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National Advisory Committee for Aeronautics, Technical Notes - Normal Component of Induced Velocity in the Vicinity of a Lifting Rotor with a Nonuniform Disk Loading

Part I presents a method for computing, from available calculations
for uniform disk loading, the effect of nonuniform circularly summetrical
disk loading on the normal comp0nent of induced velocity in the vicinity
of a lifting rotor. Charts of the normal component of induced velocity
are given for the longitudinal plane of symmetry and for the major axes
of rotors with two different,_nonuniform_circularly symmetrical disk
load distributions. It is shown that the normal component of induced
velocity must be zero at the center of any practical rotor.

A comparison of the results of this paper with those for a uniform
disk loading shows that nonuniform disk loading has a powerful effect
on the induced velocity distribution.and that it must be taken into
account in estimating-the effect of the rotor on most components of an
aircraft.

Part II develops certain symmetry relations for the induced veloc-
ities in the plane of a uniformly loaded rotor and also develops relations
between the radial load distribution of the rotor and the radial varia—
tion of induced velocities in.the wake.

Recent rotary—wing designs incorporate tails for increased s+ibility
and auxiliary wings for improved forward—flight performance. Any estimate
of the behavior of the complete aircraft depends upon a knowledge of the
flow induced by the rotor in the neighborhood of these auxiliary lifting
surfaces. Such information is relatively meager. The only available
analytical treatment is that of reference 1, which calculates the normal
component of induced velocity of a uniformly loaded lifting rotor along
its major axes and in its longitudinal plane of symmetry. Although the
assumption of uniform.disk loading and the fact that the calculations
were made for only one plane are obvious limitations of reference.l, it
was nevertheless hoped that the results would give useful indications
of the downwash over small-span auxiliary lifting surfaces.