Macy 



Many of the earlier drilling platforms were equipped for drilling off one 

 end or over the side. Aside from stability and trim control problems, this is 

 undesirable because the vertical components due to rolling or pitching are 

 added to the heaving motion. If the drilling is done at the center of flotation, 

 the vertical component of roll and pitch is zero, and there remains only the 

 small horizontal components. But unless the platform contains some type of 

 slot in one end, or has a Y, A, or catamaran configuration, the platform could 

 not be withdrawn from a permanent pile supported production platform. This 

 has led to the development of sub-sea completions, of which many forms have 

 been proposed and some tried with success. However, it is still far from a 

 routine operation. 



The natural period for unresisted rolling or pitching in still water is 



1.108 K 



T = 



x/GM 



where T is period for a complete roll, K is radius of gyration, and GM is the 

 metacentric height. 



The heaving period is 



T = 



2tt 



where t is tons per foot of immersion and D is displacement in tons. 



In the case of a wall- sided vessel, where the tons per foot of immersion is 

 constant, D/t may be replaced by the draft d, and the formula becomes 



277 



There are two basic philosophies in adopting motion criteria. One is to 

 maintain all of the natural frequencies below the range of periods of the larger 

 waves expected. This will not avoid the possibility of synchronism, because 

 wave periods will be encountered all the way from zero to the maximum con- 

 templated, and at least one period will give synchronism for each of the roll, 

 pitch, and heave conditions. There may also be secondary peaks in the response 

 curves. However, if the platform is a type with short roll, pitch, and heave 

 periods, the amplitudes even at synchronous motion may not be too great. 



The second approach is to design all of the natural frequencies to be 

 greater than the period of the maximum or the nearly maximum expected wave. 

 In this case, synchronism will never be reached. The column stabilized plat- 

 form and the less common spar platform are the only ones which can attain this 

 criterion. The determination of the design wave period for a particular loca- 

 tion is an oceanographic matter, but generally in the Gulf of Mexico a 16-second 

 wave is about the maximum to be expected, and in the Pacific 20- second waves 



466 



