Kats iO 
(M+M, cos? 0)%., -(Q, cos0)0 = F, +W 
-(Q, C08 O)Zcg + (I+1,)6 = Fo 
These equations also represent the case of the craft (model) being towed through CG at 
CONSTANT speed. Based upon the previously described equations of motion, a computer 
program has been written in FORTRAN language to compute the motions of a prismatic body, 
planing in regular head waves at high speed. A listing of the program along with the 
appropriate flow chart is presented in Appendix B. The listing contains reference to thrust 
and drag terms; however, they have no significance, except to provide a starting point for 
possible updating of the program to include these terms in the future. 
COMPARISON OF COMPUTED RESULTS WITH EXPERIMENTS 
Computations of pitch and heave motions and heave and bow accelerations were made, 
using the computer program for comparison with the experimental results of Fridsma.> 
Fridsma tested a series of constant-deadrise models of various lengths in regular waves to 
define the effects of deadrise, trim, loading, speed, length-to-beam ratio and wave proportions 
on the added resistance, heave and pitch motions, and impact accelerations at the bow and 
center of gravity. Figure 3 shows the lines of the prismatic models. The models were towed 
at CG with a system that permitted freedom in surge. The computer program simulates the 
model being towed at constant speed with CG at the baseline. 
Table 1 presents some characteristics of the model and experimental conditions for 
which comparisons were made. Most of the comparisons have been made at a speed-to-length 
ratio Wile of 6.0 where the mathematical model is expected to be most representative. A 
limited comparison has also been made at Wifes = 4.0; however, no comparison has been 
made at Wilx/ ale = 2.0. At this speed, the model (or craft) operates in the displacement mode 
for which the mathematical formulation is not valid. 
The average computer run corresponded to 10-second, real-time, model scale; however, 
only the last 2 seconds were considered free of transient effects. An example of the compu- 
ter time histories of pitch and heave motions is shown in Figure 4. Although the motions 
are periodic, they are not perfectly sinusoidal; consequently, in determining phase relationship, 
the peak, positive-pitch value (bow up) and the peak, negative-heave value (maximum upward 
position of CG) were used as reference points. There was a difference when the opposite 
peaks were used. 
