Fundamentals of aerodynamics 6th edition anderson solutions manual 1

Fundamentals of Aerodynamics 6th Edition Anderson

Solutions Manual

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5.8 For the Wrights’ 1900 glider, AR1 = 3.5. For the Lilienthal data, AR2 = 6.48. Eq (5.70), written for the Wrights’ 1900 glider, is a1 = and for the Lilienthal data. a2 =

Hence, = We set ao = 2 Also, for the rectangular wing planform (taper ratio = 1 0) of the Wrights, from Eq 5 20 1 = 0 06 For the ogival planform with pointed tips (taper ratio = 0) for the Lilienthal data, 2 = 0.12. Thus, = = = 0 83

Hence, to apply the Lilienthal data the Wrights’ 1900 glider taking into account the difference in aspect ratio, the value of lift coefficient of 0 546 from the table should be reduced to η = (0.546)(0.83) = 0.45

The Wrights should have used η = 0.45 instead of 0.546.

(Note: We continue here Lilienthal’s use of η for the normal force coefficient, as seen in Figure 1.65. It is defined in conjunction with Eq. (1.63).)

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5.9

V∞

362

From Appendix E, at 18,500 ft, ρ∞ = 0 0013329 slug/ft3 In steady, level flight, L = W. Thus L = W = ½ ρ∞ V∞ 2 S CL or, CL = =

(a) AR = = = 5.385

=

mph = 362 = 530.9 ft/sec

The induced drag is only 4.5% of the total drag. This is no surprise because at Vmax, the lift coefficient is very small and therefore so is the induced drag coefficient.

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L = 0 128

CD,i=

the elliptical

of the Spitfire, e = 1 Thus

D,i= = (b) D = T = P/V∞ = = = 979 lb D = ½ ρ∞ V∞ 2 S CD CD = = = 0 0215

= = 0.045

All

C

From Eq. (5.62)

For

wing

C

Thus,

5 10 Since only the wing planform shape is different from that in Problem 5 9, everything else being the same, the lift coefficient and aspect ratio are the same as in Problem 5.9. Only the span efficiency factor, e, will be different. From Fig.

5 20, for a taper ratio of 0.4 and AR = 5 385, = 0 005 Thus

The value of obtained from Problem 5.9 is 0.000968. By changing the planform from an elliptical shape to a tapered wing with taper ratio 0 4, the increase in the induced drag coefficient is only 0 000973 – 0 000968 = 5 x 10-6 , or only a 0 5 percent increase This underscores that a tapered wing with a taper ratio around 0.4 is just about as aerodynamically efficient at the optimum elliptical wing shape

5 11 V∞ = 70 = 102 67 ft/sec

At standard sea level, ρ∞ = 0.002377 slug/ft3 . Thus,

e = = = 0.995 = = =

CL = =

For this low-speed case, the induced drag coefficient is much larger than in the high-speed case, 0.218 compared to 0.000968. Indeed, for an airplane flying at low speeds near stalling speed, induced drag is by far the dominant source of drag, whereas at high speeds it is only a small fraction of the total drag

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