DOCSLIB.ORG

Open MS Thesis Mites Vieira.Pdf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Open MS Thesis Mites Vieira.Pdf The Pennsylvania State University The Graduate School College of Engineering AN INVESTIGATION OF THE AERODYNAMICS OF MINIATURE TRAILING-EDGE EFFECTORS APPLIED TO ROTORCRAFT A Thesis in Aerospace Engineering by Bernardo Augusto de Oliveira Vieira 2010 Bernardo Augusto de Oliveira Vieira Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2010 The thesis of Bernardo Augusto de Oliveira Vieira was reviewed and approved* by the following: Mark D. Maughmer Professor of Aerospace Engineering Thesis Advisor Jacob W. Langelaan Assistant Professor of Aerospace Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School iii ABSTRACT The aerodynamics of Miniature Trailing-Edge Effectors (MiTEs) is explored in many aspects with regards to their applicability to rotorcraft. MiTEs are active Gurney flaps that have the ability to modify the lift and moment characteristics of the blades around the rotor disk. MiTEs hold strong potential to be used as active devices to improve performance, reduce vibrations, and reduce noise of rotors. The present work explores the static and unsteady aerodynamic performance of MiTEs by the aid of experimental, numerical, and analytical methods. A static experimental investigation of Gurney flaps is undertaken at The Pennsylvania State University Low-Speed, Low-Turbulence Wind Tunnel. Aerodynamic results are obtained for three distinct rotorcraft airfoils equipped with Gurney flaps of various sizes and placed at different chordwise locations. The effects of Gurney flaps are found to be very dependent on the combination of their height and location, as well as on the airfoil shape. It is observed that when positioned upstream from the trailing edge, the Gurney flap can become sometimes ineffective and provide a decrease in the cl,max of the airfoil, suggesting that great care must be taken into sizing these devices. An experimental investigation of oscillating upstream-located MiTEs is conducted at the Mid-Sized Wind Tunnel at Penn State. Measured unsteady aerodynamic data prove the effectiveness of MiTEs in providing variations in the forces and moments of the airfoil. The amplitude and phase lag of the lift results are in good agreement with the trends predicted by unsteady linear theory. In some cases, however, the occurrence of non-linear effects is observed. These effects are believed to be caused by vortex shedding iv in the lower surface of the airfoil, and seem to be aggravated as the frequency of deployment increases. Analysis of available computational fluid-dynamic (CFD) predictions on upstream MiTEs indicates the formation and convection of an unsteady vortex in the lower surface of the airfoil, right after MiTE deployment. This disturbance can introduce non-harmonic components in the aerodynamic response, substantially affecting the loads and complicating the analysis. In order to account for these effects during routine helicopter performance and design studies, available CFD results are used to develop a reduced-order, less computer- intensive model based on indicial concepts. The model extends a work previously done for trailing-edge MiTEs by incorporating a vortex model to predict the unsteady lift of upstream MiTEs. A physics-based approach is adopted to minimize the number of constants and improve overall generality. The results from the unsteady-lift model are compared with CFD for different airfoils, MiTE deployment schedules, MiTE chordwise positions, and Mach numbers. Very good agreement is shown for a wide range of conditions that are typical of rotorcraft. Different model constants and correlations may have to be considered in order to improve the predictions for different airfoil shapes. v TABLE OF CONTENTS LIST OF FIGURES ................................................................................................... vii LIST OF TABLES ..................................................................................................... xiii LIST OF SYMBOLS ................................................................................................. xiv ACKNOWLEDGEMENTS ...................................................................................... xvi Chapter 1 Introduction.............................................................................................. 1 1.1 Introduction and Motivation .......................................................................... 1 1.2 MiTE Applications to Rotorcraft ................................................................... 3 1.3 Research Objectives ...................................................................................... 8 Chapter 2 Background and Literature Review ...................................................... 10 2.1 Gurney Flaps ................................................................................................. 10 2.2 MiTEs ............................................................................................................ 21 Chapter 3 Static Wind Tunnel Investigation........................................................... 33 3.1 Wind tunnel description and validation ......................................................... 34 3.2 Model description .......................................................................................... 38 3.3 Data acquisition system ................................................................................. 38 3.4 Results ........................................................................................................... 39 3.5 Conclusions ................................................................................................... 55 Chapter 4 Unsteady Wind Tunnel Investigation .................................................... 57 4.1 Previous efforts .............................................................................................. 58 4.2 Wind Tunnel Description .............................................................................. 60 4.3 Model and acquisition system ....................................................................... 61 4.4 Experimental Results ..................................................................................... 64 4.4.1 Static Verification ............................................................................... 64 4.4.2 Dynamic MiTEs ................................................................................. 68 4.5 Comparison with unsteady aerodynamic model ............................................ 79 4.6 Conclusions ................................................................................................... 84 Chapter 5 CFD Investigation .................................................................................... 86 5.1 Flow Physics .................................................................................................. 88 5.2 Overview of Results ...................................................................................... 96 5.3 Conclusions ................................................................................................... 101 vi Chapter 6 Unsteady Aerodynamic Modeling .......................................................... 103 6.1 Indicial Methods ............................................................................................ 104 6.1.1 Incompressible Flow .......................................................................... 105 6.1.2 Subsonic Compressible Flow ............................................................. 108 6.2 Unsteady Aerodynamic Model for MiTEs .................................................... 110 6.2.1 Circulatory Lift ................................................................................... 114 6.2.2 Apparent Mass Lift ............................................................................. 116 6.2.3 Vortex Lift .......................................................................................... 119 6.3 MiTE Model Results ..................................................................................... 123 6.3.1 Effect of Deployment Time ................................................................ 128 6.3.2 Effect of Mach number ....................................................................... 133 6.3.3 Retraction Cases ................................................................................. 135 6.3.4 Sinusoidal Deployments ..................................................................... 137 6.3.5 Effects of airfoil shape and MiTE position ........................................ 141 6.4 Summary ........................................................................................................ 145 Chapter 7 Conclusions ............................................................................................... 147 7.1 Summary of Results ...................................................................................... 147 7.1.1 Static Gurney Flap Experiments ......................................................... 147 7.1.2 Unsteady MiTEs Experiments ............................................................ 148 7.1.3 Unsteady Aerodynamic Modeling ...................................................... 149 7.2 Conclusions ................................................................................................... 150 7.3 Recommendations for Future Work .............................................................. 151
Load more

Recommended publications
  • Final Annual Activity Report 2014
    Final Annual Activity Report 2014 This report is provided in accordance with Articles 8 (k) and 20 (1) of the Statutes of the Clean Sky 2 Joint Undertaking annexed to the Council Regulation (EU) No 558/2014 and with Article 20 of the Financial Rules of Clean Sky 2 Joint Undertaking. ~ Page intentionally left blank ~ CS-GB-2015-06-23 Doc9 Final AAR 2014 2 Table of Contents 1. EXECUTIVE SUMMARY 5 2. INTRODUCTION 7 3. KEY OBJECTIVES AND ASSOCIATED RISKS 10 3.1 CLEAN SKY PROGRAMME - ACHIEVEMENT OF OBJECTIVES 10 3.2 CLEAN SKY 2 PROGRAMME - ACHIEVEMENT OF OBJECTIVES 16 4. RISK MANAGEMENT 18 4.1 GENERAL APPROACH TO RISK MANAGEMENT 18 4.2 JU LEVEL RISKS 19 4.3 CLEAN SKY PROGRAMME LEVEL RISKS 23 4.4 CLEAN SKY 2 PROGRAMME LEVEL RISKS 24 5. GOVERNANCE 26 5.1 GOVERNING BOARD 26 5.2 EXECUTIVE DIRECTOR 28 5.3 STEERING COMMITTEES 28 5.4 SCIENTIFIC AND TECHNICAL ADVISORY BOARD/ SCIENTIFIC COMMITTEE 28 5.5 STATES REPRESENTATIVES GROUP 29 6. RESEARCH ACTIVITIES 31 6.1 CLEAN SKY PROGRAMME - REMINDER OF RESEARCH OBJECTIVES 31 6.1.1 General information 32 6.1.2 SFWA - Smart Fixed Wing Aircraft ITD 34 6.1.3 GRA – Green Regional Aircraft ITD 40 6.1.4 GRC – Green Rotorcraft ITD 47 6.1.5 SAGE – Sustainable and Green Engine 52 6.1.6 SGO – Systems for Green Operations ITD 55 6.1.7 ECO – Eco-Design ITD 60 6.1.8 TE – Technology Evaluator 64 6.2 CLEAN SKY 2 PROGRAMME – REMINDER OF RESEARCH OBJECTIVES 70 6.2.1 General information 74 6.2.2 LPA – Large Passenger Aircraft IADP 75 6.2.3 REG – Regional Aircraft IADP 79 6.2.4 FRC – Fast Rotorcraft IADP 82 6.2.5 AIR– Airframe ITD 86 6.2.6 ENG – Engines ITD 91 6.2.7 SYS – Systems ITD 95 6.2.8 SAT – Small Air Transport Transverse Activity 99 6.2.9 ECO – Eco Design Transverse Activity 100 6.2.10 TE – Technology Evaluator 100 7.
    [Show full text]
  • Effects of Gurney Flap on Supercritical and Natural Laminar Flow Transonic Aerofoil Performance
    Effects of Gurney Flap on Supercritical and Natural Laminar Flow Transonic Aerofoil Performance Ho Chun Raybin Yu March 2015 MPhil Thesis Department of Mechanical Engineering The University of Sheffield Project Supervisor: Prof N. Qin Thesis submitted to the University of Sheffield in partial fulfilment of the requirements for the degree of Master of Philosophy Abstract The aerodynamic effect of a novel combination of a Gurney flap and shockbump on RAE2822 supercritical aerofoil and RAE5243 Natural Laminar Flow (NLF) aerofoil is investigated by solving the two-dimensional steady Reynolds-averaged Navier-Stokes (RANS) equation. The shockbump geometry is predetermined and pre-optimised on a specific designed condition. This study investigated Gurney flap height range from 0.1% to 0.7% aerofoil chord length. The drag benefits of camber modification against a retrofit Gurney flap was also investigated. The results indicate that a Gurney flap has the ability to move shock downstream on both types of aerofoil. A significant lift-to-drag improvement is shown on the RAE2822, however, no improvement is illustrated on the RAE5243 NLF. The results suggest that a Gurney flap may lead to drag reduction in high lift regions, thus, increasing the lift-to-drag ratio before stall. Page 2 Dedication I dedicate this thesis to my beloved grandmother Sandy Yip who passed away during the course of my research, thank you so much for the support, I love you grandma. This difficult journey would not have completed without the deep understanding, support, motivation, encouragement and unconditional love from my beloved parents Maggie and James and my brother Billy.
    [Show full text]
  • Wake Vortex Alleviation Using Rapidly Actuated Segmented Gurney Flaps
    WAKE VORTEX ALLEVIATION USING RAPIDLY ACTUATED SEGMENTED GURNEY FLAPS by Claude G. Matalanis and John K. Eaton Prepared with support from the The Stanford Thermal and Fluid Sciences Affiliates and the Office of Naval Research Report No. 102 Flow Physics and Computation Division Department of Mechanical Engineering Stanford University Stanford, CA 94305-3030 January 2007 c Copyright 2007 by Claude G. Matalanis All Rights Reserved ii Abstract All bodies that generate lift also generate circulation. The circulation generated by large commercial aircraft remains in their wake in the form of trailing vortices. These vortices can be hazardous to following aircraft due to their strength and persistence. To account for this, airports abide by spacing rules which govern the frequency with which aircraft can take-off and land from their runways when operating in instrument flight rules. These spacing rules have become the limiting factor on increasing airport capacity, and with the increases in air travel predicted for the near future, the problem is becoming more urgent. One way of approaching this problem is active wake alleviation. The basic idea is to actively embed perturbations in the trailing vortex system of an aircraft which will excite natural instabilities in the wake. The instabilities should result in a wake which is benign to following aircraft in less time than would normally be required, allowing for a reduction in current spacing rules. The main difficulty with such an approach is in achieving perturbations large enough to excite instability without significantly degrading aircraft performance. Rapidly actuated segmented Gurney flaps, also known as Miniature Trailing Edge Ef- fectors (MiTEs), have shown great potential in solving various aerodynamic problems.
    [Show full text]
  • Numerical Investigation for the Enhancement of the Aerodynamic Characteristics of an Aerofoil by Using a Gurney Flap
    International Journal of GEOMATE, June, 2017, Vol.12 Issue 34, pp. 21-27 Geotec., Const. Mat. & Env., ISSN:2186-2990, Japan, DOI: http://dx.doi.org/10.21660/2017.34.2650 NUMERICAL INVESTIGATION FOR THE ENHANCEMENT OF THE AERODYNAMIC CHARACTERISTICS OF AN AEROFOIL BY USING A GURNEY FLAP Julanda Al-Mawali1 and *Sam M Dakka2 1,2Department of Engineering and Math, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, UK *Corresponding Author, Received: 13 May 2016, Revised: 17 July 2016, Accepted: 28 Nov. 2016 ABSTRACT: Numerical investigation was carried out to determine the effect of a Gurney Flap on NACA 0012 aerofoil performance with emphasis on Unmanned Air Vehicles applications. The study examined different configurations of Gurney Flaps at high Reynolds number of 푅푒 = 3.6 × 105 in order to determine the optimal configuration. The Gurney flap was tested at different heights, locations and mounting angles. Compared to the clean aerofoil, the study found that adding the Gurney Flap increased the maximum lift coefficient by19%, 22%, 28%, 40% and 45% for the Gurney Flap height of 1%C, 1.5%C, 2%C, 3%C and 4%C respectively, C represents the chord of the aerofoil. However, it was also found that increasing the height of the gurney beyond 2%C leads to a decrease in the overall performance of the aerofoil due to the significant increase in drag penalty. Thus, the optimal height of the Gurney flap for the NACA 0012 aerofoil was found to be 2%C as it improves the overall performance of the aerofoil by 21%.
    [Show full text]
  • General Aviation Aircraft Design
    Contents 1. The Aircraft Design Process 3.2 Constraint Analysis 57 3.2.1 General Methodology 58 1.1 Introduction 2 3.2.2 Introduction of Stall Speed Limits into 1.1.1 The Content of this Chapter 5 the Constraint Diagram 65 1.1.2 Important Elements of a New Aircraft 3.3 Introduction to Trade Studies 66 Design 5 3.3.1 Step-by-step: Stall Speed e Cruise Speed 1.2 General Process of Aircraft Design 11 Carpet Plot 67 1.2.1 Common Description of the Design Process 11 3.3.2 Design of Experiments 69 1.2.2 Important Regulatory Concepts 13 3.3.3 Cost Functions 72 1.3 Aircraft Design Algorithm 15 Exercises 74 1.3.1 Conceptual Design Algorithm for a GA Variables 75 Aircraft 16 1.3.2 Implementation of the Conceptual 4. Aircraft Conceptual Layout Design Algorithm 16 1.4 Elements of Project Engineering 19 4.1 Introduction 77 1.4.1 Gantt Diagrams 19 4.1.1 The Content of this Chapter 78 1.4.2 Fishbone Diagram for Preliminary 4.1.2 Requirements, Mission, and Applicable Regulations 78 Airplane Design 19 4.1.3 Past and Present Directions in Aircraft Design 79 1.4.3 Managing Compliance with Project 4.1.4 Aircraft Component Recognition 79 Requirements 21 4.2 The Fundamentals of the Configuration Layout 82 1.4.4 Project Plan and Task Management 21 4.2.1 Vertical Wing Location 82 1.4.5 Quality Function Deployment and a House 4.2.2 Wing Configuration 86 of Quality 21 4.2.3 Wing Dihedral 86 1.5 Presenting the Design Project 27 4.2.4 Wing Structural Configuration 87 Variables 32 4.2.5 Cabin Configurations 88 References 32 4.2.6 Propeller Configuration 89 4.2.7 Engine Placement 89 2.
    [Show full text]
  • Equations for the Application of to Pitching Moments
    https://ntrs.nasa.gov/search.jsp?R=19670002485 2020-03-24T02:43:10+00:00Z View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NASA Technical Reports Server NASA TECHNICAL NOTE NASA TN D-3738 00 M h U GPO PRICE $ c/l U z CFSTl PRICE@) $ ,2biJ I 1 Hard copy (HC) ' (THRU) :: N67(ACCES~ION 11814NUMBER) 5P Microfiche (MF) > Jo(PAGES1 k i ff 853 July 85 2 (NASA CR OR TMX OR AD NUMBER) '- ! EQUATIONS FOR THE APPLICATION OF * WIND-TUNNEL WALL CORRECTIONS TO PITCHING MOMENTS CAUSED BY THE TAIL OF AN AIRCRAFT MODEL by Harry He Heyson Langley Research Center Langley Stdon, Hampton, Vk NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. NOVEMBER 1966 . NASA TN D-3738 EQUATIONS FOR THE APPLICATION OF WIND-TUNNEL WALL CORRECTIONS TO PITCHING MOMENTS CAUSED BY THE TAIL OF AN AIRCRAFT MODEL By Harry H. Heyson Langley Research Center Langley Station, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - Price 61.00 , EQUATIONS FOR THE APPLICATION OF WIND-TUNNEL WALL CORmCTIONS TO PITCHING MOMENTS CAUSED BY THE TAIL OF AN AIRCRAFT MODEL By Harry H. Heyson Langley Research Center SUMMARY Equations are derived for the application of wall corrections to pitching moments due to the tail in two different manners. The first system requires only an alteration in the observed pitching moment; however, its application requires a knowledge of a number of quantities not measured in the usual wind- tunnel tests, as well as assumptions of incompressible flow, linear lift curves, and no stall.
    [Show full text]
  • Introduction to Aircraft Stability and Control Course Notes for M&AE 5070
    Introduction to Aircraft Stability and Control Course Notes for M&AE 5070 David A. Caughey Sibley School of Mechanical & Aerospace Engineering Cornell University Ithaca, New York 14853-7501 2011 2 Contents 1 Introduction to Flight Dynamics 1 1.1 Introduction....................................... 1 1.2 Nomenclature........................................ 3 1.2.1 Implications of Vehicle Symmetry . 4 1.2.2 AerodynamicControls .............................. 5 1.2.3 Force and Moment Coefficients . 5 1.2.4 Atmospheric Properties . 6 2 Aerodynamic Background 11 2.1 Introduction....................................... 11 2.2 Lifting surface geometry and nomenclature . 12 2.2.1 Geometric properties of trapezoidal wings . 13 2.3 Aerodynamic properties of airfoils . ..... 14 2.4 Aerodynamic properties of finite wings . 17 2.5 Fuselage contribution to pitch stiffness . 19 2.6 Wing-tail interference . 20 2.7 ControlSurfaces ..................................... 20 3 Static Longitudinal Stability and Control 25 3.1 ControlFixedStability.............................. ..... 25 v vi CONTENTS 3.2 Static Longitudinal Control . 28 3.2.1 Longitudinal Maneuvers – the Pull-up . 29 3.3 Control Surface Hinge Moments . 33 3.3.1 Control Surface Hinge Moments . 33 3.3.2 Control free Neutral Point . 35 3.3.3 TrimTabs...................................... 36 3.3.4 ControlForceforTrim. 37 3.3.5 Control-force for Maneuver . 39 3.4 Forward and Aft Limits of C.G. Position . ......... 41 4 Dynamical Equations for Flight Vehicles 45 4.1 BasicEquationsofMotion. ..... 45 4.1.1 ForceEquations .................................. 46 4.1.2 MomentEquations................................. 49 4.2 Linearized Equations of Motion . 50 4.3 Representation of Aerodynamic Forces and Moments . 52 4.3.1 Longitudinal Stability Derivatives . 54 4.3.2 Lateral/Directional Stability Derivatives .
    [Show full text]
  • Longitudinal Static Stability
    Longitudinal Static Stability Some definitions M pitching moment without dimensions C m 1 (so without influence of ρ, V and S) V2 Sc 2 it is a ‘shape’ parameter which varies with the angle of attack. Note the chord c in the denominator because of the unit Nm! L For the wing+aircraft we use the C L 1 surface area of the wing S! VS2 2 L For the tail we use the surface of the tail: SH ! C H LH 1 VS2 2 H Definition of aerodynamic center of a wing: The aerodynamic center (a.c.) is the point around which the moment does not change when the angle of attack changes. We can therefore use Cmac as a constant moment for all angles of attack. The aerodynamic center usually lies around a quarter chord from the leading edge. 1 Criterium for longitudinal static stability (see also Anderson § 7.5): We will look at the consequences of the position of the center of gravity, the wing and the tail for longitudinal static stability. For stability, we need a negative change of the pitching moment if there is a positive change of the angle of attack (and vice versa), so: CC 0 mm 00 0 Graphically this means Cm(α) has to be descending: For small changes we write: dC m 0 d We also write this as: C 0 m 2 When Cm(α) is descending, the Cm0 has to be positive to have a trim point where Cm = 0 and there is an equilibrium: So two conditions for stability: 1) Cm0 > 0; if lift = 0; pitching moment has to be positive (nose up) dC 2) m 0 ( or C 0 ); pitching moment has to become more negative when d m the angle of attack increases Condition 1 is easy to check.
    [Show full text]
  • Vestas Annual Report 2015 · Group Performance ­VESTAS FACTS
    Technology “ The introduction of the V136-3.45 MW™ turbine as well as various other upgrades once again proves our ability to develop very competitive offerings based on our existing product portfolio – and with a time-to-market consistent with our customers’ needs.” Anders Vedel Executive Vice President & CTO Vestas’ technology strategy During 2015, the 3 MW variants have increased their potential and Being the global wind leader requires a long-term line of sight in tech- were upgraded to a higher wind class. Also included was an upgrade nology development. ­­Vestas continuously strives to bring commercially of standard rating to 3.45 MW, power modes of up to 3.6 MW (except relevant products to the market in a profitable way. The Vestas technol- on the V136-3.45 MW™), tower heights of up to 166 metres and the ogy strategy derives its strength from a market-driven product devel- introduction of a next-generation advanced control system. The new opment and extensive testing at Vestas’ test facility in Denmark – the control system is significantly faster, and available input/output sig- largest test facility in the wind power industry. This enables Vestas to nals are significantly increased to secure availability to meet future continuously innovate new and integrate proven technologies to cre- requirements. ate high-performing products and services in pursuit of the over-riding objective: lowering the cost of energy. V136-3.45 MW™ turbine introduced In September 2015, Vestas introduced the V136-3.45 MW™ turbine, By building on existing platforms – the 2 MW and 3 MW – and using the latest and as yet largest addition to the 3 MW wind turbine family, standardised and modularised “building blocks”, it has been possible demonstrating the strong technological capabilities of the platform to offer energy-effective solutions for a wide variety of wind regimes and how far Vestas has come in utilising the advantages of standardi- across the global wind energy markets, but with minimal additional sation and modularisation.
    [Show full text]
  • THE GURNEY FLAP by Sergio Montes
    THE GURNEY FLAP by Sergio Montes Gurney flaps are bent strips attached to the trailing edge of an airfoil, normally no larger than about 2 to 5% of the chord. They have a profound effect on the lift but in many cases a surprisingly small effect on drag. They defy what conventional wisdom would recommend as good aerodynamic practice. The name of this flap derives from American car driver Dan Gurney, who sought to increase the downward force of a wing fitted at the rear of his Indy car in the 1960's. He thought that he could get even more down-force by blocking the flow on the top of the wing with a dam at the trailing edge. Aerodynamicists who heard of this idea were not supportive, fearing that this dam might act like a spoiler and reduce the downward force rather than increase it. One of the considerations in the Circulation Theory of Lift is that the flow from the upper and lower surfaces of the trailing edge must smoothly merge in the wake. It seemed reasonable to expect that the Gurney flap would interfere with this requirement. However, a very similar scheme called the "split flap" was used on airplanes as far back as the 1930's. This is a fairly simple device consisting of a hinged plate covering the last 20% of chord on the bottom of the trailing edge. The device is deployed during landings. In the 1940's, NACA ran many two-dimensional wind tunnel tests of airfoils with and without split flaps.
    [Show full text]
  • List of Symbols
    List of Symbols a atmosphere speed of sound a exponent in approximate thrust formula ac aerodynamic center a acceleration vector a0 airfoil angle of attack for zero lift A aspect ratio A system matrix A aerodynamic force vector b span b exponent in approximate SFC formula c chord cd airfoil drag coefficient cl airfoil lift coefficient clα airfoil lift curve slope cmac airfoil pitching moment about the aerodynamic center cr root chord ct tip chord c¯ mean aerodynamic chord C specfic fuel consumption Cc corrected specfic fuel consumption CD drag coefficient CDf friction drag coefficient CDi induced drag coefficient CDw wave drag coefficient CD0 zero-lift drag coefficient Cf skin friction coefficient CF compressibility factor CL lift coefficient CLα lift curve slope CLmax maximum lift coefficient Cmac pitching moment about the aerodynamic center CT nondimensional thrust T Cm nondimensional thrust moment CW nondimensional weight d diameter det determinant D drag e Oswald’s efficiency factor E origin of ground axes system E aerodynamic efficiency or lift to drag ratio EO position vector f flap f factor f equivalent parasite area F distance factor FS stick force F force vector F F form factor g acceleration of gravity g acceleration of gravity vector gs acceleration of gravity at sea level g1 function in Mach number for drag divergence g2 function in Mach number for drag divergence H elevator hinge moment G time factor G elevator gearing h altitude above sea level ht altitude of the tropopause hH height of HT ac above wingc ¯ h˙ rate of climb 2 i unit vector iH horizontal
    [Show full text]
  • Aerodynamic Center1 Suppose We Have the Forces and Moments
    Aerodynamic Center1 Suppose we have the forces and moments specified about some reference location for the aircraft, and we want to restate them about some new origin. N ~ L N ~ L M AAM z ref new x x ref xnew M ref = Pitching moment about xref M new = Pitching moment about xnew xref = Original reference location xnew = New origin N = Normal force ≈ L for small ∝ A = Axial force ≈ D for small ∝ Assuming there is no change in the z location of the two points: MxxLMref=−() new − ref + new Or, in coefficient form: xx− new ref CCCmLM=− + ref cN new mean ac.. The Aerodynamic Center is defined as that location xac about which the pitching moment doesn’t change with angle of attack. How do we find it? 1 Anderson 1.6 & 4.3 Aerodynamic Center Let xnew= x ac Using above: ()xx− CCC=−ac ref + M refc LM ac Differential with respect to α : ∂CM xx− ∂C ref ac ref ∂CL M ac =− + ∂∂∂αααc By definition: ∂CM ac = 0 ∂α Solving for the above ∂C xxac− ref M ref ∂C =−L , or c ∂∂αα ∂C xxac− ref x ref M ref =− ccC∂ L Example: Consider our AVL calculations for the F-16C • xref = 0 - Moment given about LE ∂C • Compute M ref for small range of angle of attack by numerical ∂CL differences. I picked αα= −=300 to 3. x • This gave ac ≈ 2.89 . c x ∂C • Plotting Cvsα about ac shows M ≈ 0 . M c ∂α ∂C Note that according to the AVL predictions, not only is M ≈=0 @ x 2.89 , but ∂α ac also that CM = 0 .
    [Show full text]