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Center of Pressure As an object moves through a fluid, the velocity of the fluid varies around the surface of the object. The variation of velocity produces a variation of pressure on the surface of the object as shown by the the thin red lines on the figure. Integrating the pressure times the surface area around the body determines the aerodynamic force on the object. We can consider this single force to act through the average location of the pressure on the surface of the object. We call the average location of the pressure variation the center of pressure in the same way that we call the average location of the weight of an object the center of gravity. The aerodynamic force can then be resolved into two components, lift and drag, which act through the center of pressure in flight. Determining the center of pressure is very important for any flying object. To trim an airplane, or to provide stability for a model rocket or a kite, it is necessary to know the location of the center of pressure of the entire aircraft. How do engineers determine the location of the center of pressure for an aircraft which they are designing? In general, determining the center of pressure (cp) is a very complicated procedure because the pressure changes around the object. Determining the center of pressure requires the use of calculus and a knowledge of the pressure distribution around the body. We can characterize the pressure variation around

the surface as a function p(x) which indicates that the pressure depends on the distance x from a reference line usually taken as the leading edge of the object. If we can determine the form of the function, there are methods to perform a calculus integration of the equation. We will use the symbols "S[ ]dx" to denote the integration of a continuous function. Then the center of pressure can be determined from: cp = (S[x * p(x)]dx) / (S[p(x)]dx) If we don't know the actual functional form, we can numerically integrate the equation using a spreadsheet by dividing the distance into a number of small distance segments and determining the average value of the pressure over that small segment. Taking the sum of the average value times the distance times the distance segment divided by the sum of the average value times the distance segment will produce the center of pressure. There are several important problems to consider when determining the center of pressure for an airfoil. As we change angle of attack, the pressure at every point on the airfoil changes. And, therefore, the location of the center of pressure changes as well. The movement of the center of pressure caused a major problem for early airfoil designers because the amount (and sometimes the direction) of the movement was different for different designs. In general, the pressure variation around the airfoil also imparts a torque, or "twisting force", to the airfoil. If a flying airfoil is not restrained in some way it will flip as it moves through the air. (As a further complication, the center of pressure also moves because of viscosity and compressibility effects on the flow field. But let's save that discussion for another page.) To resolve some of these design problems, aeronautical engineers prefer to characterize the forces on an airfoil by the aerodynamic force, described above, coupled with an aerodynamic moment to account for the torque. It was found both experimentally and analytically that, if the aerodynamic force is applied at a location 1/4 chord back from the leading edge on most low speed airfoils, the magnitude of the aerodynamic moment remains nearly constant with angle of attack. Engineers call the location where the aerodynamic moment remains constant the aerodynamic center of the airfoil. Using the aerodynamic center as the location where the aerodynamic force is applied eliminates the problem of the movement of the center of pressure with angle of attack in aerodynamic analysis. (For supersonic airfoils, the aerodynamic center is nearer the 1/2 chord location.) When computing the trim of an aircraft, model rocket, or kite, we usually apply the aerodynamic forces at the aerodynamic center of airfoils and compute the center of pressure of the vehicle as an area-weighted average of the centers of the components.

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by Tom Benson Please send suggestions/corrections to: [email protected] Last Updated Thu, Feb 26 10:02:16 AM EST 2004 by Tom Benson

There are many factors which influence the amount of aerodynamic lift which a body generates. Lift depends on the shape, size, inclination, and flow conditions of the air passing the object. For a three dimensional wing, there is an additional effect on lift, called downwash, which will be discussed on this page. For a lifting wing, the air pressure on the top of the wing is lower than the pressure below the wing. Near the tips of the wing, the air is free to move from the region of high pressure into the region of low pressure. The resulting flow is shown on the figure at the left by the two circular blue lines with the arrowheads showing the flow direction. As the aircraft moves to the lower left, a pair of counter-rotating vortices are formed at the wing tips. The lines marking the center of the vortices are shown as blue vortex lines leading from the wing tips. If the atmosphere has very high humidity, you can sometimes see the vortex lines on an airliner during landing as long thin "clouds" leaving the wing tips. The wing tip vortices produce a downwash of air behind the wing which is very strong near the wing tips and decreases toward the wing root. The local angle of attack of the wing is increased by the flow induced by the downwash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing. The downstream component of the force is called induced drag because it faces downstream and has been "induced" by the action of the tip vortices. The lift near the wing tips is defined to be perpendicular to the local flow. The local flow is at a greater angle of attack than the free stream flow because of the induced flow. Resolving the tip lift back to the free stream reference produces a reduction in the lift coefficient of the entire wing. The analysis for the reduction in the lift coefficient is fairly tedious and relies on some theoretical ideas which are beyond the scope of the Beginner's Guide. The result of the analysis is an equation for the reduction of the lift coefficient. The final wing lift coefficient Cl is equal to the basic free stream lift coefficient Clo divided by the quantity: 1.0 plus the basic lift coefficient divided by pi (3.14159) times the aspect ratio AR. Cl = Clo / (1 + Clo /[pi * AR]) The aspect ratio is the square of the span s divided by the wing area A. For a rectangular wing this reduces to the ratio of the span to the chord. Long, slender, high aspect ratio wings have less lift reduction than short, thick, low aspect ratio wings as shown in the graph on the right of the figure. Reduced lift coefficient is a three dimensional effect related to the wing tips. The longer the wing, the farther the tips are from the main portion of the wing, and the smaller the lift reduction.

This picture dramatically shows airplane downwash. The picture was sent to us by Jan-Olov Newborg, from Stockholm, Sweden, and was originally taken by Paul Bowens. In the picture, the Cessna Citation has just flown above a cloud deck shown in the background. The downwash from the wing has pushed a trough into the cloud deck. The swirling flow from the tip vortices is also evident. Another slide describes the interesting problems downwash caused for early aerodynamicists.

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Drag is the aerodynamic force that opposes an aircraft's motion through the air. Drag is generated by every part of the airplane (even the engines!). How is drag generated? Drag is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field or an electromagnetic field, where one object can affect another object without being in physical contact. For drag to be generated, the solid body must be in contact with the fluid. If there is no fluid, there is no drag. Drag is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid. If there is no motion, there is no

drag. It makes no difference whether the object moves through a static fluid or whether the fluid moves past a static solid object. Drag is a force and is therefore a vector quantity having both a magnitude and a direction. Drag acts in a direction that is opposite to the motion of the aircraft. Lift acts perpendicular to the motion. There are many factors that affect the magnitude of the drag. Many of the factors also affect lift but there are some factors that are unique to aircraft drag. We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the aircraft. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the solid surface, a boundary layer of low energy flow is generated and the magnitude of the skin friction depends on conditions in the boundary layer. We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This source of drag depends on the shape of the aircraft and is called form drag. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the momentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating (or adding up) the local pressure times the surface area around the entire body. The component of the aerodynamic force that is opposed to the motion is the drag; the component perpendicular to the motion is the lift. Both the lift and drag force act through the center of pressure of the object. There is an additional drag component caused by the generation of lift. Aerodynamicists have named this component the induced drag. This drag occurs because the flow near the wing tips is distorted spanwise as a result of the pressure difference from the top to the bottom of the wing. Swirling vortices are formed at the wing tips, which produce a down wash of air behind the wing which is very strong near the wing tips and decreases toward the wing root. The local angle of attack of the wing is increased by the induced flow of the down wash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing. This additional force is called induced drag because it has been "induced" by the action of the tip vortices. It is also called "drag due to lift" because it only occurs on finite, lifting wings. The magnitude of induced drag depends on the amount of lift being generated by the wing and on the wing geometry. Long, thin (chordwise) wings have low induced drag; short wings with a large chord have high induced drag. Additional sources of drag include wave drag and ram drag. As an aircraft approaches the speed of sound, shock waves are generated along the surface. There is an

additional drag penalty (called wave drag) that is associated with the formation of the shock waves. The magnitude of the wave drag depends on the Mach number of the flow. Ram drag is associated with slowing down the free stream air as air is brought inside the aircraft. Jet engines and cooling inlets on the aircraft are sources of ram drag.

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This slide gives technical definitions of a wing's geometry, which is one of the chief factors affecting airplane lift and drag. The terminology is used throughout the airplane industry and is also found in the FoilSim interactive airfoil simulation program developed here at NASA Glenn. Actual aircraft wings are complex threedimensional objects, but we will start with some simple definitions. The figure shows the wing viewed from three directions; the upper left shows the view from the top looking down on the wing, the lower left shows the view from the front looking at the wing leading edge, and the right shows a side view from the left looking in towards the centerline. The side view shows an airfoil shape with the leading edge to the left. Top View The top view shows a simple wing geometry, like that found on a light general aviation aircraft. The front of the wing (at the bottom) is called the leading edge; the back of the wing (at the top) is called the trailing edge. The distance from the leading edge to the trailing edge is called the chord, denoted by the symbol c. The ends of the wing are called the wing tips, and the distance from one wing tip to the other is called the span, given the symbol s. The shape of the wing, when viewed from above looking down onto the wing, is called a planform. In this figure, the planform is a rectangle. For a rectangular wing, the chord length at every location along the span is

the same. For most other planforms, the chord length varies along the span. The wing area, A, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips. Note: The wing area is NOT the total surface area of the wing. The total surface area includes both upper and lower surfaces. The wing area is a projected area and is almost half of the total surface area. Aspect ratio is a measure of how long and slender a wing is from tip to tip. The Aspect Ratio of a wing is defined to be the square of the span divided by the wing area and is given the symbol AR. For a rectangular wing, this reduces to the ratio of the span to the chord length as shown at the upper right of the figure. AR = s^2 / A = s^2 / (s * c) = s / c High aspect ratio wings have long spans (like high performance gliders), while low aspect ratio wings have either short spans (like the F-16 fighter) or thick chords (like the Space Shuttle). There is a component of the drag of an aircraft called induced drag which depends inversely on the aspect ratio. A higher aspect ratio wing has a lower drag and a slightly higher lift than a lower aspect ratio wing. Because the glide angle of a glider depends on the ratio of the lift to the drag, a glider is usually designed with a very high aspect ratio. The Space Shuttle has a low aspect ratio because of high speed effects, and therefore is a very poor glider. The F-14 and F-111 have the best of both worlds. They can change the aspect ratio in flight by pivoting the wings--large span for low speed, small span for high speed. Front View The front view of this wing shows that the left and right wing do not lie in the same plane but meet at an angle. The angle that the wing makes with the local horizontal is called the dihedral angle. Dihedral is added to the wings for roll stability; a wing with some dihedral will naturally return to its original position if it encounters a slight roll displacement. You may have noticed that most large airliner wings are designed with diherdral. The wing tips are farther off the ground than the wing root. Highly maneuverable fighter planes, on the other hand do not have dihedral. In fact, some fighter aircraft have the wing tips lower than the roots giving the aircraft a high roll rate. A negative dihedral angle is called anhedral . Historical Note: The Wright brothers designed their 1903 flyer with a slight anhedral to enhance the aircraft roll performance. Side View A cut through the wing perpendicular to the leading and trailing edges will show the cross-section of the wing. This side view is called an airfoil, and it has some geometry definitions of its own as shown at the lower right. The straight line drawn from the leading to trailing edges of the airfoil is called the chord line. The chord line cuts the airfoil into an upper surface and a lower surface. If we plot the points that lie halfway between the upper and lower surfaces, we obtain a curve called the mean

camber line. For a symmetric airfoil (upper surface the same shape as the lower surface) the mean camber line will fall on top of the chord line. But in most cases, these are two separate lines. The maximum distance between the two lines is called the camber, which is a measure of the curvature of the airfoil (high camber means high curvature). The maximum distance between the upper and lower surfaces is called the thickness. Often you will see these values divided by the chord length to produce a non-dimensional or "percent" type of number. Airfoils can come with all kinds of combinations of camber and thickness distributions. NACA (the precursor of NASA) established a method of designating classes of airfoils and then wind tunnel tested the airfoils to provide lift coefficients and drag coefficients for designers.

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A glider is a special kind of aircraft that has no engine. Paper airplanes are the most obvious example, but gliders come in a wide range of sizes. Toy gliders, made of balsa wood or styrofoam, are an excellent way for students to study the basics of aerodynamics. Hang-gliders are piloted aircraft that are launched by leaping off the side of a hill. The Wright brothers perfected the design of the first airplane and gained piloting experience through a series of glider flights from 1900 to 1903. More sophisticated gliders are launched by ground based catapults, or are towed aloft by a powered aircraft then cut free to glide for hours over many miles. If a glider is in a steady (constant velocity and no acceleration) descent, it loses altitude as it travels. The glider's flight path is a simple straight line, shown as the inclined red line in the figure. The flight path intersects the ground at an angle a called the glide angle. If we know the distance flown d and the altitude change h, we can calculate the glide angle using trigonometry: tan(a) = h / d where tan is the trigonometric tangent function. The ratio of the change in altitude h to the change in distance d is often called the glide ratio.

If the glider is flown at a specified glide angle, the trigonometric equation can be solved to determine how far the glider can fly for a given change in altitude. d = h / tan(a) Notice that if the glide angle is small, the tan(a) is a small number, and the aircraft can fly a long distance for a small change in altitude. Conversely, if the glide is large, the tan(a) is a large number, and the aircraft can travel only a short distance for a given change in altitude. We can think of the glide angle as a measure of the flying efficiency of the glider. On another page, we will show that the glide angle is inversely related to the lift to drag ratio. The higher the lift to drag ratio, The smaller the glide angle, and the farther an aircraft can fly.

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There are many factors which influence the amount of aerodynamic drag which a body generates. Drag depends on the shape, size, inclination, and flow conditions of the air passing the object. For a three dimensional wing, there is an additional component of drag, called induced drag, which will be discussed on this page. For a lifting wing, the air pressure on the top of the wing is lower than the pressure below the wing. Near the tips of the wing, the air is free to move from the region of high pressure into the region of low pressure. The resulting flow is shown on the figure by the two circular blue lines with the arrowheads showing the flow direction. As the aircraft moves to the lower left, a pair of counter-rotating vortices are formed at the wing tips. The line of the center of the vortices are shown as blue vortex lines leading from the wing tips. If the atmosphere has very high humidity, you can sometimes see the vortex lines on an airliner during landing as long thin "clouds" leaving the wing tips. The wing tip vortices produce a down wash of air behind the wing which is very strong near the wing tips and decreases toward the wing root. The local angle of attack of the wing is increased by the induced flow of the down wash, giving an additional, downstream-facing, component to the aerodynamic force acting over the entire wing. This additional force is called induced drag because it faces

downstream and has been "induced" by the action of the tip vortices. It is also called "drag due to lift" because it only occurs on finite, lifting wings and varies with the square of the lift. The derivation of the equation for the induced drag is fairly tedious and relies on some theoretical ideas which are beyond the scope of the Beginner's Guide. The induced drag coefficient Cdi is equal to the square of the lift coefficient Cl divided by the quantity: pi (3.14159) times the aspect ratio AR times an efficiency factor e. Cdi = (Cl^2) / (pi * AR * e) The aspect ratio is the square of the span s divided by the wing area A. AR = s^2 / A For a rectangular wing this reduces to the ratio of the span to the chord c. AR = s / c Long, slender, high aspect ratio wings have lower induced drag than short, thick, low aspect ratio wings. Induced drag is a three dimensional effect related to the wing tips. The longer the wing, the farther the tips are from the main portion of the wing, and the lower the induced drag. Lifting line theory shows that the optimum (lowest) induced drag occurs for an elliptic distribution of lift from tip to tip. The efficiency factor e is equal to 1.0 for an elliptic distribution and is some value less than 1.0 for any other lift distribution. The outstanding aerodynamic performance of the British Spitfire of World War II is partially attributable to its elliptic shaped wing which gave the aircraft a very low amount of induced drag. A more typical value of e = .7 for a rectangular wing. The total drag coefficient, Cd is equal to the base drag coefficient at zero lift Cdo plus the induced drag coefficient Cdi. Cd = Cdo + Cdi The drag coefficient in this equation uses the wing area for the reference area. Otherwise, we could not add it to the square of the lift coefficient, which is also based on the wing area.

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Lift is the force that directly opposes the weight of an airplane and holds the airplane in the air. Lift is generated by every part of the airplane, but most of the lift on a normal airliner is generated by the wings. Lift is a mechanical aerodynamic force produced by the motion of the airplane through the air. Because lift is a force, it is a vector quantity, having both a magnitude and a direction associated with it. Lift acts through the center of pressure of the object and is directed perpendicular to the flow direction. There are several factors which affect the magnitude of lift. HOW IS LIFT GENERATED?

There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments. To help you understand lift and its origins, a series of pages will describe the various theories and how some of the popular theories fail. Lift occurs when a moving flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton's Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow. For an aircraft wing, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface's part in turning the flow leads to an incorrect theory of lift. NO FLUID, NO LIFT Lift is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field,or an electromagnetic field, where one object can affect another object without being in physical contact. For lift to be generated, the solid body must be in contact with the fluid: no fluid, no lift. The Space Shuttle does not stay in space because of lift from its wings but because of orbital mechanics related to its speed. Space is nearly a vacuum. Without air, there is no lift generated by the wings. NO MOTION, NO LIFT Lift is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift. It makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. Lift acts perpendicular to the motion. Drag acts in the direction opposed to the motion. You can learn more about the factors that affect lift at this web site. There are many small interactive programs here to let you explore the generation of lift.

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For a solid object moving through a fluid or gas, drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust. Types of drag are generally divided into two categories: parasitic drag and lift-induced drag. Parasitic drag includes form drag, skin friction and interference drag. Lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed only in the aviation perspective of drag. Beyond these two kinds of drag there is a third kind of drag, called wave drag, that occurs when the solid object is moving through the fluid at or near the speed of sound in that fluid. The overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation.

See also
• • •

Atmospheric drag Gravity drag Drag Resistant Aerospike

parasitic drag Parasitic drag is drag caused by moving a solid object through a fluid. Parasitic drag is made up of many components, the most prominent being form drag. Skin friction and interference drag are also major components of parasitic drag. In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift. However, as speed increases the induced becomes much less, but parasitic drag necessarily increases because the fluid is flowing faster. At even higher speeds in the transonic, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximise endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Mentioned In parasitic drag is mentioned in the following topics:
skin friction drag (physics) lift-induced drag interference drag form drag winglet

Horten brothers

manifold vacuum

form drag In aerodynamics, form drag, profile drag, or pressure drag, is a component of parasitic drag created by wind hitting the body. The general size and shape of the body is the most important factor in form drag; bodies with a larger apparent crosssection will have a higher drag than thinner bodies. "Clean" designs, or designs that are streamlined and change cross-sectional area gradually are also critical for achieving minimum form drag. Form drag follows the drag equation, meaning that it rises with the square of speed, and thus becomes more important for high speed aircraft. This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Mentioned In form drag is mentioned in the following topics:
atmospheric drag parasitic drag air brake (aircraft) E.T. bracket race spoiler (aeronautics) fairing drag (physics) tricycle gear Brenneke slug

drag equation

Wikipedia drag equation In physics, the drag equation gives the drag experienced by an object moving through a fluid.

where D is the force of drag,

Cd is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car), Ï is the density of the fluid*, v is the velocity of the object relative to the fluid, and A is the reference area. Units used SI force newtons fps gravitational pounds force feet per second square feet fps absolute poundals feet per second square feet

density kilograms per cubic meter slugs per cubic foot pounds per cubic foot velocity meters per second area square meters

* Note that for the Earth's atmosphere, the density can be found using the barometric formula. In the case of air as a fluid at 15 °C and standard atmospheric pressure:
•

Density= 1.225 kilograms per cubic meter or 0.002378 slugs per cubic foot.

The reference area A is related to, but not exactly equal to, the area of the projection of the object on a plane perpendicular to the direction of motion (ie cross-sectional area). Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given. The reference for a wing would be the plan area rather than the frontal area. The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area. No real object exactly corresponds to this behavior. Cd is the ratio of drag for any real object to that of the ideal object. In practice a rough unstreamlined body (a bluff body) will have a Cd around 1, more or less. Smoother objects can have much lower values of Cd. The equation is precise, it is the Cd (drag coefficient) that can vary and is found by experiment. Of particular importance is the v² dependence on velocity, meaning that fluid drag increases with the square of velocity. Contrast this with other types of friction that generally do not vary at all with velocity. Another interesting relation, though it is not part of the equation, is that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). This is because the force exerted by drag quadruples (2² = 4), and the power required equals force times velocity.

See also

• • •

angle of attack stall terminal velocity

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Mentioned In drag equation is mentioned in the following topics:
skin friction interference drag constitutive equation terminal velocity List of equations form drag drag (physics) angle of attack power-to-weight ratio lift-induced drag

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SmokeDog's Note: Much of this article is taken from a 1929 textbook. Some of the most clear and simple explanations were written in the early stages of the development of a field of study. Most of this text can be absorbed by people ages 12 and up. If you are not ready to comprehend some of the math, don't worry. The verbal descriptions of properties of air will give you insights into the problems of traveling though the atmosphere. Definition. Aerodynamics treats of the forces produced by air in motion, and is the basic subject in the study of the aeroplane. It is the purpose of this chapter to describe in detail the action of the wing in flight and the aerodynamic behavior of the other bodies that enter into the construction of the aeroplane. At present, aerodynamic data is almost entirely based on experimental investigations. The motions and reactions produced by disturbed air are so complex and involved that no complete mathematical theory has yet been advanced that permits of direct calculation. Properties of Air. Air being a material substance, possesses the properties of volume, weight, viscosity and compressibility. It is a mechanical mixture of the two elementary gases, oxygen and nitrogen, in the proportion of 23 per cent of oxygen to 77 percent of nitrogen. It is the oxygen element that produces combustion, while the nitrogen is inert and does not readily enter into combination with other elements, its evident function being to act as a dilutant for the energetic oxygen. Air is considered as a fluid since it is capable of flowing like water, but unlike water, it is highly compressible. Owing to the difference between air and water in regard to compressibility, they do not follow exactly the same laws, but at ordinary flight speeds and in the open air, the variations in the pressure are so slight as to cause little difference in the density. Hence for flight alone, air may be considered as incompressible. It should be noted that a compressible fluid is changed in density by variations in the pressure, that is, by applying pressure, the weight of a cubic foot of a compressible fluid is greater than the same fluid under a lighter pressure. This is an important consideration since the density of the air greatly affects the forces that set it in motion. Every existing fluid resists the motion of a body, the opposition to the motion being commonly known as “resistance.” This is due to the cohesion between the fluid particles. The resistance is the actual force required to break them apart and make room for the moving body. Fluids exhibiting resistance are said to have “viscosity.” In early aerodynamic researches, and in the study of hydrodynamics, the mathematical theory is based on a “perfect fluid,” that is, on a theoretical fluid possessing no viscosity. Such theory would assume that

a body could move in a fluid without encountering resistance, which in practice is, of course, impossible. In regard to viscosity, it may be noted that air is highly viscuous—relatively much higher than water. Density for density, the viscosity of air is about 14 times that of water, and consequently the effects of viscosity in air are of the utmost importance in the calculation of resistance of moving parts. Atmospheric air at sea level is about 1/800 of the density of water. Its density varies with the altitude and with various atmospheric conditions, and for this reason the density is usually specified “at sea level” as the sea level altitude gives a constant base of measurement for all parts of the world. As the density is also affected by changes in temperature, a standard temperature is also specified. Experimental results, whatever the pressure and temperature at which they were made, are reduced to the corresponding values at standard temperature and at the normal sea level pressure, in order that these results may be readily comparable with other data. The normal (average) pressure at sea level is 14.7 pounds per square inch, or 2,119 pounds per square foot at a temperature of 60° Fahrenheit. At this temperature, 1 pound of air occupies a volume of 13.141 cubic feet. At 0° F. the volume shrinks to 11.58 cubic feet, the corresponding densities being 0.07610 at 60° and 0.08633 pounds per cubic foot at 0°, respectively. This refers to dry air only as the presence of water vapor makes a change in the density. With a reduction in temperature, the pressure decreases as the density increases so that the effect of heat is twofold. With a constant temperature, the pressure and density both decrease as the altitude increases. For example, a density at sea level of 0.07610 pounds per cubic foot is reduced to 0.0357 pounds per cubic foot at an altitude of 20,000 feet. During this increase in altitude, the pressure drops from 14.7 pounds per square inch to 6.87 pounds per square inch. This variation, of course, greatly affects the performance of aeroplanes flying at different altitudes, and still more, affects the performance of the motor, since the latter cannot take in as much fuel-air mixture per stroke at high altitudes as at low. As a result the power is diminished as we gain in altitude.

The attached air table gives the properties of air through the usual range of flight altitudes. The pressures corresponding to the altitudes are given both in pounds per square inch and in inches of mercury so that barometer and pressure readings can be compared. In the fourth column is the percentage of the horsepower available at different altitudes, the horsepower at sea level being taken as unity (one). For example, if an engine develops 100 horsepower at sea level, it will develop 100 x 0.66 = 66 horsepower at an altitude of 10,000 feet above sea level. The barometric pressure in pounds per square inch can be obtained by multiplying the pressure, in inches of mercury, by the factor 0.4905, this being the weight of a mercury column 1 inch high. In aerodynamic laboratory reports, the standard density of air is 0.07608 pounds per cubic foot at sea level, the temperature being 15 degrees Centigrade (59 degrees Fahrenheit). This standard density will be assumed throughout the book, and hence for any other altitude or density, the corresponding corrections must be made.

Air Pressure on Normal Flat Plates. When a flat plate or “plane” is held at right angles or “normal” to an air stream, it obstructs the flow and a force is produced that tends to move it with the stream. The stream divides, as shown in Fig. 1 and passes all around the edges of the plate (points P and R in the drawing), the stream reuniting at a point (M) far in the rear. Assuming the air flows from left to right, as in the figure, it will be noted that the rear of the plate at (H) is under a slight vacuum, and that it is filled with a complicated whirling mass of air. The general trend of the eddy paths are indicated by the arrows.

Figure 1. Air Travel about Normal Plate At the front where the air current first strikes the plate there is a considerable pressure due to the impact of the air particles. In the figure, pressure above the atmospheric pressure is indicated by ++++ symbals, while the vacuous space at the rear is indicated by fine clots. As the pressure in front, and the vacuum in the rear, both tend to move the surface to the right in the direction of the air stream, the total force tending to move the plate will be the difference of pressure on the front and rear faces multiplied by the area of the plate. Thus if (F) is the force due to the impact pressure at the front, and (G) is the force due to the vacuum at the rear, then the total resistance (D) or “Drag” is the sum of the two forces. Contrary to the common opinion, the vacuous (vacuum at the rear) part of the drag is by far the greater, say in the neighborhood of from 60 to 75 per cent of the total. When a body experiences pressure due to tile breaking up of an air stream, as in the present case, the pressure is said to be due to “turbulence,” and the body is said to produce “turbulent flow.” This is to distinguish the forces due to impact and suction, from the forces due to the frictional drag produced by the air stream rubbing over the surface.

Forces due to turbulent flow do not vary directly as the velocity of the air past the plate, but at a much higher rate. If the velocity is doubled, the plate not only meets with twice the volume of air, but it also meets it twice as fast. The total effect is four times as great as in the first place. The forces due to turbulent flow therefore vary as the square of the velocity, and the pressure increases very rapidly with a small increase in the velocity. The force exerted on a plate also increases directly with the area, and to a lesser extent, the drag is also affected by the shape and proportions. Expressed as a formula, the total resistance (D) becomes: D=KAVsqared where K = co-efficient of resistance determined by experiment, A = area of plate in square feet, and V = velocity in miles per hour. The value of K takes the shape and proportion of the plate into consideration, and also the air density. Example. If the area of a flat plate is 6 square feet, the co-efficient K = 0.003, and the velocity is 60 miles per hour, what is the drag of the plate in pounds? Solution: D = KAVsqared = 0.003 x 6 x (60 X 60) = 64.80 pounds drag. For a square flat plate, the co-efficient K can he taken as 0.003. SmokeDog's Note: In discussions of aerodynamics, we will often use the term "coefficient". A coefficient is a number often found through experimentation or observation, which allows you to compute results in convenient units (pounds, hours, dollars, etc.) For example, you observe the results of cook times for a fully cooked turkey, given a variety of different trial weights of turkeys. Weight of Turkey 8 pounds 10 pounds 12 pounds Cook Time 4 hours 5 hours 6 hours

Turkey #1 Turkey #2 Turkey #3

You invent a coefficient, "cT" or "coefficient of turkey done time". For the Turkeys shown in the table, the coefficient cT=0.5. Pounds of Turkey x cT = hours until cooked. Different brands of turkeys may have different cT values. Different aircraft parts may have different drag coefficients. Next week we will explore the use of "streamlining' to produce a reduced drag coefficient. SmokeDog's Note: Much of this article is taken from a 1929 textbook. Some of the most clear and simple explanations were written in the early stages of the development of a field of study.

Most of this text can be absorbed by people ages 12 and up. If you are not ready to comprehend some of the math, don't worry. The verbal descriptions of properties of air will give you insights into the problems of traveling though the atmosphere. The last article ended with illustrations of the term coefficient. Lets repeat these concepts........ Example. If the area of a flat plate is 6 square feet, the co-efficient K = 0.003, and the velocity is 60 miles per hour, what is the drag of the plate in pounds? Solution: D = KAVsqared = 0.003 x 6 x (60 X 60) = 64.80 pounds drag. For a square flat plate, the co-efficient K can he taken as 0.003. SmokeDog's Note: In discussions of aerodynamics, we will often use the term "coefficient". A coefficient is a number often found through experimentation or observation, which allows you to compute results in convenient units (pounds, hours, dollars, etc.) For example, you observe the results of cook times for a fully cooked turkey, given a variety of different trial weights of turkeys. Weight of Turkey 8 pounds 10 pounds 12 pounds Cook Time 4 hours 5 hours 6 hours

Turkey #1 Turkey #2 Turkey #3

You invent a coefficient, "cT" or "coefficient of turkey done time". For the Turkeys shown in the table, the coefficient cT=0.5. Pounds of Turkey x cT = hours until cooked. Different brands of turkeys may have different cT values. Different aircraft parts may have different drag coefficients. Different cars have different drag coefficients.

.....Before we move on lets relate the coefficient of drag to modern automobiles. The drag coefficient for autos is expressed in different units that the traditional aircraft drag coefficient. The traditional aircraft drag coefficients usually give a number to multiply square feet of frontal area (the area of a structure or part as seen from the front) in order to give drag in pounds of force. The modern automotive coefficient of drag, "Cd", appears to be in units of square meters of frontal area with results relating to horsepower

required to push the car through the air given the drag produced. (Actually the force units are given in watts, but we know that 746 watts = 1 horsepower.) The Cd of automobiles range from .25 to .5. The sleek, little Honda Insight has a Cd of .25. The low coefficient of drag, multiplied by a small frontal area, (multiplied again by velocity squared), give it a gas mileage of over 60 miles per gallon (MPG) at 60 MPH. A low Cd really helps gas mileage. The smallish Honda CRV sport utility vehicle has a Cd of .5 and gives you 25 miles per gallon (MPG) on the highway. The big Chrysler Town and Country family van has a Cd of just .35 and gets 26 MPG, better than the smaller Honda CRV. As your read in the last article, a blunt, square-ish front end and rear end contribute to a poor coefficient of drag. The rear end contributes more than the front end. Let's continue with the 1929 text on aeronautics. Remember that this author uses the terms: K for coefficient of drag D for pound of drag A for square feet of frontal area V for velocity in Miles Per Hour Streamline Forms. When a body is of such form that it does not cause turbulence when moved through the air, the drag is entirely due to skin friction. Such a body is known as a “streamline form” and approximations are used for the exposed structural parts of aeroplanes in order to reduce the resistance. Streamline bodies are fish-like or torpedo-shaped, as shown by Fig. 2, and it will be noted that the air stream hangs closely to the outline through nearly its entire length. The drag is therefore entirely due to the friction of the air on the sides of the body since there is no turbulence or “discontinuity.” In practical bodies it is impossible to prevent the small turbulence (I), but in well-designed forms its effect is almost negligible.

Fig. 2. Air Flow Around Streamline Body.

In poor attempts at streamline form, the flow discontinues its adherence to the body at a point near the tail. The poorer the streamline, and the higher the resistance, the sooner the stream starts to break away from the body and cause a turbulent region. The resistance now be comes partly turbulent and partly frictional, with the resistance increasing rapidly as the percentage of the turbulent region is increased.

Figs. 3-4. Imperfect Streamline Bodies. The fact that the resistance is clue to two factors, makes the resistance of an approximate streamline body very difficult to calculate, as the frictional drag and the turbulent drag do not increase at the same rate for different speeds. The drag due to turbulence varies as V while the frictional resistance only varies at the rate of V° hence the drag due to turbulence increases much faster with the velocity than the frictional component. If we could foretell the percentage of friction, it would be fairly easy to calculate the total effect, but this percentage is exactly what we do not know. The only sure method is to take the results of a full size test.

Fig. 2 gives the approximate section through a streamline strut such as used in the interplane bracing of a biplane. The length is (L) and the width is (d), the latter being measured at the widest point. The relation of the length to the width is known as the “fineness ratio” and in interplane struts this may vary from 2.5 to 4.5, that is, the length of the section ranges from 2.5 to 4.5 times the width. The ideal streamline form has a ratio of from 5. to 5.75. Such large ratios are difficult to obtain with economy on practical struts as the small width would result in a weak strut unless the weight were unduly increased. Interplane struts reach a maxi mum fineness ratio at about 3.5 to 4.5. Fig. 3 shows the result of a small fineness ratio, the short, stubby body causing the stream to break away near the front and form a large turbulent region in the rear. Results published by the National Physical Laboratory show streamline sections giving 0.07 of the resistance of a flat plate of the same area, with fineness ratio=6.5. In Fig. 4 the effects of flow about a circular rod is shown, a case where the fineness ratio is 1. The stream follows the body through less than one-half of its circumference, and the turbulent region is very large; almost as great as with the flat plate. A circular rod is far from being even an approach to a perfect form. In all the cases shown, Figs. 1-2-3-4, it will be noticed that the air is affected for a considerable distance in front of the plane, as it rises to pass over the obstruction be fore it actually reaches it. The front compression may be perceptible for 6 diameters of the object. From the examination of several good low-resistance streamline forms it seems that the best results are obtained with the blunt nose forward and the thin end aft. The best position for the point of greatest thickness lies from 0.25 to 0.33 per cent of the length from the front end. From the thickest part it tapers out gradually to nothing at the rear end. That portion to the rear of the maximum width is the most important from the standpoint of resistance, for any irregularity in this region causes the stream to break away into a turbulent space. From experiments it has been found that as much as one-half of the entering nose can be cut away without materially increasing the resistance. The cut-off nose may be left flat, and still the loss is only in the neighborhood of 5 per cent SmokeDog's Note: In the last article we discussed drag and the use of streamlining to reduce drag. We will come back to drag in future parts in order to introduce another form of drag ... drag which is caused by lift. Before we come back to drag we will discuss lift. I wrote the following article in 1984 as a manual which came with a computer flight simulation. Lift

Lift is created by the wing passing through air. A cross-section of the wing (airfoil) is shown in Figure 2, where some important terms are introduced.

Figure 2. Airfoil Terminology The mean chord line is an imaginary line that extends from the leading edge to the trailing edge of the airfoil. It is further extended in Figure 2. Relative wind is the airflow caused by passing the aircraft through an airmass. Relative wind is approximately opposite to the flight path. Angle of attack is the angle between the relative wind and the mean chord line. Figure 3 illustrates these terms in level, climbing, and descending flight.

Figure 3. Angle of Attack: Shown in level, climbing, and descending flight. (Angle of attack is the same in all three examples illustrated.) Note that angle of attack does not have the same meaning as aircraft pitch attitude. The angle of attack in Figure 3 is purposely the same in all three examples (level, climbing, and descending flight) so as to emphasize this difference. In actual flight your angle of attack will often be different during different phases of the flight. In order to understand how lift is produced, we must explore the theories of Bernoulli and Newton. Bernoulli addressed the conservation of energy in fluid flow. Assuming a constant density (no compression) of the fluid, energy is held constant by decreasing pressure with increasing velocity or, conversely, by increasing pressure with decreasing velocity. This incompressibility assumption holds nearly true for airflow as well, at least at the low speeds flown by light aircraft. The classic graphic illustration of this theory usually depicts a tube of varying diameter (Figure 4).

Figure 4. Bernoulli's Favorite Tube Figure 4 shows an enclosed tube with airflow. Mass flow within the enclosed tube is the same at all points since the air can’t escape. An incompressible fluid (or low-speed airflow) must increase velocity at the narrow point to maintain mass flow. If energy is to be conserved, then an increase in velocity (kinetic energy) must be balanced by a decrease in pressure (potential energy). Figure 5 illustrates airflow past an airfoil at a positive angle of attack. The airflow over the top of the wing has a higher velocity than the airflow under the wing and, consequently, a lower pressure. A basic rule in physics states that when an imbalance exists, a force will result tending to relieve that imbalance. In the case of our airfoil this force is directed upwards, from the higher pressure to the lower pressure. This force is known as lift.

Figure 5. Bernoulli Explanation of Lift The Bernoulli Controversy As late as the mid 1960’s many flight instructors were emphasizing Bernoulli’s law as the major contributor to lift theory. This concept does go a long way in explaining lift when looking just at airflow immediately adjacent to the wing. Bernoulli’s law, however, doesn’t explain the forces of airflow deflected by the wing. Indeed, most modern instructors give credit to Newton for explaining the majority of lift production. Newton’s third law states that for every action there is an equal and opposite reaction. Figure 6 is a repeat of Figure 5 with labels changed to emphasize action-reaction theory.

Figure 6. Newton Explanation of Lift

Down wash is caused by the airfoil altering the direction of airflow downwards. This will occur as long as there is a positive angle of attack. Downwash is easy to understand no matter what shape the airfoil takes. In this age when fighter jets use thin, symmetrical airfoils, you can see why deflected air is considered to be the major contributor to lift. Controlling Lift As a pilot, you must learn how to control lift during takeoff, climbs, level flight, turns, descents, and landing. You can generally increase lift in two ways; increase airspeed or increase your angle of attack. Given a constant angle of attack, an increase in airspeed increases pressure differential and downwash, and therefore increases lift. Given a constant airspeed, an increased angle of attack increases pressure differential and downwash, thereby increasing lift. As a pilot, you must manage both airspeed and angle of attack in order to gain the desired flight goals. A good example would be an airspeed transition from fast cruise flight to slower flight when entering a crowded airport traffic pattern. You reduce power and the aircraft decelerates. Since the weight of your aircraft is unchanged, you must produce constant lift during the deceleration. In order to produce constant lift, you must increase the angle of attack slowly until the aircraft is stable at its new slower speed. The Stall There is a limit to the angle of attack that you can use to generate lift. You can alter the relative wind airflow only so far before the wind refuses to change anymore. Figure 7 shows an airfoil at three different angles of attack. The top illustration shows an airfoil at the same angle of attack used in the previous discussion of lift generation. The middle airfoil shows an increased angle of attack. Notice that the airflow is separating from the surface near the upper trailing edge of the wing. The bottom airfoil is at stall angle of attack. The point of airflow separation is so far forward that we don’t even see a downwash vector; Newton’s downwash is gone. Velocity in the area aft of the separation point is very low; Bernoulli’s suction is gone. And with neither law still in effect, there is no way to maintain lift.

Figure 7. Airflow Separation With Increasing Angle of Attack Important Note! What is a stall? A sudden loss of lift due to airflow separation from the wing. How do you stall an airfoil? Stall is a function of angle of attack. You can stall an aircraft at any airspeed and pitch attitude if you exceed the stall angle of attack. How do you recover from a stall? Simply reduce the angle of attack.

Stall angle of attack depends on the airfoil shape, and is usually somewhere between 10 and 20 degrees. Generally speaking, thin airfoils will stall at a lower angles of attack while thick airfoils will stall at a higher angles of attack. Also, symmetrical airfoils will stall at lower angles of attack than airfoils with more bulge on the upper surface (higher camber). Figure 8 shows the lift characteristics of a typical airfoil used on training aircraft. Lift increases steadily until stall angle is reached. After this point, lift drops off suddenly.

Figure 8. Lift versus Angle of Attack SmokeDog's Note: Part 3 illustrated the generation of lift. This lesson will quantify the amount of lift you can generate and the trade-off between producing lift versus generating a new type of drag. This lesson will end by contrasting the lift generation/drag generation properties of two airfoils. In Part 1 we were presented with a formula to calculate drag.

D=K x A x Vsquared where D=drag, K = co-efficient of resistance determined by experiment, A = area of plate in square feet, and V = velocity in miles per hour. We also have a formula for lift. Lift = (some) Coefficient X Area X Velocitysquared. (Area is the total wing area). Early texts used "K" for coeffients but modern science uses "C" to denote coeffients. Since were about to show some modern charts, we’ll designate the coefficient of lift as ‘CL’ and the coefficient of drag as ‘Cd’. The coefficient of lift will vary with angle of attack. The last lesson ended with a chart showing that lift increases with angle of attack until the stall is reached.

The following chart shows the coefficient of lift for a particular airfoil at

different angles of attack. The lift coefficient line is the tallest one and is labeled ‘CL’. The numerical lift coefficient is shown just to the right of the chart.

A standard graph of coefficient of lift versus angle of attack. Lift Coefficient is just to the right of the graph. Angle of attack is on the bottom. The maximum coefficient of lift for an airfoil with this shape is 1.6. The maximum occurs at 22 degrees angle of attack. (This NACA 2312 airfoil is a very nice, general purpose airfoil for cruise speeds between 100 and 200 MPH.) But there is another column of numbers to the right of the lift coefficients. It’s a column of “drag coefficients”. We discussed parasitic drag in the first two lessons. This was drag caused by a structure getting in the way of airflow. As

you increased speed, this "parasitic" drag increased by Velocitysquared. The drag on the airfoil chart is a different type of drag. It is caused by the creation of lift (nothing comes for free). It is called "induced" drag. Induced Drag While creating lift, your airfoil changes the direction of airflow in many ways. You’re already familiar with downwash. This downward deflection of air changes the relative wind in the vicinity of the wing to a slighty downward direction. As a result, the true angle of attack is different from the apparent angle of attack. In the last lesson, we described this apparent angle of attack by stating that the relative wind is opposite the flight path. But the airfoil alters the relative wind. This is described in the following diagram as “induced relative wind.”

Lift is produced perpendicular to the real, induced relative wind direction. A relative wind in a slighty downward direction will give us a real lift vector with a component toward the rear. This rearward component is known as induced drag. The following figure illustrates the concept of induced drag.

Since higher angles of attack tilt the lift vector even further back, induced drag is increased when the angle of attack increases. Let’s repeat the chart that we showed earlier. Now, note the line showing the coefficient of drag ‘Cd’. Notice that it is not a straight line. ‘Cd’ increases quickly with an increase in angle of attack.

Let’s relate “angle of attack” to flight at different airspeeds. If weight, bank angle, and other factors are held constant, a slower airspeed demands a higher angle of attack to produce the same lift. Therefore, the slower the airspeed, the greater the induced drag. The next figure shows a graph of Induced Drag vs. Airspeed. Note that it is nonlinear. As velocity decreases, induced drag increases inversely proportional to the square of the velocity. This phenomenon can be explained when you remember that dynamic pressure from the airstream increases as the square of velocity. Greater dynamic pressure means more lift production capability. Drop your airspeed by one-half and you only get one-quarter the lift production capability. Therefore, you will need a large increase in angle of attack to produce the same lift, and induced drag will also increase dramatically.

Total Drag Total drag equals parasitic drag plus induced drag. The next figure shows both parasitic and induced drag on the same graph. Total drag is simply both types of drag added together vertically on the graph.

This graphically-illustrated concept of total drag is important for proper aircraft control. Since you need thrust to oppose drag, think of the vertical axis as required thrust rather than drag. You’ll note that at airspeeds below the minimum drag point, more power is needed to sustain level flight than at the minimum drag point. Flying at airspeeds below the minimum drag point can cause problems for the novice pilot. Different Airfoils for Different Purposes We now know that ‘CL’ varies with angle of attack. It is interesting to note that different airfoils have different ‘CL’ charts.

We will compare a thin vs. a thick airfoil in the previous and next chart. Note the line on the charts labeled L/D (lift / drag). The peak of this curve is an efficient angle of attack for maximum flight duration. The NACA 0006 airfoil is very thin. After 3 degrees angle of attack, drag rises rapidly. The NACA 0018 airfoil is fat. It has more drag at low angles of attack but its ‘Cd’ does not rise as rapidly as the 0006 airfoil when you increase angle of attack. Also its coefficient of lift, ‘CL’ keeps on increasing up to 20 degrees angle of attack while the thin airfoil gave up at 14 degrees. Jet fighters usually use thin

airfoils at low angles of attach (low drag but in a small range of angles of attack). Heavy transport aircraft use thick airfoils. They give up a narrow range of speed for a wide range of load carrying capability at various airspeeds.

We have discussed lift and 2 forms of drag. But there are four forces in balanced flight. Next lesson we will begin a discussion of thrust.

SmokeDog's Note: In previous lessons we’ve presented 2 of the classic “4 forces of flight”, drag and lift. We will now move on to thrust, the force which will move our aircraft forward. Note a concept presented in the first diagram on our “How an Airplane Flies” page. The thrust arrow opposes drag. This concept is not totally accurate. As we stated in the “New This Week” article “Need More Engine Power? Supercharge it!”, In a climb, the thrust arrow [term - vector] points up slightly. For the purposes of this lesson, we will ignore this fact. Those arrows presented in previous lessons which represent forces are termed “vectors”. A vector is simply a representation of both direction and quantity. If you represented a force vector of a person throwing a ball, weakly at a 45 degree angle up from the ground, you would draw a vector representation as a line, perhaps 1 inch long, aiming up at 45 degrees to level. To represent the force of a person throwing a ball very hard, straight up, you would draw a vector representation as a line, perhaps 2 inches long, aiming up. And so … the concept of vectors is simple, a representation of both direction and quantity. Should you advance in the study of physics, you will learn that the power of vectors comes from adding (or subtracting) vectors from each other in order to determine the resulting motion in terms of both force and direction. Thrust vs. Speed from Car Engines In this lesson we will use the thrust and opposing drag vector in order to determine the resulting force. When you start moving in a car the resulting force is forward. In the following figure we assume that the car’s engine will produce constant thrust, no matter what its speed. (The real thrust varies with engine RPM, so we are assuming that the car has a variable speed, constant RPM drive as found on modern hybrid autos.)

The term acceleration is defined as a change in speed. Acceleration will occur whenever opposing forces are not equal. You can quantify the amount of acceleration by subtracting the drag vector line length from the thrust vector line length. Once the drag vector length equals the thrust vector line length, there is no more acceleration. The car has reached “equilibrium” speed. You’ve just learned a new term, equilibrium. Equilibrium exists when all force vectors are balanced. They cancel each other out. Note that at 30 MPH the drag vector is only 1/4 the length of the drag vector at 60 MPH. We just want to reinforce the fact that parasitic drag increases as the square of velocity. Review the parasitic drag curve in the next figure. While cars have other forms of drag, parasitic drag is the major drag factor opposing speed. The next figure is our good-ole parasitic drag curve with a constant thrust line added. The equilibrium speed will be where the drag line meets the thrust line.

Speed vs. Parasitic Drag Curve plus a constant power line. Given constant power, a car will accelerate until power = thrust. This is termed a point of "equilibrium". Thrust From Aircraft Engines Piston Engines Driving Propellers: The thrust produced by an aircraft piston engine is illustrated in the following figure. This figure is for a 260 HP Lycoming brand engine turning a “constant speed” propeller. A constant speed prop changes the bite of its blades (term – blade pitch) in order to keep the RPM and resulting horsepower the same, no matter what the airspeed. The horsepower may be constant, no matter what the airspeed, but the thrust produced drops off quickly with airspeed. This is due to a problem of propeller efficiency, not engine efficiency.

Illustration of thrust produced by an aircraft piston engine driving a constant speed propeller. Thrust is excellent at low airspeeds but drops off quickly with increasing airspeed. Jet Engines: The next figure shows the thrust curve of a representative jet engine. The power drops off as airspeed increases but not as quickly as the piston engine. At approximately 500 MPH the power decrease levels off. This is primarily due to the fact that the jet engine has a big mouth. Air rams into this big mouth to help increase the pressure needed to produce power.

Illustration of thrust produced by a jet engine. Thrust reduction curve is much flatter than the curve for a piston engine/propeller combination. Our last figure shows both the piston engine and jet engine thrust curve superimposed onto the aircraft total drag curve. The more powerful jet engine should be placed further up the chart, but for the purposes of this lesson, the figure illustrates that, assuming equal piston power vs. jet power, the piston

engine gives more thrust (and acceleration) at low airspeeds while the jet engine gives more thrust at higher airspeeds.

Illustration of piston engine and jet engine thrust (shown in blue) superimposed over the aircraft total drag curve. The equilibrium points for top speed are shown as red dots. Which engine will give better low speed acceleration? Which engine will give a better top speed? We have discussed thrust, lift and 2 forms of drag. But there are four forces in balanced flight. Next lesson we will begin a discussion of weight.

SmokeDog's Note: In previous lessons we’ve presented 3 of the classic “4 forces of flight”, drag, lift and thrust. We will now move on to weight. Weight is the last of the classic “four forces of flight” to be discussed. In the last lesson we discussed the meaning of vectors. If the vectors of the four forces balance we will have non-accelerated flight, that is, no changes in airspeed and no changes in climb (or descent) rate. In the last lesson we discussed the balance of thrust vs. drag. In this lesson we will discuss the balance of lift vs. perceived weight. “Perceived” weight

includes the concept of weight, which we are accustomed to, plus the affects of other accelerations.

Figure 1 - Classic Four Forces of Flight Weight = mass x acceleration. Our normal notion of weight is noted as we exist on earth. You may not think of yourself as accelerating but you would be accelerating if the solid earth didn’t stop you. The gravitational pull of the earth produces an acceleration of 32 feet per second, each second. If earth had no atmosphere to produce drag and you jumped from an aircraft, after one second you would have accelerated to 32 feet per second. After two seconds you would have accelerated to 64 feet per second. After three seconds you would be traveling at 96 feet per second …. And so on. While you are floating down to earth, you would not feel any force. You’d feel weightless. When you are on the ground, you feel the force pulling you toward earth’s center at 32 feet per second, each second. An aircraft’s weight, caused by the gravitation of earth, acts toward the center of earth. Lift acts perpendicular (at a 90 degree angle) to an aircraft’s relative wind. As discussed in lesson 3, relative wind is approximately opposite to the flight path. If we are in a climb or descent, the lift vector will not point opposite to the weight vector. Figure 2 shows the vectors in a descent.

Figure 2 - Four Forces of Flight in a Descent Note the “component of weight aiding thrust”. Since the weight vector is tilted forward (relative to the aircraft) we can compute the amount of thrust aid by drawing a line from the dashed lift axis to the point representing the force of weight. Add this “component of weight aiding thrust” to the thrust vector and you would notice that its length equals the length of the drag vector. This balance of forces assumes that you are not accelerating. The thrust line was reduced (the pilot reduced power) during the descent to prevent acceleration. If you are in a car and travel from level ground to a downhill portion of the road, you would accelerate forward unless you reduced power. An interesting side note to this discussion pertains to gliders. You can see why you don’t need power to go downhill. You can also see how a glider pilot can control his airspeed and descent rate by controlling the up and down pitch of his aircraft. A similar, opposite analysis, applies to an aircraft in a climb. Figure 3 shows an aircraft in a climb. The “component of weight opposing thrust” plus drag must equal thrust in order to produce steady flight.

Figure 3 - Classic Four Forces of Flight in a Climb This is a good place to discuss weight’s affect on both, an aircraft’s ability to climb and on its top speed. Thrust in excess of that need to oppose drag is necessary to produce a climb. For analytical purposes lets call this thrust “excess thrust”. In light aircraft of moderate performance, thrust is much more limited than in an average car. Add to this limitation, the fact that unlike a car, if your aircraft is going too slow as well as too fast, drag increases rapidly. Review the power curves/drag curves diagram that was introduced in the last lesson.

Figure 4 (from last lesson)

Power curves/Drag curves At any airspeed you can measure the amount of “excess thrust” available for climb by noting the vertical distance between thrust and total drag. An increase in weight has the same effect on climb performance as lowering the thrust curve. At some point of weight increase, the aircraft would have no excess thrust to produce a climb. This factor of reduced margin of thrust is exaggerated at high altitudes where engines produce less power. In the western United States (at high airport elevations), many aircraft accidents are caused each year, by an overloaded aircraft. The “excess thrust” needed to support a climb is not available. In a car, excess weight causes slower acceleration and a reduced climb ability, however, since you have to oppose only parasitic drag, you can affect a climb up a road at a slower speed. While a heavy car would accelerate slower, top speed would be affected very little. Aircraft top speed is affected more that a car but not by much. A heavier aircraft must fly at a higher angle of attack to produce more lift. The higher angle of attack causes more induced drag and usually more parasitic drag. Luckily, since the lifting ability of a wing increases by Velocitysquared, The damaging affect of weight on speed is moderated by high cruise speeds. Aircraft manuals often show airspeed reductions of only 1 to 3 percent when comparing light loads vs. maximum gross weight. In contrast, aircraft manuals often show a 30 to 50 percent reduction in climb rate when comparing light loads vs. maximum gross weight. Perceived Weight A big factor on aircraft performance is caused by an increase in the weight vector in turns, as well as sudden (accelerated) entries into climbs. Another acceleration is added to earths acceleration. In a turn, force is required to pull an airplane to the center of a circle. This pull [term - centripetal force] increases with bank angle. An increase in the percieved weight vectors require an increase in the offsetting lift vector. A steeper bank angle is needed to support a faster turn. A classic analogy used to illustrate centripetal force is a person swinging a pail. The faster you swing it, the steeper the angle to the ground as well as the bigger the force felt by your arm.

Figure 5 - Lift Force in a Turn. Assuming level flight, a 60 degree bank produces a 2G (2 X gravity) acceleration. The perceived weight of the aircraft is twice its normal weight. As you can imagine, climb performance suffers in steep turns. This article concludes the six part discussion of Simple Aerodynamics. We hope that we touched on knowledge areas which will expand you interest in the physics of flight. You will find good discussion of flight physics in the many texts published for private pilot training.

THE STREAM FUNCTION In the present analysis of an irrotational plane flow, the velocity field can be obtained in terms of a stream function instead of a potential function. We can in fact define a (scalar) stream function

that satisfies identically the continuity equation for the Schwarz theorem on mixed derivatives. Such a function

is called the stream function because its isolines are streamlines (that is lines such that at any given time they are tangent to the velocity vector). Note that, by definition, the component of the velocity normal to a streamline is always zero so that there is no mass flux across a streamline. Every solid body or boundary must then be represented by a streamline. If we now make use of the irrotationality of the flow we obtain:

So the stream function satisfies the Laplace equation, hence being a harmonic function of space. Stream function and velocity potential are both harmonic functions of space and are related by the following equations

Two bi-dimensional harmonic functions that satisfy the above conditions (the so-called Cauchy-Riemann conditions) are said to be conjugate. It is not difficult to demonstrate that by using the Cauchy-Riemann conditions, lines along which the stream function is constant (streamlines) and lines along

which the velocity potential is constant (isopotential lines) always intersect at right angles.

As described on the forces slide, the aircraft lift is the sum of the lift of all of the parts of the airplane and acts through the aircraft center of pressure. Each part of the aircraft has its own lift component and its own center of pressure. The major part of the lift comes from the wings, but the horizontal stabilizer and elevator also produce lift which can be varied to maneuver the aircraft. The average location of the weight of the aircraft is the center of gravity (cg). Any force acting at some distance from the cg produces a torque about the cg. Torque is defined to be the product of the force times the distance. A torque is a "twisting force" that produces rotations of an object. In flight, during maneuvers, an airplane rotates about its cg. But when the aircraft is not maneuvering, we want the rotation about the cg to be zero. When there is no rotation about the cg the aircraft is said to be trimmed.

On most aircraft, the center of gravity of the airplane is located near the center of pressure of the wing. If the center of presure of the wing is aft of the center of gravity, its lift produces a counter-clockwise rotation about the cg. The center of pressure for the elevator is aft of the center of gravity for the airliner shown in the figure. A positive lift force from the tail produces a counter-clockwise rotation about the cg. To trim the aircraft it is necessary to balance the torques produced by the wing and the tail. But since both rotations are counter-clockwise, it is impossible to balance the two rotations to produce no rotation. However, if the tail lift is negative it then produces a clockwise rotation about the cg which can balance the wing rotation. Let us look carefully at the torques produced by the wing and the tail. The torque from the wing TW is equal to the lift of the wing W times the distance from the cg to the center of pressure of the wing dw. TW = W * dw The torque from the tail TT is equal to the lift of the tail T times the distance from the cg to the center of pressure of the tail dt. The lift of the wing and the lift of the tail are both forces and forces are vector quantities which have both a magnitude and a direction. We must include a minus sign on the lift of the tail because the direction of this force is negative. TT = -T * dt In trimmed flight, these two torques are equal: TW = TT W * dw = -T * dt W * dw + T * dt = 0 The torque equation, as written here, is a vector equation. All of the quantities are vector quantities having a magnitude and a direction. If the distances are both positive (same side of the center of gravity), then the direction of the tail force must be different than direction of the wing force to produce no net torque or rotation. However, if the distance to the tail were negative, then the lift of the of the tail could be positive and there would be no net torque. A negative distance to the tail would imply that the tail is on the front of the aircraft, ahead of the center of gravity. A tail at the front of the aircraft is called a canard and was the configuration first used by the Wright brothers.

The total lift of the aircraft is the vector sum of the wing lift and the tail lift. For the airliner, the total lift is less than the wing lift; for the Wright brothers, the total lift is greater than the wing lift. The added lift was important for the Wright brothers because their aircraft had a very small engine and flew at low speeds (35mph). Since lift depends on the square of the velocity, it is hard to generate enough lift for flight at such low speeds.

Dr. Hanley's Aerodynamics: Wing-Tail Calculator
Standard 2.0 & Plus 2.0 Now Available

Dr. Hanley's Aerodynamics: The Wing-Tail Calculator

Welcome to WingTail/WingTail Plus!
WingTail Standard: Only $395.00. | Buy CD Online | Mail Order | WingTail Plus!: Only $695.00. | Buy CD Online | Mail Order |

Summary: There are a number of factors that aerospace engineers must consider for a successful airplane design. Dr. Hanley's WingTail calculator addresses three of the most important. (1) The load capability of the airplane (i.e. accurate lift prediction); (2) the efficiency of the wings (profile/induced drag analysis)and (3) longitudinal stability. The WingTail Calculator is an inexpensive and powerful CFD tool for engineers, designers and students who design and analyze aircraft wings, sailboat keels/rudders and race car spoilers. The software can be used to reduce or eliminate costly repetitive experimental studies needed to optimize the airfoil and planform shapes. The WingTail Calculator is Three-Tools-in-One; It accurately computes lift, drag (vortex and profile) and moment (about the center of gravity) for single wings or two-wing systems (or keel-rudder interaction); It predicts the neutral point (or aerodynamic center) location and the angle of trim; It is a complete airfoil analysis utility. The WingTail calculator is not just simple approximations. The analysis is based on the vortex lattice method (vortex rings) which makes Wing-Tail a powerful yet easy-to-use tool for load prediction and longitudinal stability analysis. Please note that Version 2.0 of WingTail is for Tapered Wings Only. It is not compatible with Version 1.0. For general planform shapes, please see MultiSurface Aerodynamics. Applications: Engineers use The Wing-Tail Calculator for Airfoil Analysis, Wing Analysis, Wing-Canard Analysis, Wing-Tail analysis, Hydrofoil Analysis, WIG Analysis and other aerodynamics calculations. WingTail can also be used for

education, science projects and airplane design. You will find the Wing-Tail an indispensable preliminary design tool for free flight gliders, sail planes, light aircraft stability, ground effect vehicles, spoilers, sail, keels/rudders & education. Details The Wing-Tail Calculator was developed using a vortex lattice (vortex rings) CFD method. The program is quite powerful and yet easy-to-use.

The Wing-Tail Calculator Results Window.

Wing-Tail can be used to: 1. Compute lift and drag coefficients for an isolated tapered wing with sweep, camber, twist and different airfoil sections at root and tip (new function). The Standard Version will analyze ONLY NACA 4-, 5- & 6-digit Airfoils. The Plus Version can analyze NACA 4-, 5- & 6-Digit Airfoils in addition to Custom airfoils. 2. Compute lift and drag coefficients for a wing-tail system . 3. Determine the neutral point for wing-tail system. 4. Compute the trim angle and corresponding aerodynamic forces for the system. 5. Compute the aerodynamic coefficients at the trim angle 6. Simulate ground effect. The program might also be used to model the lift and vortex drag on a keel-rudder system or perhaps a double sail configuration. In these applications, however, one half of the wing-tail will model the actual device while the other half can model a surface image. (note: no explicit calculations are made in the software for this modification).

Tail Input Tab for Wing-Tail.

Wing-Tail accepts the following inputs for both the wing and tail: span, taper, sweep (forward and back), airfoils and angle. The wing & tail can be placed at arbitrary locations along the x-axis. The user must also enter the center of gravity location, airplane weight & speed and whether or not to include ground effect in the calculations. The Wing-Tail Calculator will compute lift, drag and moment coefficients, lift, drag and moment forces, location of the neutral point, mean aerodynamic chords, Cl_alpha, Cm_alpha,. Lift-drag ratio and the minimum sink rate.

Stability and Trim Analysis.

Wing-Tail is intended as an educational aide for learning about 3-d wings, induced drag, sweep, taper and longitudinal stability. Wing Analysis Both WingTail Standard and WingTail Plus allow the analysis of tapered wings and tapered horizontal tails. Each wing half can have different root and tip angles (geometric twist), different root and tip airfoils (aerodynamics twist), a sweepback angles (positive or negative) and a dihedral angle. The surfaces can be any size and inputs can be made in units of inches, feet, centimeters and meters. The vortex lattice technique computes lift, drag and moment about the CG (arbitrary location). The program analyzes the problem on the cambered surface and can compute the effects of a nearby ground plane. Airfoil Analysis In addition to Wing and Wing-Tail analysis, the Wing-Tail Calculator will also perform isolated airfoil analysis.

WingTail Calculator is Ideal for Airfoil Analysis

The Standard Version will analyze ONLY NACA 4-, 5- & 6-digit Airfoils. The Plus Version can analyze NACA 4, 5 & 6-Digit Airfoils in addition to Custom airfoils. Airfoils in the Standard Version The Standard Version of WingTail Calculator comes with NACA 4-, 5- & 6-Digit Airfoils. Airfoils in the Plus Version The Plus Version of WingTail Calculator ($695.00) comes with NACA 4-, 5- & 6Digit Airfoils. It contains a library of over 1000 airfoils. It allows you to input custom airfoil in the form of an ASCII file. Graphs The Wing-Tail calculator will graph lift vs. span, Cl vs Angle of Attack, Cl vs Cd, Cl vs. Cd and Cl/Cd vs Angle of attack for Wings, Wing-Tail Combinations and Isolated Airfoils. Requirements The Wing-Tail Calculator requires a PC with a Pentium 120 or later running Windows 95 or later. Purchase Options

WingTail Standard: $395.00. | Buy CD Online | WingTail Plus!: $695.00. | Buy CD Online | Telephone Orders: 1-888-282-5887 Checks or Money Orders: Please click here. Other Options: Email us

Technical Questions can be answered by calling: (352) 687-4466. Other Software The following chart shows how other aerodynamics software developed at hanleyinnovations.com compares with the Wing-Tail calculator.
Glider Wing-Tail WAPlus VisualFoil MultiElement MultiSurface Airfoil Analysis Airfoil/Plain Flap Airfoil/Slotted Flap No Yes No Yes Yes No Yes Yes No No Yes Yes Yes No No No No No Yes Yes Yes Yes more... Yes Yes No No Yes No No No No No No No Yes Yes Yes Yes more... Yes Yes Yes Yes (20) Yes No No 2-D 2D Yes (2D) Yes (2D) Yes Yes Yes Yes Yes more...

Yes
Yes 3-D/Camber 3-D/Camber Yes Yes Yes Yes Yes (30 ) Yes Yes Yes Yes Yes Yes Yes more...

No No Multiple Airfoils Yes Airfoil Stall Prediction Yes Yes Yes 3-D Wing (Tapered) No No 3-D Wing (General) Yes Yes Biplanes 2 2 Multiple 3-D Wings Yes Yes Wing & Tail Yes Yes Wing & Canard Yes Yes Ground Effect Yes Yes Atmospheric Table Yes Yes Water Properties Yes NACA Airfoil Library Yes Yes Plus! Custom Airfoils More Information more... more...

About Dr. Hanley Dr. Patrick E. Hanley, is the owner and founder of Hanley Innovations, a small business specializing in the development of aerodynamics and fluid dynamics simulation software for education and industry. Dr. Hanley earned his B.S. degree (summa cum laude) in aerospace engineering from Polytechnic Institute of New York and his S.M. and Ph.D. degrees from the department of Aeronautics and Astronautics of Massachusetts Institute of Technology (MIT). He also completed a minor in the area of management of innovation and technology at MIT's Sloan School of Management. After graduating from MIT, Dr. Hanley joined the Mechanical Engineering faculty at the University of Connecticut where he formulated and taught courses in

aerodynamics, compressible fluids, introductory fluid mechanics and heat transfer. As a faculty member, he won the highly competitive National Science Foundation Research Initiation Award, the NASA-ASEE Summer Faculty Fellowship and three consecutive research awards from NASA Lewis Research center to study compressible viscous flows in turbomachinery using pseudospectral methods. This research led to the successful education of four (4) Ph.D students and four (4) Masters degree students. In addition Dr. Hanley can be credited with a number of publications including the pioneering work in multi-domain pseudospectral methods for compressible viscous flows entitled "A Strategy for the Efficient Simulation of Viscous Compressible Flows using a Multi-domain Pseudospectral Method" which can be found in Journal of Computational Physics, Vol 108, No. 1, pp. 153-158, September 1993. As owner and chief software author of Hanley Innovations, Dr. Hanley has written a number of software packages including AirfoilBrowser, Airfoil Organizer, Science Graphs, VisualFoil, ModelFoil, Aerodynamics in Plain English, Center of Gravity Calculator, WingAnalysis, SmockSoft, PerpeturalPaper amongst other titles.