How Airplanes Really Fly Karthik Mahesh Deptt. of Aerospace - - PowerPoint PPT Presentation

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AE-705: Introduction to Flight

How Airplanes Really Fly

Karthik Mahesh

• Deptt. of Aerospace Engineering

IIT Bombay

AE-705 Introduction to Flight Lecture No 8 Capsule-04

HOW DO WINGS GENERATE LIFT?

Let’s have a look at three theories from NASA

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AE-705 Introduction to Flight Lecture No 8 Capsule-04

THESE THEORIES ARE ALL

Let’s debunk each of these one by one

AE-705 Introduction to Flight Lecture No 8 Capsule-04

WHAT’S WRONG WITH EQUAL TIME THEORY ?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Upper surface path longer, hence upward Lift ?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

https://www.youtube.com/watch?v=w78JT6azrZU&feature=youtu.be&t=5m33s

AE-705 Introduction to Flight Lecture No 8 Capsule-04

In which direction is Lift acting ?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Speed of flow over both surfaces

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Pre-WW1 aircraft had thin airfoils like these  Wouldn’t produce lift as per equal time theory !

Thin Airfoils

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Blowing across a sheet of paper makes it lift up Fast moving air across the upper surface has a lower pressure… Does this explain lift generation ?

http://www.terrycolon.com/1features/ber.html

This demonstrates Coandă effect, not Bernoulli’s principle

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Spoon in stream of water

Bernoulli v/s Coandă conundrum

 Jet follows spoon curvature  Spoon feels force opposite to

deflection

Source 1

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Coandă effect - jet of flow attaches itself to a surface  Jet deflects due to force  Jet exerts equal and opposite force on surface  The flow over the wing is not a jet  Flow underneath wing not stationary  Coandă effect can’t be used

AE-705 Introduction to Flight Lecture No 8 Capsule-04

WHAT’S WRONG WITH SKIPPING STONE THEORY ?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

The Bullet Theory !

Bullet Theory

 Bullets hit the bottom

• f the wing,

transferring upward momentum to it

Aerofoil

 Air molecules hit the

bottom wing, transferring upward momentum to it

AE-705 Introduction to Flight Lecture No 8 Capsule-04

The Bullet Fallacy !

Bullet Theory

 Bullets don’t hit top of the wing  The shape of the top of the

wing doesn’t matter to the bullets

 Bullets don’t hit each other  Bullets weighs a few grams  Bullets that miss the wing are

un-deflected

Aerofoil

 Air goes over the wing also  Air pressure on top of wing is

• nly a few % lower than the

pressure on the bottom

 Air molecule collide with

neighbours 1012 times / s

 N2 molecules weigh ½*10-22 g  Wings deflect even far-away

bits of fluid

AE-705 Introduction to Flight Lecture No 8 Capsule-04

SKIPPING STONE THEORY

 Move a plank through sand  Sand particles simply

pushed aside

Source 2

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Water and air, however, aren’t sand

In fact, something very different happens when we move a plate through water, or a wing through air !

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Moving a plank through water

• Swirling around Leading Edge
• Water appears to flow around
• Diffusion of force in fluid
• Vortex/Circulation

http://www.terrycolon.com/1features/fly.html

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Circulation

• Mathematical quantity
• Defined as line integral

𝜐 = 𝑊 ∙ 𝑒𝑡

• Kutta Condition –
• Τ takes on value ensuring this
• Why? Otherwise – this happens
• Enforced by FRICTION!
• Question – What is the Kutta

Condition, Mathematically?

Answer via Moodle !

AE-705 Introduction to Flight Lecture No 8 Capsule-04

It’s not just the air below the wing that is pushed down Most of the air is pulled down from above the wing

http://amasci.com/wing/airgif2.html http://www.terrycolon.com/1features/fly.html

AE-705 Introduction to Flight Lecture No 8 Capsule-04

STREAMLINE CURVATURE

New idea!

Confusion of Cause and Effect?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Flow turning and pressure behaviour are connected  Inviscid flow equations in ‘Natural coordinates’–

• 𝜍 𝑊

𝜖𝑊 𝜖𝑡 = − 𝜖𝑞 𝜖𝑡 (Streamwise)

• 𝜍

𝑊2 𝑆 = 𝜖𝑞 𝜖𝑠

(Normal)

Streamline curvature

Source : edX course 16.101x_2

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 𝜍 𝑊

𝜖𝑊 𝜖𝑡 = − 𝜖𝑞 𝜖𝑡 (Streamwise)

 Assuming constant ρ, we get Bernoulli’s equation  Normal equation – similar to circular motion?  A car going around a curve experiences?  Same for a fluid particle

Streamline Curvature

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Pressure Gradients

Upper Surface

𝜖𝑞𝑣 𝜖𝑠 = 𝜍𝑊2 𝑆 > 0 ⇒ 𝑞∞ − 𝑞𝑣 > 0

Lower Surface

𝜖𝑞𝑚 𝜖𝑠 = 𝜍𝑊2 𝑆 > 0 ⇒ 𝑞𝑚 − 𝑞∞ > 0

Combining, 𝑞𝑚 > 𝑞𝑣

V change doesn’t cause p change It’s the OTHER WAY AROUND !

Source : edX course 16.101x_2

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AERODYNAMIC COEFFICIENTS

Quantifying Dependencies since 1848

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Lift Coefficient

Density? Freestream Velocity? Shape? Angle of Attack? Wing Area? Viscosity? Compressibility?

Lift depends on many things Required:- Simple equation 𝑀 = 𝑑𝑀 × 1 2 𝜍∞𝑊

∞ 2 × 𝑇

Intuitively; Any fluid force proportional to 𝜍∞𝑊

∞ 2 and Area

Lift Coefficient CL

• Non-dimensional
• Coefficient of lift
• Captures all dependencies
• Determined experimentally

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Two More Coefficients

Drag Coefficient

 𝐸 = 𝑑𝐸 ×

1 2 𝜍∞𝑊 ∞ 2 × 𝑇

 Components

• Form Drag
• Skin Friction Drag
• Others…

Moment Coefficient

 Describes pitching moment  𝑁 = 𝑑𝑁 ×

1 2 𝜍∞𝑊 ∞ 2 × 𝑇 × 𝑑

 Moment is force x length 

c added to keep Cm dimensionless

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Pressure Coefficient

• Quantifies difference

in pressure

• 𝐷𝑞 =

𝑞 −𝑞∞ 𝑟∞

• More useful than

absolute difference

• Similar dependencies

AE-705 Introduction to Flight Lecture No 8 Capsule-04

CP : MORE THAN A SPEED MEASURE?

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 𝑀 =

𝑀𝐹 𝑈𝐹 𝑞𝑀 − 𝑞𝑉 cos 𝜄 𝑒𝑡

 =

𝑀𝐹 𝑈𝐹

𝑞𝑀 − 𝑞∞ − 𝑞𝑉 − 𝑞∞ cos 𝜄 𝑒𝑡

• Dividing by 𝑟∞𝑇,
• S = c x 1
• 𝑑𝑀 =

𝑑 𝐷𝑞,𝑀 − 𝐷𝑞,𝑉 𝑒( 𝑦 𝑑)

• Refer Anderson Chapter V

for more details

Obtaining cl from cp

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Effect of Aerofoil Camber

• Symmetric airfoil, zero AoA
• Curvature same on both surfaces
• Δp same, and –ve
• No lift
• Cambered airfoil
• Both surfaces curve upward,

𝜖𝑞 𝜖𝑠 = 𝜍𝑊2 𝑆 > 0

• ΔCp nearly opposite
• Net positive lift

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Symmetric Airfoil

Zero AoA Curvature same on both surfaces Δp same and –ve Zero lift

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Cp curves intersect, and

• US goes towards 1 => Stag. Pt.
• LS curves sharply upwards => flow turns sharp corner
• Adverse pressure gradient –separation at high AoA
• LE ‘suction peak’

 Sharp LE bad at low speed

AE-705 Introduction to Flight Lecture No 8 Capsule-04

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Effect of THICKNESS

Thickness reduces Cp on both sides Rupper and Rlower increase 𝜖𝑞𝑣 𝜖𝑠 = 𝜍𝑊2 𝑆 ↑, 𝑞∞ − 𝑞𝑣 ↑, 𝑞𝑣 ↓ 𝜖𝑞𝑚 𝜖𝑠 = 𝜍𝑊2 𝑆 ↑, 𝑞∞ − 𝑞𝑚 ↑, 𝑞𝑚 ↓ Cp curves shifted up accordingly Lift unaffected much However, no adverse gradients due to sharp corners Thick/Rounded Edge airfoils better at low speed

AE-705 Introduction to Flight Lecture No 8 Capsule-04

Variation of Cp with AoA

AE-705 Introduction to Flight Lecture No 8 Capsule-04

 Source 1 - http://www.terrycolon.com/1features/ber.html  Source 2 - http://www.terrycolon.com/1features/fly.html  Source 3 - http://amasci.com/wing/airgif2.html  Source 4 – Including all Pressure coefficient diagrams – edX

course 16.101x_2 (Intro to Aerodynamics – MIT)

References