Newman 



coL _ IrrL 

 ~ D~ 



where B is the distance run in one cycle. Typical values of this distance are six 

 to ten ship lengths* and it follows that the reduced frequency parameter is 

 roughly in the range of from one-half to one. Thus a 20° -20" zig-zag maneuver 

 is marginal from the viewpoint of frequency effects. Ship maneuvers which take 

 place more rapidly than this can be expected to involve significant frequency ef- 

 fects, which can only be accounted for by Laplace transform techniques or the 

 equivalent thereof, as outlined by Brard (1964). It remains to be determined, 

 however, what magnitude of error is incurred by neglecting this complication, 

 and it would seem desirable to carry out a numerical comparison of the two 

 predictions for realistic maneuvers. 



BIBLIOGRAPHY 



The items listed herein are restricted primarily to those cited in the text 

 and to the period 1960-1966. A bibliography of the period prior to 1960 is in- 

 cluded in the survey of Norrbin (1960) and a current, but as yet unpublished, 

 broad account of the field is given by Mandel (1966). 



Abkowitz, M. A., 1964. Lectures on ship hydrodynamics— steering and maneu- 

 verability. Hydro- and Aerodynamics Laboratory, Lyngby, Denmark, Re- 

 port No. Hy-5. 



anon., 1950. Nomenclature for treating the motion of a submerged body through 

 a fluid. Society of Naval Architects and Marine Engineers, Technical and 

 Research Bulletin No. 1-5. 



Brard, R., 1964. A vortex theory for the maneuvering ship with respect to the 

 history of her motion. Fifth Symposium on Naval Hydrodynamics, Bergen. 

 (Revised March 1965.) 



Casal, Pierre, 1962. Theorie tourbillonnaire de I'aile portante de tres faible 

 envergure (vortex theory of low aspect-ratio lifting surfaces). Publ. Scien- 

 tifiques et Techniques du Ministere de I'Air, No. 384. 



Chislett, M. S., and Strj^m-Tejsen, J., 1965. Planar motion mechanism tests 

 and full-scale steering and maneuvering predictions for a Mariner class 

 vessel. Hydro- and Aerodynamics Laboratory, Lyngby, Denmark, Report 

 No. Hy-6. 



Cummins, W. E., 1962. The impulse response function and ship motions. 



Schiffstechnik, Band 9, Heft 47, pp. 101-109. Reprinted as DTMB Report 

 1661. 



'''Cf. Motora and Couch (1961). 



226 



