An Analysis of Free-running Model Trajectories of the Experimental Submarine SST

Abstract

The theoretical problem of predicting the course which a ship follows 1n response to a prescribed stern-plane or rudder motion has not been satisfactorily solved. A satisfactory solution of this problem would have considerable practical value, particularly for the motion of a submarine where "maneuverability in depth" is so important. The theory is unsatisfactory in the sense that trajectories describing the motion cannot reliably be predicted from the results of captive model tests. The commonly accepted reason for this failure is that the hydrodynamic characteristics which are determined from captive model tests are not known with sufficient precision or reliability. This reason is quite plausible in view of the discrepant results which are often obtained from different model tests of the same prototype. The present study was undertaken with the object of ascertaining whether it is possible to combine information from captive model tests with information from free-running model tests for the purpose of constructing hydrodynamic characteristics which may be introduced into differential equations of a given form, such equations being used to characterize the motion, and thus allowing one to predict new trajectories. Only hand computation methods have been used in this investigation. Although no very fixed conclusions can be drawn, it appears that more accurate free-running tests (as well as captive model tests) are required to obtain positive results. However, it is misleading to imply that nothing of value can be learned from this type of approach. One can, in fact, roughly predict some trajectories and, given enough patience, one could, perhaps, continue to modify the equations so that they fit more and more trajectories. It is known that nonlinear differential equations must be used to characterize the motion and it is, therefore, evident a priori that theoretically there must always exist some ambiguity regarding the validity of the equations. However, from a practical point of view one may say that if equations have been constructed which have as one solution a given trajectory, then these equations should be approximately valid for trajectories which are not too different, i.e., trajectories which do not involve a different type of maneuver and do not involve large differences in the magnitudes of any of the parameters which directly influence the motion.