than the rudder angle δ relative to the midship plane. Comparing these small attack angles with the large stall angles of Table 3 for full-scale Rn, it is obvious that larger maximum rudder angles than the usual 35° are a simple, cost-efficient means of improving the turning ability of ships.

However, in yaw checking large rudder angles opposite to the turning motion would lead to stall and the accompanied decrease of rudder transverse force. This is easily avoided by limiting the shaft moment which the rudder gear can generate to about the stall angle moment; then in yaw checking the rudder will just operate at the stall angle, producing maximum lift. This better manoeuvring for smaller maximum rudder gear moment was also observed practically by FSG on trial trips. For large ships this may result in difficulties to satisfy the IMO requirement of turning the rudder, at full ship speed, within 28s from 35° on one side to 30° on the other side. This rule, which is criticized also because the 28s limit should better depend on ship size and speed, should be substituted.

As demonstrated in Tables 1 to 3, to generate large lift (both for fixed α and maximum lift), rudders should have concave profiles with small or zero trailing edge angle. This holds especially for thicker profiles of, say, 20 to 25% c. The now most used NACA00xx profiles should be avoided, especially in thick profiles.

Thicker profiles generate both larger lift gradient and larger maximum lift. The lift/drag ratio, however, is worse than for thinner profiles.

Finite end thickness of rudder profiles increases the lift, but also the drag; therefore thin profile ends should be preferred. For hollow profiles this results in structural difficulties if the usual rudder construction ending in 3 plates (a middle plate and two outer skin plates) is used. An asymmetrical structure as scetched in Fig. 11 may be better; however this requires some care to avoid asymmetrical deformations due to weld shrinking, or to use these deformations intentionally to adapt the rudder to the propeller slipstream twist.

For higher speed exceeding, say, 23 knots, rudder cavitation even at small or zero rudder angle may become a problem especially for thick rudders and highly loaded, slow running propellers. The panel method is an easy and, presumably, reliable means to determine whether zero absolute pressure (which is, in full scale, not far from the cavitation limit) occurs. If problems are expected, special symmetrical profile shapes (7) or unsymmetrical profiles adapted to the propeller slipstream may be used as a remedy, and their effect predicted by a panel method. Whether such profiles can provide also better propulsive efficiency is not yet clear.

To decrease scale effects in manoeuvring model experiments, the maximum lift coefficient of the model rudder should be increased. A way to do this is to use a flap rudder in the model instead of a non-flapped rudder in the ship. The flap (area and angle) should be designed such as to produce the same maximum lift coefficient in model conditions as the ship rudder is expected to produce in full-scale conditions. To compensate for the larger dCL/dα of the model flap rudder, the model rudder angles should be decreased appropriately.

References

1. Chau, S.-W., “Computation of rudder force and moment in uniform flow”, Ship Techn. Res. Vol. 45 No. 1, pp. 3–13

2. El Moctar, O.A.M., “Numerical determination of rudder forces”, Euromech 374 (1998), Poitiers

3. Söding, H. “Forces on rudders behind a maneuvering ship”, 3rd Int. Conf. Num. Ship Hydrodyn. (1981), Paris

4. Lee, J.-T., “A potential based panel method for the analysis of marine propellers in steady flow”, Rep. 87–13, Dept. of Ocean Eng., MIT

5. Abbott, I. and Doenhoff, A., Theory of wing sections, Dover Publ., New York 1959

6. Whicker, L.F. and Fehlner, L.F., “Freestream characteristics of a family of low-aspect-ratio, all-movable control surfaces for application to ship design”, Rep. 933 (1958) David Taylor Model Basin

7. Brix, J., Manoeuvring Technical Manual, Seehafen Verlag 1993, ISBN 3–87743–902–0

8. Chau, S.-W. “Numerical investigation of free-stream rudder characteristics using a multi-block finite volume method”, Rep. 560, 1997, Institut für Schiffbau, Hamburg

9. Thieme, H., “Zur Formgebung von Schiffsrudern”, Jahrbuch Schiffbautechn. Gesellschaft 1962, Springer



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