2.1 Model Scaling
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        The boat models used in this program were made to scales of 1/43, 1/32, and 1/10. For a model test to correctly simulate a full-scale event it is necessary that all the forces on the full-scale boat be scaled down by the same ratio. The important forces are the gravity forces, pressure forces, inertia forces and viscous forces. By constructing the models with the correct weight, stability and moment of inertia about the roll and pitch axes, it is possible to correctly scale all the forces except the viscous forces. Thus models can be tested at the correct Froude number (Fr ) but not at the correct Reynolds number (Re ). In a capsize event, the gravity forces, pressure forces and inertia forces predominate. Viscous forces, which largely affect skin friction drag, should have little effect on the trajectory of the boat. As a check on the possible effect of Re, similar tests were conducted on a 1/32 scale and 1/10 scale model of the same boat. No significant differences were noted. It is believed that the model tests can be used to predict the full-scale capsizing behaviour with an acceptable accuracy.

        Froude number, Fr , is the ratio of the inertial forces to the gravity forces, i.e.,

               V   
F r    = gL

where V is velocity, g is the acceleration of gravity, and L is the relevant length parameter. Dynamic similarity principles have shown that if geometric similarity is maintained, length, time, and force will scale proportionately. Thus,

Fr (full-scale) = Fr (model),  or
   
V             =             V   
Lfs                       Lm

If we define a scale factor, a , then

Lm       
     L
fs        =    a

and therefore,

V m = a V Vfs

Noting that for deep water waves L = 5.12T2 , we can show

Tm = a Tfs

Model characteristics were scaled as follows:

Length a
Area a 2
Force a 3
Displacement a3
Moment (Stability) a4
Moment of Inertia a5
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