# Modern Lift Equation Interactive

## Objective

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.

## Operation

• You can change the values of the velocity, angle of attack, 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.

## Lift

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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