The mass, wing span, and wing aspect ratio of a Boeing 747-400 are approximately M = 400,000 kg, s = 64 m, and Λ = 7.4, respectively. What lift coefficients are needed for this aircraft to cruise at 900 km/hr at an altitude of 11 km, and land at 300 km/hr at sea level?

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Accepted Answer

For both flight conditions, the aircraft’s lift = L must balance its weight = Mg:

[latex]L=\frac{1}{2} ho U^2AC_L=\mathrm{Mg},\quad ext{ or }\quad C_L=\frac{2\mathrm{Mg}}{ ho U^2A}=\frac{2\mathrm{Mg}\Lambda}{ ho U^2s^2}[/latex],

where the final equality follows from (14.1). Using Appendix A.5, standard-atmospheric air density is 0.362 and 1.225 kg/m³ at altitudes of 11 km and sea level, respectively. Thus, the requisite lift coefficients are:

[latex]\Lambda\equiv s^2/A=s/\overline{c}[/latex], (14.1)

[latex]\left(C_L ight)_{11 \mathrm{km}}=\frac{2\left(4 imes 10^5 \mathrm{kg} ight)\left(9.81 \mathrm{ms}^{-2} ight)7.4}{\left(0.362 \mathrm{kgm} ^{-3} ight)\left(9 imes 10^5 \mathrm{m}/3600s ight)^2(64 \mathrm{m})^2}\cong0.627[/latex], and

[latex]\left(C_L ight)_{sea level}=\frac{2\left(4 imes 10^5 \mathrm{kg} ight)\left(9.81 \mathrm{ms}^{-2} ight)7.4}{\left(1.225 \mathrm{kgm} ^{-3} ight)\left(3 imes 10^5 \mathrm{m}/3600 s ight)^2(64 \mathrm{m})^2}\cong1.67[/latex].

Modern articulated wings that can change geometry in flight produce such variation in liftcoefficient with only minor changes in the aircraft fuselage’s orientation.

Question 14.2: The mass, wing span, and wing aspect ratio of a Boeing 747-4...

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