Flight and Orbital Mechanics
|
|
- Beverly Curtis
- 5 years ago
- Views:
Transcription
1 Flight and Orbital Mechanics Lecture slides Challenge the future 1
2 Flight and Orbital Mechanics Lecture hours 3, 4 Minimum time to climb Mark Voskuijl Semester Delft University of Technology Challenge the future
3 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 2
4 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 3
5 Introduction Question What is the most efficient way (minimum time) to go from take-off at sea-level to Mach 1.5 at 15,000 m? A. Climb at airspeed for max. At 15,000 m accelerate to Mach 2 B. Climb at airspeed for max RC. At 15,000 m accelerate to Mach 2 C. Climb at at airspeed for for max max RC to RC 11,000 to 11,000 m. Descent m. and accelerate Descent and to Mach accelerate 1.2 at 9,000 to Mach m, climb 1.2 at and 9,000 accelerate m, to climb Mach and 2 at accelerate 11,000 m. Decelerated to Mach 2 at climb 11,000 to 15,000 m. m, Mach Decelerated 1.5 climb to 15,000 m, Mach 1.5 D. Accelerate at sea-level to Mach 1.5, climb to 15,000 m at airspeed for max RC AE2104 Flight and Orbital Mechanics 4
6 Introduction Solution Altitude [m] M = Subsonic M = 2 M = 1.2 (Supersonic) 0 AE2104 Flight and Orbital Mechanics 5
7 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 6
8 Summary previous lecture A typical climb (civil subsonic aircraft) is performed at constant indicated airspeed and at a constant power setting. Therefore, the true airspeed is actually increasing. Since airspeed is not constant, it is an unsteady climbing flight The climb is almost a straight line. It is therefore a quasi-rectilinear flight Corresponding equations of motion: W dv T D W sin g dt L W AE2104 Flight and Orbital Mechanics 7
9 Summary previous lecture The rate of climb in an unsteady climb is smaller than in a steady climb because part of the excess energy is used to accelerate RC RC st 1 V dv 1 g dh dv ; 0 dh You must be able to derive this ratio from the equations of motion You must be able to calculate this ratio (see example exam question) For more background information: read Ruijgrok Elements of airplane performance section 14.2 AE2104 Flight and Orbital Mechanics 8
10 Content Introduction Summary previous lecture Performance diagram Optimal climb Energy height Solution low speed aircraft Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 9
11 P Performance diagram P a W P r RC steady P a P r V AE2104 Flight and Orbital Mechanics 10
12 Aerodynamic forces (year 1) Lift Drag polar C D C D 0 C 2 L Ae AE2104 Flight and Orbital Mechanics 11
13 Aerodynamic forces (year 1) Lift L W 1 2 C V S W C L 2 W 2 1 S V L 2 Drag C D C D 0 C 2 L Ae 1 2 D C V S D C 1 L 1 2 D C D V S V S Ae W D C D V S V S S V Ae W D C D V S Ae V S 2 So, one part of the drag decreases (!) with airspeed (1/V 2 ) and one part increases with airspeed (V 2 ) AE2104 Flight and Orbital Mechanics 12
14 Aerodynamic forces (year 1) Drag as a function of airspeed Aircraft are quite unique in the sense that drag increases when airspeed decreases! D D D D0 C D V S 2 2 W Di Ae 0 i V S AE2104 Flight and Orbital Mechanics 13
15 AE2104 Flight and Orbital Mechanics 14
16 P P a Pa Pr W RC steady P r V V 1 V 2 V 3 V 4 RC steady Determine magnitude of difference and divide by aircraft weight (W) V V 1 V 2 V 3 AE2104 Flight and Orbital Mechanics 15
17 Performance diagram How does it change with altitude? Note: this sheet is from the first year lecture AE2104 Flight and Orbital Mechanics 16
18 P P a Pa Pr W RC steady P r V 3 V 4 V RC steady H 1 H 2 V AE2104 Flight and Orbital Mechanics 17
19 Performance diagram Rate of climb as a function of airspeed and altitude AE2104 Flight and Orbital Mechanics 18
20 Performance diagram Rate of climb as a function of airspeed and altitude H RC = 6 m/s RC = 2 m/s V AE2104 Flight and Orbital Mechanics 19
21 Content Introduction Summary previous lecture Performance diagram Optimal climb Energy height Solution low speed aircraft Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 20
22 Optimal climb During climb at constant indicated airspeed, the aircraft is accelerating. V(H) is fixed Easy flight technique for the pilot But is this optimal??? What is optimal? AE2104 Flight and Orbital Mechanics 21
23 Optimal climb What is optimal? Minimum time to climb (time) Minimum fuel consumed during climb (fuel) Distance covered during climb (distance) Noise during climb (noise) AE2104 Flight and Orbital Mechanics 22
24 Optimal climb What is optimal? Minimum time to climb (time) Minimum fuel consumed during climb (fuel) Distance covered during climb (distance) Noise during climb (noise) We will focus on the first option, but the other three are optimal as well AE2104 Flight and Orbital Mechanics 23
25 Optimal climb Objective: to find the true airspeed as a function of altitude that yields the minimum time to climb dh RC dt dt t dt H H 2 1 dh RC dh RC Time t is not minimal if the integrand is minimal at every altitude H because the term dv/dh is in the integrand Variational calculus is necessary RC RC steady 1 1 V dv g dh 0 t H H 2 1 V dv 1 g0 dh RC steady dh AE2104 Flight and Orbital Mechanics 24
26 Variational calculus? t H H 2 1 V dv 1 g0 dh RC steady dh Minimize integrand: RC steady maximum dv/dh <0 dv/dh<0 RC steady max At H = 0, RC st is maximal at V = 100 The integrand can be minimized more by choosing (dv/dh) 1 < 0 Choosing maximum RC steady at sea level At seems altitude like a H good > 0 starting no point optimum V can be chosen Conclusion: No local optimum but global optimum (consider complete flight path) AE2104 Flight and Orbital Mechanics 25
27 Optimal climb H H 2 t 1 V dv 1 g0 dh RC steady dh Solution Simplify (low speed aircraft) Energy method (high subsonic / supersonic aircraft) AE2104 Flight and Orbital Mechanics 26
28 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 27
29 Low speed aircraft AE2104 Flight and Orbital Mechanics 28
30 Low speed aircraft t H dh RC H 0 0 V dv 1 g0 dh RC st dh Assumption: Low speed, low altitude dv/dh is small t H 0 dh RC st Choose maximum steady rate of climb at each altitude AE2104 Flight and Orbital Mechanics 29
31 Low speed aircraft W dv T D W sin g dt Pa Pr W dv RC V W g dt Pa Pr RC W steady P H 1 H RC steady 2 H V V AE2104 Flight and Orbital Mechanics 30
32 Low speed aircraft Solution propeller aircraft RC P a st P P a r W can be assumed constant as function of airspeed for propeller aircraft 3 V RC P C C Ae opt st max r,min L, opt D0 W S C L, opt Note: this optimal C L was determined in the first year lectures! P a Corresponding V V V constant because V V e i i e 0 constant P r V P r,min AE2104 Flight and Orbital Mechanics 31
33 Low speed aircraft Summary Conclusion: if the pilot selects the airspeed for the maximum steady rate of climb at the ground and if he / she keeps the indicated airspeed constant, then the climb will be optimal Optimal in this case means minimum time to climb (assuming dv/dh is small) AE2104 Flight and Orbital Mechanics 32
34 Low speed aircraft Story World War I AE2104 Flight and Orbital Mechanics 33
35 Low speed aircraft Story World War I Allied airfoils (British / French) versus German airfoils Thin airfoils have low C L,max Therefore, German aircraft were able to fly slower British / French) versus German airfoils AE2104 Flight and Orbital Mechanics 34
36 Low speed aircraft Story World War I P r P a Numerical example C 3C Ae L D o CD A 6 e 0.8 C V L, opt E V 1.26 (large!) ground W 2 1 S C 0 L, opt V min (thick profiles) V min (thin profiles) AE2104 Flight and Orbital Mechanics 35
37 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 36
38 AE2104 Flight and Orbital Mechanics 37
39 Energy height Concept to solve the minimum time to climb problem Altitude and flight speed are rapidly interchangeable (exchange of kinetic energy and potential energy) Increasing the total energy is much slower because it depends on the excess power 1 2 1W 2 Energy 2mV mgh 2 V WH g H Line of constant energy V AE2104 Flight and Orbital Mechanics 38
40 Energy height H H e e Energy W 2 V H 2g D B A C AE2104 Flight and Orbital Mechanics 39
41 Energy height H Large energy Small energy Optimal combination of V and H to increase the energy So: Minimum time to climb problem approximated by another problem: find V opt (H) at which minimum time to total energy V AE2104 Flight and Orbital Mechanics 40
42 Energy height Energy method Energy height E mg H mv W E WH 2 V g H e 0 E H W 2 V 2g dhe dh 1 dv dt dt 2g dt dhe Pa Pr dt W RC steady Equation of Motion W dv T D W sin g dt 0 1 dv sin T D g dt W 0 V dv Pa P V r sin g dt W dv dh Pa Pr 2g dt dt W 0 AE2104 Flight and Orbital Mechanics 41
43 Minimum time to climb dh dt e RC s dt dh RC e st t H e2 H e1 dh RC e st (time to energy height) AE2104 Flight and Orbital Mechanics 42
44 Optimum path subsonic aircraft (for each constant energy height line, find the maximum steady rate of climb) AE2104 Flight and Orbital Mechanics 43
45 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 44
46 Solution high speed aircraft Excess power, h 1 <h 2 <h 3 h 1 ft/sec h 2 h 3 Altitude h Mach AE2104 Flight and Orbital Mechanics 45
47 Supersonic aircraft Dip in excess power is caused by transonic drag rise: 0 C C M k M C 2 D D L supersonic aircraft High subsonic aircraft AE2104 Flight and Orbital Mechanics 46
48 Solution high speed aircraft AE2104 Flight and Orbital Mechanics 47
49 Solution high speed aircraft Example performance Mig-29: Climb from sea level to 6000 m in less than 1 minute AE2104 Flight and Orbital Mechanics 48
50 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 49
51 Example exam question AE2104 Flight and Orbital Mechanics 50
52 Example exam question AE2104 Flight and Orbital Mechanics 51
53 Content Introduction Summary previous lecture Performance diagram Optimal climb Solution low speed aircraft Energy height Solution high speed aircraft (M>1) Example exam question Summary AE2104 Flight and Orbital Mechanics 52
54 Summary AE2104 Flight and Orbital Mechanics 53
55 Questions? AE2104 Flight and Orbital Mechanics 54
Flight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and orbital mechanics Flight Mechanics practice questions Dr. ir. Mark Voskuijl 20-11-2013 Delft University of Technology Challenge
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Introduction Aerospace Engineering Flight Mechanics Dr. ir. Mark Voskuijl 15-12-2012 Delft University of Technology Challenge
More informationFlight and Orbital Mechanics. Exams
1 Flight and Orbital Mechanics Exams Exam AE2104-11: Flight and Orbital Mechanics (23 January 2013, 09.00 12.00) Please put your name, student number and ALL YOUR INITIALS on your work. Answer all questions
More informationFlight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics Lecture 7 Equations of motion Mark Voskuijl Semester 1-2012 Delft University of Technology Challenge the
More informationGliding, Climbing, and Turning Flight Performance! Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2016
Gliding, Climbing, and Turning Flight Performance! Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2016 Learning Objectives Conditions for gliding flight Parameters for maximizing climb angle and rate
More informationChapter 8 Performance analysis IV Accelerated level flight and climb (Lecture 27) Keywords: Topics 8.1 Introduction 8.2 Accelerated level flight
Chapter 8 Performance analysis I Accelerated level flight and climb (Lecture 7) Keywords: Accelerated level flight; accelerated climb; energy height. Topics 8.1 Introduction 8. Accelerated level flight
More informationGliding, Climbing, and Turning Flight Performance Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2018
Gliding, Climbing, and Turning Flight Performance Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2018 Learning Objectives Conditions for gliding flight Parameters for maximizing climb angle and rate
More informationFundamentals of Airplane Flight Mechanics
David G. Hull Fundamentals of Airplane Flight Mechanics With 125 Figures and 25 Tables y Springer Introduction to Airplane Flight Mechanics 1 1.1 Airframe Anatomy 2 1.2 Engine Anatomy 5 1.3 Equations of
More informationChapter 5 Performance analysis I Steady level flight (Lectures 17 to 20) Keywords: Steady level flight equations of motion, minimum power required,
Chapter 5 Performance analysis I Steady level flight (Lectures 17 to 20) Keywords: Steady level flight equations of motion, minimum power required, minimum thrust required, minimum speed, maximum speed;
More informationPrediction of Top of Descent Location for Idle-thrust Descents
Prediction of Top of Descent Location for Idle-thrust Descents Laurel Stell NASA Ames Research Center Background 10,000 30,000 ft Vertical profile from cruise to meter fix. Top of Descent (TOD) idle thrust
More informationMDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag. G. Leng, MDTS, NUS
MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag 2.1. The design of supersonic airfoils For efficient lift generation at subsonic speeds, airfoils look like : So why can t a similar
More informationStability and Control Some Characteristics of Lifting Surfaces, and Pitch-Moments
Stability and Control Some Characteristics of Lifting Surfaces, and Pitch-Moments The lifting surfaces of a vehicle generally include the wings, the horizontal and vertical tail, and other surfaces such
More informationMDTS 5734 : Aerodynamics & Propulsion Lecture 1 : Characteristics of high speed flight. G. Leng, MDTS, NUS
MDTS 5734 : Aerodynamics & Propulsion Lecture 1 : Characteristics of high speed flight References Jack N. Nielsen, Missile Aerodynamics, AIAA Progress in Astronautics and Aeronautics, v104, 1986 Michael
More informationDEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS M.Tech. Curriculum
DEPARTMENT OF AEROSPACE ENGINEERING, IIT MADRAS M.Tech. Curriculum SEMESTER I AS5010 Engg. Aerodyn. & Flt. Mech. 3 0 0 3 AS5020 Elements of Gas Dyn. & Propln. 3 0 0 3 AS5030 Aircraft and Aerospace Structures
More informationApplied Aerodynamics - I
Applied Aerodynamics - I o Course Contents (Tentative) Introductory Thoughts Historical Perspective Flow Similarity Aerodynamic Coefficients Sources of Aerodynamic Forces Fundamental Equations & Principles
More informationExample of Aircraft Climb and Maneuvering Performance. Dr. Antonio A. Trani Professor
Example of Aircraft Climb and Maneuvering Performance CEE 5614 Analysis of Air Transportation Systems Dr. Antonio A. Trani Professor Example - Aircraft Climb Performance Aircraft maneuvering performance
More informationSupersonic Aerodynamics. Methods and Applications
Supersonic Aerodynamics Methods and Applications Outline Introduction to Supersonic Flow Governing Equations Numerical Methods Aerodynamic Design Applications Introduction to Supersonic Flow What does
More informationAerodynamics SYST 460/560. George Mason University Fall 2008 CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH. Copyright Lance Sherry (2008)
Aerodynamics SYST 460/560 George Mason University Fall 2008 1 CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH Copyright Lance Sherry (2008) Ambient & Static Pressure Ambient Pressure Static Pressure 2 Ambient
More informationCruising Flight Envelope Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2018
Cruising Flight Envelope Robert Stengel, Aircraft Flight Dynamics, MAE 331, 018 Learning Objectives Definitions of airspeed Performance parameters Steady cruising flight conditions Breguet range equations
More informationAeroelasticity. Lecture 9: Supersonic Aeroelasticity. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 9
Aeroelasticity Lecture 9: Supersonic Aeroelasticity G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 9 1 Introduction All the material presented up to now concerned incompressible
More informationPerformance. 5. More Aerodynamic Considerations
Performance 5. More Aerodynamic Considerations There is an alternative way of looking at aerodynamic flow problems that is useful for understanding certain phenomena. Rather than tracking a particle of
More informationMechanics of Flight. Warren F. Phillips. John Wiley & Sons, Inc. Professor Mechanical and Aerospace Engineering Utah State University WILEY
Mechanics of Flight Warren F. Phillips Professor Mechanical and Aerospace Engineering Utah State University WILEY John Wiley & Sons, Inc. CONTENTS Preface Acknowledgments xi xiii 1. Overview of Aerodynamics
More informationAE Stability and Control of Aerospace Vehicles
AE 430 - Stability and ontrol of Aerospace Vehicles Static/Dynamic Stability Longitudinal Static Stability Static Stability We begin ith the concept of Equilibrium (Trim). Equilibrium is a state of an
More informationPerformance. 7. Aircraft Performance -Basics
Performance 7. Aircraft Performance -Basics In general we are interested in finding out certain performance characteristics of a vehicle. These typically include: how fast and how slow an aircraft can
More informationAOE Problem Sheet 9 (ans) The problems on this sheet deal with an aircraft with the following properties:
AOE Problem Sheet 9 (ans) The problems on this sheet deal with an aircraft with the following properties: W = 600,000 lbs T_max~=~180,000 lbs S = 5128 ft 2 = 0.017 K = 0.042 = 2.2 TSFC = 0.85 (lbs/hr)/lb
More informationME 425: Aerodynamics
ME 425: erodynamics r..b.m. oufique Hasan Professor epartment of Mechanical Engineering Bangladesh University of Engineering & echnology (BUE), haka ecture-25 26/0/209 irplane pa Performance toufiquehasan.buet.ac.bd
More informationI would re-name this chapter Unpowered flight The drag polar, the relationship between lift and drag.
Chapter 3 - Aerodynamics I would re-name this chapter Unpowered flight The drag polar, the relationship between lift and drag. Aerodynamically: = and = So the lift and drag forces are functions of the
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering 5. Aircraft Performance 5.1 Equilibrium Flight In order to discuss performance, stability, and control, we must first establish the concept of equilibrium flight.
More informationJet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay
Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Lecture No. #03 Jet Engine Basic Performance Parameters We are talking
More informationAircraft Performance, Stability and control with experiments in Flight. Questions
Aircraft Performance, Stability and control with experiments in Flight Questions Q. If only the elevator size of a given aircraft is decreased; keeping horizontal tail area unchanged; then the aircraft
More informationfor what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?
1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first
More informationChapter 9. Nonlinear Design Models. Beard & McLain, Small Unmanned Aircraft, Princeton University Press, 2012, Chapter 9, Slide 1
Chapter 9 Nonlinear Design Models Beard & McLain, Small Unmanned Aircraft, Princeton University Press, 2012, Chapter 9, Slide 1 Architecture Destination, obstacles Waypoints Path Definition Airspeed, Altitude,
More informationBallistic Atmospheric Entry (Part II)
Ballistic Atmospheric Entry (Part II) News updates Straight-line (no gravity) ballistic entry based on altitude, rather than density Planetary entries (at least a start) 1 2010 David L. Akin - All rights
More informationAER1216: Fundamentals of UAVs PERFORMANCE
AER1216: Fundamentals of UAVs PERFORMANCE P.R. Grant Spring 2016 Introduction What we will cover: 1 Simplified Standard Atmosphere 2 Simplified Airspeed measurements 3 Propulsion Basics 4 Fixed Wing Performance
More informationBasic Information to Help Select the Correct Propeller
Propeller Performance Factors - Basic Information to Help Select the Correct Propeller The performance of a propeller in flight involves several complex subjects, and the high performance propellers we
More informationIntroduction to Aerospace Engineering
4. Basic Fluid (Aero) Dynamics Introduction to Aerospace Engineering Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible,
More informationProblem Sheet 8 (ans) above
Problem Sheet 8 (ans) 41. A high speed aircraft has a parabolic drag polar with the coefficients varying according to Mach number. This variation is such that the values of the coefficients are constant
More informationFLIGHT DYNAMICS. Robert F. Stengel. Princeton University Press Princeton and Oxford
FLIGHT DYNAMICS Robert F. Stengel Princeton University Press Princeton and Oxford Preface XV Chapter One Introduction 1 1.1 ELEMENTS OF THE AIRPLANE 1 Airframe Components 1 Propulsion Systems 4 1.2 REPRESENTATIVE
More informationPerformance analysis II Steady climb, descent and glide 3
Chapter 6 Lecture 3 Performance analysis II Steady climb, descent and glide 3 Topics 6.6. Climb hydrograph 6.7. Absolute ceiling and service ceiling 6.8 Time to climb 6.9 Steady descent 6.0 Glide 6.0.
More informationPerformance analysis II Steady climb, descent and glide 2
Chapter 6 Lecture Performance analysis II Steady climb, descent and glide Topics 6.5 Maximum rate of climb and imum angle of climb 6.5. Parameters influencing (R/C) of a jet airplane 6.5. Parameters influencing
More informationChapter 1 Lecture 2. Introduction 2. Topics. Chapter-1
Chapter 1 Lecture 2 Introduction 2 Topics 1.4 Equilibrium of airplane 1.5 Number of equations of motion for airplane in flight 1.5.1 Degrees of freedom 1.5.2 Degrees of freedom for a rigid airplane 1.6
More informationAircraft Stability and Performance 2nd Year, Aerospace Engineering
Aircraft Stability and Performance 2nd Year, Aerospace Engineering Dr. M. Turner March 6, 207 Aims of Lecture Part. To examine ways aircraft turn 2. To derive expressions for correctly banked turns 3.
More informationBasic Ascent Performance Analyses
Basic Ascent Performance Analyses Ascent Mission Requirements Ideal Burnout Solution Constant & Average Gravity Models Gravity Loss Concept Effect of Drag on Ascent Performance Drag Profile Approximation
More informationAE 2020: Low Speed Aerodynamics. I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson
AE 2020: Low Speed Aerodynamics I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson Text Book Anderson, Fundamentals of Aerodynamics, 4th Edition, McGraw-Hill, Inc.
More informationChapter 5 Wing design - selection of wing parameters 2 Lecture 20 Topics
Chapter 5 Wing design - selection of wing parameters Lecture 0 Topics 5..4 Effects of geometric parameters, Reynolds number and roughness on aerodynamic characteristics of airfoils 5..5 Choice of airfoil
More informationFlight Dynamics and Control. Lecture 3: Longitudinal stability Derivatives G. Dimitriadis University of Liege
Flight Dynamics and Control Lecture 3: Longitudinal stability Derivatives G. Dimitriadis University of Liege Previously on AERO0003-1 We developed linearized equations of motion Longitudinal direction
More informationA SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN
A SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN ROBBIE BUNGE 1. Introduction The longitudinal dynamics of fixed-wing aircraft are a case in which classical
More informationPART ONE Parameters for Performance Calculations
PART ONE Parameters for Performance Calculations As an amateur designer/builder of homebuilt aircraft, you are chief aerodynamicist, structural engineer, dynamicist, mechanic, artist and draftsman all
More informationJAA Administrative & Guidance Material Section Five: Licensing, Part Two: Procedures
Introduction: 1 - To fully appreciate and understand subject 032 Performance (Aeroplanes), the applicant will benefit from background knowledge in Subject 081 Principles of Flight (Aeroplanes). 2 For JAR-FCL
More informationAEROSPACE ENGINEERING
AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics
More informationThe Boltzmann, Normal and Maxwell Distributions
Chapter The Boltzmann, ormal and Maxwell Distributions Topics The heart of the matter, numerical simulation of the Boltzmann distribution The two-dimensional Maxwell distribution The isothermal atmosphere
More informationTechnology of Rocket
Technology of Rocket Parts of Rocket There are four major parts of rocket Structural system Propulsion system Guidance system Payload system Structural system The structural system of a rocket includes
More informationRocket Science 102 : Energy Analysis, Available vs Required
Rocket Science 102 : Energy Analysis, Available vs Required ΔV Not in Taylor 1 Available Ignoring Aerodynamic Drag. The available Delta V for a Given rocket burn/propellant load is ( ) V = g I ln 1+ P
More informationChapter 5 Lecture 19. Performance analysis I Steady level flight 3. Topics. Chapter-5
Chapter 5 Lecture 19 Performance analysis I Steady level flight 3 Topics 5.8 Influence of level flight analysis on airplane design 5.9 Steady level flight performance with a given engine 5.10 Steady level
More informationMechanics. Flight Lessons 1: Basic Flight. Position, starting with 2 dimensions
Position, starting with 2 dimensions Mechanics We can measure our position forward with positive numbers and backwards with negative numbers. The bike is at 0. Speed (Average) If we take two odometer readings,
More informationRobotic Mobility Atmospheric Flight
Robotic Mobility Atmospheric Flight Gaseous planetary environments (Mars, Venus, Titan)! Lighter-than- air (balloons, dirigibles)! Heavier-than- air (aircraft, rotorcraft) 1 2014 David L. Akin - All rights
More informationEntry Aerodynamics MARYLAND U N I V E R S I T Y O F. Entry Aerodynamics. ENAE Launch and Entry Vehicle Design
Atmospheric Regimes on Entry Basic fluid parameters Definition of Mean Free Path Rarified gas Newtonian flow Continuum Newtonian flow (hypersonics) 2014 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 7 JJ II. Home Page. Title Page.
Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics Fall 2015 Lecture 7 Page 1 of 31 Midterm 1: Monday October 10th Motion in one, two and three dimensions Forces and Motion
More informationTitle: Space flight landing a Space Shuttle
Title: Space flight landing a Space Shuttle Topics: exponentials, derivatives, temperature, speed, distance and time, air density, energy conversion Time: 35 minutes Age: 6+ Differentiation: Higher level:
More informationConfiguration Aerodynamics
Configuration Aerodynamics William H. Mason Virginia Tech Blacksburg, VA The front cover of the brochure describing the French Exhibit at the Montreal Expo, 1967. January 2018 W.H. Mason CONTENTS i CONTENTS
More informationMissile Interceptor EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P Ryan Donnan, Herman Ryals
EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P- 2011121203 Ryan Donnan, Herman Ryals Georgia Institute of Technology School of Aerospace Engineering Missile Interceptor December 12, 2011 EXTROVERT ADVANCED
More informationChapter 9b: Numerical Methods for Calculus and Differential Equations. Initial-Value Problems Euler Method Time-Step Independence MATLAB ODE Solvers
Chapter 9b: Numerical Methods for Calculus and Differential Equations Initial-Value Problems Euler Method Time-Step Independence MATLAB ODE Solvers Acceleration Initial-Value Problems Consider a skydiver
More informationGiovanni Tarantino, Dipartimento di Fisica e Tecnologie Relative, Università di Palermo (Italia)
THE INTERACTIVE PHYSICS FLIGHT SIMULATOR Giovanni Tarantino, Dipartimento di Fisica e Tecnologie Relative, Università di Palermo (Italia) Abstract This paper describes a modelling approach to the dynamics
More informationAE 245 homework #4 solutions
AE 245 homework #4 solutions Tim Smith 14 February 2000 1 Problem1 Consider a general aviation aircraft with weight of 3300 lbs and wing surface area of 310 ft 2. It is powered by a piston engine that
More informationDefinitions. Temperature: Property of the atmosphere (τ). Function of altitude. Pressure: Property of the atmosphere (p). Function of altitude.
Definitions Chapter 3 Standard atmosphere: A model of the atmosphere based on the aerostatic equation, the perfect gas law, an assumed temperature distribution, and standard sea level conditions. Temperature:
More informationPERFORMANCE ANALYSIS OF A PISTON ENGINED AIRPLANE - PIPER CHEROKEE PA E.G.TULAPURKARA S.ANANTH TEJAS M. KULKARNI REPORT NO: AE TR
Appendix - A PERFORMANCE ANALYSIS OF A PISTON ENGINED AIRPLANE - PIPER CHEROKEE PA-28-180 E.G.TULAPURKARA S.ANANTH TEJAS M. KULKARNI REPORT NO: AE TR 2007-1 FEBRUARY 2007 Performance Analysis of a piston
More informationAn Investigation of the Attainable Efficiency of Flight at Mach One or Just Beyond
An Investigation of the Attainable Efficiency of Flight at Mach One or Just Beyond Antony Jameson Department of Aeronautics and Astronautics AIAA Aerospace Sciences Meeting, Reno, NV AIAA Paper 2007-0037
More information( ) for t 0. Rectilinear motion CW. ( ) = t sin t ( Calculator)
Rectilinear motion CW 1997 ( Calculator) 1) A particle moves along the x-axis so that its velocity at any time t is given by v(t) = 3t 2 2t 1. The position x(t) is 5 for t = 2. a) Write a polynomial expression
More information9.4 Miscellaneous topics flight limitations, operating envelop and V-n diagram Flight limitations Operating envelop 9.4.
Chapter 9 Lecture 31 Performance analysis V Manoeuvres 4 Topics 9.4 Miscellaneous topics flight limitations, operating envelop and V-n diagram 9.4.1 Flight limitations 9.4.2 Operating envelop 9.4.3 V-n
More informationSection 4.1: Introduction to Jet Propulsion. MAE Propulsion Systems II
Section 4.1: Introduction to Jet Propulsion Jet Propulsion Basics Squeeze Bang Blow Suck Credit: USAF Test Pilot School 2 Basic Types of Jet Engines Ramjet High Speed, Supersonic Propulsion, Passive Compression/Expansion
More informationSummer AS5150# MTech Project (summer) **
AE1 - M.Tech Aerospace Engineering Sem. Course No Course Name Lecture Tutorial Extended Tutorial Afternoon Lab Session Time to be spent outside of class 1 AS5010 Aerodynamics and Aircraft 3 0 0 0 6 9 performance
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationPhysics 114A Introduction to Mechanics (without calculus)
Physics 114A Introduction to Mechanics (without calculus) A course about learning basic physics concepts and applying them to solve real-world, quantitative, mechanical problems Lecture 6 Review of Vectors
More informationFREQUENCY DOMAIN FLUTTER ANALYSIS OF AIRCRAFT WING IN SUBSONIC FLOW
FREQUENCY DOMAIN FLUTTER ANALYSIS OF AIRCRAFT WING IN SUBSONIC FLOW Ms.K.Niranjana 1, Mr.A.Daniel Antony 2 1 UG Student, Department of Aerospace Engineering, Karunya University, (India) 2 Assistant professor,
More informationIntroduction to Flight Dynamics
Chapter 1 Introduction to Flight Dynamics Flight dynamics deals principally with the response of aerospace vehicles to perturbations in their flight environments and to control inputs. In order to understand
More informationFlight Vehicle Terminology
Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes
More information4 Compressible Fluid Dynamics
4 Compressible Fluid Dynamics 4. Compressible flow definitions Compressible flow describes the behaviour of fluids that experience significant variations in density under the application of external pressures.
More informationAir Loads. Airfoil Geometry. Upper surface. Lower surface
AE1 Jha Loads-1 Air Loads Airfoil Geometry z LE circle (radius) Chord line Upper surface thickness Zt camber Zc Zl Zu Lower surface TE thickness Camber line line joining the midpoints between upper and
More informationSPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30
SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the
More informationConsider a wing of finite span with an elliptic circulation distribution:
Question 1 (a) onsider a wing of finite span with an elliptic circulation distribution: Γ( y) Γo y + b = 1, - s y s where s=b/ denotes the wing semi-span. Use this equation, in conjunction with the Kutta-Joukowsky
More informationMAE SUMMER 2015 HOMEWORK 1 SOLUTION
MAE 04 - SUMMER 205 HOMEWORK SOLUTION Problem :. Plot the drag coefficient, c D, the aerodynamic efficiency, AE, and the center of pressure, x cp, of the airplane as a function of the angle of attack.
More informationContinuity Equation for Compressible Flow
Continuity Equation for Compressible Flow Velocity potential irrotational steady compressible Momentum (Euler) Equation for Compressible Flow Euler's equation isentropic velocity potential equation for
More informationRocket Performance MARYLAND U N I V E R S I T Y O F. Ballistic Entry ENAE Launch and Entry Vehicle Design
Rocket Performance Parallel staging Modular staging Standard atmospheres Orbital decay due to drag Straight-line (no gravity) entry based on atmospheric density 1 2014 David L. Akin - All rights reserved
More informationIntroduction to Flight
l_ Introduction to Flight Fifth Edition John D. Anderson, Jr. Curator for Aerodynamics, National Air and Space Museum Smithsonian Institution Professor Emeritus University of Maryland Me Graw Higher Education
More informationDetermination of a Light Helicopter Flight Performance at the Preliminary Design Stage
Paper received: 0.01.2008 UDC:5.661:629.01 Paper accepted: 02.07.2010 Determination of a Light Helicopter Flight Performance at the Preliminary Design Stage Zlatko Petrović - Slobodan Stupar - Ivan Kostić
More informationAOE 3104 Problem Sheet 10 (ans)
AOE 3104 Problem Sheet 10 (ans) Our class business jet has the following characteristics: Gross Weight = 10,000 lbs b = 40 ft C Lmax = 1.8 (normal flight) S = 200 ft 2 C D = 0.02 + 0.05 (C L ) 2 C Lmax
More informationCompressible Potential Flow: The Full Potential Equation. Copyright 2009 Narayanan Komerath
Compressible Potential Flow: The Full Potential Equation 1 Introduction Recall that for incompressible flow conditions, velocity is not large enough to cause density changes, so density is known. Thus
More informationManeuver of fixed-wing combat aircraft
Loughborough University Institutional Repository Maneuver of fixed-wing combat aircraft This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: RENDER,
More informationb) What does each letter (or symbol) stand for in this equation? c) What are the corresponding SI units? (Write: symbol $ unit).
First Name: Last Name: 1. a) What is Newton s Second Law in formula form? b) What does each letter (or symbol) stand for in this equation? c) What are the corresponding SI units? (Write: symbol $ unit).
More informationMODIFICATION OF AERODYNAMIC WING LOADS BY FLUIDIC DEVICES
Journal of KONES Powertrain and Transport, Vol. 21, No. 2 2014 MODIFICATION OF AERODYNAMIC WING LOADS BY FLUIDIC DEVICES Institute of Aviation Department of Aerodynamics and Flight Mechanics Krakowska
More informationRobotic Mobility Atmospheric Flight
Robotic Mobility Atmospheric Flight Gaseous planetary environments (Mars, Venus, Titan) Lighter-than- air (balloons, dirigibles) Heavier-than- air (aircraft, rotorcraft) 1 2014 David L. Akin - All rights
More informationME 425: Aerodynamics
ME 45: Aerodynamics r. A.B.M. oufique Hasan Professor epartment of Mechanical Engineering Bangladesh University of Engineering & echnology (BUE), haka Lecture-4 //9 Airplane pa Performance toufiquehasan.buet.ac.bd
More informationPHYS 124 Section A1 Mid-Term Examination Spring 2006 SOLUTIONS
PHYS 14 Section A1 Mid-Term Examination Spring 006 SOLUTIONS Name Student ID Number Instructor Marc de Montigny Date Monday, May 15, 006 Duration 60 minutes Instructions Items allowed: pen or pencil, calculator
More informationDrag (2) Induced Drag Friction Drag Form Drag Wave Drag
Drag () Induced Drag Friction Drag Form Drag Wave Drag Outline Nomenclature and Concepts Farfield Drag Analysis Induced Drag Multiple Lifting Surfaces Zero Lift Drag :Friction and Form Drag Supersonic
More informationHigh Speed Aerodynamics. Copyright 2009 Narayanan Komerath
Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil
More informationAircraft Design I Tail loads
Horizontal tail loads Aircraft Design I Tail loads What is the source of loads? How to compute it? What cases should be taken under consideration? Tail small wing but strongly deflected Linearized pressure
More informationPropeller theories. Blade element theory
30 1 Propeller theories Blade element theory The blade elements are assumed to be made up of airfoil shapes of known lift, C l and drag, C d characteristics. In practice a large number of different airfoils
More informationDrag Computation (1)
Drag Computation (1) Why drag so concerned Its effects on aircraft performances On the Concorde, one count drag increase ( C D =.0001) requires two passengers, out of the 90 ~ 100 passenger capacity, be
More informationThrust and Flight Modeling
Thrust and Flight Modeling So just how did OpenRocket or Rocksim predict the trajectory, velocity, and acceleration of our vehicle? What did we input into these numerical tools? Rocket Motors Device for
More informationTransonic Aerodynamics Wind Tunnel Testing Considerations. W.H. Mason Configuration Aerodynamics Class
Transonic Aerodynamics Wind Tunnel Testing Considerations W.H. Mason Configuration Aerodynamics Class Transonic Aerodynamics History Pre WWII propeller tip speeds limited airplane speed Props did encounter
More information