the dock may sug- gest. Sheets are also proposed for the dock as a whole and for each in- dependent unit of the dock for each position assumed in eelf-docking. It should be remembered that at the so-called critical points such as at the pontoon deck and the top of keel blocks, the least inclination will result in the cutting of a greater water-plane, thus increasing the sta- bility. "As: 'a matter of fact, docks without altars can heel farther at a point midway between tops and bot- toms of keel blocks than at either of those points, That part of the paper treating of the strength of floating docks is well stated and covers the general theory of the subject. On a former occasion the speaker has made the recommen- dation that a book containing com- plete data for each naval floating dock be placed in the hands of every dock operator. For this book such curves as are given in Figs. 16, 17, 18 and 19, of the paper, are ideal. It is the custom of the navy depart- ment to specify the assumption of a flexible ship for purposes of dock design. This is virtually the same as the assumption, recommended by the author, that the weights of both dock and ship act virtually downward against the vertical buoyancy op- posed, but that the resultant moments are withstood by the dock alone. Stiffness and rigidity are desirable qualities in a naval floating dock and their attainment is favored by designing the side-walls as beams car- rying the total load _ transmitted through 'the transverse pontoon gird- ers. etch an assumption 1s very nearly the correct one in the case of the solid trough dock or docks of the Cunningham type, the Clark and Stanfield bolted sectional type, or the Maryland Steel Co. type as ex- emplified in the "Dewey." In--the actual design 'of a dock, after preliminary shear and moment diagrams are drawn from assumed dimensions and the test ship, each member is taken up and designed in detail for local leading. The trans- verse pontoon girders are designed with the ship on three supports, i. e., the keel and bilge blocks; then the keel and intermediate longitudinal bulk- heads together with the frames; then the side-walls to which the trans- verse girder reactions are transmitted; and finally the innumerable details of connections, skin plating, etc. With these data, new. calculations of weights and moments of inertia are made, and new shear and moment diagrams are drawn. Reinforcement is applied where indicated by the his Sk aiaai