Chapter 2 – Aerodynamics: the Wing Is the Thing
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8. Level, Non-Accelerated Flight
Performance 8. Level, Non-Accelerated Flight For non-accelerated flight, the tangential acceleration, , and normal acceleration, . As a result, the governing equations become: (1) If we add the additional assumptions of level flight, , and that the thrust is aligned with the velocity vector, , then Eq. (1) reduces to the simple form: (2) The last two equations tell us that the altitude is a constant, and the velocity is the range rate. For now, however, we are interested in the first two equations that can be rewritten as: (3) The key thing to remember about these equations is that the weight,W,isagivenand it is equal to the Lift. Consequently, lift is not at our disposal, it must equal the given weight! Thus for a given aircraft and any given altitude, we can determine the required lift coefficient (and hence angle-of-attack) for any given airspeed. (4) Therefore at a given weight and altitude, the lift coefficient varies as 1 over V2. A sketch of lift coefficient vs. speed looks as follows: 1 It is clear from the figure that as the vehicle slows down, in order to remain in level flight, the lift coefficient (and hence angle-of-attack) must increase. [You can think of it in terms of the momentum flux. The momentum flux (the mass flow rate time the velocity out in the z direction) creates the lift force. Since the mass flow rate is directional proportional to the velocity, then the slower we go, the more the air must be deflected downward. We do this by increasing the angle-of-attack!]. -
Circular Motion Dynamics
Problem Solving Circular Motion Dynamics Problem 1: Double Star System Consider a double star system under the influence of gravitational force between the stars. Star 1 has mass m1 and star 2 has mass m2 . Assume that each star undergoes uniform circular motion about the center of mass of the system. If the stars are always a fixed distance s apart, what is the period of the orbit? Solution: Choose radial coordinates for each star with origin at center of mass. Let rˆ1 be a unit vector at Star 1 pointing radially away from the center of mass. Let rˆ2 be a unit vector at Star 2 pointing radially away from the center of mass. The force diagrams on the two stars are shown in the figure below. ! ! From Newton’s Second Law, F1 = m 1a 1 , for Star 1 in the radial direction is m m ˆ 1 2 2 r1 : "G 2 = "m1 r 1 ! . s We can solve this for r1 , m r = G 2 . 1 ! 2s 2 ! ! Newton’s Second Law, F2 = m 2a 2 , for Star 2 in the radial direction is m m ˆ 1 2 2 r2 : "G 2 = "m2 r 2 ! . s We can solve this for r2 , m r = G 1 . 2 ! 2s 2 Since s , the distance between the stars, is constant m2 m1 (m2 + m1 ) s = r + r = G + G = G 1 2 ! 2s 2! 2s 2 ! 2s 2 . Thus the angular velocity is 1 2 " (m2 + m1 ) # ! = $G 3 % & s ' and the period is then 1 2 2! # 4! 2s 3 $ T = = % & . -
Assignment 2 Centripetal Force & Univ
LAST NAME______________________________ FIRST NAME_____________________DATE______ CJ - Assignment 2 Centripetal Force & Universal Gravitation, 5.4 Banked Curves Draw the vectors for a free body diagram of a car in an unbanked turn and a banked turn. For this situation assume the cars are turning to the left side of the drawing. Car in Unbanked Turn Car in Banked turn Is this car in Equilibrium? Is this car in Equilibrium? Do the same for the airplane. Airplane in Unbanked Turn Airplane in Banked turn Let’s be careful to fully understand what is going on with this one. We have made an assumption in doing this for the airplane which are not valid. THE BANKED TURN- car can make it a round a turn even if friction is not present (or friction is zero). In order for this to happen the curved road must be “banked”. In a non-banked turn the centripetal force is created by the friction of the road on the tires. What creates the centripetal force in a banked turn? Imagine looking at a banked turn as shown to the right. Draw the forces that act on the car on the diagram of the car. Is the car in Equilibrium? YES , NO The car which has a mass of m is travelling at a velocity (or speed) v around a turn of radius r. How do these variables relate to optimize the banked turn. If the mass of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the VELOCITY of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the RADUS OF THE TURN is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY To properly show the relationship an equation must be created. -
April 2018 the Privileged View Steve Beste, President
Volume 18 – 04 www.FlyingClub1.org April 2018 The Privileged View Steve Beste, President Maker Faire. When something breaks, who you gonna call? If it’s your car or your Cessna, you put it into the shop and get out your checkbook. But if you fly an experimental or Part 103 aircraft, it’s not so simple. That’s why - when newbies ask me about our sport - I find out if they’re tinkerers and do-it-yourselfers. If all they bring to a problem is their checkbook, then they’re better off going with the Cessna. The tinkerers and builders, though, they’re my kind of people. That’s why I went with Dick Martin to the annual Maker Faire at George Mason in mid-March. I thought we’d find a modest event that focused on 3D printing for adult hobbyists, but I was so wrong. They had 140 exhibitors filling three buildings. With several thousand visitors, there were lines outside the buildings by mid-afternoon. Yes, they had 3D printers, but so much more. And so many kids! The focus of the event was clearly on bringing young people into the world of making stuff. The cleverest exhibit was the one shown below. They set up four tables with junk computer gear and told kids to just take things apart. Don’t worry about putting anything back together again. It’s all junk! Rip it apart! See how it’s made! Do it! It looked like a destruction derby, with laptops and printers and even a sewing machine being reduced to screws and plates. -
FAA-H-8083-3A, Airplane Flying Handbook -- 3 of 7 Files
Ch 04.qxd 5/7/04 6:46 AM Page 4-1 NTRODUCTION Maneuvering during slow flight should be performed I using both instrument indications and outside visual The maintenance of lift and control of an airplane in reference. Slow flight should be practiced from straight flight requires a certain minimum airspeed. This glides, straight-and-level flight, and from medium critical airspeed depends on certain factors, such as banked gliding and level flight turns. Slow flight at gross weight, load factors, and existing density altitude. approach speeds should include slowing the airplane The minimum speed below which further controlled smoothly and promptly from cruising to approach flight is impossible is called the stalling speed. An speeds without changes in altitude or heading, and important feature of pilot training is the development determining and using appropriate power and trim of the ability to estimate the margin of safety above the settings. Slow flight at approach speed should also stalling speed. Also, the ability to determine the include configuration changes, such as landing gear characteristic responses of any airplane at different and flaps, while maintaining heading and altitude. airspeeds is of great importance to the pilot. The student pilot, therefore, must develop this awareness in FLIGHT AT MINIMUM CONTROLLABLE order to safely avoid stalls and to operate an airplane AIRSPEED This maneuver demonstrates the flight characteristics correctly and safely at slow airspeeds. and degree of controllability of the airplane at its minimum flying speed. By definition, the term “flight SLOW FLIGHT at minimum controllable airspeed” means a speed at Slow flight could be thought of, by some, as a speed which any further increase in angle of attack or load that is less than cruise. -
Powered Paraglider Longitudinal Dynamic Modeling and Experimentation
POWERED PARAGLIDER LONGITUDINAL DYNAMIC MODELING AND EXPERIMENTATION By COLIN P. GIBSON Bachelor of Science in Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 2014 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE December, 2016 POWERED PARAGLIDER LONGITUDINAL DYNAMIC MODELING AND EXPERIMENTATION Thesis Approved: Dr. Andrew S. Arena Thesis Adviser Dr. Joseph P. Conner Dr. Jamey D. Jacob ii Name: COLIN P. GIBSON Date of Degree: DECEMBER, 2016 Title of Study: POWERED PARAGLIDER LONGITUDINAL DYNAMIC MODELING AND EXPERIMENTATION Major Field: MECHANICAL AND AEROSPACE ENGINEERING Abstract: Paragliders and similar controllable decelerators provide the benefits of a compact packable parachute with the improved glide performance and steering of a conventional wing, making them ideally suited for precise high offset payload recovery and airdrop missions. This advantage over uncontrollable conventional parachutes sparked interest from Oklahoma State University for implementation into its Atmospheric and Space Threshold Research Oklahoma (ASTRO) program, where payloads often descend into wooded areas. However, due to complications while building a powered paraglider to evaluate the concept, more research into its design parameters was deemed necessary. Focus shifted to an investigation of the effects of these parameters on the flight behavior of a powered system. A longitudinal dynamic model, based on Lagrange’s equation for adaptability when adding free-hanging masses, was developed to evaluate trim conditions and analyze system response. With the simulation, the effects of rigging angle, fuselage weight, center of gravity (cg), and apparent mass were calculated through step thrust input cases. -
Static Pressure Distribution on Long Cylinders As a Function of the Yaw Angle and Reynolds Number
fluids Article Static Pressure Distribution on Long Cylinders as a Function of the Yaw Angle and Reynolds Number William W. Willmarth 1,† and Timothy Wei 2,* 1 Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA 2 Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA * Correspondence: [email protected] † Deceased author. Abstract: This paper addresses the challenges of pressure-based sensing using axisymmetric probes whose axes are at small angles to the mean flow. Mean pressure measurements around three yawed circular cylinders with aspect ratios of 28, 64, and 100 were made to determine the effect of changes in the yaw angle, g, and freestream velocity on the average pressure coefficient, CpN, and drag coeffi- cient, CDN. The existence of four distinct types of circumferential pressure distributions—subcritical, transitional, supercritical, and asymmetric—were confirmed, along with the appropriateness of scaling CpN and CDN on a streamwise Reynolds number, Resw, based on the freestream velocity and the fluid path length along the cylinder in the streamwise direction. It was found that there was a distinct difference in the values of CDN and CpN at identical Resw values for cylinders yawed between 5◦ and 30◦, and for cylinders at greater than a 30◦ yaw. For g < 5◦, there did not appear to be any large-scale vortices in the near wake, and CDN and CpN appeared to become independent of ◦ ◦ Resw. Over the range of 5 ≤ g ≤ 30 , there was a complex interplay of freestream speed, yaw angle, and aspect ratio that affected the formation and shedding of Kármán-like vortices. -
Modelling & Implementation of Aerodynamic Zero-Lift Drag
School of Innovation, Design and Engineering BACHELOR THESIS IN AERONAUTICAL ENGINEERING 15 CREDITS, BASIC LEVEL 300 Modelling & implementation of Aerodynamic Zero-lift Drag into ADAPDT Author: David Bergman Report code: MDH.IDT.FLYG.0215.2009.GN300.15HP.Ae Dokumentslag Type of document Reg-nr Reg. No REPORT TDA-2009-0200 Ägare (tj-st-bet, namn) Owner (department, name) Datum Date Utgåva Issue Sida Page TDAA-EXB, David Bergman 2009-11-03 1 1 (46) Fastställd av Confirmed by Infoklass Info. class Arkiveringsdata File TDAA-RL, Roger Larsson PUBLIC TDA-ARKIV Giltigt för Valid for Ärende Subject Fördelning To Modelling & implementation of Aerodynamic Zero-lift TDAA-RL, TDAA-PW, TDAA-SH, Drag into ADAPDT TDAA-ET, TDAA-HJ, Gustaf Enebog (MDH) ABSTRACT The objective of this thesis work was to construct and implement an algorithm into the program ADAPDT to calculate the zero-lift drag profile for defined aircraft geometries. ADAPDT, short for AeroDynamic Analysis and Preliminary Design Tool, is a program that calculates forces and moments about a flat plate geometry based on potential flow theory. Zero-lift drag will be calculated by means of different hand-book methods found suitable for the objective and applicable to the geometry definition that ADAPDT utilizes. Drag has two main sources of origin: friction and pressure distribution, all drag acting on the aircraft can be traced back to one of these two physical phenomena. In aviation drag is divided into induced drag that depends on the lift produced and zero-lift drag that depends on the geometry of the aircraft. used, disclosedused, How reliable and accurate the zero-lift drag computations are depends on the geometry data that can be extracted and used. -
42O0kg)(25Ky = 30,000N 25In
Unit 4: Uniform Circular Motion Name_______Key_______________________ WS-3 Vertical Motion and Banked Turns Date_______________ Block___________ 1. A car travels through a valley at constant speed, though not at constant velocity. a. Explain how this is possible. thereto - its direction e The car is constantly changing it is accelerating b. Is the car accelerating? What direction is the car's acceleration? (Explain how you know.) towards the center of the circle yes , c. Construct a qualitative force diagram for the car at the moment it is at the bottom of the valley. Are the forces balanced? Justify the relative sizes of the forces. ^ F w F T ÷ 8 " mg d. If the car's speed is 25 m/s, its mass is 1200 kg and the radius of valley (r) is 25 meters, determine the magnitude of the centripetal force acting on the car. t.my?42o0kg)(25kY = 30,000N 25in e. Construct a quantitative force diagram for the car at the bottom of the valley. - a N = 42,000 n mg 30,000N = (10%2) ÷ mg 1200kg u 12,000N 2. A car travels over a hill at constant speed. ftw • Img a. Is the car accelerating? What direction is the car's acceleration? (Explain how you know.) The car is accelerating. At the top the acceleration is down. The acceleration is always perpendicular to the tangent at the location b. If the speed of the car is 43 km/h, its mass is 1200 kg and the radius of the hill (r) is 25m, determine the magnitude of the centripetal force acting on the car. -
Department of Transportation Federal Aviation Administration
Tuesday, November 26, 2002 Part II Department of Transportation Federal Aviation Administration 14 CFR Parts 1, 25, and 97 1-g Stall Speed as the Basis for Compliance With Part 25 of the Federal Aviation Regulations; Final Rule VerDate 0ct<31>2002 14:24 Nov 25, 2002 Jkt 200001 PO 00000 Frm 00001 Fmt 4717 Sfmt 4717 E:\FR\FM\26NOR2.SGM 26NOR2 70812 Federal Register / Vol. 67, No. 228 / Tuesday, November 26, 2002 / Rules and Regulations DEPARTMENT OF TRANSPORTATION Docket you selected, click on the For example, under part 25, V2 must be document number for the item you wish at least 1.2 times VS, the final takeoff Federal Aviation Administration to view. climb speed must be at least 1.25 times You can also get an electronic copy VS, and the landing approach speed 14 CFR Parts 1, 25, and 97 using the Internet through the Office of must be at least 1.3 times VS. [Docket No. 28404; Amendment Nos. 1–49, Rulemaking’s Web page at http:// The speed margin, or difference in 25–108, 97–1333] www.faa.gov/avr/armhome.htm or the speed, between VS and each minimum Federal Register’s Web page at http:// operating speed provides a safety RIN 2120–AD40 www.access.gpo.gov/su_docs/aces/ ‘‘cushion’’ to ensure that normal aces140.html. operating speeds are sufficiently higher 1-g Stall Speed as the Basis for You can also get a copy by submitting than the speed at which the airplane Compliance With Part 25 of the Federal a request to the Federal Aviation stalls. -
5 | Newton's Laws of Motion 207 5 | NEWTON's LAWS of MOTION
Chapter 5 | Newton's Laws of Motion 207 5 | NEWTON'S LAWS OF MOTION Figure 5.1 The Golden Gate Bridge, one of the greatest works of modern engineering, was the longest suspension bridge in the world in the year it opened, 1937. It is still among the 10 longest suspension bridges as of this writing. In designing and building a bridge, what physics must we consider? What forces act on the bridge? What forces keep the bridge from falling? How do the towers, cables, and ground interact to maintain stability? Chapter Outline 5.1 Forces 5.2 Newton's First Law 5.3 Newton's Second Law 5.4 Mass and Weight 5.5 Newton’s Third Law 5.6 Common Forces 5.7 Drawing Free-Body Diagrams Introduction When you drive across a bridge, you expect it to remain stable. You also expect to speed up or slow your car in response to traffic changes. In both cases, you deal with forces. The forces on the bridge are in equilibrium, so it stays in place. In contrast, the force produced by your car engine causes a change in motion. Isaac Newton discovered the laws of motion that describe these situations. Forces affect every moment of your life. Your body is held to Earth by force and held together by the forces of charged particles. When you open a door, walk down a street, lift your fork, or touch a baby’s face, you are applying forces. Zooming in deeper, your body’s atoms are held together by electrical forces, and the core of the atom, called the nucleus, is held together by the strongest force we know—strong nuclear force. -
Chapter 9 Energy
VOLUME I PERFORMANCE FLIGHT TEST PHASE CHAPTER 9 ENERGY >£>* ^ AUGUST 1991 USAF TEST PILOT SCHOOL EDWARDS AFB, CA I Approved for public rate-erne; ! Distribution Uni;: r<cA 19970116 079 Table of Contents 9.1 INTRODUCTION 9.1 9.1.1 AIRCRAFT PERFORMANCE MODELS 9.1 9.1.2 NEED FOR NONSTEADY STATE MODELS 9.1 9.2 STEADY STATE CLIMBS AND DESCENTS 9.2 9.2.1 FORCES ACTING ON AN AIRCRAFT IN FLIGHT 9.2 9.2.2 ANGLE OF CLIMB PERFORMANCE 9.5 9.2.3 RATE OF CLIMB PERFORMANCE 9.9 9.2.4 TIME TO CLIMB DETERMINATION 9.14 9.2.5 GLIDING PERFORMANCE 9.16 9.2.6 POLAR DIAGRAMS 9.18 9.3 BASIC ENERGY STATE CONCEPTS 9.22 9.3.1 ASSUMPTIONS 9.22 9.3.2 ENERGY DEFINITIONS 9.23 9.3.3 SPECD7IC ENERGY 9.24 9.3.4 SPECD7IC EXCESS POWER 9.24 9.4 THEORETICAL BASIS FOR ENERGY OPTIMIZATIONS 9.25 9.5 GRAPHICAL TOOLS FOR ENERGY APPROXIMATION 9.25 9.5.1 SPECD7IC ENERGY OVERLAY 9.26 9.5.2 SPECmC EXCESS POWER PLOTS 9.28 9.6 TIME OPTIMAL CLIMBS 9.36 9.6.1 GRAPHICAL APPROXIMATIONS TO RUTOWSKI CONDITIONS 9.36 9.6.2 MINIMUM TIME TO ENERGY LEVEL PROFILES 9.37 9.6.3 SUBSONIC TO SUPERSONIC TRANSITIONS 9.38 9.7 FUEL OPTIMAL CLIMBS 9.40 9.7.1 FUEL EFFICIENCY 9.41 9.7.2 COMPARISON OF FUEL OPTIMAL AND TIME OPTIMAL PATHS 9.43 9.8 MANEUVERABILITY 9.44 9.9 INSTANTANEOUS MANEUVERABILITY 9.44 9.9.1 LIFT BOUNDARY LIMITATION 9.45 9.9.2 STRUCTURAL LIMITATION 9.46 9.9.3 qLIMTTATION 9.46 9.9.4 PILOT LIMITATIONS 9.46 9.10 THRUST LIMITATIONS/SUSTAINED MANEUVERABILITY 9.47 9.10.1 SUSTAINED TURN PERFORMANCE 9.47 9.10.2 FORCES IN ATURN 9.47 9.11 VERTICAL TURNS 9-52 9.12 OBLIQUE PLANE MANEUVERING 9.53 9.13