A Simple Prediction Formula of Roll Damping of Conventional Cargo Ships on the Basis of lkeda#39;s Method and Its Limitation

Yuki Kawahara, Kazuya Maekawa and Yoshiho Ikeda
Department of Marine System Engineering, Osaka Prefecture University, Sakai 599-8531rsquo; Japan

Abstract:Since the roll damping of ships has 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, Ikedarsquo;s one is widely used in many ship motion computer programs. Using 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. 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 Ikedarsquo;s method for various ships, a very simple prediction formula of the roll damping of ships is deduced in the present 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 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 flow 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, some 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 authorscarried out a research project to develop a roll damping prediction method which has the same concept and the same 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 Ikedarsquo;s method, divides the roll damping into the frictional (BF), 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 (= roll damping moment (kgfm)/roll angular velocity (rad/sec)) can be expressed as follows: B44 Bbk (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 friction component is predicted by Katorsquo;s 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 been widely used.
For these 30 years, the original Ikedarsquo;s 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, sometimes, different conclusions of roll motions were derived even though the same Ikedarsquo;s method was used in the calculations. Then, to check the accuracy of the computer programs of the same Ikedarsquo;s method, a more simple prediction method with the almost same accuracy as the Ikedarsquo;s original one has been expected to be developed. It is said that in design stages of ships, Ikedarsquo;s 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 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 Ikedarsquo;s 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 condition that the center of gravity is low and the lower one on the condition that the center of gravity is high.
From this figure, the roll damping estimated by this prediction formula is in good agreement with the roll damping calculated by the Ikedarsquo;s method for low position of center of gravity, but the error margin grows for the high position of center of gravity. The results suggest that the previous prediction formula is necessary to be revised.

Methodical Series Ships
Modified prediction formula will be developed on the basis of the predicted results by Ikedarsquo;s method using the methodical series ships. This series ships are constructed based on the Taylor Standard Series and its hull shapes are methodically changed by changing length, beam, draft, midship sectional coefficient and longitudinal prismatic coeff

A Simple Prediction Formula of Roll Damping of Conventional Cargo Ships on the Basis of lkeda#39;s Method and Its Limitation

Yuki Kawahara, Kazuya Maekawa and Yoshiho Ikeda
Department of Marine System Engineering, Osaka Prefecture University, Sakai 599-8531rsquo; Japan

Abstract:Since the roll damping of ships has 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, Ikedarsquo;s one is widely used in many ship motion computer programs. Using 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. 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 Ikedarsquo;s method for various ships, a very simple prediction formula of the roll damping of ships is deduced in the present 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 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 flow 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, some 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 authorscarried out a research project to develop a roll damping prediction method which has the same concept and the same 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 Ikedarsquo;s method, divides the roll damping into the frictional (BF), 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 (= roll damping moment (kgfm)/roll angular velocity (rad/sec)) can be expressed as follows: B44 Bbk (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 friction component is predicted by Katorsquo;s 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 been widely used.
For these 30 years, the original Ikedarsquo;s 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, sometimes, different conclusions of roll motions were derived even though the same Ikedarsquo;s method was used in the calculations. Then, to check the accuracy of the computer programs of the same Ikedarsquo;s method, a more simple prediction method with the almost same accuracy as the Ikedarsquo;s original one has been expected to be developed. It is said that in design stages of ships, Ikedarsquo;s 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 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 Ikedarsquo;s 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 condition that the center of gravity is low and the lower one on the condition that the center of gravity is high.
From this figure, the roll damping estimated by this prediction formula is in good agreement with the roll damping calculated by the Ikedarsquo;s method for low position of center of gravity, but the error margin grows for the high position of center of gravity. The results suggest that the previous prediction formula is necessary to be revised.

Methodical Series Ships
Modified prediction formula will be developed on the basis of the predicted results by Ikedarsquo;s method using the methodical series ships. This series ships are constructed based on the Taylor Standard Series and its hull shapes are methodically changed by changing length, beam, draft, midship sectional coefficient and longitudinal prismatic coeff

资料编号：[3759]