The Unconventional Tribune Profiles in Architectural Designing of Stadiums

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.

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].

The solutions of profiles of the stadium stands, commonly used in today’s architectural practice, can be described as the profiles of the bowl-shaped. They form two or three-tier structures [2, 3]. The lower tiers are characterized by the slightest inclination. This slope is gradually increasing on the upper tiers, reaching the maximum allowable angle of 35º [4, 5]. This arrangement results in that the images of the pitch surface seen from the lower tiers are flat, having a small height, while the images of the players figures are reaching the greatest height. Paradoxically, the images of the playing field are the highest from the upper tiers, characterized by the highest readability of further and closer plans. At the same time, however, the sizes of the images of player figures are the smallest, due to the significant distance from the observer. The above-described circumstances constitute a justification of the undertaken research. Their aim is to determine whether it is possible to use stand profiles with better characteristics than conventional one and to determine the conditions for their application in practice. The second objective is to define the determinants of visibility for spectators located at the lowest tiers. It is necessary to establish a strict criterions regulating the minimum standards for images quality which can be achieved of these places. Another, taken into account, issue is the impact of new profiles on architectural forms of stadium interior (Fig. 1).

Fig. 1.

(Photo: author).

An example of the interior of a modern soccer stadium of medium size. Commerzbank Arena, Frankfurt, 2005

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.

Figure 2 presents fragment of a classical arrangement of the spectator zone on the stadium. A horizontal shift of the eye points is equal to the predetermined width of the rows. This parameter affects the degree of comfort and safety of spectators, as it affects the size of the space assigned to the individual seats and the space devoted to communication and evacuation [6]. Mutual elevation of the eye points, situated as adjacent to each other, ensures proper raise of the line of sight over the head of the viewer situated below, allowing to see the so-called point of focus.

Fig. 2.

(Source: author)

The definition of the line of eye points (LEP) and the lowest line of sight (LLS)

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

As mentioned earlier, the quality of vision of the playing field surface is determined mainly by the so-called vertical viewing angle. The essence of the meaning of this angle explains Fig. 3. For the analysis has been chosen theoretical point of the eye EP (n), distant horizontally from the nearer point of focus F1 by the value SEP(n) and raised above the surface of the arena of value HEP(n). The graph is a vertical section of the pyramid of pitch view, running through the center line of the playing field. 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.

Fig. 3.

(Source: author).

The vertical angle of view of the pitch field (α) and the relative retinal image of this field (F1”–F2”);

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 dependences, graphically shown on Fig. 4, suggest that the greater is the vertical viewing angle of the pitch, the greater is its relative retinal image. It is also clear that the vertical viewing angle is greater while the position of the point of eye is closer in relation to the observed object and raised higher above it.

Fig. 4.

(Source: author).

The impact of the eye point position in the space on the size of the vertical angle of view of the playing field and the size of its relative retinal image

Fig. 5.

(Source: author).

The characteristics of relative images of the playing field at a constant vertical angle of view (α) and different positions of the eye points (EP)

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

As has been earlier mention, commonly used in today’s architectural practice profiles of the stadium stands can be named as the profiles of the bowl-shaped. The lowest tiers of these profiles are characterized by the slight slope. The height of eye points elevation for that part of the tribunes is small. This results in a slight vertical viewing angles of the playing field, what gives a flat images of it. Figure 6 presents the results of studies of this problem. According to the author, it is necessary to establish a criterion defining the minimum standards for image quality. This criterion should be to determine that the line of view of the further point of focus (F2) from the lowermost eye point of the lower tier (EP1) should take place tangentially to the top of the player’s head located at the center of the pitch. In Fig. 6 has been shown that such a line, drawn from the point F2 reaches a height equal of the two heights of the player figures over the point F1.

Fig. 6.

(Source: author).

The postulated rules for determining the minimum vertical angle of view of the pitch and the position of lowest points of the eye at lowest tiers

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

As previously has been shown (Fig. 4) the height of the image of the field is all the higher the larger is the vertical viewing angle. This angle whereas is all the greater the closer and the higher above the pitch is located the point of the eye. These statements indicates the guidelines for searching profiles of grandstands which are characterized by the best parameters of visibility. It results from them that profiles the best visibility should be located in a space that provides the greatest vertical angles of view. Meeting that condition requires that the lines of eye points defining these profiles should have the inclination much greater than accepted by today standards. The farther part of the discourse presents several examples of unconventional solutions. Their common feature are the significant slopes of the profiles achieved by the use of large vertical offsets of the position of the adjacent eye points. Conventional communication and evacuation systems in the interiors of modern stadiums are based on the use of corridors in the form of stairs between sectors. The slope of these stairs is equal to the slope of the terraces of the rows of seats and cannot exceed 35º (Fig. 7). The inclination of the lowest line of view, reached in this type of stands, is the result of its minimal raising (c = 12 cm) above the point of the eye, situated in the next row below or above balustrade. The profiles characterized by the slope greater than 35º require very different solutions of communication and evacuation. Due to the significant height differences between adjacent rows, repeatedly exceeding the height of 50 cm, these solutions require the use of the balustrades or countertops at the edges of the rows. The presence of these elements in the space in front of the eye points determines the course of the lowest line of view, which must run tangentially into the upper edges thereof, or above them. The significant inclination angle of the line of view determines one of the essential values represented by a steep profiles. Thanks to these characteristics, these profiles can be placed in the close proximity of the borders of the observation field. This statement contains a conclusion, that The most important parameter determining the quality of the profile is the slope of the lowest line of sight. When this slope is larger the quality of vision become higher. Studies of the presented examples of non-conventional profiles show that the steepest slope of the lowest line of sight is achieved in these solutions in which the communication passage is located on the back, behind the seats (Figs. 9 and 11). In the proposals when the communication paths ere running in front of rows of seating the inclinations of the lowest lines of vision are smaller, although the slope of the lines of eye are very large (Fig. 8). Particularly noteworthy is in the author’s opinion the example shown in Fig. 10. In this case were used the high seats (the barium type), rotating with pneumatically adjustable height. As a result, the eye point of the sitting and standing person are at the same level. High situated point of the eye in such a sitting position allows to achieve a much greater slope of lowest line of sight over the tip of the railings than in normal sitting position. The advantage of this profile is also the fact that the lowest line of sight of the eye point in a sitting position extends above the head of a person standing close to the balustrade at the level of the row situated below. The proposed solution responds to the demands of the fans, who argue that welding them to the seats reduces the spontaneous cheering.

Fig. 7.

(Source: author)

The proposal of lowered passage in front of a seat

Fig. 8.

(Source: author).

The proposal of classic width arrangement of the rows and their significant vertical offset

Fig. 9.

(Source: author).

The proposal of lowered passage at the back of a seat and the countertop at edge of the row

Fig. 10.

(Source: author).

The proposal of the rotating barium type seats, with pneumatically adjustable height and passage in front of a seats

In the discussed example there is possibility of the participation in a match in both position simultaneously - sitting or standing - while visibility conditions for the latter are even better than the first.

Fig. 11.

(Source: author).

The arrangement of the spectator zone with a reverse angle of inclination by using stands of the double rows

6 Conclusions

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

On Fig. 12 has been presented the profiles of several modern stadiums in confrontation with the proposed profiles which are based on unconventional, presented earlier, new functional arrangements of the rows. The analyzed profiles of stadium stands are presented in the form of lines of eye points. At the points of intersection of the horizontal and vertical lines of the grid, simulating the theoretical points of the eyes, has been indicated the vertical viewing angles of the playing field, which are achieved from each of them. As a result, when reading the charts of each profile one can easily determine their characteristics in terms of the vertical viewing angles, and thus can compare each other of considered profiles. The analysis shown in Fig. 12 indicates clearly that all tiers of, postulated by the author, unconventional theoretical profiles PTP-1 and PTP-2 are situated in the zone of large vertical angles of view of the pitch. At the same time all the points of the eye of each of these profiles are much closer to the line of focus points F1 than their counterparts from the stands of the exemplary stadiums. The special emphasis requires fact, that lines of the eye points representing the lowest tiers has a very steep slope reaching up a value exceeding 50º. The effects of the application of postulated by the author a new profiles are fully apparent on Fig. 13. It presents the cross section of the stadium, which allows for an assessment of the shape and scale of this space, defined by the presence of closing it stands. Even more clearly the features of this space are illustrated on Figs. 14A and B as the schematic silhouettes of stadium interiors. These silhouettes, derived from the application of unconventional profiles PTP-1 and PTP-2, have been compared with the one of most representative contours characteristic for contemporary stadium interiors (Fig. 14C).

Fig. 12.

(Source: author).

The comparative analysis of the postulated theoretical profiles of stands and the selected profiles of modern stadiums (should be considered together with Fig. 13)

Fig. 13.

(Source: author).

The juxtaposition of analyzed profiles in the form of a cross section through the interiors of stadiums

In conclusion, we can say that the interior resulting of the PTP-2 profile deserves to be determine as “interior of a flowerpot shape”, interiors resulting of the PTP-1 can be called as “interiors of a plate shape”, while most of existing today stadiums belong to the “interiors of bowl shape” category. In the author’s opinion, the proposals of new, unconventional grandstand profiles improve significantly the parameters of visibility, comfort and safety of spectators. They could 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.

Fig. 14.

(Source: author).

Comparison of the silhouettes of stadium interiors resulting from the use of postulated profiles with the classic profile of contemporary stadium