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CHAPTER 5. COASTAL STRUCTURE MODELS
The elastic properties of the mooring system are modeled according to
the Cauchy scale criterion which states that the ratio of inertia forces to
elastic forces must be the same in prototype and model. Representing the
elastic force, Fe, as the modulus of elasticity, E, times the cross-sectional
area of the mooring line, A, the Cauchy criterion gives (in the linear elastic
range)
(Fe)p = (EA)P
(FB)m
(EA)m
or in terms of scale ratios
NFe = Ne Na
(5.56)
(5.57)
The elastic force scale must be the same as the mooring line weight
scale (and the hydrodynamic force scale). Equating the Froude criterion
of Eqn. 5.55 with the Cauchy criterion of Eqn. 5.57 and requiring that the
mooring line be geometrically undistorted so NA = (Nl)2 yields11
The subscript, ml, in Eqn. 5.58 refers to properties of the mooring line.
(5.58)
which is the elasticity requirement for selection of model mooring lines that
correctly model elastic effects in the linear range resulting from hydrodynamic loading in a Froude-scaled model.
In the likely event that a model material cannot be found to exactly
match the requirement of Eqn. 5.58, choose a material that comes close in
order to minimize elastic scale effects. For example, if the mooring lines
are heavy chains, it is more important to correctly scale the weight of
the chain rather than its elastic properties. Conversely, lightweight highly
elastic mooring lines should be modeled to reproduce the elastic, elongation
properties of the mooring line because nonsimilitude of mooring line weight
will have a minor impact (Hudson, et al. 1979).
Example 5.2. Scaling Elastic Mooring Lines
A geometrically undistorted model using fresh water has been constructed at a
scale of Nl = 75 to simulate an actual salt-water harbor. It is proposed that the
model be used to study moored ship motions. The primary consideration for modeling is that the hydrodynamic forces acting on the ship and the elastic forces in
the mooring line be in similitude. Assume that the mooring lines in the prototype
and model will have linear behavior, and neglect viscous effects on the model ship
CHAPTER 5. COASTAL STRUCTURE MODELS
The elastic properties of the mooring system are modeled according to
the Cauchy scale criterion which states that the ratio of inertia forces to
elastic forces must be the same in prototype and model. Representing the
elastic force, Fe, as the modulus of elasticity, E, times the cross-sectional
area of the mooring line, A, the Cauchy criterion gives (in the linear elastic
range)
(Fe)p = (EA)P
(FB)m
(EA)m
or in terms of scale ratios
NFe = Ne Na
(5.56)
(5.57)
The elastic force scale must be the same as the mooring line weight
scale (and the hydrodynamic force scale). Equating the Froude criterion
of Eqn. 5.55 with the Cauchy criterion of Eqn. 5.57 and requiring that the
mooring line be geometrically undistorted so NA = (Nl)2 yields11
The subscript, ml, in Eqn. 5.58 refers to properties of the mooring line.
(5.58)
which is the elasticity requirement for selection of model mooring lines that
correctly model elastic effects in the linear range resulting from hydrodynamic loading in a Froude-scaled model.
In the likely event that a model material cannot be found to exactly
match the requirement of Eqn. 5.58, choose a material that comes close in
order to minimize elastic scale effects. For example, if the mooring lines
are heavy chains, it is more important to correctly scale the weight of
the chain rather than its elastic properties. Conversely, lightweight highly
elastic mooring lines should be modeled to reproduce the elastic, elongation
properties of the mooring line because nonsimilitude of mooring line weight
will have a minor impact (Hudson, et al. 1979).
Example 5.2. Scaling Elastic Mooring Lines
A geometrically undistorted model using fresh water has been constructed at a
scale of Nl = 75 to simulate an actual salt-water harbor. It is proposed that the
model be used to study moored ship motions. The primary consideration for modeling is that the hydrodynamic forces acting on the ship and the elastic forces in
the mooring line be in similitude. Assume that the mooring lines in the prototype
and model will have linear behavior, and neglect viscous effects on the model ship