150 



THEORY OF SEAKEEPING 



impact force at the initial contact with water is not large, 

 but it increases rapidly with sulimersion (up to the deck 

 level) because of the summation of displacement and 

 dynamic forces. Theoretically the problem differs from 

 that of seaplane impact (Wagner, 1931) by the slower 

 rate of immersion which does not permit neglect of grav- 

 ity forces. Time history of the force development and 

 decay is needed. 



32 Total Impact Force in Slamming of the fast ships 

 mentioned in the aljove project should also be measured. 

 This is a project similar to 30, but it is listed separately 

 because the relatively slow rate of acceleration develop- 

 ment"' may reciuire different sensing and recording 

 equipment. Experiments in towing tanks are therefore 

 simpler with fast ship models than with the conventional 

 cargo ship models, and a greater number of lal)oratories 

 will be capable of conducting project 32 than 30. On 

 full-size ships, however, the elasticity of slender ships 

 makes the evaluation of the impact force from accelerom- 

 eter readings less certain. 



Nomenclature 



Note 1 : NASA" nomenclature shown herewith is used 

 for ship and fluid motions in three dimensions. 



Note 2: Symbols defined locally in connection with a 

 particular topic are not necessarilj' included in the list of 

 symbols. 



Note 3: The symbols listed on pages 13-15 of the 

 Proceedings of the Sixth International Conference of Ship 

 Tank Superintendents (Washington, September 10-15, 

 1951, published by SNAME) are used whenever appli- 

 cable. Symbols not contained therein are chosen from 

 the ones frecjuently used in recent literature on ship 

 motions. 



a = a coefficient 



a = coefficient of inertia! term in differential eciiiation of 

 heaving motion 

 coefficients of equation (3f ) defining attenuation of 



ship rolling aniplitvides 

 modified value of n in linearized equation 

 coefficients of series expansion, equations (12), (14) 



and (18) 

 a coefficient 



an area; sectional area of a ship 

 coefficient of inertial term in differential equation 

 of pitching motion of a ship (also in rolling when 

 considered separately) 

 half-breadth 

 6 = a coefficient 



b = coefficient of damping term in differential equation 

 of heaving motion of a ship 



b = asymptotic value of damping in heave at co — ► 



equation (5.3) 

 B = beam 

 B = coefficient of damping term in differential equation 



of pitching motion (also rolling when considered 



separately) 



6 = 



h = B/ 



"^ Some data on this will be found in Chapter 5. 

 2' National Aeronautics and Space Administration. 



B = asymptotic value of B for co — 0, equation (60) 

 c = coefficient of restoring force in differential e<iuation 



of heaving motion 

 c = wave celerity 

 C = wetted semi-breadth in slamming impact (time 



dependent. Fig. 31) 

 C = coefficient of restoring force in differential equation 

 of pitching motion (also rolling when considered 

 separately ) 

 C = added-mass coefficient in two-dimensional flow 

 based on comparison with that of a circular 

 cylinder (I^ewis, 1929, equation 1.5). C,, in verti- 

 cal oscillation, C'j in horizontal oscillation 

 f/ = draft 



/ = depth at which a source, simidating heaving oscil- 

 lation, is located 

 Fo = amplitude of exciting force in heaving oscillation 

 caused by waves 

 g = acceleration of gravity 

 i, j, k = unit vectors along :r, i/, j-axes 

 i = V-^ 



/ = moment of inertia 

 /o = moment of inertia of a body 

 /' = moment of inertia of water displaced by a body 

 /" = added moment of inertia 

 *; = tt/X 



= u'/g — wave number 

 k = radius of gyration 

 k = coefficient of accession to inertia 



coefficient of accession to inertia along x, y, z-axig 



coefficient of accession to inertia in rotation of a 

 spheroid about the minor axis (Lamb's notation) 

 kzi,,j,,,i! = coefficient of accession to moment of inertia in rota- 

 tion about x, y, j-axis 

 ^4 = correction coefficient for free surface effect on added 

 masses in heaving motion, eciuation (19) 

 / = L/2 = half-length of a ship 

 L = ship length 

 L = rolling moment 

 m = an index or subscript 

 m = a mass; mass of a ship 

 ??(' = virtual mass 

 ?"" = added mass 

 ^[ = a moment; pitching moment 



il/o = amplitude of time-de|K>ndent pitching moment 

 caused b}' waves 

 n = an index or subscript 

 n = unit vector in direction of normal to a surface 



element 

 n = number of oscillations 

 A^(^) = damping coefficient per unit of a shiji's length, 

 equation (21) 

 p = pressure 

 q = total fluid velocity (equivalent to f often used for 



total fluid velocity) 

 r = radius; radius vector 

 R = radius in polar co-ordinates 

 S = wetted-surface area 

 S = stagnation point (slamming, Fig. 31) 

 T = kinetic energy of a fluid 

 T = wave period; period of undamped oscillation of a 



body 

 Ti = period of damped oscillations 



^1 .2.3 or ) 

 preferablv j 



k' 



