Davis and Oates 



S^ = reference area (usually the area of the selected foil in sq ft), 



v^ - reference velocity (ft/sec). 



The specific parameters required representing mass, time, and force are 

 obtained from products or divisions of the four standard parameters. 



All inertias 



Development of the Normalised Equations 



As stated earlier the forces and moments impressed on the craft are non- 

 linear functions of craft position and motion. Expressions for these forces and 

 moments in terms of hydrodynamic derivatives are subject to significant errors 

 unless high order derivatives are used. Therefore all forces are derived for 

 each foil element as functions of angle of attack and immersion depth. These 

 are the simplest functions which can describe adequately the forces developed 

 by each foil. Thus for example, the foil lift Cl at a depth h is Cl^C^q, where 

 a is the total angle of attack on the foil element due to all motions. That is 



a total = (a^+a^) radians 



where 



a^ = the reference angle of attack for a given foil in calm water, 



a^ = the "dynamic" contribution to angle of attack and represents the angle 

 between the longitudinal axis and the free stream direction, and 



h = the foil element normalised immersion depth. 



h and a are derived as follows. Consider a foil element at a longitudinal dis- 

 tance X and lateral distance y from the craft e.g. Then it can be shown that 



^^foii = ti'^o + ^^^.g. - x^ + y^ - 1^ cos <p] 



= ['^^o + ^^.g. - x^ + y0- hj (42) 



(assuming cos cp ^ 1.0 ), where 



hf^jj = the reference immersion depth of the foil [Fig. No. (iii)], 



Ah^ = the perturbation about the reference height due to heave of the com- 

 plete craft. 



620 



