1 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: I choose Cessna 205 NACA 2412
For the following part of your research, you can utilize David Lednicer’s (2010) Incomplete
Guide to Airfoil Usage at http://m-selig.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 on-line 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.
Text search input Library links Search result display
Airfoil details tab This document was developed for online learning in ASCI 309.
File name: Ex_3_Lift&Airfoils
Updated: 06/23/2015 Please note the airfoil
database designator (in
parenthesis) in your
answer to 2 above. 2 Concentrate for this exercise on the Cl/alpha (coefficient of lift vs angle of attack) plot. Start by
de-cluttering the plot and leaving only the curve for the highest Reynolds-number (R e) selected
(i.e. remove all checkmarks, except the second to last, and press the “Update plots” tab). Details Link
“Update plots”
tab 3. From the plot, find the CLmax 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 CL value for an AOA of 5 for your selected airfoil:
6. Find the Zero-Lift AOA for your airfoil (again, the numerical table values can be used to more
precisely interpolate Zero-Lift 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=naca4412-il). This document was developed for online learning in ASCI 309.
File name: Ex_3_Lift&Airfoils
Updated: 06/23/2015 3
a) How do the two CLmax 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 CLmax. (Use your knowledge about airfoil designation
together with the airfoil drawings and details in the on-line 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 Zero-Lift AOA compare to each other? Evaluate how the differences
in
airfoil characteristics between your airfoil and the given NACA 4412 affect Zero-Lift
AOA.
8. Compare your researched airfoil plot to the NACA 0012 plot.
a) How do the two Zero-Lift AOA compare to each other? Evaluate how the differences
in
airfoil characteristics between your airfoil and the given NACA 0012 affect Zero-Lift
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 = CL * * S * V2 / 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
found (if no Average Chord is directly
in your research) This document was developed for online learning in ASCI 309.
File name: Ex_3_Lift&Airfoils
Updated: 06/23/2015 4 11. Find the Maximum Gross Weight [lbs] for your selected aircraft:
A. Calculate the Wing Area ‘S’ [ft2] based on your aircraft’s Wing Span (from 9.) and Average
Chord Length (from 10.):
12. Use the CL 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)
Airspeed:
0 KTAS
40 KTAS
80 KTAS
120 KTAS
160 KTAS
200 KTAS 0 Pressure Altitude (PA) ft
10,000 40,000 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. to
lift 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
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
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
This document was developed for online learning in ASCI 309.
File name: Ex_3_Lift&Airfoils
Updated: 06/23/2015 5
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 CL 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 CL; then insert the different Airspeeds into V, calculate the
corresponding CL 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 CL 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): THIS PLOT IS AN
EXAMPLE ONLY
AND NOT
APPLICABLE FOR
YOUR AIRFOIL –
PLEASE USE YOUR
RESEARCHED LIFT
CURVE FROM 3.
THROUGH 8.
ABOVE. Enter
with CL
in the
vertical,
left
scale Read corresponding AOA on the bottom scale 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
CLmax 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”).
This document was developed for online learning in ASCI 309.
File name: Ex_3_Lift&Airfoils
Updated: 06/23/2015

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