Lifting-Surface Theory of a Fully Submerged Hydrofoil

Lifting-surface theory of a fully submerged hydrofoil advanced at constant forward speed under the fixed submersion depth is developed, and then the properties of the lift and resistance are discussed in detail in relation with the effect of the Froude number. The disturbing velocity potential is, first of all, derived from the linearized condition on the free water surface. Then, from the boundary condition over the lifting surface, constructed on the Küchemann's conception, a basic integral equation is obtained for the distribution of circulation over the span, from which the lift-curve slope and the sum of the induced and wave-making resistance can be computed readily. This integral equation is solved by DeYoung and Harper's method. Comparisons of theoretical lift and resistance with the experimental data by NASA confirm the appropriateness of the construction of the present theory; and also the effects of the Froude number on the characteristics is definitely clarified. Damping and Inertia Coefficients for a Rolling or Swaying Vertical Strip 1Discussion by W. R. Porter2IN Table 2, of this paper, the author presents values of the damping constant for a vertical strip in horizontal (sway) oscillation for tabular values of nondimensional frequency. In the Addendum, he relates that another table, Table 3, was independently checked and found to vary only by 1 in the fourth decimal place. An unwary person may assume the same to be probably true for Table 2; and, therefore, the misprinted value at frequency 2.000 is hereby reported. The interval in the table at this frequency is sufficiently large that the irregular value may be otherwise undetected. Table 2 Table 3 In addition to correcting the misprint, the table as calculated by the writer at the Computation Center, MIT, presents confirmation that the original Table 2, except at 2.000, varies at most by 1 in the fourth decimal place. This new table provides entry at more closely spaced and more conventional frequencies with digit zero in the third decimal place. The new table also presents the wave-height ratio for convenience. The relation between wave-height ratio and damping constant is mentioned in the Addendum to the paper. To complete the presentation, a graph is shown here for the wave-height ratio for the vertical strip and also for the circular cylinder in horizontal (sway) oscillation as calculated by the writer. Fig. 01Wave-height ratio as a function of nondimensional frequency for vertical strip and circular cylinder in horizontal (sway) oscillation