Fig. 10 |JT| vs. D curve.
λ = alnD + b (18)
Equation (18), however, only expresses the qualitative relation between λ and D. In order to estimate coefficients a and b quantitatively, measured data are to be used.
5. Quantitative Estimation of λ based upon Measured Data
The measured values of λ are plotted in Figure 11. The coefficients a and b are determined in such manner which makes all measured values equal to or less than their estimations in accordance with Equation (18). As a result, λ is given by the following Equation (19).
λ = 0.44lnD + 0.578 (19)
Fig. 11 λ vs. D curve.
6. Conclusion
The rate of increase in torque in the crash astern condition compared with that in the steady ahead condition has been correlated successfully with major parameters of a ship such as the power of the main engine, total mass of the ship, and the like by examining the speed of a ship when the propeller rotates astern at resonant rotational speed, as seen in Equations (10) and (14). Furthermore, in order to simplify the expression of the rate of increase in torque for practical use, it is approximately expressed as a function of the propeller diameter. This is done by using the regressive relationships between the propeller diameter and the major parameters of the ship, together with the measured data of the rate of increase in torque from more than ten ships.
The authors hope that the results described in this paper will contribute to the proper design of propellers.
Acknowledgments
The opinions expressed in this paper were examined by a sub-committee on machinery of the NIPPON KAIJI KYOKAI Technical Committee. The authors would like to express their sincere appreciation to the chairman of the sub-committee, Professor Emeritus Shinji Hayama of the University of Tokyo for his continuous guidance and encouragement. Appreciation is also extended to other members of the sub-committee for their helpful comments.
References
1) Michio TAKAGI and Senichi SASAKI, Some Considerations on the Behavior of Propulsion Diesel Engines in Transient Condition, PROCEEDINGS OF ISME YOKOHAMA '95, (1995-7), 43.
2) H. Kume, Establishment of Requirements for the Pull-up Length of Keyless Propellers, TRANSIACTIONS of NIPPON KAIJI KYOKAI, No.119 (Sep., 1969), 100. (in Japanese)
3) NIPPON KAIJI KYOKAI, Part D MACHINERY INSTALLATIONS, RULES FOR THE SURVEY AND CONSTRUCTIONS OF STEEL SHIPS (Mar. 1997), 34.
4) Lloyd's Register of Shipping, Rules and Regulations for the Classification of Ships, Section 10, Part 5, Chapter 8 (1993).
5) NIPPON KAIJI KYOKAI, PROCEEDINGS OF THE SEMINAR ON AMENDMENTS TO RULES FOR THE SURVEY AND CONSTRUCTIONS OF STEEL SHIPS, (Sep. 1994) (in Japanese).
Discussion
Mr. Motohiro Takai, Ship Research Institute
In your paper, the torque acting on propeller shafts in the crash astern condition was estimated in order to calculate the pull-up length of a keyless propeller. On the other hand, it is generally known that in heavy weather, the torque acting on propeller shafts is often considerably increased especially in the case of small ships due to the racing of the vessel. Do you think that this effect should be taken into account?
