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Unformatted text preview: 1 MATLAB Digest www.mathworks.com In this article, we will derive analytical models of the loads and bending moments on the wing of a small passenger aircraft to determine whether the wing design meets strength requirements. We will derive the models in the notebook interface in Symbolic Math Toolbox. We will then use the data management and analysis tools in MATLAB to simulate the models for different scenarios to verify that anticipated bending moments are within design limits. While this example is specific to aircraft design, analytical models are useful in all engineering and scientific disciplines for example, they can be used to model drug interactions in biological systems, or to model pumps, compressors, and other mechanical and electrical systems. Deriving Analytical Model of Wing Loads We will evaluate the three primary loads that act on the aircraft wing: aerodynamic lift, load due to wing structure weight, and load due to the weight of the fuel contained in the wing. These loads act perpendicu lar to the wing surface, and their magnitude varies along the length of the wing (Figures 1a, 1b, and 1c). By Dan Doherty Analytical Modeling of Aircraft Wing Loads Using MATLAB and Symbolic Math Toolbox MATLAB Digest When modeling engineering systems, it can be difficult to identify the key parameters driving system behavior because they are often buried deep within the model. Analytical models can help because they describe systems using mathematical equations, showing exactly how differ ent parameters affect system behavior. Figure 1a. Lift on the wing. 2 MATLAB Digest www.mathworks.com We derive our analytical model of wing loads in the Symbolic Math Toolbox notebook interface, which offers an environment for managing and documenting symbolic calculations. The notebook in terface provides direct support for the MuPAD language, which is optimized for handling and operating on symbolic math expressions. We derive equations for each load component separately and then add the individual components to obtain total load. Lift We assume an elliptical distribution for lift across the length of the wing, resulting in the following expression for lift profile: where L = length of wing x = position along wing ka = lift profile coefficient Figure 1c. Load due to the weight of the fuel stored in the wing. Figure 1b. Load due to wing structure weight. 3 MATLAB Digest www.mathworks.com We can determine the total lift by integrating across the length of the wing: Within the notebook interface we define q l (x) and calculate its integral (Figure 2). We incorporate math equations, descriptive text, and images into our calculations to clearly document our work. Completed notebooks can be published in PDF or HTML format....
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 Spring '10
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