Lift Equation And CaE PDF

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Information regarding the aircraft climb and lift calculations. Complete information, provided by the teacher, to help students understand the terms and formulas....

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AVS 2102 – Lift Equation and CL vs. AOA Course Topics Lift equation -Aerodynamic force coefficients -Basic lift equation CL vs. AOA -Airfoil lift characteristics -CL vs AOA -Camber effect -Thickness effect

Associated Textbook Reading Topics and Learning Modules -Aerodynamic force coefficients -The basic lift equation -Interpretation of the lift equation Airfoil lift characteristics

Text Pages 22-27

Associated Study Questions Lift Equation and CL vs. AOA

27-29

Read ANA 22-29 Aerodynamic force coefficients The basic lift equation Interpretation of the lift equation Airfoil lift characteristics Overview Aerodynamic force coefficients The basic lift equation CL vs. AOA Airfoil lift characteristics – thickness and camber Controlling Lift In-class quiz

Student

Aerodynamic Force Coefficients Question 1 previewhhhurt What variables could influence aerodynamic forces such as lift and drag? df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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Velocity VKTAS q Air density σ Airfoil shape Cf Angle of attack Surface area S

S

These can be combined into three major factors affecting aerodynamic forces. Dynamic pressure q (which includes air density σ and velocity VKTAS) Coefficient of force Cf (which includes angle of attack and airfoil shape) Surface area S F = f(q, Cf, S) Mathematically, any aerodynamic force can be calculated from: F = CfqS F Cf = ----- = qS

F/S ----- = q

average aerodynamic force pressure --------------------------------------------dynamic pressure

For lift: L = CLqS CL (σVKTAS2) S L = ---------------------------295 L CL = ----- = qS

L/S ----- = q

lift pressure ---------------------dynamic pressure

CL = f(airfoil shape, angle of attack). For drag: D = CDqS df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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CD (σVKTAS2) S D = ----------------------------295 D CD = ----- = qS

D/S ----- = q

drag pressure ---------------------dynamic pressure

Question 1 answer *The Basic Lift Equation Question 2 preview

L q c L S 2

 V KTAS q 295 2

 S L  V KTAS c L 295 L = lift, pounds, lbs., # q = dynamic pressure, psf σ = density ratio CL = lift coefficient, no units S = wing area, sf Question 2 answerCL vs. angle of attack Question 3 preview Question 4 preview Figure 4-10 CL vs. AOA and flow pattern (source unknown). df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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*CL = f(airfoil shape, angle of attack). Determined from wind tunnel tests. Symmetric airfoil CL = 0 at AOA = 0 Linear portion. Attached flow. Deviation from linear Some separation. CLmax Maximum lift. Stall angle of attack Separation. df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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Question 5 preview ANA fig. 1.12. Lift characteristics of typical airfoil sections. Note that the curve characteristics depends only on the airfoil shape!

Cambered airfoil CL > 0 at AOA = 0 Stall/handling characteristics inferred from the CL vs. angle of attack graph. If I choose to add airspeeds to the chart (figure 1.11), I must specify a particular airplane weight and S.

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Lift characteristics of typical airfoil sections. Note that the curve characteristics depends only on the airfoil shape… like thickness and camber. Question 5 answer Airfoil Lift Characteristics – Thickness and Camber effect. CL = f(airfoil shape, angle of attack) Question 6 preview Question 7 preview ANA figure 1.10, Airfoil terminology. Thickness and camber.

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Figure 4-2 and 4-3. Thickness and camber effect. (Generalized, qualitatively)

Effect of thickness on the CL vs. AOA curve. Airfoils NACA 23012 (12% thick) and 23018 (18% thick).

Increasing thickness lengthens the CL vs. AOA curve. Increases CLmax. df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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Increases stall AOA. Effect of camber on the CL vs. AOA curve. Airfoils NACA 0012 (symmetric), 2412 (2 % camber), and 4412 (4 % camber).

Figure 4-3. Camber and thickness effect. Increasing camber shifts the CL vs. AOA curve to the left. Increases CLmax. Decreases stall AOA maybe! See http://airfoiltools.com/airfoil/details? airfoil=n63412-il Question 6 answer Question 7 answer Interpretation of the Lift Equation – Controlling Lift in the Airplane Question 8 preview Question 9 preview df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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2

 S L  V KTAS cL 295 Recall from the Airspeed Measurement LP:

V

KTAS

V KEAS 

and if VKEAS ≈ VKCAS ≈ VKIAS, then

V

V

KTAS



KIAS



Therefore,

L V

2 KIAS

c

L

S

295

What is the effect on lift L of changing flight conditions such as altitude, velocity, and angle of attack. 2

L

 V KTAS cL S

L V

295 2 KIAS

c

L

S

295

Lift has 4 variables if using VKTAS, and 3 variables if using VKIAS.

We want to maintain straight and level flight so we want

L=W

.

The pilot controls lift by changing airspeed, angle of attack (usually pitch), and, sometimes, wing area. Velocity

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2

S  L  V KTAS cL 295 L V

2 KIAS

c

L

S

295

As velocity increases, L increases non-linearly (squared) to velocity if all other variables are held constant. If velocity doubles, dynamic pressure quadruples and therefore lift quadruples. If velocity is deceased by ½, dynamic pressure and lift reduces to ¼ its original value. So how does a pilot maintain L = W as velocity increases? Decrease AOA which decreases CL which deceases L. So how does a pilot maintain L = W as velocity decreases? Increase AOA which increases CL which increases L. CL (and AOA) 2

L

 V KTAS cL S

L V

295 2 KIAS

c

L

S

295

Pilot controls lift by controlling CL by controlling AOA. Altitude 2

S  L  V KTAS cL = W = constant 295 Altitude is represented by σ. As altitude increases, σ decreases and lift decreases if all other variables (including df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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VKTAS) are held constant. So how does a pilot maintain L = W as altitude increases? 1. Increase VKTAS by adding thrust. or 2. Increase CL by increasing AOA.

L V

2 KIAS

c

L

S

Lift equation with VKIAS.

295

There is no altitude term in the VKIAS lift equation! Altitude has no effect on lift IF a constant V KIAS is maintained.

Remember that

V

V

KTAS



KIAS

so V KTAS increases “automatically” if the



pilot holds constant VKIAS. Said another way, if V KIAS remains constant as altitude is increased, lift remains constant. Question 8 answer Question 9 answer S wing area Question 10 preview Pilot does not normally control S except perhaps with Fowler wing flaps or variable geometry wings.

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Question 10 answer Summary See

Lift Equation and CL vs. AOA Study Questions

Formulas to memorize

L q c L S df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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2

 S L  V KTAS c L 295 L V

2 KIAS

c

L

S

295

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Lift Equation and CL vs. AOA Study Questions (v0) Aerodynamic Force Coefficients 1.

top

Lift coefficient is the ratio between ____________ pressure and _____________ pressure. Drag coefficient is the ratio between ____________ pressure and ____________ pressure.

The Basic Lift Equation

top

2.

*Write the four-term lift equation and the name and English units of each term.

3.

*The lift coefficient used in the lift equation is only a function of the __________________ and the ______________________________.

4.

Using ANA 1.11 figure, calculate the lift produced by the 280 sf wing at 120 KTAS (sea level) and 12.7 degrees angle of attack.

CL vs. AOA 5.

*Draw a graph depicting the lift coefficient (y axis) versus angle of attack (x axis) for a conventional airplane wing planform (symmetrical airfoil). Label the x and y axis with typical values. Identify CLmax and stall angle of attack on the appropriate axis. (ANA fig. 1.11, 1.12, and 1.13.)

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6.

*Draw a graph depicting the lift coefficient (y axis) versus angle of attack (x axis) for a conventional airplane wing planform (cambered airfoil). Label the x and y axis with typical values. Identify CLmax and stall angle of attack on the appropriate axis. (ANA fig. 1.12.)

7.

Refer to ANA figure 1.12, lift characteristics of typical airfoil sections. a. Compare the stall characteristics (angle of attack, CLmax, and aircraft handling/stall warning) of the NACA 63-006 wing versus the NACA 63-009 wing.

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b. Compare qualitatively the lift produced at zero angle of attack for the NACA 631-012 wing vs. the NACA 631-412 wing.

c. Calculate the lift produced by a NACA 631-412, 280 sf wing at 120 KTAS (sea level) and 8 degrees angle of attack. Show work.

Camber effect top 8.

*Draw a CL vs. AOA graph that shows the typical effect of increasing camber. Accurately depict and label the effect on CLmax and AOAstall. (ANA fig. 1.15 top and 1.17 bottom.)

9.

As camber of an airfoil is increased, its CL at any given AOA less than stall a. is less b. remains the same c. is greater

Thickness effect

top

10. *Draw a CL vs. AOA graph that shows the typical effect of increasing thickness. Accurately depict and label the effect on CLmax and AOAstall. (Lecture notes.) df35eadf1a6ba0ae24a5124416cbc8ec.doc 9/1/2021 12:28 AM

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11. Two features an airfoil designer can change to increase CLmax are a. thickness and wing area b. chord length and aspect ratio c. camber and wing span d. thickness and camber Interpretation of the Lift Equation – Controlling Lift 12. As altitude increases the KTAS necessary to maintain straight and level flight, i.e., constant lift, must a. Increase b. Remain the same c. Decrease 13. As altitude increases the KCAS necessary to maintain straight and level flight, i.e., constant lift, must a. Increase b. Remain the same c. Decrease 14. If a pilot wishes to increase KCAS yet maintain straight and level flight at a given altitude, what aircraft control action (relative to aerodynamics and the lift equation) must the pilot perform to avoid climbing with the airspeed increase? How does this translate to actual aircraft control inputs?

15. If a pilot wishes to decrease KCAS yet maintain straight and level flight at a given altitude, what aircraft control action (relative to the lift equation) must the pilot perform to avoid descending with the airspeed decrease? How does this translate to actual aircraft control inputs? df35eadf1a6ba0ae24a5124416cbc8ec.doc 17 9/1/2021 12:28 AM

16. Which flap type increases wing area when deployed? a. Variable geometry flaps b. Fowler flaps c. Slider flaps d. Slats

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