Mooring and Positioning of Vehicles in a Seaway 



X„=\ \ p cos e'R de de = 2paJ \ e'^^S'C^) d^ • cos cot (63) 



The surge damping force expression due to wave generation (pro- 

 portional to x) in [11] and to this should be added the surge daraping 

 due to real fluid drag effects, which is nonlinear. This drag term 

 is represented in the form 



l-^ApJ^ [x + (e - eg)e] |x + (e - ig)e| de 



(64) 



where Ap is the lateral projected submerged area of the buoy and 

 Cjj is a drag coefficient whose value is «^ 1.2, the value for long 

 slender bodies and sections in an oncoming normal flow. 



The pitch equation for the spar hull form is represented by 



ly'e = - p j s'(e)[ X + (e - eg)e] (e - eg) de 



-Pgj (e - eg)S'(e) dl • e +Md +M^+ Hn (65) 

 and the wave induced exciting moment is given by 



nO 

 = 2paa)2 \ (e - iq)e^S^{i) di • cos wt 



(66) 



The pitch damping moment coefficient due to wave generation is 

 given by [ 11] , and as with the surge damping above, the pitch 

 moment equation has additional nonlinear damping given by 



2T^^p{ tx + (e - eg)e] |x + (e - eg)e|(e - eg) de 



(67) 



which must also be induced. By considerations of symmetry^ a 

 cross -coupling damping term due to pitch angular velocity, 9, will 

 appear in the surge equation, which is given by 



x^ = - £i^y e'^s'(e) de • y_ (e - eg)e''^s'(e) de • e (68) 



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