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[boyboy]

[FONT=Arial, Helvetica, sans-serif] This slide shows the shapes for a variety of wings and rocket fins as viewed from the side while looking onto the fin. This view is called a planform of the wing or fin. You can see that wings come in many different planforms: rectangular, triangular, trapezoidal, or even elliptical. To determine the lift and drag that a wing generates, you must be able to calculate the area of any of these shapes. This skill is taught in middle school and used every day by design engineers. The area is the two-dimensional amount of space that an object occupies. Area is measured along the surface of an object and has dimensions of length squared; for example, square feet of material, or centimeters squared.
On the slide we have listed the formula to calculate the area of a variety of shapes: The area of a rectangle is equal to the height h times the base b;
A = h * b
The equation for the area of a trapezoid is one half the sum of the top t and bottom b times the height h;
A = h * [ t + b ] / 2
The area of a triangle is equal to one half of the base b times the height h;
A = .5 * b * h
Some fins are elliptically shaped. For an ellipse with a semi-axis a and semi-axis b, the area is given by:
A = pi * a * b
where pi is the ratio of the circumference to the diameter of a circle and is equal to 3.1415. A special case of the ellipse is a circle, in which the semi-axis is equal to the radius r. The area of a circle is:
A = pi * r^2
If the root of an elliptical fin is given by cr and the distance from the root to the tip is given by ct, the area of the fin is:
A = pi * cr *ct
For a compound configuration like the Space Shuttle, you have to break up the wing into simple shapes which you can compute, and then add them to

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[boyboy]

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Lift depends on the density of the air, the square of the velocity, the air's viscosity and compressibility, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow. In general, the dependence on body shape, inclination, air viscosity, and compressibility is very complex.
One way to deal with complex dependencies is to characterize the dependence by a single variable. For lift, this variable is called the lift coefficient, designated "Cl." This allows us to collect all the effects, simple and complex, into a single equation. The lift equation states that lift L is equal to the lift coefficient Cl times the density r times half of the velocity V squared times the wing area A.
L = Cl * A * .5 * r * V^2
For given air conditions, shape, and inclination of the object, we have to determine a value for Cl to determine the lift. For some simple flow conditions and geometries and low inclinations, aerodynamicists can determine the value of Cl mathematically. But, in general, this parameter is determined experimentally.
In the equation given above, the density is designated by the letter "r." We do not use "d" for density, since "d" is often used to specify distance. In many textbooks on aerodynamics, the density is given by the Greek symbol "rho" (Greek for "r"). The combination of terms "density times the square of the velocity divided by two" is called the dynamic pressure and appears in Bernoulli's pressure equation.
You can investigate the various factors that affect lift by using the FoilSim III Java Applet. (Have fun!) Use the browser "Back" button to return to this page. If you want your own copy of FoilSim to play with, you can download it at no charge.
You can view a short movie of "Orville and Wilbur Wright" discussing the lift force and how it affected the flight of their aircraft. The movie file can be saved to your computer and viewed as a Podcast on your podcast player.
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[boyboy]

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All that is necessary to create lift is to turn a flow of air. An aerodynamic, curved airfoil will turn a flow. But so will a simple flat plate, if it is inclined to the flow. The fuselage of an airplane will also generate lift if it is inclined to the flow. For that matter, an automobile body also turns the flow through which it moves, generating a lift force. Lift is a big problem for NASCAR racing machines and race cars now include spoilers on the roof to kill lift in a spin. Any physical body moving through a fluid can create lift if it produces a net turning of the flow.
There are many factors that affect the turning of the flow, which creates lift. We can group these factors into(a) those associated with the object, (b) those associated with the motion of the object through the air, and (c) those associated with the air itself:

1. Object: At the top of the figure, aircraft wing geometry has a large effect on the amount of lift generated. The airfoil shape and wing size will both affect the amount of lift. The ratio of the wing span to the wing area also affects the amount of lift generated by a wing.
2. Motion: To generate lift, we have to move the object through the air. The lift then depends on the velocity of the air and how the object is inclined to the flow.
3. Air: Lift depends on the mass of the flow. The lift also depends in a complex way on two other properties of the air: its viscosity and its compressibility.

We can gather all of this information on the factors that affect lift into a single mathematical equation called the Lift Equation. With the lift equation we can predict how much lift force will be generated by a given body moving at a given speed.
You can investigate the various factors that affect lift by using the FoilSim III Java Applet. Have fun! You can use the browser "Back" button to return to this page. If your want your own copy of FoilSim to play with, you can download it at no charge.
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[boyboy]

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Lift can be generated by a wide variety of objects, including airplane wings, rotating cylinders, spinning balls, and flat plates. Lift is the force that holds an aircraft in the air. Lift can be generated by any part of the airplane, but most of the lift on a normal airliner is generated by the wings. How is lift generated?
Force = Mass x Acceleration
Lift is a force. From Newton's second law of motion, a force F is produced when a mass m is accelerated a:
F = m * a
An acceleration is a change in velocity V with a change in time t.
F = m * (V1 - V0) / (t1 - t0)
We have written this relationship as a difference equation, but it is recognized that the relation is actually a differential from calculus.
F = m * dV/dt
The important fact is that a force causes a change in velocity; and, likewise, a change in velocity generates a force. The equation works both ways. A velocity has both a magnitude called the speed and a direction associated with it. Scientists and mathematicians call this a vector quantity. So, to change either the speed or the direction of a flow, you must impose a force. And if either the speed or the direction of a flow is changed, a force is generated.
Lift Generated in a Moving Fluid
For a body immersed in a moving fluid, the fluid remains in contact with the surface of the body. If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body. It is very important to note that the turning of the fluid occurs because the molecules of the fluid stay in contact with the solid body since the molecules are free to move. Any part of the solid body can deflect a flow. Parts facing the oncoming flow are said to be windward, and parts facing away from the flow are said to be leeward. Both windward and leeward parts deflect a flow. Ignoring the leeward deflection leads to a popular incorrect theory of lift.
Interactive Simulator
Let's investigate how lift is generated by flow turning by using a Java simulator.

Here we see a yellow flat plate immersed in a flow of air. The air appears as small blue and white particle traces which move from left to right. The plate is inclined at an angle and notice that both the flow above and below the plate are turned along the plate. The white lines are the streamlines which intersect the plate and are called stagnation streamlines. You can vary the angle of the plate by using the slider below the view window or by backspacing over the input box, typing in your new value and hitting the Enter key on the keyboard. On the right side of the simulator is a gage with some buttons and some sliders. The gage tells you the value of the velocity or pressure at the location of the probe (little purple dot) in the left view window. You can change the location from side to side by using the slider located below the gage, and you can change the location up and down by using the slider to the left of the gage. You select which variable to display by using the white buttons labeled Velocity, Pressure, or Smoke. Smoke causes green particles to be released from the probe. The blue buttons control the type of display shown in the left view window.
You can download your own copy of the program to run off-line by clicking on this button:

You can further investigate the effect of airfoil shape and the other factors affecting lift by using the FoilSim III Java Applet. You can also download your own copy of FoilSim to play with for free.
Changes in Speed or Direction
Lift is a force generated by turning a flow. Since a force is a vector quantity (like the velocity), it has both a magnitude and a direction. The direction of the lift force is defined to be perpendicular to the initial flow direction. (The drag is defined to be along the flow direction.) The magnitude depends on several factors concerning the object and the flow.
Summary
Lift and drag are mechanical forces generated on the surface of an object as it interacts with a fluid. The net fluid force is generated by the pressure acting over the entire surface of a closed body. The pressure varies around a body in a moving fluid because it is related to the fluid momentum (mass times velocity). The velocity varies around the body because of the flow deflection described above.
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