Engineering Aerodynamics Homework

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AERO 309 – Module 7 Homework In this assignment, you may work in either the SI or BGS system, but you must be consistent.

1. Performance curves a. List the aircraft you have been using for the previous assignments. List your

cruise altitude and the corresponding air density value at that altitude. List the wing area (if you have a multi-wing aircraft, only provide the information for one wing). Provide your cruise speed. Provide your takeoff weight. Provide your aspect ratio. b. In the Module 5 Homework, you created a drag polar for a wing (question 9).

What is the minimum CD for your wing? Multiply this minimum CD by 4. We will use this value as the CD0 for this assignment. What is your CD0? (If your question 9 in Module 5 was incorrect, make sure to correct it before finishing this problem and

homework) c. Assuming an Oswald efficiency factor of 0.8, you can now write the equation for

the drag polar of the full aircraft

CD=CD0+ [CL2] / [πeAR] What is the drag polar equation for your aircraft? (CL is not known and is part of the equation; you are just substituting in values [CD0, e, AR] that you know.)

d. For this question, assume CL=0, so CD=CD0. At standard sea level conditions and at cruise speed, what is the drag using CD=CD0? (Your answer is a force: N or lb)

e. We will assume that a turbojet engine is used, so the thrust available can be

considered constant with respect to the velocity. For this problem, let TA at sea level equal 2.5 times the drag you calculated in part d. What is your TA at sea

level?

f. Assume that the CLmax is 1.8, calculate the stall speed of your aircraft at takeoff weight and at sea level.

g. Use Excel to plot the TA and TR curves (together on one plot) for your aircraft at sea level and at takeoff weight. Plot your TR from stall speed to just past Vmax. Use a small enough interval with V so the curve is smooth. Remember that weight

(lift) is constant. The CL will change with airspeed. In Excel, have at least the following columns: V CL CD Required T Available T

h. From your thrust curves, what is Vmin and Vmax? How did you arrive at these values?

i. Use Excel to calculate and plot the PA vs V and PR vs V curves (together on one plot) for your aircraft at sea level and at takeoff weight.

j. Repeat f-i but at standard sea level and 90% takeoff weight.

k. Repeat f-i but at cruise altitude and 90% takeoff weight. Assume that TA at altitude is directly proportional to air density. [TS is the thrust available at sea level

that you calculated in part e]

TA=TS [ρ] / [ρS]

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l. Plot all three sets of thrust curves together. Plot all three sets of power curves together. Explain the behavior of the thrust and power curves as the altitude and weight changed.

2. Gliding Flight a. Let us assume that the engine suddenly stopped while your aircraft is at cruise

altitude. What would be the best glide ratio possible for your aircraft? (Hint: you

will need to find maximum CL/CD using results in question 1 or through the equation in the textbook and lecture)

b. At what airspeed would the aircraft need to glide for the best glide ratio at cruise altitude and 90% weight?

c. Calculate the range of the aircraft if it started its glide at cruise altitude and ended at sea level

d. What is the minimum sink rate for your aircraft at cruise altitude and 90% weight? (Hint: you will need to calculate the sink rate using the results from question 1)

3. Climb

a. Find the maximum excess thrust (TA-TR) for your aircraft at sea level and takeoff weight (use your Excel data from question 1).

b. Using this maximum excess thrust, calculate the maximum climb angle

c. Find the maximum excess power (PA-PR) for your aircraft at sea level and takeoff weight.

d. Using this maximum excess power, calculate the maximum rate of climb 4. Endurance and Range. For this problem, we will assume that the aircraft starts at 90%

takeoff weight and ends at 80% takeoff weight. Note the non-standard units for ct and c (Hint: you will need to convert to standard units for the equations).

a. Assume that the aircraft uses a jet for thrust. Calculate the maximum endurance

and range for your aircraft at cruise altitude. Assume ct=0.65 h-1. You will need to calculate maximum CL0.5/CD.

b. Assume that the aircraft uses a propeller for thrust. Calculate the maximum endurance and range for your aircraft at cruise altitude. Assume a propeller

efficiency of 0.88 and c of 2.98 [N] / [kW h] or 0.000908 [lb] / [ [ft∙lb] / [s] h] . You will need to calculate maximum CL3/2/CD.

5. Takeoff distance – assume that the runway is at standard sea level conditions. Ignore ground effect.

a. Assume that 15° flaps are used for takeoff and they increase CLmax by 0.35. What is the CLmax for takeoff?

b. At your takeoff weight, calculate the stall speed, liftoff airspeed, and 0.7VLO with flaps deployed

c. With flaps deployed, assume that CD0 (from problem 1b) is increased by 15%.

Using this new CD0 in your drag polar equation for the aircraft, calculate the drag at 0.7VLO

d. Calculate lift at 0.7VLO e. Calculate the takeoff distance assuming a friction coefficient of 0.025. Assume

thrust is constant and is TA from problem 1e. 6. Landing distance – assume that the runway is at standard sea level conditions. Ignore

ground effect.

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a. Assume that the landing weight of your aircraft is 77% takeoff weight. What is the landing weight?

b. Assume that 50° flaps are used for landing and they increase CLmax by 1.2. What is the CLmax for landing?

c. At your landing weight, calculate the stall speed, touchdown airspeed, and 0.7VT with flaps deployed

d. With flaps deployed, assume that the original CD0 (from problem 1b) is increased

by 25%. Using this new CD0 in your drag polar equation for the aircraft, calculate the drag at 0.7VT

e. Calculate lift at 0.7VT f. Calculate the landing distance assuming a friction coefficient of 0.52.