SOME NOTES ON SKIN TENSION
(SKIN TENSION - OVALIZATION - BALLONEMENT)

1. Skin tension defintion and importance

2. Ovalization of simple panels

3. Ovalization of real panels

4. Changes of the law of ovalization in each side of teh panel

1. Skin tension definition and importance

With the concept of "skin tension", we are referring to the methods used to convert flats panels, in curved panels (curved mainly in this transverse direction). Other equivalent ways to name this concept are "ovalitzation", "ballonement", or "increases in lateral width". We previously described this concept, in the book Paraglider Design Handbook chapter 6, and it is necessary to review the concept there. The practical application of the concept in the design of paragliders, has been implemented in the section 5 Skin tension and in the section 31 New skin tension of the program LEparagliding.

When more plan is the panel, we say that has more tension in the skin. But to get real tension in some parts (leading edge, trailing edge) it is necessary that other parts of the panel have "little" skin tension, because what counts are the differences in relation to tension. The amount of tension is defined with the "law of the variations of skin tension" (or law of variation of the increments of the widths).

The correct definition of the skin tensionand its variations along teh border of the panel is a concept essential for the final quality and solidity of the wing. For this reason, it is worth of thinking and studying in detail this. And the parameters are difficult to decide, because it is difficult to imagine the final result. Normally we use the laws of skin tension of the skin described in section 5 of the program, having been used with success in many paragliders (gnuLAB2, gnuA13, BHL1, BHL2, ...). In section 31 of the program we open a much more extensive control and new possibilities. In the following figures I try to explain what are the concepts in order to define a control more precise, and some of the geometric definitions used in the programming.

The concept of "3D-shaping" is just an extension of the concept of skin tension, but thinking in two directions, the transverse and the longitudinal. In this also we are working on.

2. Ovalization of simple panels

We consider the three cases of the figure above.
The CASE 1 is a flat and rectangular panel of width a. If we add a constant increment of width Dl and Dr on each side, we get an uniform ovalitzation throughout the panel. The CASE 2 is a trapezoidal panel of bases a and c and average width b. We can define the increases in lateral width, proportional to the average width og the panel b, where the value k is the law of variation of widths (Dl=k·b, Dr=k·b). This system is used normally, given that the paraglider panels have a width substantially constant. The CASE 3 is similar to CASE 2 except that the width of reference of the panel is calculated at each point. This without a doubt will allow for a more precise  skin tension (although still it is not possible to detect if the effect will be very noticeable). Soon to be incorporated in section 31 of the program this method 3 of calculation, as an option.

3. Ovalization of real panels using median width o local width

Soon to be incorporated in section 31 of the program this method, as an option.

And a small detail (for the purpose only of programming). The increases in width, can be set perpendicular to the contour (as it is calculated LEparagliding at present), or in prolongation of the line that joins the points corresponding to the left and right of the panel (this option is under study).

4. Changes of the law of ovalization in each side of teh panel

A comment on where to apply the tension of the skin. In the formulation traditional simplified (section 5 of the program) the skin tension is applied to the panels, all the panel of the wing, taking into account for each one of them its mean width, and a single law of increase of width. But the extended formulation (section 31) the skin tension is applied to each edge of the panel in coincidence with a rib. For this reason, we can say that we apply a tension in each "rib", to the panel on the left and the panel to its right. As it is now possible to define a law of increments of the widths differently for each rib, a panel may have a different tension on their left and to their right. And what counts is the sum of increments (or decrements if value is negative) to left and right.

See example figure. According to the new section 31, panel width increments are defined on each rib (not on each panel). For example, if in rib number "i" maximum ovalization is set to 3%, this means that the edges of the panels to the left and right increase by this amount (relative to the average width of the panel). If in rib number "i+1" we define a maximum ovalization of 2%, it is applied to the edges of the two adjacent panels. In the attached figure we drew a green panel that has an increase of 3% to the left, and 2% to the right (total 5%), and and orange panel that has an increase of 2% to the left, and 5% to the right (maximum total 7%).

January 2020