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Modern Lift Equation Interactive


The objective of this simulation is to find the flight conditions that produce an aircraft lift greater than the aircraft weight. You will be determining the combination of velocity, angle of attack, and wing area which are necessary for flight. You can check your results for a particular aircraft by comparing with the individual aircraft page to see how the Wrights solved this problem.

Please note: the simulation below is best viewed on a desktop computer. It may take a few minutes for the simulation to load.



Determining the lift is only a part of the design challenge. Real aircraft designs are a compromise imposed by several conflicting design factors. A higher angle of attack produces more lift than a lower angle, but it also produces more drag. The lift to drag ratio is the important design factor for the aircraft because it is directly related to the angle at which a glider descends in flight. The Wrights were aware that they needed both high lift and low drag (which they called “drift”). Increasing the wing area increases the lift, but it also increases the weight which you have to lift. Higher speed produces more lift, but it also increases drag. To provide higher speed for a powered aircraft you need a larger engine, which typically increases weight. All of these various design trades must be considered to arrive at a final, successful design.

Design Process

During the design process, engineers make mathematical predictions of the performance of a new aircraft. These predictions use the best data and mathematical techniques which are available to the engineer. As the Wright brothers were designing their first aircraft, the basic principles of aerodynamics were being discovered. The brothers had preliminary data on the lift coefficient of certain airfoil shapes based on Otto Lilienthal’s flights and tests.

Lift Coefficient

The lift coefficient is used in a lift equation to predict the lift of the wings. The lift coefficient is just a number which contains all of the complex effects of shape, angle of attack, compressibility, and viscosity on the lift of an object. In the modern lift equation, lift (L) is equal to the lift coefficient (cl) times one half the air density (r) times the velocity squared (V^2) times the wing area (A).

L = .5 * cl * rho * V^2 * A

If you know the lift coefficient, you can use the lift equation to determine the value of one unknown parameter when you are given the value of all the other variables. For example, you can determine how fast you have to fly to lift a certain weight with a given wing area. Or you can compute how big a wing you need to lift a certain weight at a given speed. Or you can compute how high you can fly with a given weight at a given speed with a given wing area. The lift coefficient is hard to determine in general. It is usually determined through wind tunnel testing. For some simple shapes, like a flat plate, or a plate with very small curvature, there are theories which give values for the lift coefficient.

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.

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