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Lanchester–Prandtl Wing Theory
The Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing based on its geometry. It is also known as the Lanchester–Prandtl wing theory. The theory was expressed independently by Frederick W. Lanchester in 1907, and by Ludwig Prandtl in 1918–1919 after working with Albert Betz and Max Munk. In this model, the bound vortex loses strength along the whole wingspan because it is shed as a vortex-sheet from the trailing edge, rather than just as a single vortex from the wing-tips. Introduction It is difficult to predict analytically the overall amount of lift that a wing of given geometry will generate. When analyzing a three-dimensional finite wing, the first approximation to understanding is to consider slicing the wing into cross-sections and analyzing each cross-section independently as a wing in a two-dimensional world. Each of these slices is called an airfoil, and it is easier to understand a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics. The term ''aerodynamics'' is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vortex
In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces, viscous friction within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin Airfoil Theory
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily the resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small-angle Approximation
The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: : \begin \sin \theta &\approx \theta \\ \cos \theta &\approx 1 - \frac \approx 1\\ \tan \theta &\approx \theta \end These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science. One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision. There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the order of the approximation, \textstyle \cos \theta is approximated as either 1 or as 1-\frac. Justifications Graphic The accuracy of the approximations can be seen belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Downwash
In aeronautics, downwash is the change in direction of air deflected by the aerodynamic action of an airfoil, wing, or helicopter rotor blade in motion, as part of the process of producing lift.Crane, Dale: ''Dictionary of Aeronautical Terms, third edition'', page 172. Aviation Supplies & Academics, 1997. In helicopter aerodynamics discussions, it may be referred to as induced flow. Lift on an airfoil is an example of the application of Newton's third law of motion – the force required to deflect the air in the downwards direction is equal in magnitude and opposite in direction to the lift force on the airfoil. Lift on an airfoil is also an example of the Kutta-Joukowski theorem. The Kutta condition explains the existence of downwash at the trailing edge of the wing."The main fact of all heavier-than-air flight is this: ''the wing keeps the airplane up by pushing the air down.''" In: See also * Brownout (aeronautics) *Jet blast *Slipstream *Wake turbulence *Wingtip vortices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin Airfoil Theory
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily the resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord (aircraft)
In aeronautics, the chord is an imaginary straight line joining the leading edge and trailing edge of an aerofoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading edge.L. J. Clancy (1975), ''Aerodynamics'', Section 5.2, Pitman Publishing Limited, London. The point on the leading edge used to define the chord may be the surface point of minimum radius. p.18 For a turbine aerofoil the chord may be defined by the line between points where the front and rear of a 2-dimensional blade section would touch a flat surface when laid convex-side up. The wing, horizontal stabilizer, vertical stabilizer and propeller/rotor blades of an aircraft are all based on aerofoil sections, and the term ''chord'' or ''chord length'' is also used to describe their width. The chord of a wing, stabilizer and propeller is determined by measuring the distance between leading and trailing edges in the direction of the airflow. (If a win ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oswald Efficiency Number
The Oswald efficiency, similar to the span efficiency, is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift distribution.Raymer, Daniel P., ''Aircraft Design: A Conceptual Approach'', Section 12.6 (Fourth edition) Definition The Oswald efficiency is defined for the cases where the overall coefficient of drag of the wing or airplane has a constant+quadratic dependence on the aircraft lift coefficient :C_D = C_ + \frac where : For conventional fixed-wing aircraft with moderate aspect ratio and sweep, Oswald efficiency number with wing flaps retracted is typically between 0.7 and 0.85. At supersonic speeds, Oswald efficiency number decreases substantially. For example, at Mach 1.2 Oswald efficiency number is likely to be between 0.3 and 0.5. Comparison with span efficiency factor It is frequently assumed that Oswald efficiency number is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lift-induced Drag
In aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is an aerodynamic drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in airplanes due to wings or a lifting body redirecting air to cause lift and also in cars with airfoil wings that redirect air to cause a downforce. It is symbolized as D_\text, and the ''lift-induced drag coefficient'' as C_. For a constant amount of lift, induced drag can be reduced by increasing airspeed. A counter-intuitive effect of this is that, up to the speed-for-minimum-drag, aircraft need less power to fly faster. Induced drag is also reduced when the wingspan is higher, or for wings with wingtip devices. Explanation The total aerodynamic force acting on a body is usually thought of as having two components, lift and drag. By definition, the component of force parallel to the oncoming flow is called drag; and the component perpendicular to the oncoming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Of Attack
In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is moving. Angle of attack is the angle between the body's reference line and the oncoming flow. This article focuses on the most common application, the angle of attack of a wing or airfoil moving through air. In aerodynamics, angle of attack specifies the angle between the chord line of the wing of a fixed-wing aircraft and the vector representing the relative motion between the aircraft and the atmosphere. Since a wing can have twist, a chord line of the whole wing may not be definable, so an alternate reference line is simply defined. Often, the chord line of the root of the wing is chosen as the reference line. Another choice is to use a horizontal line on the fuselage as the reference line (and also as the longitudinal axis). Some aut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspect Ratio (wing)
In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wing area. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio.Kermode, A.C. (1972), ''Mechanics of Flight'', Chapter 3, (p.103, eighth edition), Pitman Publishing Limited, London Aspect ratio and other features of the planform are often used to predict the aerodynamic efficiency of a wing because the lift-to-drag ratio increases with aspect ratio, improving the fuel economy in powered airplanes and the gliding angle of sailplanes. Definition The aspect ratio \text is the ratio of the square of the wingspan b to the projected wing area S, which is equal to the ratio of the wingspan b to the standard mean chord \text: \text \equiv \frac = \frac Mechanism As a useful simplification, an airplane in flight can be imagined to affect a circular cylinder of air with a diameter equal to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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