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Chapter 9: Problem 111

A Boeing 747 aircraft weighing 580,000 lb when loaded with fuel and 100 passengers takes off with an airspeed of 140 mph. With the same configuration (i.e., angle of attack, flap settings, etc.), what is its takeoff speed if it is loaded with 372 passengers? Assume each passenger with luggage weighs $200 \mathrm{lb}$.

Short Answer

Expert verified
The takeoff speed of a Boeing 747 loaded with fuel and 372 passengers assuming each passenger with luggage weighs 200 lb is approximately 148.4 mph.

Step by step solution

01

Identify given variables

Identify and list down all the given variables in the problem: The weight of the Boeing 747 aircraft loaded with fuel and 100 passengers is 580,000 lb, its takeoff airspeed is 140 mph, and each passenger with luggage weighs 200 lb.
02

Calculate total initial weight

Calculate the total initial weight by subtracting the weight of 100 passengers from the total aircraft weight. This can be done by multiplying the number of passengers (100) by the weight of each passenger (200 lb): Weight without passengers = total aircraft weight - (number of passengers * weight per passenger) = 580,000 lb - (100 * 200 lb) = 560,000 lb.
03

Calculate total weight with 372 passengers

Calculate the total weight when the aircraft is loaded with 372 passengers: Total weight with 372 passengers = weight without passengers + (number of new passengers * weight per passenger) = 560,000 lb + (372 * 200 lb) = 614,400 lb.
04

Determine proportionality factor

Determine the factor by which the weight has increased: weight increase factor = total weight with 372 passengers / total weight with 100 passengers = 614,400 lb / 580,000 lb = 1.06.
05

Calculate takeoff speed with increased weight

Using the weight increase factor obtained, calculate the takeoff speed when the aircraft is loaded with 372 passengers assuming that takeoff speed and weight are directly proportional: new takeoff speed = initial takeoff speed * weight increase factor = 140 mph * 1.06 = 148.4 mph.

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