• Version
• 216 Downloads
• 1.10 MB File Size
• 1 File Count
• August 30, 2016 Create Date
• August 30, 2016 Last Updated

National Advisory Committee for Aeronautics, Report - The Theory of Propellers, III - The Slipstream Contraction with Numerical Values for Two Blade and Four Blade Propellers

As the conditions of the ultimate wake are of concern both
theoretically and practically, the magnitude of the slipstream
contraction has been calculated. It will be noted that the con-
traction in a representative case is of the order of only 1 percent
of the propeller diameter. In consequence, all calculations
need involve only first-order ejects. Ourves and tables are given
for the contraction coeficient of two—blade and four-blade pro-
pellers for various values of the advance ratio; the contraction
coeflicient is defined as the contraction in the diameter of the
wake helix in terms of the wake diameter at infinity. The
contour lines of the wake helix are also shown at four values of
the advance ratio in comparison with the contour lines for an
infinitean/umber of blades.

Since reference is often made to the wake infinitely far
behind the propeller, it is desirable to establish certain
relationships between the dimensions of the propeller and
those of the wake helix at infinity. The present paper con—
siders the relationship of the propeller diameter and the wake
diameter, or the problem of the slipstream contraction.

The discussion is restricted to a consideration of first-order
effects, that is, to the determination of the contraction per
unit of loading for infinitely small loadings only. It will be
seen that the contractions are indeed very small, of the order
of a few percent of the propeller diameter, and that the
high-order terms are therefore not of concern. The inter-
ference velocity accordingly is neglected as small compared
with the stream velocity. The wake helix lies on a perfect
cylinder and the pitch angle is everywhere the same. It is
noted that the assumption of zero loading corresponds to
that used by Goldstein for a different purpose.