Novrbin 



An experimental evidence of the practical validity of the 

 superposition in Eq. (6.6) is illustrated in Fig. 15, based on force 

 measurements at SSPA on a 3.55 m model of a cargo liner with 

 rudder and bilge keels, [47] . In this diagram the quotient 

 Y/(p/2)V^LT = (2V/L^T)Y"/{u"^ + v"^) is plotted versus |3 = - arctg v/u, 

 and the viscous cross -flow component is seen to dominate the entire 

 range of iOO< p < 90°. 



The variation of cross -flow drag coefficients with drifting 

 speed and hull geometry has also been discussed in several papers 

 by Thieme and by other authors, [48, 49, 50], In lack of experimental 

 results for a special case in the non-linear range it shall be possible 

 to use these results; a typical value of cross -flow drag of a tanker 

 form is Cp =0.7, The contribution of cross -flow drag to moment- 

 due-to-sway may then be ignored. 



In a similar way it is possible to approximate the non-linear 

 rotary derivatives. If Cq (> C^) is the mean section drag coefficient 

 the moment- due-to-yaw derivative is iN'/^i^ = - (c-,/32) • (L T/2V) , 

 except for a three-dimensional correction factor. (For rough esti- 

 mates iN'i'pip =0,03 • 2Y|\,|y , which is verified from experiments.) 

 The force -yaw velocity derivative now is zero to this approximation. 

 Additional effects of skegs and screws contribute to non-zero values 

 of In;;,^ as well as iY,';,^ . 



In the general case the local cross -flow resistance is pro- 

 portional to |v + xr |(v + xr) , and from symmetry relations the 

 coupling terms are seen to include the derivatives Y|vir and Yyj^i , 

 etc. (In the cubic fits more often used these couplings are repre- 

 sented by terms in Yvvr 3-nd Y^rr > ®tc. — cf. Abkowitz , [51].) 



The contribution to Y due to the combined sway and yaw may 

 be written Yj^j^ | v | v(r/v) +Y |r|r(v/r), i.e., Yi^ir may be looked 

 upon as the derivative of Y|y|y with respect to yaw velocity r per 

 unit V, etc. 



Forward Speed and Resistance 



The principal effects of viscous and free -surface phenomena 

 on the resistance to steady forward motion are well-known to naval 

 architects. The correlations of wavemaking and separation with ship 

 geometry are still less satisfactory. However, alternative methods 

 are available for full scale powering predictions from standard series 

 or project model data. As will be further discussed in next Section 

 the adequate synthesis should supply information not only on shaft 

 horse power and r.p.m. but also on hull resistance and wake 

 fraction. Speed trial data therefore require an analysis such as 

 proposed and used by Lindgren; in case of very large and slow- 

 running ships it may be necessary to include scale effects also in 

 the open- water characteristics of the screw propeller, [ 52] . 



848 



