#### Relevance to Aero

This section is written by Robert Mendez, Spring 2008

Runge Kutta methong for solving Ordinary Differential Equations: Airflow over lifting surfaces (wings, elevator, ailerons) and around the aircraft in general are often modeled by ordinary and partial differential equations. The most popular of these equations are known as the Navier-Stokes equations, which describe the motion of fluids (both liquids and gases). These can then be solved for approximate solutions to gain a better understanding of the behavior of air around the aircraft. For example, when airflow reaches a wing, it stagnates at one point. This stagnation region can be solved for using the Runge Kutta method and the pressure distribution around the stagnation point can be modeled for analysis.

2)Interpolation of Data Points: A lot of work is done now with Computational Fluid Dynamics (CFD). It is cheaper to model the analysis on a computer instead of building it or even just a scaled model. When imported data into the CFD program (Gambit, Fluent, etc), the program needs data points to represent the model at every location. Since we do not have known coordinates for the model at every location they must be inferred from interpolation. Data acquired through wind tunnel testing can only retrieve data points every given amount of time that passes. For the space between successive data points, the curve can be determined through interpolation. What type of interpolation to be used depends on the accuracy needed and the cost for each method. (Lagrange, Newton, Piecewise Spline).

Error Analysis: Our differential equations and CFD models will give us merely rough approximations of what the actual behavior of the model looks like. These solutions can be compared to data acquired through wind tunnel testing. The error between what actually happens and what our equations give us can then be analyzed to determined if the models are within reasonable approximations of reality. Since precision within the aerospace engineering industry has to be much greater than other industries, error analysis plays a huge role in determining if given manufacturing processes are producing parts within a specified error.

Computer Arithmetic: Many computer programs are used for the analysis of the differential equations and computational fluid dynamics in Aerospace Engineering. It needs to be known if cancellation occurs which can strongly adversely affect the results. Even if the code/program is correct, computer arithmetic error can be devastating to the results if the engineer does not understand them.