Wave Analysis of Simple Hull Forms

Effects of Frameline Forms (The Second Report)

Abstract

The resultant of bow and stern waves of Model M 8 (L=2 m), the proto-type of the Series II i. c. the Frameline Series is wave-analyzed.
As the preliminary step of analysis, careful investigation is carried out with respect to the probable errors which are involved in the well-known procedure of Newman Sharma's longitudinal cut method.
First, Newman's truncation formula is found as not valid except y=0, where the elementary wave number k (θ) exactly equals to K₀=g/V².
This fact is of great importance because Newman-Sharma's method has its original basis on the asymptotic expression for the free wave system at the infinite distance (y=∞).
Secondly, the reduplicability of the amplitude function is examined at several Frounde numbers with respect to M 8 for an ideal fluid, where a finite length of “calculated” wave profiles at the center-line cut (y=0) is adopted. Coincidence is satisfactory except the transverse wave range (θ=0°20°) at hump speeds such as K₀L=14 and 10.
This suggests that the truncation error is much more important than the effect of finite transverse separation (y). Demonstration is also given as to the relation between the magnitude of truncation error and the longitudinal distance (x) behind the model, or more exactly, with the radial cut angle Θ.
In consideration of these theoretical results, the experiment was carried out not only in the small tank (b=3. 5 m, Ti. of Tokyo) but also in the large tank (b=18 m, S. R. I. No. 2 Tank).
Four parallel cut lines y/l =O.5, 1.0, 1.5 and 2.0 are adopted, which as a whole give a satisfactory coincidence in the “measured” amplitude function as well as in the “measured” wave resistance.
However a remarkable discrepancy is also observed between “measured” and “calculated” wave amplitude, particularly in the smaller range of θ or the transverse wave component, i. e. a serious reduction of amplitude combined with a clear phase-shift toward smaller value of θ.
Besides viscosity effects on the stern wave system, some invicid causes like non-linear effects as well as sheltering effects may also be suggested for this discrepancy.