Hydrofoil Motions in a Randonn Seaway 



'i^ = - V cos 6^^ . (31) 



Consider now a point where the velocity of Og is parallel to O^x^ then - o 

 and Zg = -v'e. Thus the body possesses an acceleration in the O^z^ direction 

 (centrifugal force) due to an impressed force, however, no acceleration is evi- 

 dent in the body axis component Zg. In the moving axis system (by definition) 

 there is never any component of velocity (v) along OgZg that is zg 0, hence 

 zg = 0. 



Note that no definition of displacement of Og is given with respect to its 

 own axis. Distances quoted in body axes merely serve to locate parts of the 

 body with respect to Og. To obtain displacements, velocity components in space 

 fixed axes must be integrated. 



Euler's equations take all of the above effects into account, but to ensure 

 that the results are interpreted correctly, it is recommended that the results be 

 transformed into components with respect to space fixed axes. The reverse 

 also applies and care must be taken when applying external forces to the craft. 

 These have to be correctly resolved into craft axes before substitution into the 

 equation of motion. 



The Normalised Equations 



In order to compare craft of various sizes it is convenient to normalise the 

 various parameters in the equations of motion. If this is not done, then for two 

 craft which were similar in design but different in scale size, a different trans- 

 formation law would exist between most of the sets of equivalent parameters re- 

 lating to the two craft. This comparison of results obtained for the two craft 

 would require recognition of how each variable should scale in relation to changes 

 in craft scale size. Scaling for the analog computer is also complicated if the 

 equations are not normalised. Computers operate within rather a limited volt- 

 age range so that changing the scale size of the simulated craft would involve 

 changing the voltage scaling levels within the computer for most of the problem 

 parameters. It is convenient, therefore, to make the parameters more or less 

 independent of scale size. 



Satisfactory normalising can be accomplished by dividing each parameter 

 by a reference value of that parameter to produce a set of nondimensional vari- 

 ables, the reference values being selected according to the scale size or per- 

 formance of the craft. Because differentiation in the equations is with respect 

 to time, it is necessary also to scale the time variable. 



Four reference parameters are required for the hydrofoil equations repre- 

 senting combinations of length, mass and time. They are: 



p - fluid mass density (slugs/cu ft), 



s = reference length (usually semi- span of selected foil in feet). 



619 



