Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 11, Problem 11.2P
Using the Prandtl-Glauert rule, calculate the lift coefficient for an NACA 2412 airfoil at
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The lift curve for the 4 digit NACA 2421 airfoil is shown in the Figure.
-Consider a wing with AR = 12, no sweep, and airplane flies at the Mach number equal to 0.65. The Oswald efficiency span number ?1 = 0.95 Calculate the lift slope for the finite wing. Clearly show the formula and explanations in the solution.
Compute the lift and drag coefficients for a symmetric, diamond-shaped airfoil with a
thickness-to-chord ratio t/c equal to 0.10, flying at Mach 3.5 in air (y=1.4) at zero angle of attack.
M₂ - 3.5
4. Write down the lift curve equation (lift coefficient versus angle of attack) according to the thin airfoil
theory. What is the amount of the lift curve slope for a thin airfoil ?
NACA 2412 airfoil
Eg. (4,57)
C 2.0 -
1.e
1.2
Lift coefficient
0.8
0.4
-0.4
Eg. (4,64)
-0.1
Moment
coefficient
-0.8
-0.2
-1.2
-0.3
Re - 3.1 X 10
O Re- 8.9 x 10
-0.4
16
a, degrees
de;
= ?
da
Chapter 11 Solutions
Fundamentals of Aerodynamics
Ch. 11 - Consider a subsonic compressible flow in cartesian...Ch. 11 - Using the Prandtl-Glauert rule, calculate the lift...Ch. 11 - Under low-speed incompressible flow conditions,...Ch. 11 - In low-speed incompressible flow, the peak...Ch. 11 - For a given airfoil, the critical Mach number is...Ch. 11 - Consider an airfoil in a Mach 0.5 freestream. At a...Ch. 11 - Prob. 11.7PCh. 11 - Consider the flow over a circular cylinder; the...Ch. 11 - In Problem 11.8, the critical Mach number for a...
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- Estimate the landing ground roll distance at sea level for the CJ-1. No thrust reversal is used; however, spoilers are employed such that L drag coefficient by 10 percent. The fuel tanks are essentially empty, so neglect the weight of any fuel caried by the airplane. The maximum lift coefficient, with flaps fully em- ployed at touchdown, is 2.5. 0. The spoilers increase the zero-lift,arrow_forwardThe Boeing 747 has a wingspan of 65 meters and AR of 7.7. (a)Assuming take off weight of 910,000 pounds and a take off velocity 160 knots, calculate the lift coefficient at take off for standard sea-level conditions.(b) Compare the above result with the lift coefficient for cruise at Mach number of 92% of the speed of sound.arrow_forwardWhat happens if the required CL is larger than CLmax of your airfoil, and what speed regime is usually associated with that condition?arrow_forward
- For the NACA 2412 airfoil, the lift coefficient and moment coefficient about the quarter-chord at -6° angle of attack are -0.39 and -0.045, respectively. At 4° angle of attack, these coefficients are 0.65 and -0.037, respectively. Calculate the location of the aerodynamic center. -arrow_forward1. 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.arrow_forwardConsider an NACA 2412 airfoil with a chord of 0.64 m in an airstream at standard sea level conditions. The freestream velocity is 70 m/s. The lift per unit span is 1254 N/m. Calculate the strength of the steady-state starting vortex.arrow_forward
- A given symmetrical airfoil has a lift curve slope of 6 per radian. What is the angle of attack (in degrees) corresponding to a lift coefficient of 0.4? Round off answer to the nearest tenths. (for symmetrical airfoils zero-lift angle of attack is 0°)arrow_forward6. Write down the lift curve equation (lift coefficient versus angle of attack) according to the thin airfoil theory. What is the amount of the lift curve slope for a thin airfoil ? NACA 2412 airfoil LEg. (4.57) * 2.0 1.6 1.2 Lift coefficient 0.8 0.4 -0.4 Eg. (4,64) --0.1 Moment coefficient -0.8- -1.2 -0.3 • Re -3.1 X 10 O Re -8.9 X 10 L-0.4 -8 16 24 a, degrees dc =? daarrow_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_forward
- Consider 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 the NACA 2412 airfoil, data for which is given in 4.10 and 4.11. The data are given for two values of the Reynolds number based on chord length. For the case where Rec = 3.1×106, estimate: (a) the laminar boundary layer thickness at the trailing edge for a chord length of 1.5 m and (b) the net laminar skin-friction drag coefficient for the airfoil.arrow_forwardAir 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°.arrow_forward
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