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AERO 309 – Module 5 Homework

For this assignment, you will use the same aircraft from the Module 1 and 3 homework

assignments. You may work in either the SI or BGS system, but you must be consistent.

1. Using the same aircraft from the Module 1 and 3 homework assignments, provide the

following

a. The aircraft

b. The cruise altitude and the corresponding standard atmosphere values at that

altitude

c. The wing area (if you have a multi-wing aircraft, only provide the information for

one wing)

d. The average chord

e. The wing span

f. The cruise speed

g. The takeoff weight

2. Calculate the Reynolds number based on the cruise speed, cruise altitude, and average

chord.

3. Calculate the aspect ratio AR.

4. Assume that the airfoil lift curve slope a0 is 0.11 /deg and the wing efficiency e1 is 0.92.

Calculate the wing lift curve slope.

5. If the aspect ratio was 25% larger, calculate the new wing lift slope. If the aspect ratio

was 25% smaller, calculate the new wing lift slope. Explain the effect of aspect ratio on

the wing lift slope.

6. Assume that the airfoil used for your wing is the NACA 23012. From the airfoil data in the

appendix and using the Reynolds number that most closely matches the Reynolds

number from question 2, provide the following

a. The airfoil αL=0

b. The airfoil clmax

c. The airfoil αstall

7. In Excel, replot the profile drag coefficient of the airfoil cd for the NACA 23012 from a lift

coefficient of 0 to the maximum in the drag polar plot. All you are doing is reading off the

cd values from the airfoil plot, putting them in Excel, and replotting them.

8. Calculate and plot the induced drag coefficient CDi for CL=0 to the maximum CL used in the

previous question. Assume that e=e1. Plot this curve on the same figure as the previous

question. For this problem, we are going to assume that the cl in problem 7 (the airfoil cl)

is the same as the CL (wing CL) used in this problem.

9. Calculate and plot the total drag coefficient of the wing. Plot this curve on the same

figure as the previous question. Just like problem 8, we are going to assume that the cl in

problem 7 (the airfoil cl) is the same as the CL (wing CL) used in problem 8.

10. Assume that the CLmax of your wing is 90% of the clmax of the airfoil. Calculate

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a. CLmax of the wing

b. Stall speed of your aircraft at takeoff weight and at standard sea level conditions

11. Figure 5.68 in the book shows an example of how flaps change the lift curve. Use this

figure to answer the following

a. What is the ΔCL between no flaps and δ=15° at α=0?

b. What is the ΔCL between no flaps and δ=50° at α=0?

c. Assume that these ΔCLs hold for your aircraft. What is the stall speed of your

aircraft at 15° flaps and 50° flaps at takeoff weight and at standard sea level

conditions? Hint: CLmax(15% flap) =CLmax(question 10)+ΔCL(15% flap)

12. Assume a rectangular wing has a Mcr of 0.66. Plot the theoretical upper limit Mcr versus

sweep angle for sweep angles from 0 deg to 60 deg by 5 deg increments. Explain the

major penalties of sweeping wings.

13. For this question, you will be comparing a cylinder to the NACA 23012. For a cylinder,

cd=1.0 for laminar boundary layer and cd=0.25 for turbulent boundary layer. The critical

Reynolds number for a cylinder is 300,000. You must work with BGS units.

The Reynolds number of a cylinder: Re= [ρVd] / [μ]

The drag of a cylinder: D= [1] / [2] ρV2dcd

The d is the cylinder diameter

a. For a cylinder at sea level with a diameter of 18 in. that is traveling at 150 ft/s,

what is the Reynolds number? Is the boundary layer laminar or turbulent? What

is cd for this cylinder.

b. Calculate the drag of the cylinder.

c. From question 7, what is the minimum cd of the NACA 23012?

d. Using the minimum cd of the NACA 23012, what is the drag of the airfoil that is at

sea level traveling at the same velocity of the cylinder and has the same

maximum physical thickness of the cylinder? The NACA 23012 has a maximum

thickness percentage of 12%.The airfoil and the cylinder will have the same

maximum physical thickness.

e. What is the chord and physical thickness of a NACA 23012 airfoil that has the

same drag as the cylinder found in part b?

f. From parts d and e, what can you say about the importance of streamlining?