Geometric methods for estimating representative sidewalk widths applied to Vienna’s streetscape surfaces database
Abstract
Space, and in particular public space for movement and leisure, is a valuable and scarce resource, especially in today’s growing urban centres. The distribution and absolute amount of urban space—especially the provision of sufficient pedestrian areas, such as sidewalks—is considered crucial for shaping living and mobility options as well as transport choices. Ubiquitous urban data collection and today’s IT capabilities offer new possibilities for providing a relationpreserving overview and for keeping track of infrastructure changes. This paper presents three novel methods for estimating representative sidewalk widths and applies them to the official Viennese streetscape surface database. The first two methods use individual pedestrian area polygons and their geometrical representations of minimum circumscribing and maximum inscribing circles to derive a representative width of these individual surfaces. The third method utilizes aggregated pedestrian areas within the buffered street axis and results in a representative width for the corresponding road axis segment. Results are displayed as citywide means in a 500 by 500 m grid and spatial autocorrelation based on Moran’s I is studied. We also compare the results between methods as well as to previous research, existing databases and guideline requirements on sidewalk widths. Finally, we discuss possible applications of these methods for monitoring and regression analysis and suggest future methodological improvements for increased accuracy.
Keywords
Streetscape Urban surface database Sidewalk width Inscribed circle Circumscribed circleJEL Classification
R14 R41 R521 Introduction
Today’s IT capabilities and data collection on various urban management levels provide mobility relevant data on a comprehensive basis. In the past, random tape measurements provided anecdotal evidence of characteristic dimensions of transport infrastructure. Today’s new geographic datasets enable systematic and comprehensive derivation of characteristic measurements. Besides detailed measurements for planning, the need of areawide, quick, workable and relationpreserving overview methods may prove more important to some management needs than indepth analysis. GIS is increasingly being used for deriving transportrelated state variables, e.g. catchment areas of public transport stations (Iseki and Tingstrom 2014), the accessibility to public transport (O’Sullivan et al. 2000) or network performance (Mesbah et al. 2012). Walkability is another parameter, which has gained importance in recent quantitative analyses, for example analysing the connection between quality of urban built environment and mental health in youth (Duncan et al. 2013), active school transport (Wong et al. 2011), obesity (Duncan et al. 2012; Agampatian 2014) or the dichotomy of objective and perceived walking times (Dewulf et al. 2012). Findings suggest strong correlations between walkability and likelihood of taking a walking trip, vehicle miles travelled and obesity prevalence (Frank et al. 2007) and with moderatetovigorous physical activity (Sallis et al. 2009). Due to the lack of more detailed data, a lot of studies stay on a metalevel when linking walkability with indicators such as landuse mix, residential density and intersection density (Frank et al. 2005) or pedestrian route directness. These can be calculated easily using GIS software and existing data. However, even simple indicators such as mere sidewalk presence or sidewalk width—used in a few studies (Ewing et al. 2004; Lin and Chang 2010)—need to be collected at least in part manually, which is timeconsuming and costly (Schneider et al. 2005; Frackelton et al. 2013). Systemic data collection on sidewalk widths is needed. Here, our paper steps in with the proposition of automated computation of representative sidewalk widths with differently grained methods according to data availability.
Our paper is organized as follows: the next section presents three methods to compute representative sidewalk width and applies them to a dataset from Vienna, Austria. Section 3 presents distribution parameters of resulting representative widths and the mapped study of autocorrelation in terms of position in the city. The second to last section discusses the plausibility of results and draws conclusions on result significance elaborately. In the final section, results are reviewed as well as method application and improvement is debated.
2 Materials and methods
2.1 The dataset
Dataset parameters
Surface type  GG  EE  HH 

Sample size  349,462  77,950  91,623 
Area (m^{2})  
Min  0.00  0.00  0.00 
Mean  25.16  8.48  3.84 
Max  2739.44  803.90  330.12 
Circumference (m)  
Min  0.01  0.04  0.02 
Mean  26.33  11.80  7.78 
Max  1636.47  307.47  84.15 
In effect, minimum areas are not zero, but smaller than 100 cm^{2}. As not only physical boundaries are shown in the SIS_F database, but also lines connecting house corners randomly delimit surfaces, such extremely small snippets exist. For example, the lower left corner of Fig. 2 shows such a triangular snippet—in some cases their size is less than the threshold given above.
2.2 Three methods

Method 1 uses the minimum circumscribed circle of a polygon.

Method 2 uses the maximum inscribed circle of a polygon.

Method 3 utilizes the total sidewalk area within a buffer around the street axis.
The first two methods keep the distinction between the three surface types as given by the SIS_F database for reasons of precision and smallsized permanent changes in in situ widths. The different orientation of length versus width calls for the necessity to different methodical approaches. An inclusion of EE or HH surfaces to adjoining GG surfaces would reduce the detailed representation of constant width changes.
 1.
Define a rectilinear search region R from (x _{MIN}, y _{MIN}) to (x _{MAX}, y _{MAX});
 2.
Create a grid of N _{ x } by N _{ y } nodes in R, where GarciaCastellanos and Lombardo (2007) use N _{ x } = N _{ y } = 21;
 3.
Of the points inside the polygon, find the point that is furthest from any point on the edge;
 4.
From that point define a new R with smaller intervals and bounds, where GarciaCastellanos and Lombardo (2007) reduce R by a factor of \( \sqrt 2 , \) and repeat from step two to get to any arbitrary precision.
2.3 Circumference over area
Parameters of selected regular shapes for equation
Shape  k  β  Colours in Fig. 4 

Circle  3.54  0.5  Red 
Square  4.00  0.5  Green 
Rectangle 2a  4.24  0.5  Orange 
Rectangle 10a  6.96  0.5  Violet 
Figure 4 a–c shows that sidewalk surfaces (GG) are larger than driveway entrances (EE) and walkway entrances (HH) with a tendency to grow narrower with increasing area. This is shown in Fig. 4a by the grey cloud and contour lines moving away from the circle line (red) over the rectangle 2a line (orange) to the rectangle 10a line (purple) with surface sizes around 10^{2} m^{2} and larger. Figure 4a shows for sidewalk surfaces (GG) that density isolines clearly group along the orange line with the peaks in an area range of 10^{0.5}–10^{1.5} m^{2}, this is from 3 to ca. 32 m^{2}.
Figure 4b illustrates that driveway entrances (EE) are bigger in size than walkway entrances (HH, Fig. 4c), as one would expect from door widths. Density peaks in a range around 10^{1} m^{2} for walkway entrances versus a range between 10^{0} and 10^{1} m^{2} for driveway entrances, which peak around 10^{0.5} m^{2} of area and a 10^{1} m circumference. The density spikes clearly group along the rectangle 2a line with no grey circle actually touching the red circle line. Walkway entrance (HH) density groups between the circle (red) and the rectangle 2a line (orange) as well and it can be observed that no grey dot reaches as far as the circle line. Both surface types, EE and HH, are distinctly smaller than GG surfaces and appear to be packed around the rectangle 2a line, whereas higher densities (contour lines) of the GG surfaces reach and cross the rectangle 10a line. In comparison with GG surfaces, EE and HH surfaces show a more compact form, as their density peaks appear between the lines for circles and rectangles with a side proportion of one–two times a. Although, from this point of view, it appears likely to expect that the estimation method for types EE and HH may lead to greater deviations of w _{REP} from the actual sidewalk width, we apply this method nevertheless since the C–A plots indicate that the three applied methods are legitimate and valid. On the one hand side, for GG surfaces, Method 1 is expected to underestimate w _{REP}, because the rectangularstyle polygon’s area is divided by its diagonal, which is bigger than the longitudinal side. Method 2, on the other hand, is expected to overestimate widths because it relies on the maximum circle. For types EE and HH, the circumscribed method, due to seeking for the polygon’s longest diagonal, is expected to overestimate w _{REP}. Method 3 is expected to behave indifferently, as the buffer includes sidewalk surfaces from the intersecting roads and the buffer width is added to street length as denominator in Eq. (3).
3 Results
Distribution parameters of w _{REP} (m) by datasets and methods
Parameter  Method  GG  EE + HH  GG + EE + HH 

15th percentile  1—Circumscribed  0.83  2.17  1.05 
2—Inscribed  0.97  1.77  1.19  
3—Buffered street  –  –  1.51  
Mean  1—Circumscribed  1.82  3.62  2.41 
2—Inscribed  2.11  3.04  2.42  
3—Buffered street  –  –  4.83  
85th percentile  1—Circumscribed  2.67  4.87  3.61 
2—Inscribed  3.06  4.12  3.48  
3—Buffered street  –  –  7.04 
Ranges of specific parameters of the resulting cumulative distributions
Method  w _{REP,15%} (m)  w _{REP,50%} (m)  w _{REP,85%} (m)  Districts with w _{REP,MAX}  Districts with w _{REP,MIN} 

1—Circumscribed  0.51–1.01  1.51–2.26  3.01–4.01  1, 11, 20  14, 15, 23 
2—Inscribed  1.00–1.26  1.51–2.76  2.76–4.26  1, 3, 20  13, 14, 23 
3—Buffered street  0.26–2.50  1.01–3.25  2.26–4.25  5, 6  13, 22, 23 
Ranges of specific parameters of the cumulative distributions comparison from Fig. 8
Methods and datasets  w _{REP,15%} (m)  w _{REP,50%} (m)  w _{REP,85%} (m) 

Circumscribed GG  0.51–1.00  1.25–2.25  1.76–3.75 
Circumscribed EE + HH  1.51–2.75  2.76–3.75  4.00–6.25 
Inscribed GG  0.51–1.00  1.26–2.50  2.01–3.50 
Inscribed EE + HH  1.01–2.25  2.26–3.00  3.25–5.25 
4 Discussion
Results are as granular as the input data and method characteristics determine. In our results, we have aggregated all representative sidewalk widths, either by districts or in a grid. These are two options among many, and for other use cases it may be more appropriate to aggregate on more detailed levels, such as on a building block or street level or even individual surfaces.
4.1 Context
While the results of our methods agree on some aspects, considerable differences between different method results can be observed as well, which we have presented in graphical and numerical form. Because the cumulative distributions for Vienna (Fig. 8) take a sigmoidal shape, which is often an indicator for a normal distribution, we tested it. Both, the visual evaluation of histograms as well as the Kolmogorov–Smirnov normality test, which is considered suitable for datasets bigger than 2000 specimen, reveals that all three w _{REP} data sets are not normally distributed.
The cumulative distributions of w _{REP} (Fig. 8) reveal a long tail reaching to 10 m of width and beyond. These surfaces do not necessarily represent classic sidewalk settings (as in a cross section of wall–sidewalk–lanes–sidewalk–wall) but represent squares and plazas that are not classified as type FZ (pedestrian precinct). The distributions’ long tails are one reason why the normality tests do not reveal a Gaussian distribution of data.
There is a significant difference in results when using Method 3 in comparison with Methods 1 and 2, where the circumscribed method results in the least spreading/diverging curves. While individual district results from Method 3 vary considerably from Methods 1 and 2, spanning a wider range of values, the cumulative curve for Vienna’s total datasets does not differ much. District distributions show a relative stability explicated as envelope curves to the set of curves. While district 23, a peripheral district with a lot of industrial areas, consistently appears on the list of minimum sidewalk widths, other peripheral districts (such as 13, 14 and 22) are part of the smallest widths curve sets as well. Maximum widths show more variety. Nevertheless, districts 1 and 20 bound the curve sets from the upper end in two out of three methods, indicating a intermethodical stability.
In comparison with single surface consideration in Methods 1 and 2, the buffered street axis method (3) provides an aggregate approach. Surfaces from all three types within the buffer are consolidated and divided by the street buffer’s characteristic length l + 2b. For sake of comparison with Methods 1 and 2, we assume most streets to have a left and a right sidewalk; therefore, we multiply with 0.5. The use of l + 2b instead of simply l as denominator tends to produce better results since otherwise w _{REP} would be overestimated systematically. This means that circumscribed and inscribed methods favour streets with one wide sidewalk over those with two narrower sidewalks. An improvement of the buffered street axis method would ask for the variation of buffer size within a sensitivity analysis of results. When street link datasets include lane widths and lane numbers, buffer size could be adapted accordingly for every individual link. This would improve the accuracy of results considerably, instead of running a constant buffer size analysis over every type and dimension of roads.
To our knowledge, only two approaches related to ours exist in the literature. One is Freeman and Shapira’s (1975) development of the minimum area rectangle (MAR) method for calculating the length and width of a rectangle circumscribing an entity. It is likely that this rectangle’s length reveals similar results to our circumscribing circles—Method 1. In the other approach, Zhu and Lee (2008) investigated Moran’s I for various transportrelated variables. While some variables showed a significant impact, sidewalk width did not show significant clustering.
4.2 Comparison and validation
So far, none of our methods consider the qualitative distinction between a wide onesided sidewalk and narrow twosided sidewalks. Even though the resulting numbers may be the same, e.g. in Method 3, the qualitative perception by pedestrians may differ considerably.

Finding 1: w _{MEASURED} − w _{REP} differs most for GG; HH produces the best fit, EE slightly less.

Finding 2: EE surfaces (driveway entrances) are often wider than the sidewalk width.

Finding 3: The inscribed method is more exact than the circumscribed method.
Finding 1 is due to the fact that GG surfaced are often irregular, while HH and EE surfaces are mostly perfectly rectangular.
Finding 2 results in an overestimation of w _{REP} as the surface orientation appears contrary to the method’s preconditions—in partial contrast to the conclusion drawn in Sect. 2.3. We therefore calculated a corrected width “EE*” with the method used for GG rather than HH which led to a significant increase in fit. Finding 3 is a consequence of the used calculation method where especially in rectangular surfaces the inscribed method renders perfect results for w _{REP}, while the circumscribed method overestimates distances due to the Pythagorean theorem. Given a sufficient number of HH and EE surfaces, this (adapted) method produces a good overview of w _{REP} values.
One further approach for improvement of the presented methodology is to systematically calculate the logic transversal and longitudinal orientation of sidewalk surfaces from neighbourhood relationships between surface types irrespective of actual surface orientation. This is expected to be an advancement benefitting from treating groups of surfaces instead of every surface by itself. Under ideal circumstances, a GG type surface is expected to have its longer extension oriented with the longitude of the sidewalk, while for surfaces denoting the access to buildings over the sidewalk, such a clear distinction between width and length in terms of pedestrian’s logic is not possible from geometry alone.
Sidewalk surfaces, especially in intersection setups, are segmented by lines that result from virtual alignment lines between house corners. These fragmentations reduce surface size artificially and are likely to lead—especially for Method 2—to an underestimation of w _{REP}. For example, when a square is divided in two isosceles triangles, the relation of areas is 2, but the relation of inscribed diameters changes to 1.707. Circumscribed diameters remain the same.
4.3 Requirements
Measurements of the actual space that pedestrians demand for (Schopf 1985), put our results into the following perspective: twopeople encounters ask for a width of 2.21 m at 50% share and 2.56 m at 85% share. While with the circumscribed method the 50% value is met only by the better half of districts, the 85% value is easily overachieved. A similar situation is present with the inscribed method. The buffered street axis method results in show that the total dataset meets the 50% as well as the 85% requirements. The Austrian transport engineering guidelines on sidewalk design (FSV 2015a, b) give 1.50 m as the minimum width for enabling the meeting of two opposite walking pedestrians and ask for a basic sidewalk width of 2.0 m. All three methods result in a w _{REP,50%} that meets this requirement, indicating that only selected districts assessed using the inscribed method (w _{REP,15%} up to 1.51 m), do not meet the quality standard for sidewalk infrastructure (Table 3).
5 Conclusion
In this paper, we have used three different methods for calculating a representative sidewalk width from a detailed citywide urban surfaces GIS database.
Our paper contributes insofar as it introduces three methods which can be used to quickly estimate representative sidewalk widths from existing large scale urban surface GIS data. Moreover, the methods’ quality, significance and representativeness are tested in a series of critical examinations. In one case, surface types EE, the comparison with manual measurements suggest to change the calculation algorithm accordingly when applying Methods 1 and 2 as these surfaces appear to be more oriented like GG surfaces than HH surfaces.
Results are a quantitative basis for subsequent indepth analysis. Not only can these results be precisely compared to guideline requirements, they can also evaluate in terms of spatial autocorrelation. The question “Do clusters of extra wide or extra narrow sidewalks exist?” can be answered for areal entities. We performed this examination based on a 500 by 500 m grid to show that Method 3 leads to such a clustering of likewise results.
The task, which cannot be satisfied with our methods, but is one of very high importance to real pedestrian quality, is the consideration of net sidewalk widths. Gross width encompasses the sidewalk surface from wall to kerb, while net width is determined by obstacles and hindrances such as traffic sign posts, bargain baskets, light poles and advertisements cluttering sidewalks. As Fig. 2 shows in its left lower corner, the database already includes some of these fixed obstacles: tree bases and traffic light control boxes. Other fixed obstructions are not included in the present data base. To our knowledge, only lighting post GIS data exists in Vienna to a level precise enough to be included in our kind of calculations—a task open for future endeavours. One pure geometrical approach would be to cookiecut these obstructions from its underlying sidewalk surfaces. Yet, most of these obstructions such as lamp poles and traffic signs engage only a very small horizontal space, hardly impacting on surface size. A lamp pole’s obstruction effect lies in its local space constriction—a singularity in comparison with sidewalk surfaces. Although the road engineering rules pose a carlane envelope driven demand for putting traffic signs up to 60 cm into the sidewalk surface, systematic surveys of how much these obstacles reduce gross widths have not been undertaken so far to our knowledge. But, we consider research on this issue as dearly needed. In a first approach, undergrad students at our Institute of Transportation are now conducting preliminary enquiries addressing net and gross sidewalk width discrepancy.
In general, GG surfaces due to their variety in shapes and sizes promise lower accuracy than EE and HH surfaces. But how representative are EE and HH surfaces—in their appearance discrete information—in contrast to the larger GG surfaces, representing most of the sidewalk surfaces? Therefore, the question of weighting of method’s results in aggregate analysis needs to be targeted for method improvement. As of now, every derived w _{REP} value weighs in equally. However, a weighting method for calculating w _{REP} for road sections or building blocks has to be defined. Shall GG based results are forfeited for the more precise but likely less representative EE and HHbased values? It appears conceivable to the authors that when using GG, EE and HHbased results, the individual surfaces size ought to be included as a weight in calculating aggregated representative values, e.g. for a block, a street section or an administrative unit. The question, when is it sufficient to just arithmetically average EE and HH values to achieve an acceptable degree of representation, poses a research task in need of being addressed. We see adding improved methods for dealing with all walkable surfaces—such as pedestrian precincts and separated walkways—as one additional horizon of improvement.
 1.
Automatic enrichment of street network databases with sidewalk width information (for example for the official Austrian reference network GIP as an alternative to extensive manual data collection).
 2.
Citywide systemic monitoring of sidewalk widths—as absolute values or as a proportion of the total streetscape.
 3.
Input data for surveys, e.g. Frank et al. (2007).
Thus, we consider our three methods as quick tools for enabling a better understanding of urban systems at the crossroads of transport and surface allocation—thus a step towards leaving the yardstick behind.
Footnotes
 1.
 2.
For the GIP standard documentation, please refer to http://open.gip.gv.at/ogd/gip_standardbeschreibung.pdf.
Notes
Acknowledgements
Open access funding provided by TU Wien (TUW). The SIS_F database is courtesy of Vienna city administration’s department for roads. A part of this study was funded by Wiener Linien (TB and UL). No influence was taken by the owners and funders on choice of methods and conclusions derived. Thanks to Takeru Shibayama and BernadetteJulia Felsch for proofreading and suggestions. Our thanks as well belong to two anonymous reviewers who helped shaping the final version of the paper.
Compliance with ethical standards
Conflict of interest
All authors declare no conflict of interest.
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