Graded Homework

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:

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.htmlor 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/searchand 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.

parenthesis) in your answer to 2
above.

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).

3. From
the plot, find the C_Lmaxfor your airfoil (Tip: for a numerical
breakdown of the plotted curve, you can select the “Details” link and directly
read the highest C_Lvalue, 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_Lvalue 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).

a)
How do the two C_Lmaxcompare 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 on-line tool to make conclusions about characteristics.)

b)
How do the two Stall AOAcompare 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 AOAcompare 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 AOAcompare 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
= C_L *? * 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 (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’ [ft²]based on your aircraft’s Wing Span (from 9.) and
Average Chord Length (from 10.):

12. Use the C_Lvalue 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 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 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

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 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”).