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AERO 309 – Module 8 Homework

In this assignment, you may work in either the SI or BGS system, but you must be consistent.

1. Create the CMcg versus α plot

a. List the aircraft you have been using for the previous assignments. List the wing

area and the average wing chord. We will use the average wing chord as the

reference chord in this homework.

b. Assume that the horizontal tail area is 20% of the wing area. Calculate the tail

area St.

c. Assume that the distance from the center of gravity to the aerodynamic center of

the tail is 160% of the wing’s average chord. Calculate lt. Calculate the tail

volume VH.

d. Using a tail aspect ratio of 5 and an efficiency e1 of 0.9, calculate the lift curve

slope of the horizontal tail at. Assume that the tail airfoil has a0=0.11 /deg

e. We will assume that αL=0 for the airplane is the αL=0 of the NACA 23012 airfoil.

Using the airfoil plots in the book, what is αL=0?

f. We will assume that the aerodynamic center of the wing-body is located at 0.25c

and the center of gravity is located at 0.4c. Calculate (h-hac,wb). [Remember that h

and hac,wb are nondimensional]

g. Let us use it=-2°, ε0=0, and [∂ε] / [∂α] =0.35. We now have enough information to

plot CMcg vs α

CMcg=CMac,wb+a (α-αL=0) (h-hacwb-VH [at] / [a] (1- [∂ε] / [∂α] ) ) +VHat (it+ε0)

Use CMac,wb=0.1. The “a” in the equation is the lift curve slope of your wing (found in

Homework 5). Use Excel to plot CMcg from αL=0 to at least α=10°. [Note: the letter “a”

and the Greek letter alpha look very similar in the above equation. Make sure to

use the correct values.]

h. Calculate [∂Cm,cg] / [∂α] either through your plot or by equation. Is the aircraft

stable? Why?

i. From your plot, what is the trim angle of attack? Youmay have to extend your CMcg

plot to find the answer. Remember that trim is when CMcg=0. It is possible for there

not to be a trim point. If this is the case, explain why.

2. Now you will create the CMcg versus α plot when the CG is at 0.3c.

a. Since the CG moved, calculate the new lt and VH.

b. Use Excel to plot the new CMcg versus α. Add this plot to the one created for

problem 1.

c. From your new plot, what is [∂Cm,cg] / [∂α] for the 0.3c case. Is this new CG

location stable? Why?

d. What is the new trim angle of attack?

3. Now create the CMcg versus α plot when the CG is at 0.5c. Plot all three CG locations on

one plot. Remember that lt will also have changed when the CG moved.

a. Since the CG moved, calculate the new lt and VH.

Page 2 of 2

b. Use Excel to plot the new CMcg versus α. Add this plot to the one created for

problems 1 and 2.

c. From your new plot, what is [∂Cm,cg] / [∂α] for the 0.5c case. Is this new CG

location stable? Why?

d. What is the new trim angle of attack?

4. Using the results from problems 1 through 3

a. Using the [∂Cm,cg] / [∂α] for the three CG locations, estimate where the neutral

point is on the aircraft. Remember that at the neutral point, [∂Cm,cg] / [∂α] =0. (Hint:

use linear interpolation)

b. Find the neutral point via equation.

c. Calculate the static margin for all three CG locations.

5. Using the CG location of 0.4c, now change the it to 5° and -5°. Plot all three tail incidence

angles on one plot. While we are changing the tail incidence angle, the results are

analogous to moving an elevator up or down. What are the new trim angles of attack?

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