I would re-name this chapter Unpowered flight The drag polar, the relationship between lift and drag.
|
|
- Julian Montgomery
- 6 years ago
- Views:
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
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 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 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 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 informationLecture 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 informationStability 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 informationKinesiology 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 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 informationModel 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 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 informationIntroduction 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 information3.3 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 informationEVOLVING 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 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 information3 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 informationPHYSICS. 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 informationFlight 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 informationAircraft 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 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 informationy(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 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 informationSTRAIGHT-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 informationTheory 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 informationTEKS 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 informationTheory 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 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 informationTopic 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 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 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 informationBell 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 informationThe 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 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 informationPHYSICS. 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 informationWritten 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 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 informationA 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 informationChapter 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 informationComment: 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 informationfor 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 informationKinematics 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 informationSection /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 informationN 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 informationDynamic 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 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 informationSTEP 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 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 informationPhysics 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 informationCHAPTER 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 informationThe 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 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 informationQuest 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 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 informationKinematics 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 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 informationKinematics -- 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 informationSubsonic 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 informationUnit 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 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 informationKinematics. 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 informationNewton 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 informationReview 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 informationAP 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 informationExtended 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 information4.2. 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 informationThe 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 informationMotion 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 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 informationPhysics 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 informationPhysics 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 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 informationTeacher 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 informationProblem: 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 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 informationLecture 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 information1-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 informationLesson 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 informationForces 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 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 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 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 information5 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 informationLab 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 informationMotion. 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 informationPHYSICS 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 informationUnit 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 informationDynamic 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 informationFigure 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 informationMAV 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 informationKEY 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 informationVisual 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 informationNewtonian 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 informationModule 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 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 informationLecture 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 informationDrag 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 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 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 informationChapter 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 informationDefinitions 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 informationMotion 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