Question

4-18. With no restrictions whatsoever and using the closed-form approximations of this chapter, find the time to climb, fuel used, and distance traveled for Aircraft A with C=0.95 lb/h/lb: a. From sea level to 20,000 ft From sea level to 30,000 ft b.

Answer 1

Using the work-energy principle, the time required for an airplane with engines that produce 100 MW of power to reach 250 m/s and 12.0 km altitude without air resistance can be calculated. If the airplane actually takes longer, the power and average force of air resistance can also be determined by energy and work principles.

Step-by-step explanation:

Time to Reach a Specific Speed and Altitude without Air Resistance

To find the time it would take a 1.50×105-kg airplane with engines that produce 100 MW of power to reach a speed of 250 m/s and an altitude of 12.0 km without air resistance, we can use the work-energy principle.

This principle states that the work done on the airplane by the engines will equal the airplane's change in kinetic and potential energy.

Using the Work-Energy Principle

Step 1: Calculate the kinetic energy (KE) the airplane needs to have a speed of 250 m/s.

KE = ½mv2 = ½(1.50×105 kg)(250 m/s)2.

Step 2: Calculate the potential energy (PE) needed to reach 12.0 km altitude.

PE = mgh = (1.50×105 kg)(9.81 m/s2)(12.0×103 m).

Step 3: Add KE and PE to find the total energy required.

Step 4: Divide the total energy by the power output of the engines to find the time required.

Actual Power and Air Resistance Calculation

If the airplane actually takes 900 s, we can calculate the actual power by dividing the total required energy by this time.

For the average force of air resistance when the airplane takes 1200 s, we would first find the total distance the airplane travels assuming constant acceleration and then use this distance to determine the work done against air resistance, and thus the average force.