Nowaeckt and Sharma 
need not be described here in detail . After several test runs had re- 
vealed that the two programs yielded practically identical solution of 
the design problem , we chose the Berlin program for further use and 
adapted it to a solution of the performance problem . The principal 
modification necessary was the following . In the design problem the 
hydrodynamic pitch angle 8; (R/Rp) is generally prescribed to fulfil 
the optimum ( minimum energy loss ) condition thus eliminating the 
need to solve an integral equation . In the performance problem , how- 
ever , the integral equation must be solved . This was done by the 
method of successive approximations to the unknown function B;(R/Rp). 
Starting with an initial guess ($j ),5, say corresponding to the opti- 
mum condition , a better approximation was found by cycling through 
Equations (Cl) to (C7) . In order to prevent the iteration from diverg - 
ing it was found necessary to weight the successive approximations 
as follows 
(B°x),42 os w, (Bin i wo (Bin +1 (C11) 
With w,; = 0.9 and wz = 0.1 the final error in B {(R/Rp) after ten 
iterations was found to be generally less than 1 % 
A major handicap in this algorithm was that the two-dimensional 
foil characteristics of our propeller (see Fig.2) were not explicitly 
known to us . We therefore back-calculated the foil characteristics 
from the known measured performance (thrust and torque) of the pro- 
peller (in the deeply submerged open water condition) . This was 
done by treating any given operating condition as a small perturbation 
from an assumed design (optimum) condition , i.e. 
| eee (C12) 
Cy. (fo) Rees & + 2m (a-ay ) 
LD 
a 
ie ® 2 
Cy (a) = a, |Cz,(a) -C, 5) pote (C13) 
The design angles of attack a and the corresponding lift coefficients 
Crip were specified indirectly by the choice of a design advance coef- 
ficient Jp. Let Bip be the optimum hydrodynamic pitch angle at any 
radius at the design point Jp. Then for calculating the performance 
at any other advance coefficient J (and assumed pitch angle Be ee i: 
is only necessary to evaluate the differences (see next page) 
1908 
