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National Advisory Committee for Aeronautics, Report - Experimental Investigation of the Momentum Method for Determining Profile Drag

An erperimental inrestigation has been conducted in the
full-scale tunnel to determine the accuracy of the Jones and
the Beta equations for computing profile drag from total-
and static-pressure surveys in the wake of wings. Sur-
veys were made behind 6- by 36:;‘oot airfoils of the. N. A.
0. A. 000.9, 0012, and 0018 sections at zero lift and behind
the N. A. C. A. 0012 airfoil at positive lifis. The surreys
were made at various spanwise positions and at distances
behind the airfoil ranging from 0.050 to 3.00c.

The reduction of the test data by either the Jones or the
Betz equation gate profile-drag coefficients agreeing within
2 percent with those obtained by force tests at zero lift.
The variation of the profile drag determined at stations
from 0.05:: to 3.00.: behind the trailing edge was small and
the error resulting from the induced field of a lifting aidoil
did not exceed 2.5 percent at a 0;, of 1.0 and a spanuise
station of 0.78 6/2.

The use of the momentum method for the determina-
tion of profile drag has recently increased, owing mainly
to the equations developed by Betz (reference 1) and
by Jones (reference 2) by which the method has been
made applicable in the region of increased static pres-
sure close behind a body. The derivation of these
equations, which are based on the original principle
stated by Froude in 1874, requires certain assumptions.
The errors introduced by these assumptions have been
the subject of theoretical analyses (references 2 and 3),
which have set an upper limit for the errors involved
but fail to define their actual value.

The investigation reported herein was conducted to
determine experimentally the magnitude of these errors
by determining the effect of a number of variables upon
the measured drag. (See reference 4.) The necessary
wake surveys were made in the N. A. C. A. full-scale
wind tunnel behind symmetrical airfoils of three thick-
ness ratios. The effect of distance behind the airfoils
was first investigated by a comparison of drag deter-
minations made at locations ranging from 0.05:: to
3.00c behind the trailing edge.