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Computer drawing of Wright 1900 glider. Lift equals the lift coefficient
 times the density times the area times half the velocity squared.

The amount of lift generated by an object depends on a number of factors, including the density of the air, the velocity between the object and the air, the viscosity and compressibility of the air, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow, also called the angle of attack.

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". 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 now determine the value of Cl mathematically. But, in general, this parameter is determined experimentally using models in a wind tunnel. For thin airfoils, at small angles of attack, the lift coefficient is approximately two times pi (3.14159) times the angle of attack expressed in radians.

Cl = 2 * pi * angle (in radians)

The modern lift equation states that lift is equal to the lift coefficient (Cl) times the density of the air (r) times half of the square of the velocity (V) times the wing area (A).

L = .5 * Cl * r * V^2 * A

By the time the Wrights began their studies, it had been determined that lift depends on the square of the velocity and varies linearly with the surface area of the object. Early aerodynamicists characterized the dependence on the properties of the air by a pressure coefficient called Smeaton's coefficient which represented the pressure force (drag) on a one foot square flat plate moving at one mile per hour through the air. They believed that any object moving through the air converted some portion of the pressure force into lift, and they derived a different version of the lift equation which expressed this relationship. Today we know that the lift varies linearly with the density of the air. Near sea level the value is .00237 slugs/cu ft, or 1.229 kg/cu m, but the value changes with air temperature and pressure. The pressure and temperature vary in a rather complex way with altitude. The linear variation with density and the variation with the square of the velocity suggests a variation with the dynamic pressure which we encountered in Bernoulli's equation. So modern aerodynamicists include a factor of 1/2 into the definition of the modern lift equation to reference the aerodynamic forces to the dynamic pressure (1/2 density times velocity squared).

NOTICE: The modern lift equation and the lift equation used by the Wright brothers in 1900 are slightly different. The lift coefficient of the modern equation is referenced to the dynamic pressure of the flow, while the lift coefficient of the earlier times was referenced to the drag of an equivalent flat plate. So the value of these two coefficients would be different even for the same wing and the same set of flow conditions.

Using the modern lift equation, and the lift coefficient given above, one can calculate the amount of lift produced at a given velocity for a given wing area. Or, for a given velocity, you can determine how big to make the wings to lift a certain weight. Here's a Java program that you can use to investigate the designs of the Wright aircraft from 1900 to 1905 which uses the modern lift equation.

You can download your own copy of this applet by pushing the following button:

Button to Download Applet

The program is downloaded in .zip format. You must save the file to disk and then "Extract" the files. Click on "Lift.html" to run the program off-line.

You can change the values of the velocity, angle of attack, temperature, pressure, and wing area by using the sliders below the airfoil graphic, or by backspacing, typing in your value, and hitting "Return" inside the input box next to the slider. By using the drop menu labeled "Aircraft" you can choose to investigate any of the Wright aircraft from 1900 to 1905. At the right bottom you will see the calculated lift and to the right of the lift is the weight of the selected aircraft. The aircraft designated "-K" are kites and the weight does not include a pilot. The aircraft designated "-G" are gliders and the weight does include a pilot. For design purposes, you can hold the wing area constant and vary the speed and angle of attack, or hold the speed constant and vary the wing area and angle of attack by using the drop menu next to the aircraft selection. In this simulation, the change in weight due to change in wing area has been neglected. For output, you can choose to have a plot of the lift or the lift coefficient by using the drop menu. You can plot lift versus angle of attack, velocity or wing area by pushing the appropriate button below the graph. You can perform the calculations in either English or metric units by using the drop menu labeled "Units". Finally you can turn on a "Probe" which you can move around the airfoil to display the local value of velocity of pressure. You must select which value to display by pushing a button and you move the probe by using the sliders located around the gage.

Select an aircraft and then find the flight conditions that produce a lift greater than the weight. You can check with the individual aircraft pages to see how big the Wrights designed their wings. Remember that determining the lift is only a part of the design problem. You will find that a higher angle of attack produces more lift. But it also produces more drag. The lift to drag ratio is an efficiency factor for the aircraft and directly related to the glide angle. The Wrights were aware that they needed both high lift and low drag (which they called "drift"). You will also find that increasing the wing area increases the lift. But in the total design, increasing wing area also increases the weight.

NOTICE: In this simple program we have approximated the entire aircraft (both wings and the canard) by a single flat plate. So you can expect that our answer is only going to be a very rough estimate. Engineers used to call this a "back of the envelope" answer, since it is based on simple equations which you can solve quickly. Engineers still use these kinds of approximations to get an initial idea of the solution to a problem. But they then perform a more exact (usually longer, harder, and more expensive) analysis to get a more precise answer.

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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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Jun 12 2014

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