Norrbin 



(1 + a/a+b) , [65]. Next, for the calculation of the lift carried on 

 the axially oriented body and on the wing deflected to the flow, it is 

 observed t hat the ex act theory by Mirels [ 66] may be approximated 

 by L^^ K VL?- L^?= L^(1 + a/a+b). Except for a correction factor 

 the control derivative for the ship will be calculated as 



where Y''| ^ unlike Yl is defined also for zero forward speed. 

 The modern naif spade or Mariner type rudder has a fixed horn, 

 which divides the upper part of the rudder in ratio Af,/(Ay - A^ , 

 The right-hand member of (7, i) may then be multiplied by a factor 

 1 - (1/4) . (Aj,/A,). 



The effective rudder advance velocity c (squared) is calcu- 

 lated from the mean square velocity of the screw race and an esti- 

 mated mean square velocity past the rudder outside the race. If w 

 is the wake factor as integrated by the propeller (thrust identity) the 

 effective square velocity above the race in a normal single screw 

 arrangement may be taken as u (1 - Aw) , Inside the race, which in 

 average conditions has a diameter some 10 per cent smaller than 

 the propeller, the ultimate mean square velocity is given by 

 u2(i - w )2(1 + (8/it) • (Kj/3^)), where, for u> 0, 



Ky = K^,, + ^1 « K^^ + K^/ + i K^jjJ (7. 2) 



is to be approximated from the open water propeller diagram. Where- 

 as the thrust may be analytically defined for all combinations of u 

 and n — see below — the working conditions of the rudder are known 

 only for a positive thrust, in which case 



2i22,2 ,i2||,i22 in ■i\ 



From an analysis of a large number of control derivative 

 measurements on models it appears that a correction factor of 

 0,7 - 0.8 shall be applied to (7.1) when combined with (7.3) to give 

 the force Y(u,n,6) =pV/l-* iYjU • c^6. This correction factor is 

 understood to take care of gap effects and non- ideal geometry of the 

 hull + rudder arrangement, etc. 



The four constants in Eq. (7.3) depend on screw character- 

 istics and wake factors, and they are therefore unique for the model 

 scale. To facilitate a correction for this scale effect in the control 

 derivatives the diagram in Fig, 20 has been compiled, chiefly from 

 Ref. [ 67] and data available at SSPA, The slope of curves of wake 

 factors against ship or model lengths increases with hull fullness; 

 especicilly SSPA experience of full scale tanker trials rarely include 



858 



