Question 10.24: Figure 10.30b illustrates the effects of flaps (no flap, sin...

(a)–(b) The minimum takeoff and landing speed was determined in Example Problem 10.23 above. Furthermore, the maximum lift coefficient at takeoff and landing was read from Figure 10.30a for the given angle of attack of 10^{\circ } in Example Problem 10.23 above. The lift force must equal the weight of the aircraft at takeoff and landing (see Example Problem 10.23 above). The drag force is determined by applying Equation 10.12 F_{D} = C_{D} \frac{1}{2} \rho v^{2}A , and the drag coefficient, C_{D} is determined from Figure 10.30b for the corresponding lift coefficient, C_{L} .
(a) The drag force during takeoff and landing for wings with no flaps is determined as follows:

slug: = 1 lb \frac{sec^{2}}{ft}                                   b: = 25 ft                               c: = 20 ft                               A_{plan}: = 2.b.c = 1 \times 10^{3} ft^{2}

\rho : = 0.0023768 \frac{slug}{ft^{3}}                               \alpha : = 10deg                               W: = 30000 lb                               F_{Lmin}: = W = 3 \times 10^{4} lb

C_{Lmax}: = 1.25                               C_{Dmax}: = 0.04                               V_{min}: = 96.893 mph = 142.11 \frac{ft}{s}

Guess value:                              F_{Dmin}: = 100 lb

Given

F_{Dmin} = C_{Dmax} \frac{1}{2} \rho .V_{min}^{2} . A_{plan}
F_{Dmin}  =Find (F_{Dmin}) = 959.998 lb

(b) The drag force during takeoff and landing for wings with slotted flaps is determined as follows:

C_{Lmax}: = 2.5                               C_{Dmax}: = 0.075                               V_{min}: = 68.514 mph = 100.487 \frac{ft}{s}

Guess value:                              F_{Dmin}: = 100 lb

Given

F_{Dmin} = C_{Dmax} \frac{1}{2} \rho .V_{min}^{2} . A_{plan}
F_{Dmin}  =Find (F_{Dmin}) = 900.006 lb

Therefore, although for the given angle of attack, α of 10^{\circ } , the use of slotted flaps increases the drag coefficient, C_{D} from 0.04 to 0.075, the corresponding drag force, F_{D} actually decreases from 959.998 lb to 900.006 lbs. The decrease in the drag force, F_{D} is due to a corresponding decrease in the minimum takeoff and landing speed from 96.893 mph to 68.514 mph, as the drag force is directly proportional to v^{2}_{min} .

FIGURE 10.30
(a) Variation of the lift coefficient, C_{L} with the angle of attack, α for an airfoil with no flap, single-slotted flap, and double-slotted flap. (Adapted from Abbott, I. H., and A. E., von Doenhoff, Theory of Wing Sections, including a Summary of Airfoil Data, Dover, New York, 1959.) (b) The effects of flaps (no flap, single-slotted flap, and double-slotted flap) simultaneously on the lift coefficient, C_{L} and the drag coefficient, C_{D} for an air foil. (Adapted from Abbott, I. H., and A. E., von Doenhoff, Theory of Wing Sections, including a Summary of Airfoil Data, Dover, New York, 1959.)