Basic Wing and Airfoil Theory, 1st Ed.

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More filters. Sort order. Mohamed Hamdan rated it it was amazing Nov 30, Neo Goldenstar rated it it was amazing Mar 06, Dennis Berry rated it liked it Feb 18, Tyler rated it it was amazing Oct 27, Benjamin rated it liked it Apr 28, Nicky Siga rated it it was amazing Nov 07, Joecrash rated it it was amazing Jan 28, Anindita marked it as to-read Dec 13, Per Mortensen marked it as to-read Mar 21, Chandan marked it as to-read Sep 13, Mohammed Almusawa marked it as to-read Feb 12, Joana marked it as to-read Oct 14, Josep-Angel Herrero Bajo marked it as to-read Oct 12, Subsonic flight airfoils have a characteristic shape with a rounded leading edge , followed by a sharp trailing edge , often with a symmetric curvature of upper and lower surfaces.

Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily the result of its angle of attack and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air for fixed-wing aircraft, a downward force , resulting in a force on the airfoil in the direction opposite to the deflection.

This force is known as aerodynamic force and can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines , resulting in lower pressure on one side and higher pressure on the other.

This pressure difference is accompanied by a velocity difference, via Bernoulli's principle , so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface.

A fixed-wing aircraft 's wings, horizontal , and vertical stabilizers are built with airfoil-shaped cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans , compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard and keel , are similar in cross-section and operate on the same principles as airfoils. An airfoil-shaped wing can create downforce on an automobile or other motor vehicle, improving traction. When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind.

This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag.

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Airfoils have potential for use in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering. A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve represents an airfoil with a positive camber so some lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation, called the slope of the lift curve.

At about 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The drop in lift can be explained by the action of the upper-surface boundary layer , which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, in particular it reduces its effective camber , which modifies the overall flow field so as to reduce the circulation and the lift.

The thicker boundary layer also causes a large increase in pressure drag , so that the overall drag increases sharply near and past the stall point. Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an aerobatic airplane.

In the region of the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spin — stall. Thus a large range of angles can be used without boundary layer separation. Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross section is not strictly circular, however: the radius of curvature is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge.

Supersonic airfoils are much more angular in shape and can have a very sharp leading edge, which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a low camber to reduce drag divergence.

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Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing. Movable high-lift devices, flaps and sometimes slats , are fitted to airfoils on almost every aircraft.

Text Book Theory of Flight

A trailing edge flap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into the wing if not used. Take point 2 to be at a point above the curved surface of the wing, outside of the boundary layer. It is assumed that compared to the other terms of the equation, gz 1 and gz 2 are negligible i. Thus, Equation 1 becomes:.

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For the second case, take point 1 to be again at a point on the streamline in front of the wing. Since the values for P ambient and v ambient are the same as for the first case, the constant from Equation 2 is also assumed to be the same. Take point 2 to be at a point below the wing, outside of the boundary layer. With the same assumptions as in the first case, Equation 1 and 2 become:.

Since the velocity of the fluid below the wing is slower than the velocity of the fluid above the wing, to satisfy Equation 3, the pressure below the wing must be higher than the pressure above the wing. In a qualitative look at Euler's Equations, the movement of the fluid flow around the curved upper surface of the wing may be likened to that of a car going around a bend. Similarly, as the fluid particle follows the cambered upper surface of the wing, there must be a force acting on that little particle to allow the particle to make that turn. This force comes from a pressure gradient above the wing surface.

Starting at the surface of the wing and moving up and away from the surface, the pressure increases with increasing distance until the pressure reaches the ambient pressure.

Thus, a pressure gradient is created, where the higher pressures further along from the radius of curvature push inwards towards the center of curvature where the pressure is lower, thus providing the accelerating force on the fluid particle. Thus due to the curved, cambered surface of the wing, there exists a pressure gradient above the wing, where the pressure is lower right above the surface. Assuming a flat bottom, the pressure below the wing will be close to the ambient pressure, and will thus push upwards, creating the lift needed by the airplane.

At angles of attack below around ten to fifteen degrees, the lift increases with an increasing angle. However, if the angle of attack is too large, stalling takes place. Stalling occurs when the lift decreases, sometimes very suddenly. The phenomena responsible for stalling is flow separation see Figure 9.

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Flow separation is the situation where the fluid flow no longer follows the contour of the wing surface. Fluid particles flowing along the top of the wing surface experience a change in pressure, moving from the ambient pressure in front of the wing, to a lower pressure over the surface of the wing, then back up to the ambient pressure behind the wing. The region where fluid must flow from low to high pressure adverse pressure gradient is responsible for flow separation.


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  • If the pressure gradient is too high, the pressure forces overcome the fluid's inertial forces, and the flow departs from the wing contour. Since the pressure gradient increases with an increasing angle of attack, the angle of attack should not exceed the maximum value to keep the flow following the contour. If this angle is exceeded, however, the force keeping the plane in the air will decrease, and may even disappear altogether.



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