moment coefficient is due to the moment of the induced-drag
distribution
,_b12
= !
J
"
....
°.
°L_._.
Cni
Sb_
18o y dy
-b/2
A
_
_i
:_
b Z-8_ d
i
r-i
k,,
/c_c
:
Om
18o
(2l)

20
NACA TN No. 1269
The induced-yawing-moment
coefficient for an antisymmetrical
lift
distribution is equal to zero and has little meaning inasmuch as
the lift coefficient is also zero.
The induced-yawing-moment
coefficient is a f'_nction of the lift and rolllng-_T_oment coefficients
and must be found for asymmetrical lift distributions.
?rofile-yawing-moment
coefficient.- The profile-yawing-
moment coefficient is due to the moment of the profile-drag
distribution,
1
,[
b/2
= --
CdoCY dy
Cno
St
U-b/2
r-i
_---
(CdoC)
)-- --T,m
m=!
APPLICATION OF METHOD USING NONLINEAR SECTION LIFT DATA
FOR SYMMETRICAL LIFT DISTRIBUTIONS
(22)
The method described is applied herein to a wing, the geometric
characteristics
of which arm given in table IV. Only symmetrical
lift distributions are considered hereinafter inasmuch as these
are believed to be sufficient for illustrating the method of
calculation.
The lift, profile-drag, and pltching-moment
coefficients
for the various wing sections along the span were derived from
unpublished airfoil data obtained in the Langley two-dimensional
low-turbulence
pressure tunnel.
The original a_rfoil data were
cross-plotted against Reynolds number and thickness ratio inasmuch
as both varied along the span of the wing.
Sample curves are given
in figures 1 and 2. From these plots the section characteristics
at the various spanwise stations were determined and plotted in the
conventional manner.
(See fig. 3.) The edge-velocity factor
E,
derived in reference 9 for an elliptic wing, has been applied to
the section angle of attaok for each value of section lift coefficient
as follows:

NACA TN No. 1269
21
c% = E(C_o-_tQl+
°'_o,,
lift Distribution
Computation
of the lift distribution
at an angle of attack
of 3° is shown in table V.
This table is designed
to be used wl_ere
the multiplication
is done by means
of a slide rule or simple
calculating
machine°
_lere
calculating
machines
capable
of performing
accumulative
multiplication
are available,
the si_aces for the
individual
products
in cohnnns
(6) to (15) may be omitted
and tl_
table made smaller.
(See tables
VII and VIII.)
The mechanics
of
computing
are explained
in the table;
however,
the method
for
approximating
the lift coefficient
distribution
requires
some
explanation.
The initially
assm,_ed lift-coefficlent
distribution
(column
(3) of first division)
can be taken as the d_stributlon
given by the geometric
angles
of attack
but it is best determined
by some simple method
which will give a close approxiy._atlon to the
actual
distribution.
The initial
distribution
given in table V
was approximated
by
!
t
cz =
A
l-
cZ( )
A + 1.8 2
_c
where
c_(_)
is the lift coefficient
read from the section
curves
for the geometric
angles
of attack.
This equation
weights
the lift
dlstrib_tion
according
to the average
of the chord distribution
of
the wing under consideretlon
and thst of an elliptical
wing of the
same aspect
ratio and s_an.
_.._enthe lift distributions
at several
angles