Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4, Problem 4.10P
For the NACA 2412 airfoil, the lift coefficient and moment coefficient about the quarter-chord at -6° angIe 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.
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A wing has a planform area S of 200 ft? and a total span b of 40 feet. The airfoils
are symmetric all along the span. The airfoil has a 2-D lift curve slope of 27 per
radian. The wing has a rectangular planform, and thus has zero taper. The wing
is untwisted.
a. Compute the lift coefficient C and the drag coefficient Coi at an angle of
attack of 4 degrees.
Use two terms in the series expansion for circulation.
T= 2bV,[4, sin ø + A, sin 3ø]
b. Repeat the above calculation, now with just one term T=2bVA1sino.
Compare the lift drag coefficient C and Cp values to problem #2 above.
c. Compare the results for drag coefficient from part (b) above with that for
an elliptically loaded wing at this lift coefficient.
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
The image
below is a cross-section of a Darrieus-type and
wind turbine. Find the cross Sectional moment
provided by the bottom airfoil under the following
circumstances.
Calculate the lift coefficient based on the formula
CL = 27 (α -αL=c) Assume that stall is not
occuring
The airfoil has a zero lift angle of attack of O
degrees and a sectional drag coefficient of 7x10-
-3
10 = 41-7 RPM
6 = 13 degrees
R = 188 m
V = limls
C =017 m
Airdensity = 0.91 kg/m3
Find moment in N.m
C
R
co
C
Calculate 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 1000000
Chapter 4 Solutions
Fundamentals of Aerodynamics
Ch. 4 - Consider the data for the NACA 2412 airfoil given...Ch. 4 - Consider an NACA 2412 airfoil with a 2-m chord in...Ch. 4 - Starting with the definition of circulation,...Ch. 4 - Starting with Equation (4.35), derive Equation...Ch. 4 - Consider a thin, symmetric airfoil at 1.5 angle of...Ch. 4 - The NACA 4412 airfoil has a mean camber line given...Ch. 4 - For the airfoil given in Problem 4.6, calculate...Ch. 4 - Compare the results of Problems 4.6 and 4.7 with...Ch. 4 - Starting with Equations (4.35) and (4.43), derive...Ch. 4 - For the NACA 2412 airfoil, the lift coefficient...
Ch. 4 - Consider again the NACA 2412 airfoil discussed in...Ch. 4 - For the airfoil in Problem 4.11, calculate the...Ch. 4 - In Section 3.15 we studied the case of the lifting...Ch. 4 - The question is often asked: Can an airfoil fly...Ch. 4 - The airfoil section of the wing of the British...Ch. 4 - For the conditions given in Problem 4.15, a more...
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- 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; = ? daarrow_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_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_forward
- Consider a thin, symmetric airfoil at 1.5◦ angle of attack. From the resultsof thin airfoil theory, calculate the lift coefficient and the momentcoefficient about the leading edge.arrow_forwardCompute 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 - 3.5arrow_forwardA 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_forward
- Consider an infinite wing with a NACA 1412 airfoil section and a chord length of 3 ft. The wing is at an angle of attack of 5° in an airflow velocity of 100 ft/s at standard sea-level conditions. Calculate the Reynold’s number, lift, drag, and moment about the quarter-chord per unit span. Cl = 0.67, Cmc/4 = -0.025 and Cd = 0.007Detailed solution plsarrow_forwardConsider a finite wing with an aspect ratio of 5. Assume an elliptical lift distribution. The lift slope for the airfoil section is 0.1/degree. Calculate the lift slope (in 1/rad) for a straight wing. (Round the final answer to three decimal places.) The lift slope for a straight wing is per radian.arrow_forwardEstimate 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_forward
- For a 10 deg included angle wedge at 0 deg AOA, calculate the lift and drag coefficient (Cl = 0, Cd = 0.082). Then calculate the lift and drag at AOA=4 deg (Cl = 0.16, Cd = 0.093). Let M=2.arrow_forwardA given airfoil develops a lift of 120 lb/ft at a given velocity of 120 mph under standard sea level conditions. Calculate the lift coefficient when the chord length is 9 ft. Round off answer to the nearest hundredths.arrow_forwardConsider a finite wing with an aspect ratio of 3. Assume an elliptical liftdistribution. The lift slope for the airfoil section is 0.1/degree. Calculateand compare the lift slopes for (a) a straight wing, and (b) a swept wing,with a half-chord line sweep of 45 degrees.arrow_forward
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