6.1. Introduction
6.2 Analysis of the ovalization in transverse direction to the cells
6.3 Analysis of the ovalization along the axis of the cells
6.4. Corrections to the panels

6.1. Introduction

It is well known that the upper and lower surfaces of the cells are not flat. Because the structure of the paraglider is textile, and that the internal pressure is higher than outside, the cells tend to adapt a cylindrical shape between ribs.

According to measurements made by the LE, at various paragliders, the width of the cells in flight is around 5-6% less than the width of the panels.

In this chapter we analyze the effect of this and its consequences on the geometry of the panels.

6.2 Analysis of the ovalization in transverse direction to the cells

In the figure below shows the effect of a ovalization (billow) in a cross-section to the cells.

The ribs remain flat due to equal pressure on both sides, but the upper and lower panels adopt cylindrical shapes along them. The degree of ovalization depends primarily on the wisespan tension. Measurements made on various models show ovalization degrees around 6% higher in the arco regarding the length of segment.

It is impossible to avoid ovalization and its interest lies in the need to project the top and bottom panels adapted to it.

Transversal ovalization
Fig 6.1: Ovalization in transverse direction to the cells

 Geometry of the ovalization:   

S = R * α  
L = 2 * sin (α/2)
R = f + L * cos (α/2)

data: L, S
unknowns: R,f,α (solving the previous system of three equations)

Fig 6.2: Cell ovalization

6.3 Analysis of the ovalization along the axis of the cells

Oval longitudinal

Fig 6.3: Ovalization along the axis of the cells

The figure below shows the effect of ovalization lengthwise. The main consequence is that the "virtual" airfoils contained between two textile ribs are different and bigger (from 18% to 21.5% in the case drawn). This only takes into account implicitly in the design of the wing, the study focused on the "true" or project airfoils.

An important consequence of this analysis is that the contour length of the virtual airfoils is greater than the length of real contours of the projected airfoils. In the example airfoil, the difference in length is about 2.26% in the upper surface and a 0.9% on the lower surface.

Differences in the lower surface are minor, but differences on the upper surface, are higher because of the curvature of the leading edge.

At the area of the leading edge there are two independent curvatures, one due to the ovalization efect and another due to the curvature of the leading edge. The resulting surface is not developed in a flat figure. Hence the solution is to create a micro wrinkles in the area joining the top panel with the rib to offset the differences in length.

Then two figures are attached with a cell in 3D for better understanding of the above.

oval 3D
Fig 6.4: Cell ovalization

Oval 3D
Fig 6.5: Cell ovalization

6.4. Corrections to the panels

To take into account the effects of ovalization, corrections must be made in panels obtained by the method describeb in the previos chapter.

We simpli need to increase the wide of the panels in a total of around 6% (3% on each side, and this value must be adapted in each paraglider model).

Around the LE and TE is a linear transition of wide to reduce ovalization and increase the sail tension in the area.

Normal values of transition points are as follows:

From LE
From TE
Upper panel
Lower panel

Fig. 6.6: Corrections to the panels.