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National Advisory Committee for Aeronautics, Report - The Normal Component of the Induced Velocity in the Vicinity of a Lifting Rotor and Some Examples of its Application

This paper presents a practical method for computing the
approximate values of the normal component of the induced
velocity at points in the flow field of a lifting rotor. Tables and
graphs of the relative magnitudes of the normal component of
the induced velocity are given for selected points in the longi—
tudinal plane of symmetry of the rotor and on the lateral rotor
axis.

A method is also presented for utilizing the tables and graphs
to determine the interference induced velocities arising from the
second rotor of a tandem- or side—by—side—rotor helicopter and
the induced flow angle at a horizontal tail plane.

This work, conducted at the Georgia Institute of Tech—
nology State Engineering Experiment Station under the
sponsorship and with the financial assistance of the National
Advisory Committee for Aeronautics, was undertaken in an
attempt to obtain a better understanding of the induced
flow in the vicinity of a lifting rotor.

Previous investigations, such as those of references 1 and 2,
demonstrated that the solution of the integral for the normal
component of the induced velocity at the center of the rotor
could be obtained in an elementary form provided certain
approximations were made as to the distribution of vorticity
in the wake. However, the value of the integral for the
induced—velocity component at an arbitrary point in the
rotor flow field cannot, in general, be expressed in terms of
elementary functions. Its numerical evaluation for a
specific case presents considerable difficulty.

De Leeuw, in reference 3, investigated the feasibility of
calculating the induced velocity at arbitrary points in the
vicinity of the rotor by an alternative method which con—
sisted of (1) numerically integrating the increments induced
by the votex ring wake elements within a given distance of
the point and (2) summing up the effect of the remainder of
the wake by an approximate integral. This approach is
quite general in that it can be applied to any wake which
can be approximated by an assemny of vortex rings. It
was found that the method afforded satisfactory accuracy
with the expenditure of a reasonable amount of efifort, since
the values of the normal induced-velocity component for
the isolated rings may be precomputed and tabulated for
repeated use.