Free Surface Effects tn Hull Propeller Interaction 
Ry , Rp_ are the hub and tip radius of the propeller respectively . 
There is no simple way of relating the source strength directly to 
propeller geometry , speed and rate of revolutions . However , using 
momentum theory , Dickmann derived two useful approximations con- 
necting propeller source strength to thrust loading , one of which yields 
a uniform sink disk of source density 
a(R, 0) = -(¥l+Crp -1)/4-7 
a Se Soy (B10) 
over 
and the other a discrete point sink of source strength 
-(4)1+C yy - 1) (Rp* -R,,7)/4 at (xp,0,2p) (B11) 
where 
Z 
er fen) a oes (BRE (B12) 
is the thrust loading coefficient based on disk area (excluding the hub ). 
In addition to the above we have also used the following alter- 
native relation due to Hough and Ordway (1965): 
meer 5.6) == ZG / 4.5 (B13) 
where 
GR), sa all shu Ze elec ties (B14) 
is a non dimensional function representing the radial distribution of 
bound circulation [’ along each blade of a Z bladed propeller at 
advance coefficient J = V / 2 a Rp . Here the source density is 
a function of radius R , but still independent of angle © . Since the 
circulation is obtained numerically from a computer program at dis - 
crete radii, 6 will generally be defined merely as a tabulated function. 
Unless analytical interpolation is used for further processing , it is 
tantamount to a radially stepped sink disk 
1889 
