(Op mM)n 
Subscripts: 
d 
EXP 
Wake fraction determined 
from volume mean 
longitudinal velocity 
through propeller disk 
determined from a wake 
survey, (V-Vym)/V 
Coordinate axes 
Number of blades 
Angular coordinate used 
to define location of 
blade and variation of 
loads, from vertical 
upward, positive 
counterclockwise looking 
upstream for left-hand 
propeller, positive 
clockwise looking 
upstream for right-hand 
propeller, 0= -6y 
Angular coordinate of 
wake velocity, from 
upward vertical, positive 
clockwise looking up- 
stream for left-hand 
propeller, positive 
counterclockwise looking 
upstream for right-hand 
propeller, ®w =-6 
nth harmonic force 
coefficient, 
(F) n/ (onvaD3) 
nth harmonic moment 
coefficient, 
(M) n/ ( onVaD4) 
Mass density of water 
nth harmonic phase angles 
of F,M based on a cosine 
series, 
WAG A N 
(F,M) = (F,M)+ © (F,M)n. 
n=1 
cos {né-(¢F,m) n} 
Inclination of propeller 
shaft 
Value at the near design 
condition 
Value of experimental 
measurements 
Value of hub radius 
Value of nth harmonic 
REF Value at specified 
reference advance 
coefficient 
X,VY,Z Component in x,y,z 
direction 
Superscripts: 
- Time-average value per 
revolution 
INTRODUCTION 
The once-per-revolution (or shaft 
frequency) propeller blade loads are 
important for consideration of propeller 
blade fatigue strength (1,2,3,4). 
Therefore, an investigation was 
undertaken at DTNSRDC to evaluate the 
periodic blade loads on propellers in 
inclined flow and in circumferentially 
non-uniform longitudinal velocity fields. 
Systematic experiments were 
conducted on three model propellers (see 
Table I) operating in inclined flows 
generated by shaft inclinations of 10, 
20, and 30 degrees, and in a once- 
per-revolution circumferentially 
non-uniform longitudinal velocity field 
produced by an upstream wire-grid 
screen. The inclined flow produces a 
once-per-revolution variation of the 
tangential component of velocity in the 
propeller plane; therefore, the inclined 
flows are sometimes referred to as 
tangential wake patterns. 
TABLE I — CHARACTERISTICS OF PROPELLERS 
4661, 4710, AND 4402 
PROPELLER NUMBER | 4661 | 4710 | 4402 | 
Diameter, D (feet) 
Rotation 
Number of Blades, Z 
Hub-Diameter Ratio, D,,/D 
Expanded Area Ratio 
Design Advance Coefficient 
Pitch-Diameter Ratio (P/D) 
atr/R =0.7 
The experimental results were 
correlated with predictions by the 
following theoretical methods: 
Ib A simple quasi-steady procedures 
developed by McCarthy (5) at 
DTNSRDC which utilizes the open 
