Table of Contents

# Honors Project

## Discussion

Although the data shown in figure 6 is quite wild, it is clear that there exists a strong adverse pressure gradient, meaning that it is
likely the flow will detach in the manner desired. This, then, will be the selected airfoil for the tunnel design for this honors
project.

Numerically designing a completely new airfoil would be too haphazard since the program is quite sensitive and needs occasional human
interaction on the airfoil data to get results.

Challenges in numerical programs such as these can be hard to overcome. The data size of the airfoil is unknown, so dynamic memory must
be allocated and carefully kept track of or a memory leak will occur. The data size cannot be simply guessed, because if the guess is
too small, the program will crash and if the guess is too large extra memory is wasted.

The file structure of the airfoil is also a challenge. This honors project program used data points representing boundary points on the
airfoil. Control points were then found by taking the midpoint between the boundary points.

**Equation 1.** The main equation that must be solved for lambda (source strength).

Applying the equation doesn't look too difficult, however when generating the matrix, a single piece of "bad luck" data will corrupt the
entire matrix with no chance of recovery.

Since there exists an equation for every panel, and ever equation has a term for every panel, the matrix size is quite large and could
not be solved by hand. The numerical method chosen for this program was that of a Gaussian elimination method. The matrix was first
put into row echelon form and then the source strengths are found through back substitution.

The most challenging part of the project, however, was finding a way to have the computer measure angles from the x-axis to the
*inside* of the body.

**Figure 7.** An arbitrary body has angles ascribed to it. Note that the angles are always measured in the counter-clockwise
direction and go to the inside of the body.

Getting the computer to recognize *inside* vs. *outside* panels was accomplished by averaging other data points from the body
and comparing those with the normal.

Next: Conclusions and Recommendations