User:Eas4200c.f08.carbon.orear/HW4/Matlab

 Comment: This page is identical to the previous one, except that the MATLAB section has been modified with additional work in the torsional constant calculation and centroid calculation. Here is a comparison between these two versions. Eas4200c.f08.carbon.orear 19:09, 7 November 2008 (UTC)

= Code =

The airfoil now has a centroid calculation missing from Homework 3. Instead of resubmitting HW 3, these changes are here in the new code.

AirfoilArea.m
= Debugging =

Circle
With a circular airfoil, the Number of Segments such that the computed Area of the airfoil is accurate to within 1% of the exact value is 23 segments at which the computed area was 3.1115 m3. This is 0.95% away from the actual area of a unit circle, 3.14195 m3. The Centroid of the 8 segment airfoil was found to be (1.0000, 4.2743e-018).

Code used to find ns_max



The area for a various number of segments is tabulated below.

Plotting the Area vs Number of segments up to the point of 1% accuracy we get the graph below.

At P0 = (0,0), Area computed equaled 3.1115

At P0 = (1,0), Area computed equaled 3.1115

At P0 = (1,-4), Area computed still equaled 3.1115

NACA Airfoil
With a circular airfoil, the Number of Segments such that the computed Area of the airfoil is accurate to within 1% of the previous value is 8 segments at which the computed area was 0.024616 m3. This is 0.77% away from the previous area of a unit circle, 0.024373 m3. At 10,000 segments, the computed area was 0.02569 m3. The Centroid of the 8 segment airfoil was found to be ( 0.2167, 0.0078).

Code used to find ns_max



The area for a various number of segments is tabulated below.

Plotting the Area vs Number of segments up to the point of 1% difference accuracy we get the graph below.

At P0 = (0,0), Area computed equaled 0.024616

At P0 = ( 0.2167, 0.0078) (Centroid), Area computed equaled 0.024616

At P0 = (.25,-1), Area computed still equaled 0.024616

=Torsion=

Single Cell
With a NACA 2415 airfoil, the Number of Segments such that the computed torsional constant (J) of the airfoil is accurate to within 1% of the previous value is 12 segments at which the computed area torsional constant (J) 4.7209 x 106 m4.

Code used to find ns_max

Multiple Cell
In the multiple cell case, using the code below, the torsional constant was found to be higher at torsional constant (J) 4.7518 x 106 m4, slightly higher then the single cell airfoil. The area summation of each cell was the same at 0.0251 m2