(2) A Boeing 747 weighs W = 3.5 X 10 6 newtons (~400 tons) and has wing area S =
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Question
(2) A Boeing 747 weighs W = 3.5 X 106 newtons (~400 tons) and has wing area S = 511 m2.
What is the wing loading for a 747? Show your calculation.
W/S = Wing loading
3.5 X 106 N / 511 m2 = 6849 N/m2
What is the cruising speed for a 747 (for this and all subsequent questions, assume that the plane is cruising at an altitude where the air density is 30% that at sea level)? Show your calculation.
W is proportional to pV2S
At cruising speed, W is proportional to air density (air density here = (1.25 kg/m3)(0.30) = 0.375 kg/m3, thus weight = (3.5 X 106 N)(0.3) = 1.1 X 106 N
6849 N/m2 = 0.38V2
V2 = (6849 N/m2)/(0.38) = 1.8 X 104
V = sqrt(1.8 X 104)
= 134 m/s
(above answers provided for context to next question...)
(3) The smaller Boeing 737 weighs only 5 X 105 newtons (~50 tons).
If the 737 had been designed as an isometrically scaled down version of the 747, what would the wing loading be for the 737? Show your work (for convenience, you can consider the 747 to be around eight times the weight of the 737).
Explanation / Answer
Wing loading = weight / wing surface area
weight of Boeing 737 = 5 x 105 Newtons
Boeing 737 is isometrically scaled down version of Boeing 747
Boeing 747 is approximately 8 times heavier than Boeing 737
Wing surface area of Boeing 747 = 511 m2
Wing surface area of Boeing 737 = 511/8 = 63.8
Wing loading for Boeing 737 = 5 x 105 / 63.8
= 7352 N/m2
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