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National Advisory Committee for Aeronautics, Report - A Theoretical and Experimental Investigation of the Lift and Drag Characteristics of Hydrofoils at Subcritical and Supercritical Speeds

A theoretical and experimental investigation at subcaoitation
speeds was made of the efiect of the free-water surface and rigid
boundaries on the lift and drag of an aspect-ratio-IO hydrofoil
at both subcritical and supercritical speeds and of an aspect-
ratio-4 hydrofoil at supercritical speeds. For the aspect-ratio-
10 hydrofoil, tests were madein Langley tank no. 1 and Langley
tank no. 2 at 0.84 and 3.84 chords submergence at subcavitation
speeds from 5 to 45 fps corresponding to Reynolds numbers
from 0.18 X 10“ to 1.64 X 10". For the aspect-ratio—4
hydrofoil, tests were made in Langley tank no. 2 at 0.59, 1.0.9,
3.0.9, 3.0.9, and 4.0.9 chords submergence at subcaoitation speeds
from 15 to 35 fps corresponding to Reynolds numbers fiom
0.873 X 106 to 2.04 X 10°.

Approximate theoretical solutions for the efiects of the free-
water surface and rigid boundaries on lift and drag at super-
critical speeds are developed. An approximate theoretical solu-
tion for the ejects of these boundaries on drag at subcritical
speeds is also presented. The agreement between theory and
easperiment at both supercritical and subcrz‘tical speeds is satis-
factory for engineering calculations of hydrofoil characteris-
tics from aerodynamic data.

The emperimental investigation indicated no appreciable
efiect of the limiting speed of warm propagation on lift-curve
slope or angle of zero lift. It also shozoed that the increase in
drag as the critical speed is approached from the supercritical
range is gradual. This result is contrary to the abrupt in—
crease at the critical speed predicted by theory.

Airfoils and hydrofoils operate in fluids which differ
principally in density and viscosity, properties that are
readily treated by the concept of Reynolds number. Since
such is true, the vast amount of aerodynamic data already
accumulated becomes available for use in predicting hydro-
foil characteristics. The airfoil, however, generally oper—
ates in an essentially infinite medium, whereas hydrofoil
applications usually require operation in a limited medium,
that is, in the proximity of the water surface. Aside from
the effects of cavitation then, the principal difference be-
tween airfoil and hydrofoil applications is one of boundaries.