698 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 73.20 



changing quickly the longitudinal compensating 

 moments. It is not feasible in these vessels to 

 proAdde hydrodynamic moment compensation 

 because of the increased drag, weight, and 

 mechanical complication of an adjustable sta- 

 bilizer. There is the further important fact that 

 the submarine may be running slowly or be 

 stopped when trim compensation is required. 



The trailing end of a ship hull, together with 

 such rudders or planes as may be attached to it, 

 possesses a definite but unknown stabilizing 

 property. Actually, damping in pitch and yaw 

 results from the swinging of both ends of the hull 

 about the corresponding axis, but restoring 

 moments are expected only from the after part. 

 For angular damping the area of all movable 

 rudders, planes, and fins mounted normal to 

 the direction of local motion is added to the area 

 of the fixed portions. For the most effective 

 dynamic damping from these surfaces they are 

 mounted as close as possible to the hull, to prevent 

 unnecessary leakage from the +Ap to the 

 — Ap sides. 



Just how much fixed and movable stabilizing 

 surface is demanded for stability of route is not 

 a matter for ready calculation or reUable pre- 

 diction, especially if the hull under design is of 

 essentially different shape from that of a hull 

 which has been satisfactorily stabilized in the 

 past. This matter is discussed further under 

 Maneuvering in Part 5 of Volume III. 



To insure zero restoring force or moment on 

 fixed stabilizers when none is desired, they must 

 be placed exactly in the lines of flow. For a surface 

 vessel these fines are only by accident or coinci- 

 dence parallel to the axis of the ship or its direction 

 of motion. For a stabilizing fin or skeg placed in 

 the outflow jet of a screw propeller, the water 

 follows the hull-flow pattern when the vessel is 

 self-propelled rather than the direction of the 

 propeller axis. If the stabilizers are near the surface 

 the flow directions almost certainly change with 

 speed because of the change in profile of the Velox 

 wave system. This calls for the selection of a 

 given speed at which the lines of flow are to be 

 paralleled. In the case of submersibles which must 

 perform well on the surface as well as below it 

 this procedure is further complicated by the 

 possible existence of different lines of flow for 

 the surface and submerged conditions. Usually, 

 however, the critical conditions for which fixed 

 stabilizers are required occur during submerged 

 running. When well below the surface the flow 



pattern does not change materially for small 

 variations from the normal running attitude. 



Considering only the restoring forces and mo- 

 ments produced by hydrofoil lift at an angle of 

 attack, stabilizing fins and skegs act more effi- 

 ciently as their aspect ratio is increased. However, 

 there are practical limits to the distances which 

 these appendages may project beyond the hull or 

 to which they may approach certain other 

 boundaries such as the baseplane or the planes 

 defining extreme half-beams. A reduction in the 

 aspect ratio must be accepted if the stabilizer 

 area is large. This is not a disadvantage because 

 a surface short in the direction of motion and 

 long in a direction normal to it has low dynamic 

 damping. Taking all factors into account, the 

 best fore-and-aft length for such a skeg or fin 

 appears to be approximately equal to its extension 

 from the hull. If the hull is relatively large in area 

 at the point of attachment, compared to the size 

 of the stabilizer, the effective aspect ratio is of 

 the order of 2.0, for the reasons given in Sec. 14.11. 



It is difficult to formulate design rules for the 

 different but common form of stabilizing or 

 "fulcrum fin" required on any flat-bottomed boat 

 to provide a pivot point for the rudder moment. 

 On a small centerboard sailboat, the board is 

 raised or lowered to give the required area. For 

 the balsa rafts of the Incas, exemplified by the 

 Kon-Tiki of T. Heyerdahl, thin planks pushed 

 down vertically between the fore-and-aft logs 

 at selected positions served as multiple stabilizers. 

 This gave the "rafters" a great freedom for adjust- 

 ment and relieved the builder of the burden of 

 selecting a fixed — and proper — set of positions 

 when the raft was put together. 



On a high-speed motorboat carrying a fulcrum 

 fin, a trial-and-error process of positioning is 

 indicated, at gradually increasing speeds, or else 

 a miniature centerboard may be used, mechan- 

 ically operated from the driver's seat. J. Baader 

 shows the shape, relative size, and position of 

 this forward or fulcrum fin for a number of 

 successful motorboats ["Cruceros y Lanchas 

 Veloces (Cruisers and Fast Launches)," Buenos 

 Aires, 1951, pp. 115, 119, 322-325, 341]. 



Fixed stabilizers and skegs, especially on sub- 

 marines, may often be called upon for comple- 

 mentary functions such as propeller guards and 

 docking supports for the stern. In this case their 

 outer edges may be reinforced with shallow 

 flanges simflar to those described for the roll- 

 resisting keels in Sec. 73.17. These flanges must 



