Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 4, Problem 4.14P
The question is often asked: Can an airfoil fly upside-down? To answer this, make the following calculation. Consider a positively cambered airfoil with a zero-lift angle of
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Consider a positively cambered airfoil with a zero-lift angle of −3◦. The lift slope is 0.1 per degree.
Now imagine the same airfoil turned upside-down, but at the same 5° angle of attack as part (a). Calculate the lift coefficient. (Round the final answer to one decimal place. You must provide an answer before moving on to the next part.)
The lift coefficient is ............
At what angle of attack must the upside-down airfoil be set to generate the same lift as that when it is right-side-up at a 5° angle of attack? (Round the final answer to the nearest whole number.)
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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°)
You are designing an airfoil for a new hobby RC plane. Because of your limited knowledge, you have mistakenly approximated your airfoil as an ellipse with a = 75mm and b = 12mm. Here, “a” is the depth of your wing and “b” is the thickness. Your plane travels through the air at approximately 20mph (8.9m/s). As it does so, skin friction produces a drag-induced heat of 800W on your wind, of length 1m.
Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), TInfinity = 25oC
a) What is the Reynold’s number? Hint: “D” is taken to be the thickness for an elliptical crosssection.
b) What is the Nusselt number?
c) What is the convection coefficient?
d) What is the average temperature of your wing? Assume an ellipse perimeter of approximately 200mm.
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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- You are designing an airfoil for a new hobby RC plane. Because of your limited knowledge, you have mistakenly approximated your airfoil as an ellipse with a = 75mm and b = 12mm. Here, “a” is the depth of your wing and “b” is the thickness. Your plane travels through the air at approximately 20mph (8.9m/s). As it does so, skin friction produces a drag-induced heat of 800W on your wind, of length 1m. Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), TInfinity = 25oC a) What is the average temperature of your wing? Assume an ellipse perimeter of approximately 200mm.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_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_forward
- The car shown in the figure below moves at a constant speed on a highway and has a drag coefficient Cpc of 0.32 with the windows and roof closed. What is the percent increase of horsepower needed to maintain the speed if the windows and roof are then opened? With the windows and roof open, the drag coefficient increases to Cpo = 0.43. Assume the frontal area remains the same. Windows and roof closed: CD=CDc Windows open; roof open: C₂=CDoarrow_forwardA light combat aircraft weighs 75,000 N and has a wing area of 27 m?. The maximum lift coefficient with high-lift devices is 1.8, and the structural limit load factor is 6.0. While flying at 250 km/h, the aircraft makes a 90 deg turn in 8 s at sea level holding a constant altitude and at an angle of attack such that the lift-to-drag ratio is 8.0. Find (a) the bank angle, (b) load factor, (c) radius of turn, and (d) the thrust required. [Answer: (a) µ = 54.26 deg, (b) n = 1.7120, (c) R %3D 353.7665 m, and (d) T = 16,050 N.)arrow_forwardFor 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_forward
- A NACA 2412 airfoil with a chord of 0.64m is flying in an airstream of standard sea level conditions. The freestream velocity is 70 m/s. Given the lift per unit span is 1,254 N/m. By using the experimental data for NACA 2412 data plot in Figure Q1c, investigatethe angle of attack of the airfoil and the analyze the value of drag per unit spanof the airfoil. Given that at standard sea level, ?=1.789×10-5 kg/m.s.arrow_forwardHelp me pleasearrow_forwardThe drag polar equation of a light airplane in clean configuration can be written as Cp = 0.358 + 0.0405 C₁². It has a weight of 18,681 N. The wing area is 14.41 m². Calculate the minimum power required in watts. (Round off answer with no decimal places, No units, No commas) Answer given: 1461792 A 5,000 lbs. aircraft has an excess power of 75 hp at sea level. If the service ceiling is 3,657.6 m, determine the time to climb from sea level to absolute ceiling in minutes. (Round off answer with no decimal places. No units, No commas) Answer given: 17arrow_forward
- For the shown continuously circular (i.e. not parabolic) arc airfoil with sharp corners of each 8 = 5°, at 0° angle of attack with Mo = 3 and assuming steady, two-dimensional flow, calculate the: a) pressure coefficient distribution; b) lift coefficient; c) drag coefficient. Moo 8 ********* 8arrow_forward6. For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is (where CL is the lift coefficient) (b) TAR CL 2TAR (d) TAR2 (a) TAR 7. Laminar flow airfoil is used to reduce the (a) pressure drag (b) induced drag (c) skin friction drag (d) wave drag 8. Set the aerofoil your chosen angle of incidence is gives a good installed pressure distribution. (a) twelve degree (b) ten degree (c) eight degree 9. The critical Mach number for a thick airfoil will be (a) lesser than a thin airfoil. (b) greater than a thin airfoil. (c) equal to a thin airfoil. (d) cannot be related to thin airfoil 10. What is the dimension for Lift coefficient? (a) N/s (b) kg/N (c) Dimensionlessarrow_forward2. The table below shows experimental data for the shape and pressure distribution on the upper and lower surface of an airfoil at zero angle of attack. X 0 0.25 0.5 0.75 1 Y Fx = Yu 0 0.0952 0.0922 0.0588 0 (Pu dYu dx - Calculate the drag and lift force on the airfoil by numerically evaluating the integrals Fy (P₁-P₂)dx = √ ( P₁ - 1 Pi Y₁ 0 -0.0254 -0.0144 -0.0052 0 dv) Y = Yu (x) dx y = Ye (x) Pu 1.000 -1.640 -0.786 -0.212 0 x Pi 1.000 0.589 0.426 0.322 0 Use finite difference approximations of the derivatives and the composite Simpson's rule to evaluate the integrals. Hint: Use central differences to estimate the derivatives wherever possible since they are more accurate than forward or backward differences.arrow_forward
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