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AE245F07Sol1

AE245F07Sol1 - AE 245 Performance of Aircraft and...

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AE 245 Performance of Aircraft and Spacecraft Homework 1 Solutions 1. In the development of the standard atmospheric model in Chapter 2, the variation of the acceleration of gravity with altitude is ignored; that is, the acceleration of gravity is approximated as constant with altitude. Using the Newtonian gravitational model, compute the acceleration of gravity at sea level, the acceleration of gravity at 50,000 ft altitude, and the acceleration of gravity at 100,000 ft altitude. Based on these computations, describe the accuracy of this approximation. Solution: With the Newtonian gravitational model, the acceleration may be computed as a = GM E r 2 , where G = 6 . 673 × 10 - 20 km 3 kg · s 2 , M E = 5 . 974 × 10 24 kg, R E = 6 , 378 km, h is the altitude in kilometers, and r = R E + h . At sea level, h = 0 km, and a = 9 . 800 × 10 - 3 km / s 2 = 32 . 15 ft / s 2 . At h = 50 , 000 ft = 15 . 24 km, a = 9 . 753 × 10 - 3 km / s 2 = 32 . 00 ft / s 2 . At h = 100 , 000 ft = 30 . 48 km, a = 9 . 707 × 10 - 3 km / s 2 = 31 . 85 ft / s 2 . The percent change over 100 , 000 ft is - 0 . 9331%. Therefore, a constant approximation is accurate . 2. Based on the standard atmospheric model, what are the temperature, pressure, and air density at an altitude of 8,000 ft? What are the temperature, pressure, and air density at an altitude of 18,000 ft?

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