LIFT DUE TO SLIPSTREAM
The method of Smelt and Davies (1937) can be used to estimate the added wing lift due to the slipstream. It is given by
ACL = s(XCLo – 0.6а0в)
Dx = diameter of slipstream at the wing C. P.
= Щ1 + a)/( 1 + s)]1/2 c = wing chord on center line of slipstream
Figure B.7,2 Variation of Ск^ with blade angle. (From NACA Wartime Rept. L-25, 1944, by H. S. Ribner.)
Side-force factor, SFF
Figure B.7,3 Ratio of normal force derivatives. (From NACA Wartime Rept. L-25, 1944, by H. S. Ribner.)
Distance behind root quarter-chord point, root chords
Figure B.7,4 Value of 1 — de/da on longitudinal axis of elliptic wing for aspect ratios 6, 9, and 12. (From NACA Wartime Rept. L-25, 1944, by H. S. Ribner.)
S = wing area s = a + ax/(D2l4 + x2)l/2 D = propeller diameter a = -* + 1(1 + STJtt)1’2 x = distance of wing C. P. behind propeller CLq = lift coefficient at section on slipstream center line, in absence of the slipstream
a0 = two-dimensional lift-curve slope of wing section
0 = angle of downwash of slipstream at wing C. P. calculated from the equation
1/008 = 0.016jc/£> + 1/0O08
0O = аф/( l + a)
ф = angle between propellor axis and direction of motion. A is an empirical constant given in Fig. B.7,5.
B.8 Wing Pitching Derivative Cmq
The method of USAF Datcom for estimating this derivative for a rigid wing in subsonic flow is as follows. The low-speed value (M = 0.2) of Cmq is given by
C, is the wing section lift curve slope from Sec. В. 1 (per rad). Ac/4 is the sweepback angle of the wing chord line.
A3 tan2 Л..М 3
——————– 1- —
AB + 6 cos Лс/4 В
A3 tan2 A£./4
———— — + 3
A + 6 cos Лс/4
For higher subsonic speeds the derivative is obtained by applying an approximate compressibility correction.
where A is aspect ratio, and
В = V1 — M2 cos2 Лс/4 (В.8,3)
В. 9 Wing Sideslip Derivatives Clp, Cnp
The methods that follow are simplified versions of those given in USAF Datcom. They apply to rigid straight-tapered wings in subsonic flow.
The derivative Clp.
For A > 1.0:
For A < 1.0:
(^7/i j is the wing-sweep contribution obtained from Fig. B.9,1.
CL / Л.-/2
KMa is the compressibility correction to the sweep contribution, obtained
from Fig. B.9,2.
/ is the aspect-ratio contribution, including taper-ratio effects, ob-
CL JA tained from Fig. B.9,3.
—— is the dihedral effect for uniform geometric dihedral, obtained from
Г Fig. B.9,4.
Г is the dihedral angle in degrees.
KM is the compressibility correction factor to the uniform-geometric-di
hedral effect, obtained from Fig. B.9,5.
is the wing-twist correction factor, obtained from Fig. B.9,6.
is the wing-twist between the root and tip stations, negative for washout (see Fig. B.9,6). is the sweepback angle of the midchord line, is the sweepback angle of the chord line.
(СпЛ _ ( A + 4 cos Ac/4 IA2B2 + 4AB cos Лс/4 – 8 cos2 Лс/4 у СП0
СІ /м ЛВ + 4 cos Лс/4 Д А2 + 4А cos Лс/4 – 8 cos2 Лс/4 j С )low speed
where В is given by (B.8,3).