Davis and Oates 



Forces and Moments 



In the case of the hydrofoil craft, if the foil system is considered as a 

 whole, then the foil derivatives are usually functions of more than two dependent 

 variables. However, if the foil system is divided into a number of elements, 

 then for a particular foil element the lift, drag and side forces are a function of 

 two variables only, the immersion depth and the angle of attack. These varia- 

 bles can be obtained at any instant, for a given foil element, and the forces along 

 the three body axes continuously computed. The moments about the craft e.g. 

 are then given by the product of these forces and their moment arms about the 

 e.g., the net forces and moments at the craft e.g. being obtained by a summation 

 of the forces acting on the individual foil elements. These net forces and mo- 

 ments when divided by the appropriate inertia coefficients then produce the lin- 

 ear and angular accelerations that are required in the basic Euler equations of 

 motion. 



Derivation of Forces 



The basis for computation of the forces acting on a given foil or strut ele- 

 ment is the lift- curve slope (Cl„) together with the angle of attack on that ele- 

 ment. The lift coefficient (Cl) developed being a product of Cl^ and a. The 

 lift- curve slope is a function of immersion depth (h) and aspect ratio (a) which 

 also is a function of immersion depth when the foil element is surface piercing 

 and is readily obtainable from Refs. 12, 17, 18, 19, 20 and 21. The angle of at- 

 tack experienced by a foil is due to pitch and roll, yaw and heave rates together 

 with wave orbital velocities, the actual angle of attack at any instant being de- 

 pendent upon the free stream velocity and the respective distances from the 

 craft e.g. in the x, y and z directions. 



Itnme.rs€ii Aft.a. 



Figure (iv) 



628 



