I would re-name this chapter Unpowered flight The drag polar, the relationship between lift and drag.

Size: px
Start display at page:

Download "I would re-name this chapter Unpowered flight The drag polar, the relationship between lift and drag."

Transcription

1 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 square of the speed. is the density of the air. S is a reference area (often the area of the wing). The chapter introduces the drag polar curve. This is a plot of CD vs. CL, though the independent variable (C L ) is plotted on the vertical axis and the dependent variable (C D ) on the horizontal axis. In Figure 9 of the Skript on page there are some errors, and the figure is misleading. Here s a revision of that figure: C L and C D are related to each other. As can be seen from the above curve, it looks something like a parabolic relationship. A polar curve for an aircraft is made by plotting C D vs. C L :

2 As can be seen, this curve is plotted backwards (see below). This curve is a simplified version of this relationship, a sort of prototype. This is called a square polar. Polar because it s a plot of C L vs. C D. Square because it s a parabolic relationship. The equation is = + So actually, what we have here is C D = C D(C L) not C L = C L(C D) ; it s just plotted backwards, with the independent variable on the vertical axis and the dependent variable on the horizontal axis. What s important, however, is that they are related. Why it s plotted backwards is anybody s guess. Aeronautical engineers are perverse. It was probably first done by the same guy who decided that down is up. Obviously what we want with aircraft is as much lift as possible and as little drag as possible. As we see from the equation at the start of this section of notes, both and have the same dependencies (, S, v 2 ). The place on the polar where L/D is maximum is the tangent to this curve drawn from the origin with the angle min shown. Turning our attention once again back to the polar equation = + we see that the curve has an offset C D0. This gives us the minimum drag. We have it regardless of how much lift we produce. The other term, is lift-related drag or induced drag. k is a measure of how fat the parabola will be. The smaller k is, the fatter the parabola will be. In fact, if k = 0, the curve would be a vertical line at C D0, and we could get more and more lift without increased drag. The higher k is, the more drag we will get for a given amount of lift. So we want the parabola to be as fat as possible; we want k to be a small as possible, if we consider the above equation. If it were very fat, say a straight vertical line, the drag would not increase with additional lift. k is often estimated by where = Λ e = 1 for elliptical wings e > 1 for non-elliptical wings

3 Λ = where b is the wing-span of the aircraft and A is some area, usually the area of the wing. For a fat parabola, a small k ), needs to be large. Thus we d want a lot of area for a given wing-span. Put another way, we want long wings with little area. As far as k goes, note that it depends just on properties of the aircraft and wing. So it is design conditions that determine the fatness of the parabola. Again, the polar equation here is a square polar, which is the most common. Other types of polar relationships have C L to other powers than 2. Still, here with this equation giving C D = C D(C L), we haven t said what C L depends on. Section 3.1 The relationship of lift and drag along the (square) polar Since the expressions for L and D are identical except for the coefficients of lift and drag, for any flight condition, these two forces are related as = 2 2 = This relationship will change, depending upon where you are operating on the polar. The figure above shows an aircraft with the throttles pulled back (T=0) in descent. Because of the kinematics, note that tan = = What happens if T 0? What happens, say, if the plane is flying horizontal, with = 0? We know that there is lift and drag, with D L/10. So the relationship between L, D, and does not apply to that case. In fact, only when there is no thrust is the L, D, and relationship valid, i.e. the lift and drag forces together are vertical. A pilot has the option of controlling the flight path of the aircraft. For example, if he/she turns the nose straight down to the ground, there will be no lift force. This will not make v 0, quite the contrary, nor

4 will any of the other terms be 0, so in such a case, with no lift, C L must be = 0. Since the aircraft must fly on the polar, it will be operating at the nose of the parabola, and C D = C D0. Thus, there no matter what the velocity, and = 0 2 = 0 = 2 The drag force will continue to increase as the velocity builds until it becomes equal to the gravity force, at which point we shall have reached terminal velocity, and the aircraft ceases to build speed in this balanced-force state. The other possibility is that the aircraft will exceed its structural speed and come apart. Also note that if the aircraft is headed straight down without lift, D/L =. arctan( ) = 90 ; i.e. the descent angle is 90 from the horizontal, i.e. straight down. Let s consider the other, opposite end of the flying spectrum on the polar. Rather than lowering the nose, we raise it. The lift force increases, but so does the drag force. Take again the case of unpowered flight, T = 0. If we pull the nose up, we get more get more lift, but because the parabola is mostly horizontal, we also increase the drag force inordinately. We move out along the polar, and increases. The descent rate increases again, even though we have more lift. Also because of the increased drag, the velocity drops off. Eventually the airflow cannot stay attached to the wing, so the aircraft stalls. Thus, there is a sweet spot. This is the point on the polar in between these two extremes where D/L = C D/C L is minimum. Since the tan increases as increases, this point is where a line from the origin is tangent to the parabola. This gives min, i.e. the minimum descent angle for unpowered flight. This is where a glider pilot wants to fly when he/she is hunting for the next source of lift. This is the speed at which a pilot of a powered aircraft wants to fly if his/her engine quits. This is the best glide or minimum descent speed. The moral of the story is that the airplane has a polar along which it flies. It cannot leave the polar, but it can fly at various points along it, depending upon the pitch attitude. Section 3.2 Minimum glide angle To find the sweet spot, take the derivative of with respect to C L and set this equal to 0. See Skript. This leads to = = 2 = arctan = arctan 2 = arctan 2

5 Notice what we would need to do to the square polar curve to get a small angle of descent. We need to move the parabola as close as possible to the origin (make C D0 small) and then make the parabola as fat as possible (make k small). Another way to look at this is to look at Figure 12. In this figure, if must be vertical, if increase, for whatever L we have, D will get greater and greater. In fact at = 90, L must be 0 to make vertical, and D is enormous. Minimum and maximum velocity We start with the expression for R shown in the Skript. Then we impose the condition that the resulting force needs to be equal to the weight. This would give us a descent rate that leads to no vertical acceleration. From this we can get an expression for the velocity in terms of parameters that don t change with the flight condition (m, g,, S) and those that do (C L and C D, as we move along the polar). Why are we limited to having = +? I assume it is for the reason shown in the three figures above. If we are flying along at our best L/D as in 1 above, for example, and we change the pitch angle downward, the airplane will then have and reorient as shown in 2. Now s vertical component is less than. The aircraft accelerates then downward. At the same time, now has a horizontal component, so the aircraft accelerates to the right too. The result is that the aircraft now has a steeper angle of descent and a greater speed. Thus the drag vector will be greater. We have moved away from the optimum unpowered descent angle, so we have moved to a new point on the drag polar, where there is less lift for a given drag. This is shown in 3 above. This point is then down the drag polar toward its nose. Also note that though this scenario started with us at the minimum descent angle, but there is actually no reason that that need be. We could have started at any point on the drag polar and moved to any other point on the drag polar. We could have started at 3, for example, pulled back on the stick or yoke, and wound up at 1. Then we would have moved up the drag polar away from the origin. On page 20 of the Skript, equations (3.9) and (3.10) give the values for minimum and maximum velocity along the drag polar. Since = 2 1 +

6 v max occurs when + is minimum, and that occurs at the nose of the parabola, when C D = C D0 and C L = 0. I m not sure about the assertion for v min. v min seems to me to be the stall speed, and that is not modelled on the drag polar. The condition given for i his expression is C L >> C D. The point on the curve where C L/C D is maximum is at the tangent point, as already discussed above. So this seems rather to be an approximation for the speed at minimum-descent flight-path angle. 3.3 Minimum rate of descent w is the vertical speed. So If is small, and Also So = sin sin tan = = (Note that this equation is incorrect in the Skript.) etc To get the minimum rate of descent, minimize w with respect to C L. Figure 14 is a plot of w = w(v), i.e. of the equation above it. Note that v min is really v w-min, i.e. the velocity at minimum descent angle.

PRINCIPLES OF FLIGHT

PRINCIPLES OF FLIGHT 1 Considering a positive cambered aerofoil, the pitching moment when Cl=0 is: A infinite B positive (nose-up). C negative (nose-down). D equal to zero. 2 The angle between the aeroplane longitudinal axis

More information

Chapter 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, 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 information

Introduction to Aerospace Engineering

Introduction 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 information

AE Stability and Control of Aerospace Vehicles

AE 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 information

Lecture No. # 09. (Refer Slide Time: 01:00)

Lecture No. # 09. (Refer Slide Time: 01:00) Introduction to Helicopter Aerodynamics and Dynamics Prof. Dr. C. Venkatesan Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture No. # 09 Now, I just want to mention because

More information

Stability and Control

Stability and Control Stability and Control Introduction An important concept that must be considered when designing an aircraft, missile, or other type of vehicle, is that of stability and control. The study of stability is

More information

Kinesiology 201 Solutions Fluid and Sports Biomechanics

Kinesiology 201 Solutions Fluid and Sports Biomechanics Kinesiology 201 Solutions Fluid and Sports Biomechanics Tony Leyland School of Kinesiology Simon Fraser University Fluid Biomechanics 1. Lift force is a force due to fluid flow around a body that acts

More information

Flight and Orbital Mechanics. Exams

Flight 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 information

Model Rocketry. The Science Behind the Fun

Model Rocketry. The Science Behind the Fun Model Rocketry The Science Behind the Fun Topics History of Rockets Sir Isaac Newton Laws of Motion Rocket Principles Flight of a Model Rocket Rocket Propulsion Forces at Work History Rockets and rocket

More information

Chapter 1 Lecture 2. Introduction 2. Topics. Chapter-1

Chapter 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 information

Introduction to Aeronautics

Introduction to Aeronautics Introduction to Aeronautics ARO 101 Sections 03 & 04 Sep 30, 2015 thru Dec 9, 2015 Instructor: Raymond A. Hudson Week #8 Lecture Material 1 Topics For Week #8 Airfoil Geometry & Nomenclature Identify the

More information

3.3 Acceleration An example of acceleration Definition of acceleration Acceleration Figure 3.16: Steeper hills

3.3 Acceleration An example of acceleration Definition of acceleration Acceleration Figure 3.16: Steeper hills 3.3 Acceleration Constant speed is easy to understand. However, almost nothing moves with constant speed for long. When the driver steps on the gas pedal, the speed of the car increases. When the driver

More information

EVOLVING DOCUMENT ME 5070 Flight Dynamics

EVOLVING DOCUMENT ME 5070 Flight Dynamics EVOLVING DOCUMENT ME 5070 Flight Dynamics Homework Date of this version: March 20, 2015 Hyperlinks look like this Dates in headings below are the dates of the associated lecture Due January 27, 2015 1

More information

PART ONE Parameters for Performance Calculations

PART 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 information

3 Fluids and Motion. Critical Thinking

3 Fluids and Motion. Critical Thinking CHAPTER 3 3 Fluids and Motion SECTION Forces in Fluids BEFORE YOU READ After you read this section, you should be able to answer these questions: How does fluid speed affect pressure? How do lift, thrust,

More information

PHYSICS. Chapter 5 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. Chapter 5 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc. PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 5 Lecture RANDALL D. KNIGHT Chapter 5 Force and Motion IN THIS CHAPTER, you will learn about the connection between force and motion.

More information

Flight and Orbital Mechanics

Flight and Orbital Mechanics Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics Lecture hours 3, 4 Minimum time to climb Mark Voskuijl Semester 1-2012 Delft University of Technology Challenge

More information

Aircraft stability and control Prof: A. K. Ghosh Dept of Aerospace Engineering Indian Institute of Technology Kanpur

Aircraft stability and control Prof: A. K. Ghosh Dept of Aerospace Engineering Indian Institute of Technology Kanpur Aircraft stability and control Prof: A. K. Ghosh Dept of Aerospace Engineering Indian Institute of Technology Kanpur Lecture- 05 Stability: Tail Contribution and Static Margin (Refer Slide Time: 00:15)

More information

AOE 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: 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 information

y(t) = y 0 t! 1 2 gt 2. With y(t final ) = 0, we can solve this for v 0 : v 0 A ĵ. With A! ĵ =!2 and A! = (2) 2 + (!

y(t) = y 0 t! 1 2 gt 2. With y(t final ) = 0, we can solve this for v 0 : v 0 A ĵ. With A! ĵ =!2 and A! = (2) 2 + (! 1. The angle between the vector! A = 3î! 2 ĵ! 5 ˆk and the positive y axis, in degrees, is closest to: A) 19 B) 71 C) 90 D) 109 E) 161 The dot product between the vector! A = 3î! 2 ĵ! 5 ˆk and the unit

More information

Performance analysis II Steady climb, descent and glide 3

Performance 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 information

STRAIGHT-LINE MOTION UNDER CONSTANT ACCELERATION

STRAIGHT-LINE MOTION UNDER CONSTANT ACCELERATION STRAIGHT-LINE MOTION UNDER CONSTANT ACCELERATION Problems involving a body moving in a straight line under constant acceleration have five relevant variables: u = Initial velocity in m/s v = Final velocity

More information

Theory of Flight Flight Instruments and Performance Factors References: FTGU pages 32-34, 39-45

Theory of Flight Flight Instruments and Performance Factors References: FTGU pages 32-34, 39-45 Theory of Flight 6.09 Flight Instruments and Performance Factors References: FTGU pages 32-34, 39-45 MTPs: 6.09 Flight Instruments and Performance Factors Pitot Static Instruments Asymmetric Thrust Precession

More information

TEKS 8.7. The student knows that there is a relationship between force and motion. The student is expected to:

TEKS 8.7. The student knows that there is a relationship between force and motion. The student is expected to: TEKS 8.7 The student knows that there is a relationship between force and motion. The student is expected to: A. demonstrate how unbalanced forces cause changes in the speed or direction of an object's

More information

Theory of Flight. Pitot Static Instruments Flight Instruments and Performance Factors. MTPs:

Theory of Flight. Pitot Static Instruments Flight Instruments and Performance Factors. MTPs: Theory of Flight 6.09 Flight Instruments and Performance Factors References: FTGU pages 32-34, 39-45 6.09 Flight Instruments and Performance Factors MTPs: Pitot Static Instruments Asymmetric Thrust Precession

More information

Giovanni Tarantino, Dipartimento di Fisica e Tecnologie Relative, Università di Palermo (Italia)

Giovanni 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 information

Topic 2: Mechanics 2.2 Forces

Topic 2: Mechanics 2.2 Forces Representing forces as vectors A force is a push or a pull measured in Newtons. One force we are very familiar with is the force of gravity, AKA the weight. The very concepts of push and pull imply direction.

More information

Performance. 7. Aircraft Performance -Basics

Performance. 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 information

Flight and Orbital Mechanics

Flight 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 information

Bell Ringer: What is constant acceleration? What is projectile motion?

Bell Ringer: What is constant acceleration? What is projectile motion? Bell Ringer: What is constant acceleration? What is projectile motion? Can we analyze the motion of an object on the y-axis independently of the object s motion on the x-axis? NOTES 3.2: 2D Motion: Projectile

More information

The Force Is with You

The Force Is with You The Force Is with You Learning Objectives The learner will interpret free-body force diagrams Review: Newton s 1 st Law An object in motion stays in motion in a straight line, unless acted upon by unbalanced

More information

Aircraft Stability and Performance 2nd Year, Aerospace Engineering

Aircraft 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 information

PHYSICS. Chapter 5 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. Chapter 5 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc. PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 5 Lecture RANDALL D. KNIGHT Chapter 5 Force and Motion IN THIS CHAPTER, you will learn about the connection between force and motion.

More information

Written in August 2017 during my holiday in Bulgaria, Sunny Coast

Written in August 2017 during my holiday in Bulgaria, Sunny Coast Electric ucted Fan Theory This paper describes a simple theory of a ducted fan. It is assumed that the reader knows what it is an electric ducted fan (EF), how it works, and what it is good for. When I

More information

Fundamentals of Airplane Flight Mechanics

Fundamentals 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 information

A model of an aircraft towing a cable-body system

A model of an aircraft towing a cable-body system ANZIAM J. 47 (EMAC2005) pp.c615 C632, 2007 C615 A model of an aircraft towing a cable-body system C. K. H. Chin R. L. May (Received 2 November 2005; revised 31 January 2007) Abstract We integrate together

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapter 5 Force and Motion Chapter Goal: To establish a connection between force and motion. Slide 5-2 Chapter 5 Preview Slide 5-3 Chapter 5 Preview Slide 5-4 Chapter 5 Preview Slide 5-5 Chapter 5 Preview

More information

Comment: Unlike distance, displacement takes into consideration the direction of motion from the point of origin (where the object starts to move).

Comment: Unlike distance, displacement takes into consideration the direction of motion from the point of origin (where the object starts to move). Chapter 3 Kinematics (A) Distance Vs Displacement 1. Compare distance and displacement in terms of: (a) definition Distance is the total length of travel, irrespective of direction. Displacement is the

More information

for any object. Note that we use letter, m g, meaning gravitational

for any object. Note that we use letter, m g, meaning gravitational Lecture 4. orces, Newton's Second Law Last time we have started our discussion of Newtonian Mechanics and formulated Newton s laws. Today we shall closely look at the statement of the second law and consider

More information

Kinematics in Two Dimensions; Vectors

Kinematics in Two Dimensions; Vectors Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors

More information

Section /07/2013. PHY131H1F University of Toronto Class 9 Preclass Video by Jason Harlow. Based on Knight 3 rd edition Ch. 5, pgs.

Section /07/2013. PHY131H1F University of Toronto Class 9 Preclass Video by Jason Harlow. Based on Knight 3 rd edition Ch. 5, pgs. PHY131H1F University of Toronto Class 9 Preclass Video by Jason Harlow Based on Knight 3 rd edition Ch. 5, pgs. 116-133 Section 5.1 A force is a push or a pull What is a force? What is a force? A force

More information

N W = ma y = 0 (3) N = W = mg = 68 kg 9.8 N/kg = 666 N 670 N. (4) As to the horizontal motion, at first the box does not move, which means

N W = ma y = 0 (3) N = W = mg = 68 kg 9.8 N/kg = 666 N 670 N. (4) As to the horizontal motion, at first the box does not move, which means PHY 309 K. Solutions for Problem set # 6. Non-textbook problem #I: There are 4 forces acting on the box: Its own weight W mg, the normal force N from the floor, the friction force f between the floor and

More information

Dynamic trajectory control of gliders

Dynamic trajectory control of gliders Dynamic trajectory control of gliders Rui DILãO and João FONSECA Institut des Hautes Études Scientifiques 35, route de Chartres 91440 Bures-sur-Yvette (France) Avril 2013 IHES/M/13/09 Dynamic trajectory

More information

Aircraft Performance, Stability and control with experiments in Flight. Questions

Aircraft 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 information

STEP Support Programme. Mechanics STEP Questions

STEP Support Programme. Mechanics STEP Questions STEP Support Programme Mechanics STEP Questions This is a selection of mainly STEP I questions with a couple of STEP II questions at the end. STEP I and STEP II papers follow the same specification, the

More information

Introduction to Flight Dynamics

Introduction 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 information

Physics 380: Physics and Society Lecture 2: Newton s Laws, Mass, Force, and Motion

Physics 380: Physics and Society Lecture 2: Newton s Laws, Mass, Force, and Motion Physics 380: Physics and Society Lecture 2: Newton s Laws, Mass, Force, and Motion [Instructor] Slide #1 Physics and Society Physics 380: Physics and Society Lecture 2: Newton s Laws, Mass, Force, and

More information

CHAPTER 3 ANALYSIS OF NACA 4 SERIES AIRFOILS

CHAPTER 3 ANALYSIS OF NACA 4 SERIES AIRFOILS 54 CHAPTER 3 ANALYSIS OF NACA 4 SERIES AIRFOILS The baseline characteristics and analysis of NACA 4 series airfoils are presented in this chapter in detail. The correlations for coefficient of lift and

More information

The Physics of Boomerangs By Darren Tan

The Physics of Boomerangs By Darren Tan The Physics of Boomerangs By Darren Tan Segment 1 Hi! I m the Science Samurai and glad to have you here with me today. I m going to show you today how to make your own boomerang, how to throw it and even

More information

Mechanics of Flight. Warren F. Phillips. John Wiley & Sons, Inc. Professor Mechanical and Aerospace Engineering Utah State University WILEY

Mechanics 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 information

Quest Chapter 09. Eliminate the obviously wrong answers. Consider what is changing: speed, velocity, some part of velocity? Choose carefully.

Quest Chapter 09. Eliminate the obviously wrong answers. Consider what is changing: speed, velocity, some part of velocity? Choose carefully. 1 A dragster maintains a speedometer reading of 100 km/h and passes through a curve with a constant radius. Which statement is true? 1. The dragster rounded the curve at a changing speed of 100 km/h. 2.

More information

Aerodynamics 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 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 information

Kinematics in Two Dimensions; 2D- Vectors

Kinematics in Two Dimensions; 2D- Vectors Kinematics in Two Dimensions; 2D- Vectors Addition of Vectors Graphical Methods Below are two example vector additions of 1-D displacement vectors. For vectors in one dimension, simple addition and subtraction

More information

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC 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 information

Kinematics -- Conceptual Solutions. 1.) Without using a formal presentation of formulas, determine the following in your head:

Kinematics -- Conceptual Solutions. 1.) Without using a formal presentation of formulas, determine the following in your head: Kinematics Kinematics -- Conceptual Solutions 1.) Without using a formal presentation of formulas, determine the following in your head: a.) The units you get when you multiply velocity and time. Solution:

More information

Subsonic flight. Copyright c , Benny Lautrup Revision 7.7, January 22, 2004

Subsonic flight. Copyright c , Benny Lautrup Revision 7.7, January 22, 2004 27 ubsonic flight The takeoff of a large airplane never ceases to wonder passengers and bystanders alike After building up speed during a brief half-minute run, gravity lets go and the plane marvellously

More information

Unit 1: Equilibrium and Center of Mass

Unit 1: Equilibrium and Center of Mass Unit 1: Equilibrium and Center of Mass FORCES What is a force? Forces are a result of the interaction between two objects. They push things, pull things, keep things together, pull things apart. It s really

More information

Introduction to Aerospace Engineering

Introduction 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 information

Kinematics. Vector solutions. Vectors

Kinematics. Vector solutions. Vectors Kinematics Study of motion Accelerated vs unaccelerated motion Translational vs Rotational motion Vector solutions required for problems of 2- directional motion Vector solutions Possible solution sets

More information

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction. Newton s Laws Newton s first law: An object will stay at rest or in a state of uniform motion with constant velocity, in a straight line, unless acted upon by an external force. In other words, the bodies

More information

Review of General 1D Kinematics The instantaneous velocity and acceleration are:

Review of General 1D Kinematics The instantaneous velocity and acceleration are: Review of General 1D Kinematics The instantaneous velocity and acceleration are: If we know the position and velocity at the initial point i, we can find the position and velocity at point f by: PhET Computer

More information

AP Physics 1 Summer Assignment

AP Physics 1 Summer Assignment Name: Email address (write legibly): AP Physics 1 Summer Assignment Packet 3 The assignments included here are to be brought to the first day of class to be submitted. They are: Problems from Conceptual

More information

Extended longitudinal stability theory at low Re - Application to sailplane models

Extended longitudinal stability theory at low Re - Application to sailplane models Extended longitudinal stability theory at low Re - Application to sailplane models matthieu.scherrer@free.fr November 26 C L C m C m W X α NP W X V NP W Lift coefficient Pitching moment coefficient Pitching

More information

4.2. Visualize: Assess: Note that the climber does not touch the sides of the crevasse so there are no forces from the crevasse walls.

4.2. Visualize: Assess: Note that the climber does not touch the sides of the crevasse so there are no forces from the crevasse walls. 4.1. Solve: A force is basically a push or a pull on an object. There are five basic characteristics of forces. (i) A force has an agent that is the direct and immediate source of the push or pull. (ii)

More information

The physics and mathematics of javelin throwing

The physics and mathematics of javelin throwing The physics and mathematics of javelin throwing Professor Les Hatton CISM, University of Kingston May 24, 2005 Abstract Javelin flight is strictly governed by the laws of aerodynamics but there remain

More information

Motion along a straight line. Physics 11a. 4 Basic Quantities in Kinematics. Motion

Motion along a straight line. Physics 11a. 4 Basic Quantities in Kinematics. Motion Physics 11a Motion along a straight line Motion Position and Average velocity and average speed Instantaneous velocity and speed Acceleration Constant acceleration: A special case Free fall acceleration

More information

Consider a wing of finite span with an elliptic circulation distribution:

Consider 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 information

Physics 207 Lecture 9. Lecture 9

Physics 207 Lecture 9. Lecture 9 Lecture 9 Today: Review session Assignment: For Thursday, Read through Chapter 8 (first four sections) Exam Wed., Feb. 17 th from 7:15-8:45 PM Chapters 1-6 One 8½ X 11 hand written note sheet and a calculator

More information

Physics 8 Wednesday, October 19, Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes!

Physics 8 Wednesday, October 19, Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes! Physics 8 Wednesday, October 19, 2011 Troublesome questions for HW4 (5 or more people got 0 or 1 points on them): 1, 14, 15, 16, 17, 18, 19. Yikes! Troublesome HW4 questions 1. Two objects of inertias

More information

Flight Vehicle Terminology

Flight 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 information

Teacher Content Brief

Teacher Content Brief Teacher Content Brief Vectors Introduction Your students will need to be able to maneuver their Sea Perch during the competition, so it will be important for them to understand how forces combine to create

More information

Problem: Projectile (CM-1998)

Problem: Projectile (CM-1998) Physics C -D Kinematics Name: ANSWER KEY AP Review Packet Vectors have both magnitude and direction displacement, velocity, acceleration Scalars have magnitude only distance, speed, time, mass Unit vectors

More information

Propeller theories. Blade element theory

Propeller 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 information

Lecture 3 - Pull! A Puzzle... m g. m g. = d Sin[θ] F μ N 1 (2)

Lecture 3 - Pull! A Puzzle... m g. m g. = d Sin[θ] F μ N 1 (2) Lecture 3 - Pull! A Puzzle... Recall from last time that we computed the stability criterion 1 an[] for a leaning ladder (of length d): 2 μ We computed the stability using the base of the ladder as the

More information

1-D Motion: Free Falling Objects

1-D Motion: Free Falling Objects v (m/s) a (m/s^2) 1-D Motion: Free Falling Objects So far, we have only looked at objects moving in a horizontal dimension. Today, we ll look at objects moving in the vertical. Then, we ll look at both

More information

Lesson 3: Climbs and Descents

Lesson 3: Climbs and Descents Page 1 of 12 Lesson 3: Climbs and Descents Fly This Lesson Now by Rod Machado In the fifth grade, my teacher asked me to come to the front of the class and name the parts of speech. I walked up, turned

More information

Forces on a banked airplane that travels in uniform circular motion.

Forces on a banked airplane that travels in uniform circular motion. Question (60) Forces on a banked airplane that travels in uniform circular motion. A propeller-driven airplane of mass 680 kg is turning in a horizontal circle with a constant speed of 280 km/h. Its bank

More information

Performance analysis II Steady climb, descent and glide 2

Performance 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 information

Chapter 5 Lecture Notes

Chapter 5 Lecture Notes Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414 - Strauss Constants: G = 6.67 10-11 N-m 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular

More information

A SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN

A 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 information

5 Projectile Motion. Projectile motion can be described by the horizontal and vertical components of motion.

5 Projectile Motion. Projectile motion can be described by the horizontal and vertical components of motion. Projectile motion can be described by the horizontal and vertical components of motion. In the previous chapter we studied simple straight-line motion linear motion. Now we extend these ideas to nonlinear

More information

Lab 5: Projectile Motion

Lab 5: Projectile Motion Concepts to explore Scalars vs. vectors Projectiles Parabolic trajectory As you learned in Lab 4, a quantity that conveys information about magnitude only is called a scalar. However, when a quantity,

More information

Motion. Ifitis60milestoRichmondandyouaretravelingat30miles/hour, itwilltake2hourstogetthere. Tobecorrect,speedisrelative. Ifyou. time.

Motion. Ifitis60milestoRichmondandyouaretravelingat30miles/hour, itwilltake2hourstogetthere. Tobecorrect,speedisrelative. Ifyou. time. Motion Motion is all around us. How something moves is probably the first thing we notice about some process. Quantifying motion is the were we learn how objects fall and thus gravity. Even our understanding

More information

PHYSICS 1050 Test 1 University of Wyoming 25 September 2008

PHYSICS 1050 Test 1 University of Wyoming 25 September 2008 Name: PHYSICS 15 Test 1 University of Wyoming 25 September 28 This test is closed-note and closed-book. No written, printed, or recorded material is permitted, with the exception of a formula sheet with

More information

Unit 08 Work and Kinetic Energy. Stuff you asked about:

Unit 08 Work and Kinetic Energy. Stuff you asked about: Unit 08 Work and Kinetic Energy Today s Concepts: Work & Kinetic Energy Work in a non-constant direction Work by springs Mechanics Lecture 7, Slide 1 Stuff you asked about: Can we go over the falling,

More information

Dynamic trajectory control of gliders

Dynamic trajectory control of gliders Proceedings of the EuroGNC 2013, 2nd CEAS Specialist Conference on Guidance, Navigation & Control, Delft University of Technology, Delft, The Netherlands, April 10-12, 2013 ThCT1.3 Dynamic trajectory control

More information

Figure 3.71 example of spanwise loading due to aileron deflection.

Figure 3.71 example of spanwise loading due to aileron deflection. 3.7 ILERON DESIGN 3.7.1 Introduction It s very important for preliminary design to analyze the roll and turn performances of the aircraft, paying attention on its use and category. the system used for

More information

MAV Unsteady Characteristics in-flight Measurement with the Help of SmartAP Autopilot

MAV Unsteady Characteristics in-flight Measurement with the Help of SmartAP Autopilot MAV Unsteady Characteristics in-flight Measurement with the Help of SmartAP Autopilot S. Serokhvostov, N. Pushchin and K. Shilov Moscow Institute of Physics and Technology Department of Aeromechanics and

More information

KEY NNHS Introductory Physics: MCAS Review Packet #1 Introductory Physics, High School Learning Standards for a Full First-Year Course

KEY NNHS Introductory Physics: MCAS Review Packet #1 Introductory Physics, High School Learning Standards for a Full First-Year Course Introductory Physics, High School Learning Standards for a Full First-Year Course I. C ONTENT S TANDARDS Central Concept: Newton s laws of motion and gravitation describe and predict the motion of 1.1

More information

Visual Tutorial. Pitot Static System Simulator. Adobe (formerly Macromedia) Flash Requirements

Visual Tutorial.  Pitot Static System Simulator. Adobe (formerly Macromedia) Flash Requirements Visual Tutorial Tutorial Version 1.01 Pitot Static System Simulator Adobe (formerly Macromedia) Flash Requirements Thank you for using the Pitot Static System Simulator from luizmonteiro.com. Please note

More information

Newtonian Mechanics. Dynamics. Marline Kurishingal

Newtonian Mechanics. Dynamics. Marline Kurishingal Newtonian Mechanics Dynamics Marline Kurishingal Newton s laws of Motion Newton's laws of motion are three physical laws which provide relationships between the forces acting on a body and the motion of

More information

Module No. # 01 Lecture No. # 22

Module No. # 01 Lecture No. # 22 Introduction to Helicopter Aerodynamics and Dynamics Prof. Dr. C. Venkatesan Department of Aerospace Engineering Indian Institute of Technology, Kanpur Module No. # 01 Lecture No. # 22 Lead lag dynamics

More information

Introduction to Aerospace Engineering

Introduction 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 information

Lecture AC-1. Aircraft Dynamics. Copy right 2003 by Jon at h an H ow

Lecture AC-1. Aircraft Dynamics. Copy right 2003 by Jon at h an H ow Lecture AC-1 Aircraft Dynamics Copy right 23 by Jon at h an H ow 1 Spring 23 16.61 AC 1 2 Aircraft Dynamics First note that it is possible to develop a very good approximation of a key motion of an aircraft

More information

Drag Analysis of a Supermarine. Spitfire Mk V at Cruise Conditions

Drag Analysis of a Supermarine. Spitfire Mk V at Cruise Conditions Introduction to Flight Aircraft Drag Project April 2016 2016 Drag Analysis of a Supermarine Spitfire Mk V at Cruise Conditions Nicholas Conde nicholasconde@gmail.com U66182304 Introduction to Flight Nicholas

More information

ME 425: Aerodynamics

ME 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 information

Jet 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 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 information

Chapter 10. Projectile and Satellite Motion

Chapter 10. Projectile and Satellite Motion Chapter 10 Projectile and Satellite Motion Which of these expresses a vector quantity? a. 10 kg b. 10 kg to the north c. 10 m/s d. 10 m/s to the north Which of these expresses a vector quantity? a. 10

More information

Definitions In physics we have two types of measurable quantities: vectors and scalars.

Definitions In physics we have two types of measurable quantities: vectors and scalars. 1 Definitions In physics we have two types of measurable quantities: vectors and scalars. Scalars: have magnitude (magnitude means size) only Examples of scalar quantities include time, mass, volume, area,

More information

Motion under the Influence of a Central Force

Motion under the Influence of a Central Force Copyright 004 5 Motion under the Influence of a Central Force The fundamental forces of nature depend only on the distance from the source. All the complex interactions that occur in the real world arise

More information