CHAPTER 62 



Estimating the Added Mass of Water Around a 

 Ship in Unsteady Motion 



62.1 

 62.2 



62.3 



62.4 



General 417 62,5 



Added-Liquid Masses for Some Geometric 



Shapes and for Selected Modes of Motion . 419 62.6 



Comparison of a Vibrating Ship with a Vibrat- 

 ing Geometric Shape 423 62 . 7 



The Change of Added Mass Near a Large 

 Boundary 432 62.8 



Estimating the Added-Mass Coefficients of 



Vibrating Ships in Confined Waters .... 433 

 Estimating the Added-Mass Coefficients for 



Vibrating Propulsion Devices 436 



Added-Mass Data for Water Surrounding Ship 



Skegs and Appendages 438 



Partial Bibliography on Added-Mass and 



Damping Effects 439 



62.1 General. In Sec. 3.4 of Volume I there 

 is explained the concept of the added mass of 

 the entrained liquid surrounding a body or ship 

 in unsteady motion. In a recent paper, K. Wendel 

 gives a superb exposition of this concept in both 

 physical and mathematical terms [STG, 1950, 

 Vol. 44, pp. 207-255. EngHsh version in TMB 

 Transl. 260 of Jul 1956]. Moreover, his discussion 

 is extended to cover the accelerative-force and 

 pressure features not treated in Sec. 3.4 or in 

 the present chapter, as well as other modes 

 of motion. It should be possible for the reader 

 who is familiar with the preceding portions 

 of Parts 1, 2, and 3 of this book to follow Wendel's 

 development intelligently, and to derive great 

 benefit from it, even though some of the details 

 are passed over. His description of the derivation 

 of added liquid masses for ships which are heaving 

 and rolling, with and without bilge keels, apphes 

 to the discussion of wavegoing in Part 6 of 

 Volume III. 



The effect of the added mass of entrained 

 liquid aroimd a body in unsteady motion, in a 

 relationship of (1) the forces applied to the body, 

 and (2) the resulting body accelerations, is often 

 called the inertia effect. The added mass itself is 

 sometimes called the accession of inertia for the 

 body. In other quarters it is called the hydrody- 

 namic mass. Similarly, the 0-diml coefficients 

 relating the added mass of liquid to the mass of 

 the body, called here the added-mass (or added 

 mass moment of inertia) coefficients, are often 

 called the inertia (or moment of inertia) co- 

 efficients. These important definitions are dis- 

 cussed further in Sec. 62.2. 



For the treatment in Parts 5 and 6 of Volume 

 III of ship motions in maneuvering and wavegoing, 

 both of which involve unsteady motions, the 

 added mass of the entrained water almost 

 always enters as a sizable factor. In general, the 

 added masses are of the same order of magnitude 

 as the ships themselves. For the design of a 

 new ship, or for estimating the performance of an 

 existing one, numerical values must be known or 

 estimated. Knowledge of the quantitative effects 

 of the entrained water in adding to the mass is 

 also necessary in a study of body and ship 

 vibration in liquids, discussed at some length in 

 Sec. 20.11 of Volume I and in subsequent sections 

 of this chapter. 



It is indicated in Sec. 3.4 that the magnitude 

 of the added mass is determined normally from a 

 knowledge of the kinetic energy in the velocity 

 field around the body for a given mode of motion. 

 This energy, in turn, is calculated from an ex- 

 pression defining the velocity potential throughout 

 the field around the body. 



For practically every case cited throughout the 

 present chapter, where the added-mass coefficient 

 is derived by analytic instead of by empirical 

 methods, the value is calculated on the basis of 

 the following assumptions: 



(1) The potential theory is valid for the case in 

 hand. This means that the body is completely 

 surroimded by an ideal liquid of great extent 

 in all directions, in which only potential flow 

 takes place. This liquid is without viscosity, 

 therefore no boundary layer exists. 



(2) The flow pattern and the added mass of 



417 



