The Criterion of Access to the Sky View in Residential Environment Architectural Designing

From the dawn of time, a feature of urban structures is the increasing density of their buildings. For thousands of years, this was due to the spatial limitations of defensive cities. Today, however, it is the result of many new factors mostly of an economic nature. One of the basic problems of urban living space development is and has been to satisfy the age-old need for sensual and physical relations between man protected by utility interiors and the surrounding external environment. These vital connections are and have been realized through the window, which explains why the history of architecture is largely the history of the window.

Man functions alternately both in the natural conditions of the external environment and in architectural interiors separated from it. Both of these environments create one existential living space necessary for his health and well-being. The primary sense of perception of this space is the sight, which provides its visual representation in the human mind [1, 2].

The need for eye contact with the external space through the window is primarily psychological but window also has basic role in ensuring the flow of physical factors of the external environment into living interiors. The inviolability of the window functions may be protected by the law. An example of this was English Property Law known as Ancient Lights (1663). These regulations ensured the owner of a building or house the right to light received from and through windows – and thus also to an unobstructed view through the window. Windows used for light by an owner for 20 years or more could not be obstructed by the erection of an edifice or by any other act by an adjacent landowner [3].

The research undertaken is part of the interest in the issue of view through windows, represented by many scientific fields and in the broader context of the relationship between the internal and external environment. Studies of a wide spectrum of issues represented by numerous items of scientific literature in this field confirm the high rank of these problems in the modern world. Particular emphasis should be placed on their multidisciplinary nature and unquestionable relations to the impact of the doctrine of sustainable development. Due to the limited scope of this article, the author does not discuss these works in detail, limiting himself to listing them in the list of references. The purpose of referring to them is to show the general scientific background, and thus to show the importance of the research topic undertaken. Parallel to Town Planning, Architecture and Construction, this issue is of interest to researchers from other fields, such as: Environmental Psychology [4, 5, 6]. Environment and Behaviour [7, 8, 9]. Construction and Environment [10, 11, 12, 13], Lighting Research and Technology [14, 15, 16, 17, 18, 19] as well as the Human Factors, Ergonomics and Medicine [20, 21, 22].

One of the key undertakings in this research area was an interdisciplinary project initiated by the National Research Council of Canada under the name “The Physiological and Psychological Effects of Windows, Daylight and View at Home: Review and Research Agenda” [23]. This program allowed to identify over 270 items of scientific papers prepared by 2012, which indicates the importance scale of these issues. The research program was aimed at supporting architectural and lighting solutions that are beneficial to the health and well-being of the inhabitants. The summary of the report contains conclusions that should be emphasized as important for the research undertaken. The first is that separation from the view of sky and the outside world should be avoided. The second indicates that the view outside also contributes to well-being, especially if it's nature.

The effects of these strictly scientific activities constitute the theoretical basis of a real strategy for the implementation of the concept of sustainable urban development. An example of this could be the statutory requirements to provide city residents with access to the sky and sunlight. A good example of the effective application of such a strategy in practice is the activity of the city of Toronto. In their building design guidelines, they established an obligation to protect access to sunlight and the view of the sky, defined as the measurable amount of sky seen above and between urban building blocks [24]. The importance of these essential regulations is expressed in a clear, simple statement: Losing the view of the sky restricts access to light, affecting comfort, quality and enjoyment of the public sphere [25].

The high rank of the window view criterion in the assessment of the apartment value is well reflected in the real estate market. Research of scientific publications in the field of real estate economics confirms the dependence of the value of apartments and houses on the quality of the view from their windows – the more sky and open space to the horizon, the higher the price [26]. It is well known that houses on the shoreline have twice the market value of houses located a mile inland. The quality of the view from the windows translates directly into the price of a flat or house. According to estimates by one of New York's largest real estate appraisals and consultancy firms, an apartment on a higher floor with nearly unobstructed views can cost 25 percent more than an apartment without views on the lower levels [27].

Literature studies on the topic have shown two cases of a method that directly uses the optics of the human visual apparatus to obtain a view of the sky from the window of living quarters. One of them comes from the work of Marcus Vitruvius Pollio: de Architectura, Book VI, Chapter 6, dated to the 1st century BC [28]. A Roman architect wrote: (...) in the city, the height of the party walls or the tightness of the situation may obscure the light. In that case, we should proceed as follows. In the direction from which the light is to be received, a line should be drawn from the top of the obscuring wall to that part where the light is to be introduced, and if looking up along this line, a large area of open space can see the sky, light can be obtained from that quarter without fear that it will be covered; (...), which was summed up a few lines later: (...) In short, one can assume as a general rule that where the sky is visible, openings for windows should be left in such a part so that the building is bright. (…).

The second case is about 200 years old and comes from the provisions of Prussian Law. A simple visual-optical method was used to determine the distance between the buildings. Namely, it was required to provide a view of the sky above the newly erected building from the ground floor of the existing building, Fig. 1(A).

Figure 1

Only the industrial revolution brought significant changes in the functional and spatial organization of cities. The flagship example of this is the great reconstruction of Paris (1853–1870), Fig. 1(B). From the point of view of the subject of this work, the precise rules of shaping the transverse profile of a city street, introduced at that time, are important. They strictly determined the height of the buildings and the distances between their opposite frontage [29]. In this way, they regulated the access of daylight to the apartments on individual floors, and also provided a view through windows with access to the sky.

In European urbanism, these principles survived until the renewal movement initiated by the Athens Charter and the CIAM conferences, known as Modern Architecture. Due to the subject matter of the presented research, the most important was the introduction of the then common in estate planning rule that the minimum distance between residential buildings should be twice their height, Fig. 1(C). After World War II, the urban planning of housing estates in the countries of the Soviet-dominated Eastern bloc was based on the rigorous application of this algorithm, and these principles survived until the 1990s [33].

Until recently, the standards specifying the requirements for daylight in shaping the interiors of residential buildings resulted only from elementary physiological and health conditions of the human body. The term “window” was used only in relation to its dimensions due to the amount of light introduced into the interior and not due to the viewing opening. Matters related to visual perception, with the role of light as a carrier of images of the outside world, were not subject to unambiguous normative regulation. In this context, the 2018 edition of the European Lighting Standard should be considered a breakthrough. For the first time, a building code clearly indicates the need for a view of external environment. It also tries to define the view from the window in terms of its essential elements, specifying the minima required in this respect [34]. The most important of the three elements of the view presented in the standard is, according to the author, the image of the sky. Its lack in the view from the window significantly weakens the visual relationship of the user of the residential interior with the outside world.

It is obvious that in the psychological dimension it is the sky that is the basic reference element in the human perception of natural space. Therefore, one of the most important criteria for sustainable housing construction should be to ensure that every apartment user has access to a view of the sky through the window. The implementation of this postulate is closely related to the problem of the distance between buildings that make up the urban spatial structure of housing estates. The above statements were the basis for determining the goals and scope of the undertaken research. The main goal is to identify the broadly understood full spectrum of conditions for ensuring access to the sky view from apartments in buildings of high-intensity housing estates.

The undertaken research topic concerns the key issue in the field of architectural design of housing estates. This issue is the rules for determining the distance between buildings in the context of qualitative and quantitative factors ensuring physical and mental comfort, health and well-being of residents. Among them, the most important factors are provided by the window. The most important of them are: daylight, direct sunlight and eye contact with the external environment. The design conditions of the first two are precisely defined in the relevant building standards. The same cannot be said for the view through the window, however. It is true that the new European Lighting Standard for Buildings raises issues related to the view through the window in general, but they cannot be treated as strict normative regulations.

The applied research methods are based on the use of previous scientific works as well as theoretical and practical experiences of the author in the design and implementation of visibility profiles of large-size stadium stands [35, 36, 37, 38]. The author, focusing strictly on the phenomenon of visual perception, has developed a research apparatus capable of simulating the real visual perception of images of the external environment space through a window opening [39]. It was possible thanks to the use of the method of the relative image of the retina and the underlying conceptual apparatus [40a].

In this framework, the main attention is on the spatial and physical nature of the sky, as a component of the external landscape. The field of work interest also included the determinants of access to its view through the window. The subject of research is the image of the sky, which is an important element of the image of the wider external environment, reflected on the retina of the eye of the observer looking through the window from inside the living space. The assumed goal, scope and methodology of the research required the use of strictly optical principles of the functioning of the human visual apparatus and the definition of the view through the window adequate to these principles. In this context, this view can be thought of as a flat image projected onto a plane simulating the retina of the eye. Thus, an important research tool was created on the basis of the author's concepts developed in earlier works. This allowed for a series of analyzes, which are presented in detail later in the paper. They include issues such as: –

The dependence of the image size in the window opening on the observer's position in the residential interior;

The following presentation of the terms used and the definitions of their meanings is intended to facilitate the understanding of the analyzes described in the following chapters of the paper.

Terms used in the works preceding current research:

Line of sight – A straight line connecting the observed material point in the external space to the centre of the retinal yellow spot, passing through the geometric centre of the eye's lens

Terms created for the purposes of the current research:

The horizon plane – The horizontal plane through the line of the horizon and the theoretical eye point.

The method of simulating real images recorded by the human visual apparatus is based on the use of a simple optical and geometric principles of the eye's operation, which we owe to the perspective vision. The lines of sight of observed objects pass through the centre of the lens and hit the retina inside the eyeball. The most important geometrical fact is that the distance between the lens and the retina has a constant dimension, while a distances from the lens of the points situated in the external space can be arbitrary. The angle between the lines of sight of the extreme points of the observed object is called the viewing angle, and its value on both sides of the central point of the lens is the same. It follows from the above-mentioned relationships that the viewing angles of objects of the same size will be different depending on the position in relation to the eye. This angle will be larger for object of closer distance to the eye, than the one lying further. Due to the differences in the sizes of the described angles of view, the images of objects displayed on the retina of the eye have the characteristics of an optical perspective. Images of objects of the same height or width decrease when moving away from the observer, and the lines of sight of their edge points converge on the horizon line, at the so-called vanishing points. The finding of the principle of the constant distance of the central point of the lens from the retina in the inside of the eye became the inspiration for the original graphic concept called the relative retinal image method. It involves the use of a back or front projection plane that simulates the retina of the eye. These planes should be perpendicular to the central line of sight and equidistant from the eye point, in front of and behind that point. This distance should have a constant value for all analyzed images, which is an indispensable condition for their comparability.

Details of image formation on the back and front projection planes are shown in Fig. 2. For simplified research models of the sky image size in the window opening frame, the analysis of the vertical viewing angle was the most useful. They were achieved by graphs made in the vertical plane, passing through the observer's theoretical eye point and the vertical axis of the window opening. The width of this images was obtained by examining the horizontal viewing angles in a horizontal plane, passing through the eye point and the horizon line.

Figure 2

Several factors (parameters) simultaneously determine the size and scope of the image of a sector of external space, seen by an observer from of a residential interior. They are: observer's distance from the window opening; the size and shape of the window opening; relation of the position of the window opening in regard to the central line of sight and the horizon line.

Fig. 3 shows an example analysis of these relationships performed using the relative retinal image method. In order to make it easier to read, a simplified, synthetic model based on the following geometric assumptions was tested:

The window opening is a square with a side equal to 1.4 m, (approximate to the most popular size and proportions meet in a mass housing construction);

The Central Line of Sight elevation is 1.6 m, (the mean anthropometric elevation of the eye of the observer in a standing position);

The horizon line divides the height of the window opening in half;

The vertical plane of the graph passes through the vertical axis of the window opening;

The positions of the theoretical points of the eye in relation to the outer plane of the window opening are determined by the multiplicity of the 1 m scale;

Figure 3

The distance of the projection plane for individual points of the eye is constant and amounts to 1 m.

These assumptions mean, that characteristic for individual points of the eye, a horizontal and vertical viewing angles, are the same. The results of the conducted research show that the most important factor influencing dramatically the size and scope of the image recorded in the frame of the window opening is the distance of the observer from the outer plane of this opening. This is due to the fact that the values of vertical and horizontal viewing angles rapidly decrease as the eye point moves away from the window, with the former being the most important for the view of the sky.

Fig. 3 presents a summary of the graphs of relative retinal images of the window opening for points of the eye distant from this opening by the values of 1 m, 2 m, 4 m and 8 m. As seen, both the dimensions of the images of the sides of square window openings and their surfaces are rapidly decreasing, being respectively 1/4, 1/16, 1/64 part of the sizes registered from a distance of 1 m. The vertical and horizontal viewing angles of the images in the window frame decrease in similar proportions, and so do the viewing angles of the sky segment contained in them.

The above conclusions played an important role in the further stages of the search for the definition of the criterion of minimum access to the view of the sky from the windows of living quarters. They contributed, inter alia, to the definition of the essential parameter in the research which is the distance of the eye point from the outer plane of the window equal to 1 m.

Applied research model is based on the three dimensional Cartesian coordinate system, (see Fig. 2 at the top). The traces of the line of sight are examined in two planes: vertical (xz) known as the central vertical plane of symmetry and horizontal (xy) defined as the horizon plane. The intersection of the x, y, and z axis marks so-called the theoretical eye point, being the common point of three planes xz, xy, and yz. The edges of the window opening delimit a bundle of lines of sight of the external space converging at the theoretical eye point. In the case of a square-shaped opening, the beam will be in the form of a pyramid. When the hole is circular, the beam will be a cone. In both cases, the point of the eye is the apex of these forms. For the purposes of this description, they are given the names of a pyramid or a cone of vision. Due to the subject of the research, the most important are the lines of sight running in the plane of the central vertical section (in the xz plane). They allow for the analysis of determinants affecting the height of the sky image that is part of the image defined by the window opening frame.

As shown in Fig. 3 the height of the image of the external space is determined by two extreme sight lines – from the top, the line tangent to the upper outer edge of the window opening, and from the bottom, it is tangent to its lower edge. In this image, an important reference is the horizon plane on which the central line of sight lies.. The image recorded by the visual apparatus is divided into two parts, the one above the horizon and the one below it. It follows from the laws of the eye's optics and human range of vision that the maximum height of the sky view extends upwards from the horizon plane, represented by the central line of sight, to the vertical line of sight, reaching a vertical viewing angle of 90°. In the view through the window, the vertical angle of the sky view (β) is significantly limited by the presence of a lintel. Another limitation of the size of this angle may also be the presence in the image of the window frame of an object exceeding the height of the horizon plane. This height difference is represented by the vertical viewing angle γ. In the described situation, the height of the sky image is reduced to the size defined by the so-called sky view entry angle (δ).

Fig. 4 also shows the method of analysing the relationship between the human vertical range of vision and the vertical viewing angles of the external space through the window opening specified in the research model. It shows that below the horizon, these angles fall within the range of vision achieved solely by eyeballs movement, and above it slightly fall within the normal range of vision achieved by a combination of eye movements and head movements [40c].

Figure 4

The research was based on the analysis of the theoretical model. Using the previously developed conceptual apparatus in order to conduct more detailed analysis, a research model was created. Its basis is presented with a vertical and horizontal cross-section, of a window opening, together with a fragment of the interior of the theoretical apartment. The obscuring object is drawn on the same scale as the residential interior, in terms of height, elevation above the horizon and distances. Reflecting the real viewing angles requires that both the interior and the obscuring object are plotted on the same scale. As shown earlier, the size of the image in the frame of the window opening depends on the distance of the theoretical point of the observer's eye from the outer plane of the opening. In the research model, it was assumed that for the first eye point this distance is 1m. Subsequent analysed positions of the eye point are a multiple of this distance.

For the research model, strict assumptions were made for the creation of relative retinal images. Accordingly, the front projection plane lies on the outer plane of the window opening and is thus distant from the first point of the eye by 1 m. The rear projection plane coincides with the vertical axis of the next point of the eye, which runs at a distance of 1 m. The method of constructing the relative image of the retinal view through the window is shown in Fig. 5 (detail “a”). It consists in transferring the course of three lines of sight: tangent to the upper edge of the opening (Sue), tangent to the lower edge of the opening (SLe) and tangent to the highest edge of the screening object (SBe), to an enlarged drawing of the vertical cross-section of the window opening.

Figure 5

The first two pass through the extreme edges of the opening, while the third cuts off the boundary between the sky view and the view of the obscuring object, on the front projection plane (Fp). Extending these lines to the intersection with the trace of the rear projection plane creates an image identical to the above, but inverted. Plotting the horizontal dimension, i.e. the width of the window opening image, is carried out on the plane of the horizontal, central cross-section of the window opening. It is defined by the points of intersection of the line of sight of the side edges of the opening with the front and rear projection planes. The full image of the sky in the image of the window opening is obtained by combining both image parameters, i.e. its height and width.

Fig. 6 illustrates an example of the application of the previously presented research methodology on the issue of access to the view of the sky from residential interiors. The conducted analysis concern the relationship between the sky view in the window frame image and the distance between neighbouring residential buildings. The goal defined in this way required the extension of the research model to include the possibility of stacking individual modules of residential interiors. The subject of research in this case are not only individual apartments, but also entire, multi-storey buildings. Their representation in the model is the vertical cross-section through the building, including the living spaces, adherent to the external façade wall with windows.

Figure 6

In the research, a specific height module of a building story was adopted (M = 2.85 m). An important role in the analysis is played by the central lines of sight, lying on the horizon planes, which are parallel to each other and characteristic for each storey. Their mutual elevations have the dimension of the M module. The eye points are located at the intersection of the horizon lines and the eyes vertical axis, distant from the building face by a constant value (1 m). Their location is the same on the individual storeys of the building. The horizon plane passes through the points of the eye and is raised 1.6 m above the floor. This height is called the standing position eye height in anthropometry, and its value corresponds to the median of the percentile distribution. Its counterpart for a sitting position is value equal to 1.2 m.

For the purposes of increasing readability of this analysis, it was assumed that the window opening is a 1.4 m square and the central line of sight passes through its geometric centre, which means that the central planes, horizontal (xy) and vertical (xz) are dividing it symmetrically. The upper edge of the analyzed buildings is above the eye point of the highest storey at the distance of the M module. This assumption allows for the treatment of parallel horizontal central lines of sight as a modular grid, which is useful in determining the heights and distances of an obscuring buildings.

The parallelism of the central lines of sight of observers on individual storeys results from the general laws of optics of the eye. According to them, the planes of the horizon on which these lines lie rise in parallel as the point of the eye rises, the line of the horizon rises and the range of view increases. Using the research model described above, detailed analysis of access to the sky view from apartments of opposite residential buildings, depending on their distance, were carried out.

The initial assumption for these studies was to determine the acceptable, minimum vertical angle of view of the sky from the lowest apartments, previously named as the minimal entry angle of the sky view. Based on his previous research on the issues of visual perception, the author assumed that this angle should not be smaller than 7.5°. It is the upward viewing angle that is achieved by humans solely through the movement of the eyeballs. The second important assumption was that the study should focus on the impact of the designed building on the existing one. It was also established at the outset that the existing building consists of 6 residential storeys and its height, measured from the horizon of the lowest eye point, is 6 modules M.

It follows from the above-described conditions that ensuring the minimum entry angle of the sky view (δmin = 7.5°) for the lowest point of the eye in the existing building (A6) requires that the highest edges of the designed building do not exceed the line of the lower arm of this angle (SBe}, and were at most tangent with this line. The intersections of the SBe line with the lines of the horizon planes of individual storeys determine the potential heights of the designed building B (4–8), which meet the above condition. They also define its potential distances from building A.

However, it turns out in the summary that not all the positions of the designed building B determined in this way can be taken into account, which results of the influence of building A on building B in terms of meeting the criterion δmin = 7.5°. This is evidenced by the analysis of the route of the SBe line derived from the eye points of the lowest storey of building B. It shows that only the location variant of B6 and the subsequent ones provide their lowest apartments with access to the sky view. The eye points EP1' in buildings B4 and B5 are completely deprived of this access. At this point, it should be noted that the condition of having an equal view of the outer space from the lowest apartments of both, existing and planned, buildings is fulfilled when they are of the same height, and their distance (L) results from the course of the SBe line, derived from the lowest EP1 eye point.

Fig. 6 (Detail “b”) shows the analysis of the vertical angles of the line of sight of the top edge of the window opening (Sue). These angles depend on three parameters: the elevation of the lintel above the horizon line of sight (x1), the height of the lintel (x2) and the distance of the theoretical eye point from the outer plane of the window opening. The study were carried out for the assumed values of these parameters, such as: x1 = 0.7 m; x2 = 0.25 m; distance of the eye point, as a multiple of 1.0 m modulus. For these values, the slope of the SUe line (β) for the eye point EP1 is 35°. This value was considered minimal for the standing position of the observer, 1 m away from the outer surface of the window. As the observer moves away from the window, these angles quickly decrease – for a distance of 2 m the angle β is equal 19.5°, and for 3 m equal 13.3°. For a sitting position, these angles increase significantly, e.g. for point EP1 this angle reaches the value of 48°. The value of the sight-line SBe inclination angle (γ= 27.5°) is the difference between the value of the sightline SUe inclination angle (β= 35°) and the assumed minimal sky view entry angle (δ= 7.5°).

Knowing the value of the inclination angle γ = 27.5° allows to present the relationship between the height of the analyzed buildings (H) and the distance between them (L) in the form of a trigonometric function tan γ = H / L or L = H / tan γ. Since the tan 27.5° is 0.5206 (very close to 0.5), the above equation shows that with a high approximation, the value of “L” is almost equal to value of two ”H”, where: “H” is the height of the upper edge of the building elevation (multiplicity of “M” modules), calculated from the lowest horizon plane (HL) of the lowest point of the eye (EP1, EP1'), and “L” is the distance of the face of the obscuring building (B6) from the eye point EP1 in the existing building (A6). Summing up, it should be stated that providing a view of the sky from the lowest storeys in both opposite buildings requires that the distance between them should be twice the height of the higher one, and with the same building heights, the height of one of them. This statement is consistent with the findings of the algorithm used by architects and town planners in the period of modernism. In Poland, this rule was in force for nearly 30 years (from 1966 to 1994) [33].

One more conclusion about the distance between the buildings comes from the analysis. It concerns the relationship between the observer's distance and the perception of objects in terms of the ability to recognize image details. The described geometrical features of the examined building arrangement enable the conclusion that the distance Lx is 17.5 m. This value is within the margin of the distance of the farthest viewer, which is commonly used in designing drama theaters, which is 24 m, and determines the limit of legibility of the actors' facial expressions.