OVERVIEW What is M crit ? Sound Barrier Critical Pressure - PowerPoint PPT Presentation

OVERVIEW  What is M crit ?  Sound Barrier  Critical Pressure Coefficient Derivation  How to find M crit ?  Drag Divergence Mach Number  Wave Drag  Swept Wings  Types of Swept Wings AE-705 Introduction to Flight Lecture-09 Capsule-05

Why are you so critical ? WHAT IS M CRIT ? AE-705 Introduction to Flight Lecture-09 Capsule-05

Source: http://www.boldmethod.com/learn-to-fly/aerodynamics/wing-sweep/ AE-705 Introduction to Flight Lecture-09 Capsule-05

When M=1  Weak shock wave Actual M crit varies from wing to wing Has lower M crit Deflects air more AE-705 Introduction to Flight Lecture-09 Capsule-05

Can be broken !!! SOUND BARRIER AE-705 Introduction to Flight Lecture-09 Capsule-05

Source: https://www.youtube.com/watch?v=ugPJYJ-BKkU AE-705 Introduction to Flight Lecture-09 Capsule-05

REVISITING PRESSURE COEFFICIENT At low V  M < ~ 0.3  C p = constant 𝐷 𝑞 = 𝐷 𝑞,0 For ~ 0.3 < M ∞ < ~ 0.7 𝐷 𝑞,0 𝐷 𝑞 = 2 1 − 𝑁 ∞ Prandtl-Glauert Rule Compressibility effects AE-705 Introduction to Flight Lecture-09 Capsule-05

Universal Curve Source: EdX course on Introduction to Aeronautical Engineering AE-705 Introduction to Flight Lecture-09 Capsule-05

Let’s get to some Math!! CRITICAL PRESSURE COEFFICIENT DERIVATION AE-705 Introduction to Flight Lecture-09 Capsule-05

We know that: 𝐷 𝑞 = 𝑞 − 𝑞 ∞ 𝑞 ∞ 𝑞 (1) = − 1 𝑟 ∞ 𝑟 ∞ 𝑞 ∞ 𝑟 ∞ = 1 𝑡𝑗𝑜𝑑𝑓 𝑁 ∞ = 𝑊 1 ∞ 2 𝑏 ∞ 2 And 2 2 𝜍 ∞ 𝑊 = 2 𝜍 ∞ 𝑁 ∞ ∞ 𝑏 ∞ 2 = 𝛿 𝜍 ∞ And 𝑏 ∞ 𝑟 ∞ 𝑟 ∞ = 1 2 𝛿𝑞 ∞ …..(2) 2 𝑁 ∞ AE-705 Introduction to Flight Lecture-09 Capsule-05

Substituting (2) in (1), we get 2𝑞 ∞ 𝑞 𝐷 𝑞 = − 1 2 𝛿𝑞 ∞ 𝑞 ∞ 𝑁 ∞ 𝛿 From the isentropic flow 𝑞 0 1 + 𝛿 − 1 𝛿−1 𝑁 2 𝑞 = relations 2 𝛿 𝑞 0 1 + 𝛿 − 1 𝛿−1 2 = 𝑁 ∞ 𝑞 ∞ 2 𝛿 1 + 1 𝛿−1 2 2 𝛿 − 1 𝑁 ∞ 𝑞 …..(3) Thus = 1 + 1 𝑞 ∞ 2 𝛿 − 1 𝑁 2 AE-705 Introduction to Flight Lecture-09 Capsule-05

Substituting (3) in (1) 𝛿 1 + 1 𝛿−1 2 2 𝛿 − 1 𝑁 ∞ 2 𝐷 𝑞 = − 1 2 1 + 1 𝛿𝑁 ∞ 2 𝛿 − 1 𝑁 2 From definition of C p,crit putting M=1 Thus we get 𝛿 2 𝛿−1 2 2 + 𝛿 − 1 𝑁 ∞ 𝐷 𝑞,𝑑𝑠𝑗𝑢 = − 1 2 𝛿 + 1 𝛿𝑁 ∞ M ∞  M crit as M=1 AE-705 Introduction to Flight Lecture-09 Capsule-05

Two methods waiting for you!! HOW TO FIND M CRIT ? AE-705 Introduction to Flight Lecture-09 Capsule-05

GRAPHICAL SOLUTION M crit  Obtain a plot of versus  Obtain the value of (usually given)  Plot from Prandtl-Glauert rule AE-705 Introduction to Flight Lecture-09 Capsule-05

ANALYTICAL SOLUTION  From Prandtl-Glauert rule C p min at max V 𝐷 𝑞,0 𝐷 𝑞 = 2 1 − 𝑁 ∞ It is seen that as C p,0 M ∞  C p at sonic condition(M=1) is C p,crit  Thus 𝛿 𝐷 𝑞,0 2 2 2 + 𝛿 − 1 𝑁 ∞ 𝛿−1 2 = − 1 2 𝛿 + 1 𝛿𝑁 ∞ 1 − 𝑁 ∞ M ∞  M crit as M=1 AE-705 Introduction to Flight Lecture-09 Capsule-05

LOCATION OF MAX V POINT ON AIRFOIL Min pressure (max velocity)  X max x/c Not corresponding 0.3 0.11 NACA 0012 Source: Anderson Max V  complete shape of airfoil AE-705 Introduction to Flight Lecture-09 Capsule-05

What’s the difference?? DRAG DIVERGENCE MACH NUMBER AE-705 Introduction to Flight Lecture-09 Capsule-05

M  Drag rapidly  at times C d (*10) Source: http://slideplayer.com/slide/8760031/ AE-705 Introduction to Flight Lecture-09 Capsule-05

M  Drag rapidly  at times C d (*10) Flow separates Due to formation of shock wave Adverse dp/dx a c r o s s P & V Source: http://slideplayer.com/slide/8760031/ AE-705 Introduction to Flight Lecture-09 Capsule-05

Drag = Wave Drag?? WAVE DRAG AE-705 Introduction to Flight Lecture-09 Capsule-05

WHAT IS IT ?  Component of drag @ V transonic/supersonic  Independent of μ effects  Seen as SW considerable energy  Drag Source: http://tousifahmed54.blogspot.in/2013/08/completed-projects-and-researches.html AE-705 Introduction to Flight Lecture-09 Capsule-05

WEDGE BODY @ V supersonic Pressure Distribution P ,T , ρ ,V , M Shock wave AE-705 Introduction to Flight Lecture-09 Capsule-05

FLAT PLATE @ V supersonic Region through which P Pressure Distribution Minimize wave  Thin profile/Sharp LE AE-705 Introduction to Flight Lecture-09 Capsule-05

FOR THIN AIRFOILS 4𝛽 𝐷 l = Lockheed 104 Starfighter  𝑁 2 ∞ − 1 4𝛽 2 𝐷 d,w =  𝑁 2 ∞ − 1 L and D as q ∞ Note: 𝐷 l and 𝐷 d,w with M ∞ Source: http://www.heartlandofamericaband.af.mil/photos/mediagallery.asp?galleryID=529&page=262 AE-705 Introduction to Flight Lecture-09 Capsule-05

TACKLING WAVE DRAG objects @ M ∞ >1  weak disturbance  objects @ M ∞ >1  shock wave   Solution:  Wing sweep  Thin wings  Fuselage shape  Anti-shock bodies  Supercritical airfoils Source: https://aviation.stackexchange.com/questions/21620/whats- Source:https://www.flickr.com/photos/multiplyleadership/529963 Source: http://empiresandallies.wikia.com/wiki/Gripen_Fighter Source: http://forum.flitetest.com/showthread.php?8139-KFM- the-reason-for-the-local-flap-extensions-at-the-shockbody-locations 7305 Airfoils-and-Swept-Back-wings AE-705 Introduction to Flight Lecture-09 Capsule-05

TRANSONIC FLIGHT  Airflow~0.8<M<1.2  Depends on T surrounding Drag  Fuel consumption   Solution: Convair F-102A Delta Dagger  Swept Wings  Area Rule  Wasp waist fuselage Source: https://www.thisdayinaviation.com/24- october-1953/ AE-705 Introduction to Flight Lecture-09 Capsule-05

SWEPT WINGS AE-705 Introduction to Flight Lecture-09 Capsule-05

HISTORY IDEA!! Swept wings V air,wing dominated by V air,n and not V air ,∞ Dr. Adolf Busemann 1901 - 1986 Shock waves formed at ↑ V!! AE-705 Introduction to Flight Lecture-09 Capsule-05

WHAT IS IT ? Lateral Axis Sweep Angle Mind it!! Can be forward swept also AE-705 Introduction to Flight Lecture-09 Capsule-05

WHY SWEPT WINGS ? AE-705 Introduction to Flight Lecture-09 Capsule-05

Drag divergence delayed to M AE-705 Introduction to Flight Lecture-09 Capsule-05

In reality….complex 3D flow Source: https://www.mentor.com/products/mechanical/engineering- edge/volume2/issue3/floefd-external-aero Although our 2D sweeping simplification 𝑁 𝑑𝑠 𝑔𝑝𝑠 𝑏𝑗𝑠𝑔𝑝𝑗𝑚 M cr for airfoil < Actual M cr for swept wing < cos 𝛻 AE-705 Introduction to Flight Lecture-09 Capsule-05

AD-1 NASA Weird isn’t it ?? Source: http://www.techeblog.com/index.php/tech-gadget/nasa-ad-1- oblique-wing-aircraft-might-be-strangest-looking-ever-here-are-5-cool-facts OBLIQUE WING AE-705 Introduction to Flight Lecture-09 Capsule-05

Introduction to Oblique Wing AE-705 Introduction to Flight Lecture-09 Capsule-05

BENEFITS OF OBLIQUE WING  Low structural mass  Centre of mass and lift not shifted  Low wave drag Induced drag   AE-705 Introduction to Flight Lecture-09 Capsule-05

PROBLEMS  Asymmetric stall  Hinge  Load of fuel tank!  Poor handling  trim and inertial coupling  Engine mounted on fuselage Learjet 45 Source: https://www.privatefly.com/private-jets/medium-jet- hire/Learjet-45-45XR.html Source: https://www.youtube.com/watch?v=UQJa_FKkYZA Source: https://www.youtube.com/watch?v=vTQwkKameLg AE-705 Introduction to Flight Lecture-09 Capsule-05

You gotta be kidding me!! FORWARD SWEPT WING AE-705 Introduction to Flight Lecture-09 Capsule-05

WHY THIS IDEA ?  Location of main spar  More space  Air flows inwards  X Tip stall Aileron control Slats X remains!!  Wingtip vortices  Improves maneuverability Source: http://blogs.bu.edu/biolocomotion/2011/10/18/ winglets-the-anti-vortex-device/ AE-705 Introduction to Flight Lecture-09 Capsule-05

WHAT WAS THE PROBLEM ?  Yaw instability  Reverse Dutch Roll  Torsional Divergence Source: http://ascelibrary.org/doi/full/10.1061/(ASCE)AS.1943- 5525.0000427  Unstable in stall Video Courtesy: https://www.youtube.com/watch?v=kOBbAFzXrRg AE-705 Introduction to Flight Lecture-09 Capsule-05

What’s the point? Is it a fashion show ?? VARIABLE SWEPT WINGS AE-705 Introduction to Flight Lecture-09 Capsule-05

General Dynamics F-111 Aardvark AE-705 Introduction to Flight Lecture-09 Capsule-05

MiG 27M Bahadur 3 Wing Sweep Positions 16 o T/O, Land, Low speed Flight 45 o Combat, Transonic Flight 72 o High Speed Dash AE-705 Introduction to Flight Lecture-09 Capsule-05

 Also called Swing Wing  Suitable for high speeds  Lowers drag  Improves lateral stability Sees the airfoil thinner Experiences less V  less drag Delays shockwaves AE-705 Introduction to Flight Lecture-09 Capsule-05

WHY DID THEY DIE OUT ?  Added weight (~ 4% extra)  Maintenance Issues  Higher radar cross-section  Tough balancing AE-705 Introduction to Flight Lecture-09 Capsule-05