HYDRODYNAMIC FORCES 



143 



8 Concluding Remarks and General Research Suggestions 



It appears that analysis of ship motions'"' has reached 

 its most complete development, from a practical point of 

 view, in using hydrodynamic forces obtained by the strip 

 theoi'y. Strip theory, at the same time, provides the 

 distribution of the hydrodynamic forces along the length 

 of a ship. This distribution is needed for analysis of 

 shear forces and bending moments acting on a ship. 

 Use of the strip theory, likewise, appears to be necessary 

 in the evaluation of rolling and yawing moments and of 

 the corresponiling translational forces acting on a ship 

 in waves coming from an oblifiue direction. An ex- 

 ample of a partial evaluation of rolling moments by this 

 method can be found in the work of Cartwright and 

 R.ydill (1957). Available material on sectional hydro- 

 dynamic forces suitalile for use with the strij) theory, 

 however, are meager and mostly theoretical. Broadly 

 speaking, there is an acute need for (a) experimental data 

 on prismatic and cylindrical bodies, (b) exi^erimental data 

 on complete ship models, (c) additional theoretical cal- 

 culations for prismatic bodies and complete ships, relat- 

 ing to added masses and damping-force coefficients in 

 oscillatory motions of all modes. The force connected 

 with the acceleration of the added mass and the damping 

 force are here imdcrstood to be two components of a 

 hydrodj'namic force, acting respecti\'elj' in phase and 

 90 deg out of phase with the oscillation of the body. 

 In theoretical work and in the analysis (jf experi- 

 mental data these appear as real and imaginary parts 

 of the total force, which is considered to be a complex 

 quantity. 



8.1 Experimental Research: 8.11 Methods of test- 

 ing. Various types of tests have been described by Dimp- 

 ker (1934), Ilolstein (1936), Haskind and Riman (1946), 

 Grim (1953), Oolovato (1956-57), and Gerritsma 

 (1957c). The papers of Haskind and Riman and of 

 Golovato gi^'e clear descriptions of the analysis of test 

 data in connection with two different basic test methods. 

 Wliile they are actually applied to complete ship models, 

 the methods are ecjuallj' applicable to prismatic bodies. 

 A third method used by Holstein (1936) consists of meas- 

 uring wave profiles and is applicable only to damping 

 forces. 



In the tests of Haskind and Riman and of Gerritsma, 

 model motion was excited harmonically through a spring 

 actuated by an eccentric, while forces were evaluated 

 from the recorded amplitude and phase of the model mo- 

 tion. A method used by Grim (1952, 1953) is similar, 

 except that unbalanced rotating weights were used in- 

 stead of springs and eccentric. In either case a known 

 harmonically varying exciting force or moment was ap- 

 plied, and the analysis was based on the assumption of 

 harmonic model motion. In practically all liody forms 

 the actual instantaneous force is not a simple harmonic 

 but is nonlinear. The tests gave the forces and moments 

 of an assumed linear or harmonic system of the same 

 amplitude and phase relationship as the true physical 



' To be discu.ssed in Chapter 3. 



system at hand. It will be shown later in Chapter 3, 

 in the section on irregular seas, that this ecjuivalent lin- 

 earization is what is needed for the present statistical 

 theory of irregular model motions. However, since the 

 forces and moments are in all likelihood not linear, the 

 experiment must be repeated for several amplitudes of 

 motion. Thes.e amplitudes, and the frec^uencies of oscil- 

 lation as well, must cover the practical range met by a 

 ship in wa\es. 



In this method of testing the model is flexibly con- 

 nected with the apparatus and, therefore, records are 

 largely free from noise. The resultant forces are inferred 

 from the model's motions, while the model itself acts as 

 an integrator of all instantaneous forces. The records, 

 therefore, are rehiti\'ely smooth and easy to interpret. 

 For these reasons great precision is not required in the 

 apparatus, which thus can be simple and inexpensive. 



In Golovato's tests at the David Taylor Model Basin, 

 the model was driven positively by an apparatus in a 

 simple harmonic motion. Dynamometers with high 

 spring constants were placed between the model and the 

 driving part of the apparatus. The deflection was so 

 small that the model motion was assumed to follow di- 

 rectly the motion of the apparatus. The dynamometers 

 measured the sum of hydrodynamic and model inertia 

 forces. These were very sensitive to any irregularity in 

 the acceleration of the driving system. The apparatus 

 at the Da-\-id Taylor Model Basin is believed to be the 

 only one of this type in existence and has taken a nimiber 

 of years to de^'elop. 



While the dynamometers were rigid enough to trans- 

 mit the apparatus motion to the model, their own fre- 

 (|uency response could not be neglected, since it was of 

 the same order of magnitude as that of the record taken. 

 Because of the large mass of the model and of the added 

 water mass it is usually not possible to secure a suffi- 

 ciently high fre(|uency response while retaining sensitiv- 

 it^^ Correction for tlie frefiuency response of dynamom- 

 eters, therefore, is reciuired and was discussed by Golo- 

 vato. 



The advantage of this method of testing lies in that it 

 is possible to get a record of nonlinear ^'ariations of the 

 added masses and damping forces. In the case of Golo- 

 vato's model the damping force was nonlinear. 



It appears that at the present stage of ship-motion 

 theory, and in particular the theory of ship motions in ir- 

 regular seas, it is not yet possible to make use of the de- 

 tailed nonlinear information provided by the DTMB 

 apparatus as used by Golovato. It is suggested that the 

 simpler methods described by Haskind-Riman (1946) 

 and Gerritsma (1957f) be u.sed in order to provide, as 

 (juickly as possible, a large amount of experimental in- 

 formation on hj'drodynamic forces. Certain other dy- 

 namometers may be added at the model in order to meas- 

 ure directly the cross-coupling forces and moments. 

 Knowledge of the nonlinear behavior of forces, howe\'er, 

 may be needed in the near future for analysis of structural 

 loads acting on ships. In view of this, it is recommendetl 

 that the Golovato-David Taylor Model Basin method 



