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

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

Thin Airfoils  Pre-WW1 aircraft had thin airfoils like these  Wouldn’t produce lift as per equal time theory ! AE-705 Introduction to Flight Lecture No 8 Capsule-04

Blowing across a sheet of paper makes it lift up http://www.terrycolon.com/1features/ber.html Fast moving air across the upper surface has a lower pressure… Does this explain lift generation ? This demonstrates Coandă effect, not Bernoulli’s principle AE-705 Introduction to Flight Lecture No 8 Capsule-04

Bernoulli v/s Coand ă conundrum  Spoon in stream of water  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  Coand ă 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 Aerofoil  Bullets hit the bottom  Air molecules hit the of the wing, bottom wing, transferring transferring upward upward momentum to it momentum to it AE-705 Introduction to Flight Lecture No 8 Capsule-04

The Bullet Fallacy ! Bullet Theory Aerofoil  B ullets don’t hit top of the wing  Air goes over the wing also  The shape of the top of the  Air pressure on top of wing is wing doesn’t matter to the only a few % lower than the bullets pressure on the bottom  Air molecule collide with  Bullets don’t hit each other neighbours 10 12 times / s  N 2 molecules weigh ½ *10 -22 g  Bullets weighs a few grams  Bullets that miss the wing are  Wings deflect even far-away un-deflected 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 http://www.terrycolon.com/1features/fly.html Most of the air is pulled down from above the wing http://amasci.com/wing/airgif2.html AE-705 Introduction to Flight Lecture No 8 Capsule-04

Confusion of Cause and Effect? New idea! STREAMLINE CURVATURE AE-705 Introduction to Flight Lecture No 8 Capsule-04

Streamline curvature  Flow turning and pressure behaviour are connected Source : edX course 16.101x_2  Inviscid flow equations in ‘Natural coordinates’– 𝜖𝑊 𝜖𝑞 𝜖𝑡 (Streamwise)  𝜍 𝑊 𝜖𝑡 = − 𝑊 2 𝜖𝑞 (Normal)  𝜍 𝑆 = 𝜖𝑠 AE-705 Introduction to Flight Lecture No 8 Capsule-04

Streamline Curvature 𝜖𝑊 𝜖𝑞 𝜖𝑡 (Streamwise)  𝜍 𝑊 𝜖𝑡 = −  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 AE-705 Introduction to Flight Lecture No 8 Capsule-04

Pressure Gradients Upper Surface 𝜖𝑠 = 𝜍𝑊 2 𝜖𝑞 𝑣 > 0 ⇒ 𝑞 ∞ − 𝑞 𝑣 > 0 𝑆 Lower Surface 𝜖𝑠 = 𝜍𝑊 2 𝜖𝑞 𝑚 Source : edX course 16.101x_2 > 0 ⇒ 𝑞 𝑚 − 𝑞 ∞ > 0 𝑆 Combining, 𝑞 𝑚 > 𝑞 𝑣 V change doesn’t cause p change It’s the OTHER WAY AROUND ! AE-705 Introduction to Flight Lecture No 8 Capsule-04

Quantifying Dependencies since 1848 AERODYNAMIC COEFFICIENTS AE-705 Introduction to Flight Lecture No 8 Capsule-04

Lift Coefficient Compressibility? Lift depends on many things Required:- Simple equation Freestream Velocity? Density? 𝑀 = 𝑑 𝑀 × 1 2 × 𝑇 2 𝜍 ∞ 𝑊 ∞ Intuitively; Any fluid force Shape? 2 and Area proportional to 𝜍 ∞ 𝑊 ∞ Wing Area? Angle of Attack? Lift Coefficient C L Non-dimensional • Viscosity? Coefficient of lift • Captures all dependencies • Determined experimentally • AE-705 Introduction to Flight Lecture No 8 Capsule-04

Two More Coefficients Moment Coefficient Drag Coefficient 1 2 × 𝑇  𝐸 = 𝑑 𝐸 × 2 𝜍 ∞ 𝑊 ∞  Components Form Drag  Skin Friction Drag  Others …  Describes pitching moment  1 2 × 𝑇 × 𝑑  𝑁 = 𝑑 𝑁 × 2 𝜍 ∞ 𝑊 ∞  Moment is force x length c added to keep C m  dimensionless AE-705 Introduction to Flight Lecture No 8 Capsule-04

Pressure Coefficient Quantifies difference • in pressure 𝑞 −𝑞 ∞ • 𝐷 𝑞 = 𝑟 ∞ More useful than • absolute difference Similar dependencies • AE-705 Introduction to Flight Lecture No 8 Capsule-04

C P : MORE THAN A SPEED MEASURE? AE-705 Introduction to Flight Lecture No 8 Capsule-04

Obtaining c l from c p 𝑈𝐹 𝑞 𝑀 − 𝑞 𝑉 cos 𝜄 𝑒𝑡  𝑀 = 𝑀𝐹 𝑈𝐹  = 𝑞 𝑀 − 𝑞 ∞ − 𝑞 𝑉 − 𝑞 ∞ cos 𝜄 𝑒𝑡 𝑀𝐹  Dividing by 𝑟 ∞ 𝑇 ,  S = c x 1 𝑑 𝐷 𝑞,𝑀 − 𝐷 𝑞,𝑉 𝑒( 𝑦  𝑑 𝑀 = 𝑑 ) 0  Refer Anderson Chapter V for more details 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 • 𝜍𝑊 2 𝜖𝑞 Both surfaces curve upward, • 𝜖𝑠 = 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 R upper and R lower increase 𝜖𝑠 = 𝜍𝑊 2 𝜖𝑞 𝑣 ↑, 𝑞 ∞ − 𝑞 𝑣 ↑, 𝑞 𝑣 ↓ 𝑆 𝜖𝑠 = 𝜍𝑊 2 𝜖𝑞 𝑚 ↑, 𝑞 ∞ − 𝑞 𝑚 ↑, 𝑞 𝑚 ↓ 𝑆 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 C p with AoA AE-705 Introduction to Flight Lecture No 8 Capsule-04

References  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) AE-705 Introduction to Flight Lecture No 8 Capsule-04