The 70s saw the application of gradient-based models for aerodynamic shapes, solving for up to 11 different variables in a three-dimensional design space. The next leap in the field, however, didn't come until the 1960s when numerical solutions became available with advances in hardware. Newton applied variational calculus to drag minimization problems. Some of the earliest wing optimization attempts can be traced back to the late 1500s. Considerations generally include lift and drag, as with the airfoil, but also noise and stability. Secondly, the overall shape of the wing can be optimized as well. The behavior of an airfoil, or cross-section, of wings in air is thoroughly studied to make efficient airplanes. The two most prominent ones are lift and drag, which correspond to a wing's ability to fly the airplane against gravity without wasting energy by moving forward. In designing the wing of an airplane, several fluid dynamic concepts come into play. A critical design consideration in any aircraft is its three-dimensional wing shape this will be explored as an example of optimization's role and importance in industry. Coming with substantial costs, nearly every aspect of the industry, from aircraft design to material selection to operation, has been optimized in at least one way. Aerospace collectively represents one of the most sophisticated technological endeavors and largest markets in the world.
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