An estimation of the accuracy of the experimental measurements, along 

 with the sources of error, is tabulated in the Table. 



A least squares analysis was performed on the digitized force data 

 to calculate the parameters, Cl, cj), k, C^^j, and Cq, of the vertical wave 

 force equation, and the coefficients, Cj^^ and Cq, corresponding to the 

 liorizontal wave force equation. Using this approach, values of the wave 

 force parameters that best fit the force data throughout the entire wave 

 cycle can be determined. These values were then substituted back into 

 the wave force equation to calculate the force over a complete wave cycle, 

 thus allowing comparison of the results with the original data. The 

 least squares analysis is given in Appendix A. Tlie computer programs 

 used for the analysis are given in Appendixes B, C, and D; the tabulated 

 results of the analysis are in Appendixes E, F, and G. Examples of the 

 computer output showing comparison of the original data with the forces 

 calculated using the results of the least squares analysis are given in 

 Figures 24 and 25. 



III. RESULTS AND DISCUSSION 



1. Resultant Force Tlirough Wave Cycle . 



Both horizontal and vertical force measurements were made for some 

 test conditions in the two-dimensional experiments using the 4-inch- 

 diameter cylinder. The resultant force throughout the wave cycle could 

 thus be determined for these conditions. Figures 26 to 32 show the 

 resultant force plotted for each bottom clearance under the same wave 

 condition, a period of 1.85 to 1.86 seconds and a wave height of 0.24 

 to 0.25 foot (7.32 to 7.62 centimeters). Values from the corresponding 

 horizontal and vertical force records were plotted at 20 evenly spaced 

 intervals (18°) through each wave cycle. The forces were plotted for 

 two consecutive wave cycles to indicate the degree of scatter in the 

 data. A rectangle was drawn at each plotted point to illustrate the 

 horizontal and vertical range of the force data over the two wave cycles, 

 and an envelope curve was drawn over these points. 



Examination of these plots as a group (Fig. 33) shows the transition 

 of the resultant wave-induced force with increasing clearance for the 

 given wave condition (T = 1.85 to 1.86 seconds, H = 0.24 to 0.25 foot). 

 The vertical component of the wave force is dominated by the lift force, 

 while the horizontal component of the resultant force is due to the iner- 

 tial and drag forces, with the inertial forces predominating for the 

 experimental conditions tested. 



For the smallest clearance (0.001 foot), in which the pipeline is 

 almost in contact with the bottom, the resultant force attains a maximum 

 upward value under the crests and troughs of the passing waves. The 

 total wave force acts in the upward (positive) direction throughout the 

 complete wave cycle, except for small downward forces in the vicinity of 

 90° and 270°, where the horizontal flow reverses. 



58 



