Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.14P
Consider a diamond-wedge airfoil such as shown in Figure 9.36, with a half-angle
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Consider the same Lockheed F-104 supersonic fighter shown, with the same flight conditions of Mach 2 at an altitude of 11 km. For these conditions the wing angle of attack is α = 0.035 rad = 1.98◦. Assume the chord length of the airfoil is 2.2 m, which is approximately the mean chord length for the wing. Also, assume fully turbulent flow over the airfoil. Calculate: (a) the airfoil skin friction drag coefficient, and (b) the airfoil wave-drag coefficient. Compare the two values of drag.
1. A flat plate airfoil with a chord length of 1 m and a width of 6 m is required to generate a lift of 40, 000 N when flying in air at a Mach number of 2.0, a temperature of −20°C and a pressure of 105 P a. What is the required angle of attack? What is the wave drag at this angle of attack? 2. A symmetrical diamond-shaped airfoil is placed at an angle of attack of 2° in a flow at Mach 2 and static pressure of 2×103 P a. The half-angle at the leading and trailing edges is 3° . If its total surface area (top and bottom) is 4 m2 , find the forces due to lift and wave drag acting on the airfoil.
Air flows at Ma = 2.5 past a half-wedge airfoil whoseangles are 4°, as in Fig. Compute the lift and dragcoefficient at α equal to (a) 0° and (b) 6°.
Chapter 9 Solutions
Fundamentals of Aerodynamics
Ch. 9 - A slender missile is flying at Mach 1.5 at low...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Equation (8.80) does not hold for an oblique shock...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Consider the flow over a 22.2 half-angle wedge. If...Ch. 9 - Consider a flat plate at an angle of attack a to a...Ch. 9 - A 30.2 half-angle wedge is inserted into a...Ch. 9 - Consider a Mach 4 airflow at a pressure of 1 atm....Ch. 9 - Consider an oblique shock generated at a...Ch. 9 - Consider the supersonic flow over an expansion...
Ch. 9 - A supersonic flow at M1=1.58 and p1=1atm expands...Ch. 9 - A supersonic flow at M1=3,T1=285K, and p1=1atm is...Ch. 9 - Consider an infinitely thin flat plate at an angle...Ch. 9 - Consider a diamond-wedge airfoil such as shown in...Ch. 9 - Consider sonic flow. Calculate the maximum...Ch. 9 - Consider a circular cylinder (oriented with its...Ch. 9 - Consider the supersonic flow over a flat plate at...Ch. 9 - (The purpose of this problem is to calculate a...Ch. 9 - Repeat Problem 9.18, except with =30. Again, we...Ch. 9 - Consider a Mach 3 flow at 1 atm pressure initially...Ch. 9 - The purpose of this problem is to explain what...
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- Consider an airfoil at 12◦ angle of attack. The normal and axial forcecoefficients are 1.2 and 0.03, respectively. Calculate the lift and dragcoefficients.arrow_forwardA straight-tapered flying-wing aircraft has the following characteristics: span, 20 ft; area, 100 ft2 ; root chord, 6 ft; tip chord, 4 ft; leading-edge sweep angle, 40 deg; sweep angle of line of maximum thickness, 24 deg; and Airfoil NACA 2412. Determine the wing's lift-curve slope and induced drag k value. Assume the flight Mach number is 0.25 in standard sea-level conditions.arrow_forwardThe NACA 64(l)–412 airfoil has a lift-to-drag ratio of 50 at 0° angle of attack. At what angle of attack does this ratio increase to 80?arrow_forward
- Consider Mach 4 flow at standard sea level conditions over a flat plateof chord 5 in. Assuming all laminar flow and adiabatic wall conditions,calculate the skin-friction drag on the plate per unit span.arrow_forwarda)What is the impact of increasing Reynolds number on skin friction and pressure drags over an airfoil? What can be happened for separation in this case? b) What is an adverse pressure gradient and where does it occur on an airfoil (show that on a sketch)? c) Why lift-to-drag ratio is an important parameter for an aircraft? d)How can changing in altitude affect the aircraft power required, PR? Show thatmathematically and graphically?arrow_forwardCalculate the lift and drag coefficiens for a flat plate at a 5◦ angle of attack in a Mach 3 flow.arrow_forward
- Consider Mach 4 flow at standard sea level conditions over a flat plateof chord 5 in. Assuming all turbulent flow and adiabatic wall conditions,calculate the skin-friction drag on the plate per unit span.arrow_forwardConsider the NACA 2412 airfoil discussed . The airfoil is flying at a velocity of 60 m/s at a standard altitude of 3 km . The chord length of the airfoil is 2 m. Calculate the lift per unit span when the angle of attack is 4◦.arrow_forwardConsider a circular cylinder in a hypersonic flow, with its axisperpendicular to the flow. Let φ be the angle measured between radiidrawn to the leading edge (the stagnation point) and to any arbitrary pointon the cylinder. The pressure coefficient distribution along the cylindricalsurface is given by Cp = 2 cos2 φ for 0 ≤ φ ≤ π/2 and 3π/2 ≤ φ ≤ 2πand Cp = 0 for π/2 ≤ φ ≤ 3π/2. Calculate the drag coefficient for thecylinder, based on projected frontal area of the cylinder.arrow_forward
- Consider a diamond-wedge airfoil such as shown , with ahalf-angle ε = 10◦. The airfoil is at an angle of attack α = 15◦ to a Mach3 freestream. Using linear theory, calculate the lift and wave-dragcoefficients for the airfoil. Compare these approximate results with thosefrom the exact shock-expansion theory obtained.arrow_forwardCalculate the lift and moment coefficients using thin airfoil theory approximations for a range of angle of attacks for the following airfoils below. 1. NACA 0008 2. NACA 0018 3. AG04 4. Clark-Y 5. NACA 2415 Angle of attacks taken to be between 0 degree to 15 degree. Also calculate value of Cm at quarter chord. (Cm at 0.25c) for each. Reynolds number 1000000arrow_forwardConsider a wedge with a 15◦ half angle in a Mach 5 flow, as sketched. Calculate the drag coefficient for this wedge. (Assume that the pressure over the base is equal to freestream static pressure, as shownarrow_forward
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