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A theoretical method is derived for predicting trim angle and speed coefficient at the inception of propoising of prismatic planing hulls. Although equations are derived for the surge, pitch, and heave degrees of freedom, it is seen that the effect of surge is small at ordinary operating trim angles. Comparisons of theoretical predictions with existing experimental data on coupled pitch and heave porpoising show reasonably good agreement for a wide range of speed coefficients, load coefficients, and deadrise angles. The theory may also be used for estimating the natural frequencies and damping characteristics of prismatic hulls in the stable, high-speed planing range.

Both theoretical and ezpermental studies of wave effects In isolation mounts have been made. From the standpoint of vibration isolation, wave effects are important in the mse that the vibration isolating properties of a mount are changed by their presence. The wel-known "lumped parameter" theory of vibration mounts predicts that the vibration isolation of a mount increases at 12 db per octave for frequencies weU above the resonant frequency of the spring-mass system. This theory holds true only when the wavelength of the elastic wave in the mount is large compared to the dimensions of the mount. Standing waves occur, as would be epected, which in certain frequency ranges decrease the vibration isolation properties of the mount by as much as 20 db. For practical mounts, wave effects are most detrimental in the most audible frequency range (500 to 1000 cps). The theoretical and euperimental treatments are in good agreement, and indicate various methods for improving the vibration isolation properties of the mount. Experimental data concerning isolation mounts fabricated of various materials are proented.

A theoretical method is derived for predicting the linearized response characteristics of constant deadrise high-speed planing boats in head and following waves. Comparisons of the theoretical predictions of the pitch and heave response amplitude operators and phase angles with existing experimental data show reasonably good agreement for a wide variety of conditions of interest. It appears that nonlinear effects are more severe at a speed to length ratio of 6 than of, say, 4 or less, principally because of the reduction of the damping ratio of the boat with increasing speed, and the consequent increase in motions in the vicinity of the resonant encounter frequency. However, it is concluded that the linear theory can provide a simple and fast means of determining the effect of various parameters such as trim angle, deadrise, loading, and speed on the damping, natural frequency, and linearized response in waves, and that this can furnish valuable insight into the actual boat dynamics, even though the accurate predictions of large motions and peak accelerations would require a nonlinear analysis.

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