HYDRODYNAMIC FORCES 



147 



the LWL ai-e given a lateral as well as x-ertical impulse. 

 This is expected to favor the development oi progi-essive 

 waves carrying the energy away from a ship and thereby 

 to increase damping. The problem can be attacked in 

 two ways: 



(a) By suitable formulation of a basic theory. 



(6) As a correction to the water flow induced Ijy a wall- 

 sided section. Guilloton's "second-order" corrections in 

 the thcorj' of ship wavemaking resistance (Korvin- 

 Kroukovsky and Jacobs, 1954) may prove to be ap- 

 plicable in this ca.se. 



This project affects project 11 inasmuch as inclined 

 sides can be expected to intensify the non-linear draft 

 effect. 



14 Experimental Measurement of Damping Forces 

 in heaving of prismatic anil cylindrical bodies, Section 

 3.21, is a companion project to No. 5. It is expected 

 that inertial and damping forces will be obtained from 

 analysis of the measm-ed data as real and imaginary parts 

 of the total hydrodynamic force. It is suggested that 

 measurements be made on Lewis' (1929) sections for 

 which Grim's (1953) theoretical calculations are avail- 

 able. For section fullness greater than that of the semi- 

 circle, Lewis' .sections closely resemble those u.sed in 

 practical ships. Tests on the.se sections have, there- 

 fore, direct practical interest. 



15 Experiments on Damping Forces at Low Section 

 Coefficients are also advi.sable. For section types finer 

 than semi-circvilar, Haskind's (1946) sections can lie sug- 

 gested. Theoretical information on these can be ob- 

 tained by reworking Haskind's three-dimensional anal- 

 ysis. These sections have shapes similar to those in the 

 bow and stern portions of actual ships, which are charac- 

 terized by sloping sides at the LWL. Since the hydro- 

 dynamic characteristics of such sections are nonlinear, 

 tests must be conducted at a series of amplitudes. 



The measured result at a given amplitude will repre- 

 sent the damping coefficient of an equivalent linear .sys- 

 tem. In the present .state of development of ship- 

 motion analysis, and in view of the ultimate application 

 to ship motions in irregular waves, the author sees 

 no need for a detailed description of the nonlinear 

 damping. 



16 Evaluation of Sectional Damping Forces by Means 

 of Wave-Amplitude Ratio (Section 3.21; Holstein, 1936) 

 is sugge.'^ted as alternate or supplemental to projects 14 

 and 15. Such measurements can be accomplished with 

 the minimum of special apparatus, and therefore, it is 

 hoped, can be collected for a large number of sections 

 in the shortest po.ssible time. A towing tank of rec- 

 tangular cross section (for a minimum of wave distortion), 

 a plunger-type wavemaker hugging the end wall of the 

 tank and a good wave-absorbing beach are the reciuired 

 e(|uipment, to be found in many laboratories. By meas- 

 uring wa\-e amplitudes at several freffuencies and ampli- 

 tudes of the existing plungers a good deal of useful in- 

 formation can be obtained. Much information can be 

 obtained by mere re-examination of wavemaker cali- 



bration data. Further data on \'arious sections can be 

 obtained by building plungers of the proper semi-section. 



17 Damping-Force Measurements on Complete Ship 

 Models should be made preferably in wide (maneuvering) 

 tanks in order to avoiil contamination of results by the 

 wave reflection from towing-tank walls. This project 

 can be subdivided and classified by the method of test- 

 ing and by the type of model. 



By the method: 



(a) Tests similar to those of Haskind and Kiman 

 (1946) and Gerritsma (1957c), in which the model is re- 

 stricted alternately in pitching and heaving, and is har- 

 monically driven by a spring link. This type of test ap- 

 paratus appears to thc^ author to lie the best combination 

 of simplicity and reliability. 



(b) Tests similai' to (iolovato's (1957a, b) in which 

 the model is driven alternately in heaving and pitching 

 by positive (rigid) mechanism and forces are measuretl 

 directly by small-deflection dynamometers. Good qual- 

 ity apparatus and extreme care are needed for proper 

 interpretation of results. Corrections for dynamometer 

 response must be included. 



(c) Analysis of the coupled pitching and heaving mo- 

 tion of a free model (Grim, 1953) excited in one of the 

 modes by rotating weights. While only one mode is 

 excited, oscillations in the other will develop under ac- 

 tion of cross-coupling forces. In particular, the heaving 

 induced by directly excited pitching will increase with 

 model speed. Unle.ss complete analysis of the coupled 

 motion is made, the results will simulate an exaggerated 

 effect of ship's speed on the damping in pitch. 



By the type of model : 



(a) A theoretically defined (parabolic) model with 

 affine sections. The model should be chosen preferably 

 from the Haskind (1946) or the Hanaoka (1957) series 

 for which complete theoretical calculations are avail- 

 able. The object of the test is to compare the measured 

 and calculated results on damping and added masses at 

 \'arious speeds. The data obtained on these idealized 

 ship forms should not be assumed directly applicable to 

 actual ships. This project is an extension and veri- 

 fication of the work of Haskind and Riman and of Hana- 

 oka. The author l)elie\'es that it deserves only low 

 priority. 



(6) A theoretically ilefined model with sections vary- 

 ing from full amidships to V or hollow V at the ends, and 

 unsymmetrical fore and aft. The object of these tests 

 is dual; i.e., to provide experimental comparison with 

 theoretical calculations, and to provide data on a (mathe- 

 matically tractable) model reasonably resembling actual 

 ships. The author is inclined to assign the highest prior- 

 ity to this project, but only after theoretical work on the 

 formulation and analvsis of these model types. Section 

 6.1. 



(c) Tests on models of conventional ships. The only 

 tests available to date arc those of CJerritsma (1957c, 1958, 

 and 1960). Additional tests on other ship models are 

 needed. These tests will provide the data on actual ship 

 forms, and also will jiroN-ide the information needed to 



