# LIFT DUE TO SLIPSTREAM

The method of Smelt and Davies (1937)[23] can be used to estimate the added wing lift due to the slipstream. It is given by

ACL = s(XCLo – 0.6а0в)

where

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

where

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

(B.8,1)

where

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:

where

(^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.

C. ■

—— 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

(B.9,4)

where В is given by (B.8,3).