Purpose Evaluate the relationships between Coefficient of Lift (CL) and Angle of Attack (AOA), Airfoil Camber, and Airfoil Thickness and the variables of the Lift Equation using graphs and equations. If you are able, review the concepts using an on-line s

Exercise 3: Lift and Airfoils

Purpose

Evaluate the relationships between Coefficient of Lift (CL) and Angle of Attack (AOA), Airfoil Camber, and Airfoil Thickness and the variables of the Lift Equation using graphs and equations. If you are able, review the concepts using an on-line simplified simulated Wind tunnel.

Scope

(Questions 1-4) Looking at Dole and Lewis textbook Figure 4.4 and Figure 4,3, you will evaluate Lift Curve slope Parameters of a Symmetrical (NACA 0012) and Cambered Airfoil (NACA 4412) of similar thickness and evaluate the thickness effect on Coefficient of Lift and AOA for cambered airfoils of different thicknesses (NACA 4412 and NACA 4406)

1. Find the CLmax for the two airfoils in Figure 4.4.What is the relationship between Camber and CLmax ?

Answer

CLmax = 1.5 (CAMBERED)

CLmax = 1.3 (SYMMETRICAL)

CLmax is directly proportional to Camber

2. Find the AOA at Zero Lift for the two airfoils in Figure 4.4.What is relationship between Camber and zero lift (CL = 0)?.

Answer

AOA for Cambered is -3 while for symmetrical is 0 and is inversely proportional to Camber

3. Find the AOA at CLmax for the two airfoils in Figure 4.4.What is the relationship between Camber and Stall AOA?.

Answer

AOA at CLmax for Cambered is 140 and for symmetrical is 180 and is inversely proportional to Camber

4. Looking at Figure 4.3, what is the relationship between airfoil thickness, CLmax and AOA?

Answer

Greater the thickness greater the CLmax and AOA

(Questions 5-7) With some algebraic analysis, find the effects of Airspeed and Altitude on Lift by finding the Lift of an airplane with the following fixed parameters with various airspeeds and altitudes. Use Equation 4.1, Table 2.1, and Figure 4.4 in Dole & Lewis .

Given:

NACA 4412

Wing Chord (c) =5 ft

Wing Span (b) = 40 ft

AOA= 7 deg

Standard Day Conditions

5. First-make a table of Airspeed (0 KTAS, 40 KTAS, 80 KTAS, 120 KTAS) vs. Lift

@ Pressure Altitude of (0 ft Altitude, 10,000 ft Altitude, 40,000 ft Altitude)

LIFT (lb)	Pressure Altitude (PA) ft
	0	10,000	40,000
0 KTAS	1050	776	0
40 KTAS		1049	257
80 KTAS	4203	3105	1031
120 KTAS	9458	6988	2320

6. What is the relationship between True Airspeed and Lift at a constant Pressure Altitude?

Answer

More airspeed more lift, in fact the increase is to the Square. Double airspeed- quadruple the lift the wing produces. Triple the airspeed –Lift increases by a factor of 9.

7. What is the relationship between Altitude and Lift at a constant True Airspeed?

Answer

Higher Altitude – Decreased density there for decreased lift. At 40 k ft the density is ¼ the density at sea level, therefore lift in decreased by ¼.

8. If the gross weight is 1050 lbs. Estimate the true airspeed in KTAS to maintain level flight (Lift = Gross Weight) at the given Angle of Attack conditions at sea level, 10,000 ft and 40,000 ft.

Answer

Using the airfoil model,

40 mph achieves a lift of 1050 lb for the given wing conditions at sea level

46.5 mph achieves a lift of 1049 lb for the given wing conditions at 10 k

80 mph achieves a lift of 1031 lb for the given wing conditions at 40 k

(Questions 9-10) With some algebraic analysis, find the effects of Airspeed and AOA on Lift by finding the Lift of an airplane during a takeoff roll. Using Figure 4.4 in Dole and Lewis, assume that the Cambered airfoil (NACA 4412) is the wing airfoil with Flaps Down and the Symmetrical Airfoil (NACA 0012) is the wing airfoil with Flaps up.

Takeoff configuration will be flaps Down (NACA-4412). On the ground and during rotation to takeoff assume that the AOA is 8 deg. Once airborne (L=W), assume staying at essentially at a constant sea level altitude and accelerating. The AOA must change to keep the same lift. Raise the Flaps at 80 KTAS and continue to accelerate to an airspeed of 120 KTAS, in preparation for a climb, by keeping Lift = ~1950 lb.

Given:

Takeoff Weight is 1950 lb

Wing Chord (c) =5 ft

Wing Span (b) = 40 ft

Sea Level Standard Day Conditions:

Make a Table of Airspeed vs. Lift and AOA using Equation 4.1 and Figure 4.4

Airspeed (KTAS)	AOA (deg)	CL	Lift (lb)	Remarks
0	8	1.1	0	No Airspeed No Lift FLAPS DN
20	10	1.3	92	No Airspeed No Lift FLAPS DN
40	10	1.2	100	Airborne
50	10	1.2	833	No Airspeed No Lift FLAPS DN
60	1.24	1.3	1450	No Airspeed No Lift FLAPS DN
80 (Flaps DN)	6.28	1.4	1481	Camber 6% Flaps still down
80 (Flaps UP)	4.12	0.6	1600	Camber 6% Flaps still down
100	2.6	1.1	1604	Camber 6% Flaps still down
120	1.8	0.9	1605	Camber 6% Flaps still down

9. Find the approximate Lift-Off Speed (KTAS).(i.e. the True Airspeed where Lift = Weight for the given configuration on the ground at lift-off)

Answer

Approximate Lift Off speed is 41.5 KTAS

10. What is the relationship between Airspeed and AOA as an airplane accelerates at a constant altitude?

Answer

Reduces with increase in Airspeed

Not required but feel free to connect on-line to NASA Glen Research Center education website to further explore aerodynamic concepts. This is an excellent this web site to use as an on-line Lab. http://www.grc.nasa.gov/WWW/K-12/airplane/foil3u.html. You may have to load the Java plugin or download the applet to enable the website to work

Similar exercise questions have been developed below to explore the relationships of Coefficient of Lift (CL) and Angle of Attack (AOA), Airfoil Camber, and Airfoil Thickness and the variables of the Lift Equation.

Page 4 of 10

This document was developed for online learning in ASCI 309.

File name: Ex_3_Lift_Airfoils

Updated: 11June12

Exercise A

Compare three airfoils that have different thickness and camber to see how thickness and camber affect Coefficient of Lift (CL) vs. Angle of Attack (AOA).

Connect to FoilSim III.

SET UP

Initial Conditions:

Imperial Units

Input:

Change Flight

Speed 100 mph

Altitude 0 ft

Change to Size

Chord-5.0 ft

Span 40.1 ft

Area-200.5 Ft2

Change to Shape

Angle-0 deg

Camber-0 %

Thickness- 12%

Change to Analysis

Stall Model

Select Plot

Cl vs Angle

Data Window-Change Lift to CL

Set up your own table in Microsoft Word or Excel (AOA vs. CL) and use Shape to answer the following questions:

(AOA = -10, -5, 0, 5, 10, 14, 16, 18)

Airfoil 1-(0 % Camber/12 % Thickness)

Airfoil 2-(6% Camber/ 12 % Thickness)

Airfoil 3-(6% Camber/ 19.8 % Thickness

Questions:

1. What is the relationship between Camber and CLmax?

Answer

Increase Camber and CLmax increases. The AOA where CLmax increases also is reduced. Example Trailing Edge Flaps which increase camber allow the aircraft to fly slower with higher CLmax and also have lower pitch attitude on approach.

2. What is relationship between Camber and zero lift (Cl =0)

Answer

Symmetrical Airfoils (Camber = 0%) have the zero lift line at 0 deg AOA. Increase Camber and zero lift line occurs at a negative AOA.

3. What is the relationship between airfoil thickness and CLmax?

Answer

Increase Thickness and increase CLmax. Effect of thickness is less than Camber for this example. Important distinction- CLmax increases at a higher AOA with thickness. Thickness permits flight at slower speeds and allows aircraft to fly at higher AOA.

Exercise B Questions

Examine how True Airspeed and Altitude affect Lift.

Set up Angle-5 deg

Camber-6 %

Thickness-12%

Chord 5 ft

Span 40.1 ft

Data Window- Lift

Set up Table Flight

Airspeed (0 mph, 40 mph, 80 mph, 120 mph) vs. Lift

@ (0 ft Altitude, 10,000 ft Altitude, 40,000 ft Altitude)

Exercise B Questions

4. What is the relationship between True Airspeed and Lift?

Answer

More airspeed more lift, in fact the increase is to the Square. Double airspeed- quadruple the lift the wing produces. Triple the airspeed –Lift increases by a factor of 9.

5. What is the relationship between Altitude and Lift?

Answer

Higher Altitude – Decreased density there for decreased lift. At 40 k ft the density is ¼ the density at sea level, therefore lift in decreased by ¼.

6. If your gross weight is 1050 lbs. Estimate the true airspeed in M PH to maintain level flight (Lift = Weight) at the given Angle of Attack conditions at sea level, 10,000 ft and 40,000 ft.

Answer

Using the airfoil model,

40 mph achieves a lift of 1050 lb for the given wing conditions at sea level

46.5 mph achieves a lift of 1049 lb for the given wing conditions at 10 k

80 mph achieves a lift of 1031 lb for the given wing conditions at 40 k

Exercise C

This exercise will evaluate an aircraft on a takeoff roll, takeoff and accelerate to flap speed and then accelerate to climb speed. With the given conditions find when wings can support aircraft weight and takeoff can occur on a takeoff roll in (mph) and compare AOA to Lift and Airspeed (0-120 mph) while maintaining level flight accelerating at sea level.

Exercise C Conditions

Aircraft weight: 1600 lbs Wing Area: 200.5 sf

Wing Span: 40.1 ft Chord: 5 ft

Thickness: 12% C

Camber 6% at speeds less than 65 mph (flaps in takeoff position).

Camber 0% at speeds greater than 65 mph (flaps up).

Let’s use AOA for takeoff is 10 deg. Once you get enough lift to equal weight.

Keep Lift = Weight and adjust AOA, Camber, and airspeed.

Exercise C Question

Make a table of Airspeed vs. Lift and AOA. Start at 10 deg AOA.

Then when Aircraft Weight = Lift that will be takeoff.

Then extend the table to greater airspeeds simulating the aircraft accelerating to 120 mph. Keep Lift at ~1600 lbs, but the AOA must change. Raise Flaps (Camber 0%) at 65 mph. Compare Airspeed to AOA in the accelerating aircraft keeping Lift @~1600 lbs.

Answer C