where g is acceleration due to gravity, i is a characteristic length 

 (diameter or line length), and U is current velocity. Hence, if a 

 geometric scaling parameter 1s de.ined as 



» = V £ m = V d m (2) 



where d is line diameter and subscripts m and p refer to model and 

 prototype, respectively, then Froude scaling relates model to prototype 

 velocities by the following equation 



U = U / ^ (3) 



m p 



and model to prototype wave frequencies by 



m p 

 Breslin expresses the celerity (or wave speed) of longitudinal waves 

 as follows 3 



K ' T! (5) 



where A is line cross sectional area, E is Young's modulus of the 

 line material, and u is mass per unit length of the cable; and the 

 celerity of transverse waves as 



C"( m 1° \ , } H [(6)] 



I (1 + t )L' 



where To is equilibrium tension, eo is equilibrium strain, and u 1 is 

 the virtual mass per unit length. Now, Froude scaling relates model 

 to prototype area by the following 



\ = V> 2 {7) 



Mass per unit length may be expressed as follows 



u - p c A (8) 



where p is the density of the mooring line; and virtual mass as 



vA (p c + p)A (9) 



where p is the density of the fluid and the mooring line is assumed 



to have a circular cross section. Also, the equilibrium strain may 



be expressed as follows 



