# The Unconventional Tribune Profiles in Architectural Designing of Stadiums

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## Abstract

One of the key issues in designing of stadiums is to define the profile of the stands. By this term is meant a contour of the vertical cross-section of the tribunes, which is carried out in a plane perpendicular to the edges of the rows of seats. Such a profile reflects the spatial relations between theoretical points of the eye, arranged in individual rows, specifying their horizontal and vertical displacement relative to neighbouring points. It also allows you to determine the extent of visibility of the arena for each of them, using graphs of visibility. But it is also determined by considerations of communication links between the individual rows of seats by using the stairs. These stairs must however be adapted to the human motoric ability. Today, due to economic reasons, the designers completely abandoned the use of curved profile, replacing it with a sloping straight line. Existing standards limit this slope up to 35°. Reminiscent of the curved profiles are currently used broken linear profiles, as the continuous or balcony types. The author takes many years of research on the designing of modern stadiums, especially in shaping large spectator zones. Presented in this article unconventional solutions of modern stadium stands profiles are the result of these studies. These proposals improve much the parameters of visibility, comfort and safety of spectators. They contribute as well in the development on the field of stadiums designing, bringing a new values, such as quite new architectural forms in shaping interiors of these objects.

## Keywords

Architectural designing Tribune profile Modern stadium## 1 Introduction - Definition of the Research Problem

Forms of the interiors of modern stadiums are the result of a compromise between functional, technological and economical determinants. The main task of the designer is to provide every spectator a clear view of the playing field. This does not mean, however, that the image quality for each of them can be the same. The field of view of each viewer is determined by sight lines creating shape of so called the pyramid of view, which base is a rectangle of the pitch, and its top is located in his theoretical point of eye. Two parameters are crucial for the quality of the image of the pitch rectangle. These are: the height of elevation of eye point above the level of the arena, and the distance between this point and side lines of the playing field. The most essential forthe perception is the height of the image, reflected on the retina inside the eye of the observer. It depends directly on the so-called vertical viewing angle. The larger the angle is, the higher the height of the image field. In other words, the larger the vertical angle of view, the more we see from the top. On the other hand, small vertical viewing angles correspond to the flat images, with a small depth of the optical perspective [1].

## 2 Lines of Eye Points as a Representation of the Profiles of Stadium Stands

The undertaken research on the stadium stand profiles requires to introduce a few basic concepts, for the analytical reasons. One of them is a “theoretical point of eye”. This is the point embodying the geometric center of the lens of the human eye. For simplicity of the optical analysis assumed that each observer is represented by the only one point of the eye, located on the vertical axis of symmetry of the pair of eyes. With these assumptions, the location of each of the many thousands of points of the eye can be defined using the coordinates in the Cartesian system of axes x, y, z.

Drawing through each point of the eye the set of horizontal and vertical lines gives in result a grid of the stand profile. If, however, all the eye points will be connected by continuous line, in the result of this will be obtained the linear image of the profile.

The research instruments described above i.e. *Point of the Eye*, *Grid of the Stand* *Profile* and *Lines of Eye Points*, despite its simplicity and without any limitations, enable to carry out assumed studies. They are also very useful in the designing practice because, thanks to their brevity, allow the architect for simultaneous controlling of many issues in design process and taking a quick correcting decisions.

## 3 The Issue of Vertical Viewing Angle

**α)**of the width of the pitch is included between the line of sight SLF2 of further focus point F2 and line of sight SLF1of closer focus point F1. Its value is the difference between the inclination angle (ßf1) of the line of sight SLF1 and inclination angle (ßf2) of the line SLF2.

For an objective comparison of images receiving by the visual apparatus of the observers located in various places of the stadium interior, author have developed its own method of so-called *the relative retinal image*. The sight lines of focus points (F1 and F2) extended beyond the point of the eye EP(n), while piercing the back plane of projection (RPP) will appoint the images of these points (F1”and F2”). The image of the pitch width, obtained in this way, can be called *relative retinal image*, provided, however, that the distance between the rear projection plane and the point of the eye will be the same in each case of the analyses. With such an assumption have been obtained an optical system that simulates the interior of the eyeball, the essence of which is a constant distance between the central point of the lens and the surface of the retina.

The quality of the visual perception of action pending on the arena is, equally to the vertical angle of view of the pitch, determined by the height of the images of the figures of players. The analysis of this issue is presented in Fig. 5. In order to examine the relationship of viewing quality of players, depending on the position of the observer’s eye, the analysis have been based on the assumption of equal vertical angle of view of the pitch. This was possible thanks to the well-known theorem of geometry, that the measure of inscribed angle is two times less than the measure of central angle based on the same arc. Furthermore, that all inscribed angles based on the same arc are equal.

The three extremely different positions of eye points have been considered. For each of them the height of the image of the playing field is the same, because they are seen in the same vertical angle of view. As shown in the Fig. 5 in the image for the eye point EP1 (coordinates: L = 54 m, H = 5 m) the height of player silhouette housed only 3 times in height of the pitch image. In the case of the eye point EP2 (coordinates: L = 92 m, H = 21 m), this parameter reaches the number 8.5. Eye point EP3 (coordinates: L = 132 m, H = 48 m) is characterized accordingly by the number of 14.

## 4 The Visibility Determinants of Lowest Tier

The slope of this line will be ßf2 = 3º. If the lowest points of the eye will lie on that line and at the same time will ensure at least the vertical angle of view of the pitch α = 7º, it give that the depth of view of the playing field will be 3 heights of the footballer. Figure 6 shows also that the exemplary stand profiles of modern stadia have significantly lower fragments of the spectator zones, which do not meet the described criterion. These are the profile sections which are situated below the proposed regulation line.

## 5 Propositions of Unconventional Profiles of Stadium Stands

## 6 Conclusions^{1}

## Footnotes

- 1.
In the years 1994–2007 the author was the chief architect of the reconstruction of the Silesian Stadium in Chorzow, Poland.

## References

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