simulation, the smallest value of peak loading occurred near VV ony as the 
hull passed from the stern-down to the stern-up portion of the cycle; i.e., 
(W-W ay )=0, ¥>0. 
This difference in the unsteady loading between the quasi-steady and 
unsteady simulations may be due to an additional relative velocity compo- 
nent arising from the motion of the hull during dynamic pitching. As the 
hull passes through p=) the vertical velocity of the hull (and propel- 
> 
ler) is a maximum. As a hull goes from stern up to stern down through 
YVoyp the upward velocity component relative to the propeller in the 
plane of the propeller tends to increase above the values at fixed hull 
pitch at v=Voye This tends to increase the amplitude of the first harmo- 
nic of the tangential velocity, and thereby increase the unsteady loading 
(and increase the peak loading). The maximum vertical velocity of the 
propeller for sinusoidal pitching with Cbuax Yew 7d: 85 degrees and fre- 
quency=0.8 hertz is approximately 1.47 feet per second (0.448 m/s). This 
is equivalent to an additional tangential velocity ratio OND) Ose, (05 a13}3}., 
For ~ fixed at v=Voy ((V,),/V)=0.130 (see Appendix A). Therefore, 
(VM ax, i40 = 0.130 + 0.133 = 2.02% 
((V),/V) §-0,0-Voy 0.130 
This maximum occurs at a model simulated time of approximately 0.2 second 
before the maximum measured loads. The measured increase in unsteady loads 
arising from dynamic pitching was somewhat smaller than this calculated 
increase in tangential velocity, for example: 
F = 10 
. x ba 
MAX , 70 ca = LGD & i. /Mil 
: ay 0.4 
*A numerical error was found in a similar calculation presented in Ref- 
erence 2, With the numerical error corrected the results in Reference 2 
are substantially the same as those presented here. 
36 
