Str^m-Tejsen and Chislett 



airfoil having an oscillatory angle of attack. Waves generated as a result of the 

 oscillatory motions of the model (independent of the tank boundaries) and reflec- 

 tions of such waves from the tank walls are two other sources of differences. 



Since such effects, while repeatable, are frequency dependent, they can be 

 assessed by comparing force measurements made at different frequencies, the 

 agreement of which may safely be assumed to preclude the possibility of sig- 

 nificant unsteady-flow effects. 



The results of "pure sway" tests and "pure yaw" tests previously reported 

 (Figs. 4 and 5 and Tables 7 and 8 of Ref. 5), showed that forces resulting from 

 yaw velocity, yaw acceleration, and sway acceleration are quite independent of 

 frequency of oscillation, within the low-frequency range used during the tests. 

 Forces resulting from sway velocity, i.e., drift angle, were found to vary with 

 frequency but to approach the steady-state results of the "static -drift-angle" 

 test as frequency tended to zero. 



Higher Order Frequencies 



The periodic motions generated by the HyA planar -motion mechanism are 

 of almost perfect sine and cosine character, and so during a given run the re- 

 sulting hydrodynamic forces at the Y gauges must necessarily be of the same 

 frequency as the motions. There are no grounds to expect periodic forces hav- 

 ing frequencies which are integer multiples of the frequency of oscillation, as 

 opposed, for example, to analyses of fluctuating thrust and torque in a propeller 

 shaft, when integer multiples of the basic shaft frequency would depend on num- 

 ber of blades, deadwood, etc. It is not therefore considered a disadvantage of 

 the synchronous -switch technique for integration of periodic forces, that the 

 Oscil. program is sensitive to uneven integer multiples of the frequency of the 

 motion and insensitive to even multiples, and vice versa for the Const, program. 

 Neither is it thought helpful to consider an alternative method of integration, in 

 which the force signals are multiplied by sin cot and cos ^t, as yielding the first 

 harmonics of a Fourier analysis (13). 



No difficulties have been encountered due to vibration of the HyA towing 

 carriage and planar-motion mechanism, presumably because of their stiff con- 

 struction, which ensures that any small vibrations are of such low amplitude and 

 high frequency that the resulting high-frequency forces acting at the Y gauges 

 are negligible in comparison with the forces under investigation. 



CONCLUSIONS 



The method adopted at HyA for investigating steering and manoeuvring 

 qualities of surface ships has been described. A planar-motion mechanism sys- 

 tem is used for the experimental measurement of hydrodynamic coefficients, and 

 predictions of manoeuvres are obtained from solutions of the equations of motion 

 using a digital computer. 



The mathematical model at present in use at HyA for simulation of steering 

 and manoeuvring of surface ships is based on a third -order Taylor expansion of 



378 



