Concept explainers
A commercial airplane has a total mass of 150.000 Ibm and a wing planform area of 1700 ft2. The plane has a cruising speed of 625 mi1 and a cruising altitude of 38.000 ft where the air density is 0.0208 Ibm/fl3. The plane has double-slotted flaps for use during takeoff and landing. but it cruises with all flaps retracted. Assuming the lift and drag characteristics of the wings can be approximated by NACA 23012, detennine (a) the minimum safe speed for takeoff and landing with and without extending the flaps. (b) the anzle of attack to cruise steadily at the cruising altitude, and (c) the power that needs to be supplied to provide enough thrust to overcome drag. Take the air density on the ground to be 0.075 Ibm/ft3.
(a)
The minimum safe speed for takeoff and landing with the flaps.
The minimum safe speed for takeoff and landing without the flaps.
Answer to Problem 101EP
The minimum safe speed for takeoff and landing with the flaps is
The minimum safe speed for takeoff and landing without the flaps is
Explanation of Solution
Given information:
The total mass of the airplane is
Write the expression for the initial velocity of the aircraft.
Here, the weight of the aircraft is
Write the expression for the final velocity of the aircraft.
Here, the lift coefficient at final state is
Write the expression for the weight of the aircraft.
Here, the mass of the airplane is
Write the expression for the safe velocity with flaps.
Write the expression for the safe velocity without flaps.
Calculation:
Substitute
Refer to Figure 15-45 titled "Effect of flaps on the lift and drag coefficient of an airfoil" to obtain maximum lift coefficient with flaps as
Substitute
Substitute
Substitute
Substitute
Conclusion:
The minimum safe speed for takeoff and landing with the flaps is
The minimum safe speed for takeoff and landing without the flaps is
(b)
The angle of attack to cruise steadily at the cruising altitude.
Answer to Problem 101EP
The angle of attack to cruise steadily at the cruising altitude is
Explanation of Solution
Write the expression for the coefficient of the lift force.
Here, the lift force is
Calculation:
The lift force is equals to weight of the airplane that is
Substitute
Refer to Figure 15-45 "Effect of flaps on the lift and drag coefficients of an airfoil" to obtain the angle of attack of a clean flap as
Conclusion:
The angle of attack to cruise steadily at the cruising altitude is
(c)
The power to be supplied to present enough thrust to overcome the drag.
Answer to Problem 101EP
The power to be supplied the enough thrust to overcome the drag is
Explanation of Solution
Write the expression for the drag force.
Here, the drag force coefficient is
Write the expression for the drag force and the velocity of the airplane.
Calculation:
Refer to Figure 15-45 "Effect of flaps on the lift and drag coefficients of an airfoil" to obtain the drag coefficient as
Substitute
Substitute
Conclusion:
The power to be supplied the enough thrust to overcome the drag is
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Chapter 11 Solutions
Fluid Mechanics: Fundamentals and Applications
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