Exercise 3: Lift and Airfoils
The first part of this week’s assignment is to choose and research a reciprocating engine powered (i.e. propeller type) aircraft. You will further use your selected aircraft in subsequent assignments, so be specific and make sure to stay relatively conventional with your choice in order to prevent having trouble finding the required data during your later research. Also, if you find multiple numbers (e.g. for different aircraft series, different configurations, and/or different operating conditions), please pick only one for your further work, but make sure to detail your choice in your answer (i.e. comment on the condition) and stay consistent with that choice throughout subsequent work.
In contrast to formal research for other work in your academic program at ERAU, Wikipedia may be used as a starting point for this assignment. However, DO NOT USE PROPRIETARY OR CLASSIFIED INFORMATION even if you happen to have access in your line of work.
1. Selected Aircraft: Gulfstream G550
For the following part of your research, you can utilize David Lednicer’s (2010) Incomplete Guide to Airfoil Usage at http://mselig.ae.illinois.edu/ads/aircraft.html or any other reliable source for research on your aircraft.
2. Main Wing Airfoil (if more than one airfoil is used in the wing design, e.g. different between root and tip, pick the predominant profile and, as always, stay consistent):
Please note also the database designator in the following online tool (see picture below):
Find the appropriate lift curve for your Airfoil from 4. You can utilize any officially published airfoil diagram for your selected airfoil or use the Airfoil Tool at http://airfoiltools.com/search and text search for NACA or other designations, search your aircraft, or use the library links to the left of the screen. Once the proper airfoil is displayed and identified, select the “Airfoil details” link to the right, which will bring up detailed plots for your airfoil similar to the ones in your textbook.
Concentrate for this exercise on the Cl/alpha (coefficient of lift vs angle of attack) plot. Start by decluttering the plot and leaving only the curve for the highest Reynoldsnumber (R_{e)} selected (i.e. remove all checkmarks, except the second to last, and press the “Update plots” tab).
3. From the plot, find the C_{Lmax }for your airfoil (Tip: for a numerical breakdown of the plotted curve, you can select the “Details” link and directly read the highest C_{L }value, i.e. the highest number within the second column, and associated AOA in the table, i.e. the associated number in the first column):
4. Find the Stall AOA of your airfoil (i.e. the AOA associated with C_{Lmax} in 3.):
5. Find the C_{L }value for an AOA of 5° for your selected airfoil:
6. Find the ZeroLift AOA for your airfoil (again, the numerical table values can be used to more precisely interpolate ZeroLift AOA, i.e. the AOA value for which C_{L} in the second column becomes exactly 0):
7. Compare your researched airfoil plot to the given plot of NACA 4412 (http://airfoiltools.com/airfoil/details?airfoil=naca4412il).
a) How do the two C_{Lmax }compare to each other? Describe the differences in airfoil characteristics (i.e. camber & thickness) between your airfoil and the given NACA 4412, and how those differences affect C_{Lmax}. (Use your knowledge about airfoil designation together with the airfoil drawings and details in the online tool to make conclusions about characteristics.)
b) How do the two Stall AOA compare to each other? Explain how the differences in airfoil characteristics (i.e. camber & thickness) between your airfoil and the given NACA 4412 affect Stall AOA.
c) How do the two ZeroLift AOA compare to each other? Evaluate how the differences in airfoil characteristics between your airfoil and the given NACA 4412 affect ZeroLift AOA.
8. Compare your researched airfoil plot to the NACA 0012 plot.
a) How do the two ZeroLift AOA compare to each other? Evaluate how the differences in airfoil characteristics between your airfoil and the given NACA 0012 affect ZeroLift AOA.
b) What is special about the design characteristics of NACA 0012? How and where could this airfoil design type be utilized on your selected aircraft? Describe possible additional uses of such airfoil in aviation.
For the second part of this assignment use your knowledge of the atmosphere and the Density Ratio, (sigma), together with Table 2.1 and the Lift Equation, Equation 4.1, in your textbook (remember that the presented equation already contains a conversion factor, the 295, and speeds should be directly entered in knots; results for lift will be in lbs):
L = C_{L} * * S * V^{2} / 295
Additionally, for your selected aircraft use the following data when applying Equation 4.1:
9. Research the Wing Span [ft]:
10. Find the Average Chord Length [ft]:
Note: Average Chord = (Root Chord + Tip Chord) / 2 (if no Average Chord is directly found in your research)
11. Find the Maximum Gross Weight [lbs] for your selected aircraft:
A. Calculate the Wing Area ‘S’ [ft^{2}] based on your aircraft’s Wing Span (from 9.) and Average Chord Length (from 10.):
12. Use the C_{L }value for an AOA of 5° for your airfoil found in 5. above to simulate cruise conditions in the following exercise B. (Note it here for easier reference):
B. Prepare and complete a table of Lift vs. Airspeed at different Pressure Altitudes utilizing the given Lift Equation and your previous data. (For the calculation of Density Ratio ‘’ you can assume standard temperatures and neglect humidity.)
You can utilize MS^{®} Excel (ideal for repetitive application of the same formula) to populate table fields and examine additional speeds and altitudes, but as a minimum, include six speeds (0, 40, 80, 120, 160, & 200 KTAS) at three different altitudes (Sea Level, 10000, 40000 ft), as shown below:
Calculate LIFT (lb) 
Pressure Altitude (PA) ft 

Airspeed: 
0 
10,000 
40,000 
0 KTAS 



40 KTAS 



80 KTAS 



120 KTAS 



160 KTAS 



200 KTAS 



I) What is the relationship between Airspeed and Lift at a constant Pressure Altitude? Evaluate each Altitude column of your table individually and describe how changes in Airspeed affect the resulting Lift. Be specific and mathematically precise, and support your answer with the relationships expressed in the Lift Equation.
II) What is the relationship between Altitude and Lift at a constant Airspeed? Evaluate each Airspeed row of your table individually and describe how changes in Altitude affect the resulting Lift. Be specific and mathematically precise, and support your answer with the relationships expressed in the Lift Equation.
III) Estimate the Airspeed required to support the Maximum Gross Weight of your selected airplane (from 11. above) at an Altitude of 10000 ft and flying at the given AOA of 5°. (As initially indicated, a more detailed table/Excel worksheet is beneficial to precision for this task. To support the Weight of any aircraft in level flight, an equal amount of Lift has to be generated – therefore, you can also algebraically develop the lift equation to yield a precise Airspeed result, i.e. substituting L=W and solving for V in the lift equation. Remember that conditions in this question are not at sea level.)
C. In B.III) above, we noted that lift has to equal weight in order to sustain level flight. Using the same Maximum Gross Weight (from 11.), and the same Wing Area (from A.), calculate required AOA for level flight at the different airspeeds in your table under standard, sea level conditions (i.e. =1). You can start a new table or expand your existing one. (See also step by step instructions below the table.):
Airspeed (KTAS) 
Required Lift = Weight 
Required C_{L} 
Corresponding AOA for your airfoil 
0 



40 



80 



120 



160 



200 



First and similar to the note in B.III) above, develop the lift equation algebraically to yield C_{L} results based on Airspeed inputs (i.e. substitute Lift with the aircraft Weight and solve the Lift Equation for the Coefficient C_{L}; then insert the different Airspeeds into V, calculate the corresponding C_{L} values, and note them in your table).
Finally, use your researched airfoil Cl/alpha plot (from 3. through 8.) to find corresponding AOA to your calculated C_{L} values (enter the plot in the left scale with each calculated CL value, trace horizontally to intercept the graph for that CL value, then move down vertically to find the corresponding AOA and note it in your table (alternatively, you can also look up values in the detailed table):
I) Comment on your results. Are there airspeeds for which you could not find useful results? Describe where in the step by step process you’ve got stuck and why. Explain what it aerodynamically means for your airfoil if a required C_{L} value is greater than the C_{Lmax} that you found in 3.
II) What is the standard sea level Stall Speed for your selected aircraft at its Maximum Gross Weight? (Utilize above data and the Stall Speed Equation on page 44 of “Flight Theory and Aerodynamics”).
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