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1、A Simple Prediction Formula of Roll Damping of Conventional Cargo Ships on the Basis of lkedas Method and Its LimitationYuki Kawahara, Kazuya Maekawa and Yoshiho IkedaDepartment of Marine System Engineering, Osaka Prefecture University, Sakai 599-8531 JapanAbstract: Since the roll damping of ships h
2、as significant effects of viscosity, it is difficult to calculate it theoretically. Therefore, experimental results or some prediction methods are used to get the roll damping in design stage of ships. Among some prediction methods, Ikedas one is widely used in many ship motion computer programs. Us
3、ing the method, the roll damping of various ship hulls with various bilge keels can be calculated to investigate its characteristics. To calculate the roil damping of each ship, detailed data of the ship are needed to input. Therefore, a simpler prediction method is expected in primary design stage.
4、 Such a simple method must be useful to validate the results obtained by a computer code to predict it on the basis of Ikeda，s method, too. On the basis of the predicted roll damping by Ikedas method for various ships, a very simple prediction formula of the roll damping of ships is deduced in the p
5、resent paper. Ship hull forms are systematically changed by changing length, beam, draft, mid-ship sectional coefficient and prismatic coefficient. It is found, however, that this simple formula can not be used for ships that have high position of the center of gravity. A modified method to improve
6、accuracy for such ships is proposed.Key words: Roll damping, simple prediction formula, wave component, eddy component, bilge keel component.Introduction In 1970s, strip methods for predicting ship motions in 5-degree of freedoms in waves have been established. The methods are based on potential flo
7、w theories (Ursell-Tasai method, source distribution method and so on), and can predict pitch, heave, sway and yaw motions of ships in waves in fairly good accuracy. In roll motion, however, the strip methods do not work well because of significant viscous effects on the roll damping. Therefore, som
8、e empirical formulas or experimental data are used to predict the roll damping in the strip methods. To improve the prediction of roll motions by these strip methods, one of the authors carried out a research project to develop a roll damping prediction method which has the same concept and the same
9、 order of accuracy as the strip methods which are based on hydrodynamic forces acting on strips. The review of the prediction method was made by Himeno 5 and Ikeda 6，7 with the computer program. The prediction method, which is now called Ikedas method, divides the roll damping into the frictional (B
10、F), the wave (Bw)，the eddy (Be) and the bilge keel (Bbk) components at zero forward speed, and at forward speed, the lift (Bi) is added. Increases of wave and friction components due to advance speed are also corrected on the basis of experimental results. Then the roll damping coefficient B44 (= ro
11、ll damping moment (kgfm)/roll angular velocity (rad/sec) can be expressed as follows:B44Bbk (1) At zero forward speed, each component except the friction and lift components are predicted for each cross section with unit length and the predicted values are summed up along the ship length. The fricti
12、on component is predicted by Katos formula for a three-dimensional ship shape. Modification functions for predicting the forward speed effects on the roll damping components are developed for the friction, wave and eddy components. The computer program of the method was published, and the method has
13、 been widely used.For these 30 years, the original Ikedas method developed for conventional cargo ships has been improved to apply many kinds of ships, for examples, more slender and round ships, fishing boats, barges, ships with skegs and so on. The original method is also widely used. However, som
14、etimes, different conclusions of roll motions were derived even though the same Ikedas method was used in the calculations. Then, to check the accuracy of the computer programs of the same Ikedas method, a more simple prediction method with the almost same accuracy as the Ikedas original one has bee
15、n expected to be developed. It is said that in design stages of ships, Ikedas method is too complicated to use. To meet these needs, a simple roll damping prediction method was deduced by using regression analysis 8.Previous Prediction Formula The simple prediction formula proposed in previous paper
16、 can not be used for modem ships that have high position of center of gravity or long natural roll period such as large passenger ships with relatively flat hull shape. In order to investigate its limitation, the authors compared the result of this prediction method with original Ikedas one while out of its calculating limitation. Fig. 1 shows the result of the comparison with their method of roll damping. The upper one is on the conditi
