Norrbin 



From model tests with a Rhine vessel [85] it appears that the added 

 resistance at a given forward speed may be approximated by an 

 expression of the form AR = a • (BT/Wh) + b • {BT/W^ • 4> or, 

 roughly, 



AX(u, ^,^) = i X^u^:;^^;^ + ^ X,,^^-u^% (9.2) 



where r|/2 = L/W is a bank spacing parameter defined from the 

 mean width 2W of the canal cross section. (See Section X,) 



The higher resistance in confined waterways is associated 

 with a lower propeller efficiency, and the total propulsive efficiency 

 is further reduced by an increase of the thrust deduction. The 

 influence of flow restrictions on thrust deduction and wake factors 

 has also been considered in a paper by Graff, [86] .In most simu- 

 lator applications this letter influence may be ignored. Horwever, 

 the computed values of r.p.m. and speed attained at a given engine 

 setting should be compared with, say, diagrams compiled by 

 Sjostrom, [ 87] . 



Sinkage and Lateral Forces 



Within the last decade the application of slender-body theory 

 has furnished new understanding and quantitative estimates to the old 

 experience on sinkage and lateral motions in confined waters. 

 Further developments of the theories and nnore accurate measure- 

 ments are required to bridge a gap still remaining in force pre- 

 dictions. 



In an essentially forward motion of the ship in shallow water 

 the back- flow is increased all round the frame sections, and according 

 to the first-order theory of Tuck the dynamic pressure is largely 

 constant in the water around a cross section of the hull and over the 

 bottom bed close below it, [ 88] . Upon assumption of a water depth 

 of same order as the draught, the draught and beam being small 

 compared to the length of ship and waves, and by use of the new 

 technique of "matched asymptotic expansions" Tuck derived formulae 

 for the vertical forces and so also for the sinkage and trim at sub- 

 and super-critical speeds. 



In case of ships with fore-and-aft symmetry the theory pre- 

 dicts zero trim for subcritical speeds, and zero sinkage for super- 

 critical speeds. For small to moderate Froude numbers based on 

 depth the sinkage varies as speed squared, and, using the under-keel 

 clearance parameter defined here, according to the upper curve of 

 Fig. 22. 



8 70 



