AEROFOIL FITTING

LE procedure to obtain the paraglider aerofoil of any wing. Method based on the grid ripstop fabric

1. Auxiliary coordinate system
2. Taking coordinates
3. Scale corrections
4. Orthogonality corrections
5. Normalization
6. Smoothing
7. Note: ".dat" format

1. Auxiliary coordinate system

Fix an arbitrary point inside the aerofoil, which is the origin of axes that follow the main directions of the strands of ripstop fabric (axis "X1"in the warp direction, and axis Y1 in the direction of the weft) . The axes are automatically graduated in units corresponding to the grid of the fabric in the direction X1 and in the direction Y1.

2. Taking coordinates

Take the coordinates (X1, Y1) of the aerofoil contour and singular points with an offset of approximately 5 cm in areas of greater curvature (leading edge) and 10 cm in the rest. The contours of the intrados and extrados, taken separately. Check that the coordinates taken from the lower surface coincide with the coordinates taken from the top surface. Coordinates taking is facilitated by placing auxiliar crosses or points, on points of ripstop coordinates multiples of 10 units, and setting numerical references. The marking can be done with a graphite mine (to be deleted) or fine-point permanent marker.

Fig. 1: Aerofoil ripstop grid coordinates (X1,Y1)

3. Scale corrections

Having obtained the ripstop coordinates in the axes (X1, Y1), must be converted to a coordinate system with axes graded on a uniform scale, whit X and Y, graduated in centimeters. To do this, calculate the corresponding correction factors:

Kx = (X cm / units X1)
Kx = (Y cm / units Y1)

Resulting in a new uniform coordinates (X2, Y2):

X2 = Kx · X1
Y2 = Ky · Y1

To measure accurately Kx and Ky, it is desirable to measure the total length of a large number of squares, then divide by the total of them, thus obtaining the measurement side of the square (rectangle to be precise). And even by several measures, in different areas, and making the average between them.

Fig. 2: Scale corrections

4. Orthogonality corrections

This correction is purely theoretical, and rarely should be done, since the ripstop fabric is assumed perfectly orthogonal in the process of cutting and marking. Otherwise, we can estimate the angle alpha formed between the axes X2 - Y2 (assuming non-orthogonal), and a new axis system, X3 - Y3 completely orthogonal, using the following conversion:

X3 = X2 - Y2 · sin(alpha)
Y3 = Y2

Fig. 3: Orthogonality corrections

5. Normalization

The next step is the achievement of a normalized aerofoil, with a unit length chord, and with that chord located on a horizontal axis. There are several possibilities:

a) Draw the profile with a graphic design program (AutoCAD type). Making the alignment of the chord of the profile, on the segment going from point unit (0.0) to the point (0.1) and placing the leading edge in (0.0) and the trailing edge at (0 1). List thecoordinates of the line profile. Commands "align" and "list" in AutoCAD.

b) Perform a numerical conversion of coordinates, by applying transformations of displacement, rotation, and scale. To be programmed into a spreadsheet.

c) Load the airfoil in ".dat" similar format directly in the program XFLR5 or XFOIL and use the functions  "Derotate" and "Normalize".

6. Smoothing

Once the experimental profile (taken from the experimental data), aligned and normalized, we must obtain another profile that fits perfectly smooth as much as possible to all data points and correct measurement errors, or accidental, that may have occurred during the process. With the smoothing process is not intended to use even none of the points from the data collection. Only is relevant form of the aerofoil, not the value of the experimental points... Therein lies part of the power of the method.

Again there are several possibilities.

a) Working In AutoCAD, with splines or curves defined geometrically conforming to the set of points that define the profile.

b) Work the points numerically by applying a mathematical algorithm (to define...).

c) Adjust the program with XFLR5 splines.

d) Auxiliary aerofoils method: Adjust separately the upper and lower surface of the aerofoil by two auxiliary profiles by changing its main parameters (thickness, camber, and their positions, leading edge radius ...) to fit as much as possible the experimental aerofoil. We need to experiment with various profiles that can be either NACA or otherwise, to achieve the desired result. The whole points of the extrados of the first auxiliary profile, and the whole points of the intrados of the second auxiliary profile, should be merged into a single ".dat" file to define the profile adjusted to the experimental profile. The verification of geometric and aerodynamic parameters of the experimental profile and the smoothed, will verify the goodness of fitting.

Fig. 4: Smoothing method, fitting two modified aerofoils

7. Note: ".dat" format

Fig 5: ".dat" file structure
Sorry again for my writings in English, because it is not my usual language