The Aerodynamic Characteristics of Flaps

position then the corresponding change in twist near zero iift is given approximately by
C'
-- ~: .
A CL/
. .
c'
. . . . . . . . . . . . . (33)
C a 6 C
where c' is the effective chord.
On the basis of these assumptions Dent and Curtis have calculated the increment A C,,0 for
flaps of various spans and at various chordwise positions on wings of various taper ratios. Their
final formula for A C~0 takes the form
d0
AC,,o = ff2AC,,, +- ~ A,~:l-'ff~ . . . . . . . . . . . . (34)
where A C~, is the full-span pitching moment increment as defined in section 3.3 on an unswept
wing,
ff 2 is the conversion factor for part-span flaps, already discussed in sections 3.5.2.2
and 4.3.2, and shown in Fig. 14,
do is the two-dimensional lift-curve slope of the mean wing section,
/1 = tan 7 (y = angle of sweep-back),
ft, function of wing taper ratio, flap span and flap ehordwise position, shown in Figs.
27a, b, c.
The first term on the right-hand side of equation (40) represents the contribution due to the
local change of C,,o on each spanwise dement of the flapped part of the wing, the second term
represents the contribution due to the change in spanwise loading at zero lift caused by the flap.
For an unswept wing the latter term is zero.
From equation (38) we can write
+ aoA d CL:F#3 . . . . . . . . . . (35)
A C~o = ff 2A C,., 2a. " "
and using the ordinary lifting-line theory for elliptic loading, we have
Hence, we can write
d0 1
2a6 1"5
AC,.o = ff2dc,,, + ~.5 r~,Ac.~: . . . . . . . . . . . . (36)
From sections 4, '5, A Cz: is given by
=
where 2,ic:/c) is given ill Fig. 5, and Z 2(/~) is given in Fig. 6 for split and plain flaps and Fig. 7
for slotted flaps.
For flaps in the normal trailing edge position (see, for example, section 4.3)
-- A C,~, = ff ~A CL:,
where ff~ is given in Fig. 13 for split and plain flaps ; for slotted flaps see section 5.3.
For flaps not at the trailing edge we must calculate A CL': (see equation (16), section 4.1.1) and
hence A C,,', and finally apply equation (12) of section 3.5.2.1 to determine A C~,.*
Dent and Curtis 132 have compared the results of their formula with some experimental results,
and they conclude that the formula provides an acceptable guide to the magnitude of the
pitching moment change at zero lift for preliminary design purposes. A further comparison
has since been made for a number of other experimental results, and it is concluded that the
* Dent and Curtis gave curves for A C~, and ~:, deduced from split-flap data on NACA 230 sections, for use with
equation (40) ; the above procedure is, however, more in line with previous sections of this report and is more general.
25