Merging mathematical and physical models toward building a more perfect flying vehicle

phys.org | 10/20/2018 | Staff
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When designing flying vehicles, there are many aspects of which we can be certain but there are also many uncertainties. Most are random, and others are just not well understood. University of Illinois Professor Harry Hilton brought together several mathematical and physical theories to help look at problems in more unified ways and solve physical engineering problems.

"There are many equations because there are many phenomena. They are an attempt to describe mathematically the physical phenomena so that you can solve these problems. Words alone won't solve the problem. In this case, the problem is how do to build the perfect flying vehicle for specific missions and purposes," said Harry Hilton, a professor emeritus in the Department of Aerospace Engineering in the College of Engineering at the University of Illinois at Urbana-Champaign. Hilton looked at models independently of each other, then put them together.

Model - Rest - Exercise - Futility - Model

"If you don't use the right model, the rest becomes an exercise in futility. It may be a model that's self-consistent but has no reality," he said. "Of course, the only way you can validate a model is to run experiments and even then, you're introducing another reality into the picture which is the experiment and not the real airplane. So each one of these is an idealization."

Hilton began by analyzing the da Vinci-Euler-Bernoulli theory of elastic bending. "It's deterministic, that is, determined that it is true with a probability of 1, based on a set of equations that give a set of answers," Hilton said. Added to that is the Timoshenko theory that takes load and other realistic properties such as wind shear into consideration. Hilton merges those theories with properties of viscoelastic materials—which includes time dependent material behavior and is of particular importance in modern composite materials and metals at elevated temperatures.

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