Since the airfoil is an oriented two-dimensional form, several variables describes its shape. The chord line describes the length from leading edge to trailing edge via the horizontal reference of the airfoil. The optimum angle of attack, AOA, represents the steepness of wing with respect to the horizontal motion direction. In many situations, the AOA is taken as a parameter for the entire wing, although it is possible to calculate an optimum for each airfoil section.
Wings with high sweep angles are becoming more prevalent as they often impart higher fuel efficiency. However, airplane designs are limited by airport gate sizes which constrain perpendicular wing length. The efficiency effect is so tantalizing for airlines that some airplanes in development, like the Boeing X, will have wing extensions that fold away when parked in the gate.
A more conventional approach to building a functionally longer wing while still fitting in the gate requires sweeping the wing away from the wing axis.
Angling the wing forward does this, but comes with unacceptable instability. Therefore, most commercial planes sweep the wing rearwards. Most wings are also angled up, or down with respect to the horizontal plane of the aircraft. This modification, called a dihedral angle, is used to increase the functional wing length and pitch stability. The aspect ratio of the wing is closely related to the lifting area, both of which are critical variables in almost any objective function. In the most basic lift equations, the "footprint" of the wing is linearly proportional to the force:.
Of course, complete lift calculations involve substantially more variables, including altitude and surface topography that relate to the aerodynamic boundary layer thickness.
Before beginning optimization of a wing shape, several assumptions about the basic structure are made. These typically include the number of wings, vertical position on the fuselage, and sometimes airfoil shape.
An initial condition, based on lifting line theory, is designed by aerospace engineers as a starting point for the optimization. Then, in most cases, CFD is run to gather fundamental performance values e. The next iteration makes a set of small changes to the geometry and repeats the process until the algorithm converges on a form with the best objective value.
To check against a local solution, some approaches involve starting the model from several different, randomly generated points instead of the human-designed one. A few different models from the literature are described below to provide some insight into how optimization problems are structured for wing shape. The large number of potential variables requires careful consideration of computational resources and algorithms. While genetic algorithms are a candidate for global optimization of the shape, their dependence on many iterations each performing CFD makes it challenging.
Therefore, the gradient-based optimizer with adjoint gradient evaluations was chosen by University of Michigan researchers to guide consecutive iterations [2]. The adjoint state numerical methods applies the dual problem formulation of the objective and constraints to more quickly converge on solutions.
In essence, this iterative process uses CFD in conjunction with minimization algorithms for a multi-objective model. A starting design is proposed, CFD performed, results analyzed, shape changed, and repeated. The result was a design with 8. As it moves faster, the air on top of the wing also loses pressure and push. The slower moving air below the wing maintains more of its pressure, which pushes the wing, and the plane, up.
Forces of Flight On This Page. Credit: Bill Tinkler. What Are Flaps For? Learn More Flying Upside Down. Flaps at Takeoff. Flaps at Landing. Ask an Explainer Q:. Camber is a measure of the amount of airfoil curvature. The red dot shows your conditions. Below the graph is the numerical value of the lift. You can display either the lift value in English or Metric units or the lift coefficient by using the choice buttons surrounding the output box.
Click on the choice button and select from the drop-menu. As an experiment, set the camber to 0. Now increase the camber to 5 per cent. Did the lift increase or decrease? Set the camber to -5 per cent. What is the value of lift? Which way would this airfoil move? 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. 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: 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.
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