Posted: September 11th, 2023
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AERO 309 – Module 4 Homework
1. In the book and presentations, we used dimensional analysis to derive the expression
L=q∞Scl. Now use dimensional analysis to derive M=q∞Sccm.
2. Use the following airfoils from the back of the book: NACA 1412, NACA 2412, NACA
4412, NACA 0006, and NACA 0009. For this question, use the airfoil data that is closest
to a Reynolds number of 6 million. Make sure you are using the correct curve. DO NOT
use the “Standard roughness” or flap curves.
a. For each airfoil, what is the maximum percent camber, the location of the
maximum camber, and the maximum percent thickness?
b. Using the airfoil data in the back of the book, what is the αL=0, cl at α=0, and cm at
α=0 for each airfoil?
c. From the information in (b), what can you say about the effect of camber? What is
special about the lift and moment for the symmetric airfoils?
d. For the symmetric airfoils, use the data in the back of the book to find clmax and
e. From the information in (d), what is the effect of thickness on the lift curve?
3. Use the provided pressure coefficient distribution and Excel
a. Plot the Cp distribution. Make sure to use the convention where the Cp axis is
flipped (i.e. the negative Cp values are above the x-axis). Include your name in the
b. Find the minimum (most negative) Cp value.
c. Use the trapezoidal rule to find cl. Since the chord length in the provided
distribution is 1, the integral to find cl is simplified. cl=∫01Cp,l dx-∫01Cp,u dx
d. Explain the steps you took in (c) in using the trapezoidal rule to find cl
4. Using the minimum Cp from the last question and Excel
a. Let the minimum Cp from earlier be Cp,0. Use the Prandtl-Glauert rule to plot Cp
from M∞=0 to M∞=0.8 with a maximum interval of ΔM=0.01. Include your name in the
b. On the same plot, add the Cp,cr equation from the book and presentation from
M∞=0.4 to M∞=0.8
c. From the plot, what is Mcr and Cp,cr of the airfoil (to the closest 0.01 Mach)?
5. Reduce the magnitude of the minimum Cp from the previous question by 30% (multiply by
0.7). Now use the iterative method to find Mcr and Cp,cr
6. Assume you have a supersonic airfoil at M∞=1.75
a. If the airfoil has the same cl as the one you found in question 3, what is the angle
of attack α in radians and degrees?
b. What is the wave drag coefficient cdw?
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