Figure 10.30a illustrates the effects of flaps (no flap, single-slotted flap, and doubleslotted flap) on the lift coefficient, CL for a range of angles of attack, α. Consider an airplane that weighs 30,000 lb with wings with aspan width of 25 ft and a chord length of 20 ft, as illustrated in

Question

Figure 10.30a illustrates the effects of flaps (no flap, single-slotted flap, and double-slotted flap) on the lift coefficient, [latex] C_{L} [/latex] for a range of angles of attack, α. Consider an airplane that weighs 30,000 lb with wings with a span width of 25 ft and achord length of 20 ft, as illustrated in Figure EP 10.23. Assume the airplane takes off and lands at sea level (air at standard atmosphere at sea level, [latex] \rho = 0.0023768 slugs/ft^{3} [/latex]) at an angle of attack of [latex] 10^{\circ } [/latex]. (a) Determine the minimum takeoff and landing speed for wings with no flaps. (b) Determine the minimum takeoff and landing speed for wings with slotted flaps.

FIGURE 10.30
(a) Variation of the lift coefficient, [latex] C_{L} [/latex] 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, [latex] C_{L} [/latex] and the drag coefficient, [latex] C_{D} [/latex] 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.)

Accepted Answer

(a)–(b) The minimum takeoff and landing speed is determined by applying Equation 10.25 [latex] F_{L,mim} = W = C_{ L,max} \frac{1}{2} ho.V^{2}_{min} . A[/latex]. The lift force must equal the weight of the aircraft at takeoff and landing. Furthermore, the maximum lift coefficient at takeoff and landing is read from Figure 10.30a for the given angle of attack of [latex] 10^{\circ } [/latex].
(a) The minimum takeoff and landing speed for wings with no flaps is determined as follows:

[latex] slug: = 1 lb \frac{sec^{2}}{ft} [/latex] [latex] b: = 25 ft [/latex] [latex] c: = 20 ft [/latex] [latex] A_{plan}: = 2.b.c = 1 imes 10^{3} ft^{2} [/latex]

[latex] ho : = 0.0023768 \frac{slug}{ft^{3}} [/latex] [latex] \alpha := 10 deg [/latex] [latex] W: = 30000 lb [/latex] [latex] F_{Lmin}: = W = 3 imes 10^{4} lb [/latex]

[latex] C_{Lmax}: = 1.25 [/latex]

Guess value: [latex] V_{min}: = 100 \frac{ft}{sec} [/latex]

Given

[latex] F_{Lmin} = C_{Lmax} \frac{1}{2} ho .V_{min}^{2} . A_{plan} [/latex]
[latex] V_{min} : =Find (V_{min}) = 142 .11 \frac{ft}{s} [/latex] [latex] V_{min} = 96.893 mph [/latex]

Furthermore, since this is not the stall speed, it does not have to be adjusted.
(b) The minimum takeoff and landing speed for wings with slotted flaps is determined as follows:

[latex] C_{Lmax} := 2.5 [/latex]

Guess value: [latex] V_{min}: = 100 \frac{ft}{sec} [/latex]

Given

[latex] F_{Lmin} = C_{Lmax} \frac{1}{2} ho .V_{min}^{2} . A_{plan} [/latex]
[latex] V_{min} : =Find (V_{min}) = 100.487 \frac{ft}{s} [/latex] [latex] V_{min} = 68.514 mph [/latex]

Furthermore, since this is not the stall speed, it does not have to be adjusted (increased). And, finally, for the given angle of attack, α of [latex] 10^{\circ } [/latex], the use of slotted flaps increases the lift coefficient, [latex] C_{L} [/latex] from 1.25 to 2.5 and thus allows a decrease in the corresponding minimum takeoff and landing speed from 96.893 mph to 68.514mph.

Question 10.23: Figure 10.30a illustrates the effects of flaps (no flap, sin...

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