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The concept of flying has taken root only within the past 100 years or so, when the Wright brothers were credited for the first controlled manned flight in 1903 at Kitty Hawk, NC. It is to say the least that this field has “taken-off” to the point where we often take routine flights around the world.

The development of aviation has pointed to a rather obvious concern regarding the safety of large jetliners carrying numerous passengers. It has trialed many-a-obstacle from ice and wind to volcanic ash and birds. Also, the absolute design of aircraft may still be less than one-hundred percent settled. Yet, statistically, it is ten times safer than taking a train, and nineteen times safer than driving a car.

The design and development of aircraft involve thousands of personnel from almost every branch of engineering and applied science. A major part of an aircraft is the airframe - composed of structural frame members, bulkheads, wing spars, longitudinal stringers, and an outer skin. The airframe of a jetliner is primarily made from aluminum alloy, although composite materials have substituted portions of the skin in attempts to save weight. Still other parts of the airframe may require titanium for increased strength and reliability.

Major studies involving mathematical models are used to determine flight loads on an aircraft which in turn provide information for a second major mathematical study of determining the internal loads, or stresses, within the airframe itself. Further analysis, or stress detailing, is then incorporated to determine all the remaining pathways of forces until every remaining bolt and rivet are accounted for.

Mathematical modeling is a term used in trade, derived from a complex field of numerical methods. Numerical methods, or numerical analysis, has its origins since the days of Gauss and Newton. It has progressed through the efforts of mathematicians and engineers into workable and impressive mathematical modeling techniques, one of these which is called the Finite Element Method. During the process of carrying out this method, calculations in the thousands are made using a math-based microprocessor, or modern day computer.

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