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National Advisory Committee for Aeronautics, Technical Notes - 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 magni-
tudes of the normal component of the induced velocity are given for
selected points in the longitudinal 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-byhside—rotor helicopter and the induced flow
angle at a horizontal tail plane.

This work, conducted at the Georgia Institute of Technology State
Engineering Experiment Station under the sponsorship and with the finan—
cial 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, demon-
strated 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 ele-
mentary form provided certain approximations were made as to the distri-
bution 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 calcu—
lating the induced velocity at arbitrary points in the vicinity of the
rotor by an alternative method which consisted of (l) numerically inte—
grating the increments induced by the vortex 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 assembly of vortex rings. It was found that the method afforded
satisfactory accuracy with the expenditure of a reasonable amount of
effort, since the values of"the normal induced—velocity component for
the isolated rings may be precomputed and tabulated for repeated use.