Methodological issues of metrological analysis of planned medieval towns and villages


ACTA IMEKO 
ISSN: 2221-870X 
March 2021, Volume 10, Number 1, 217 - 223 

 

ACTA IMEKO | www.imeko.org March 2021 | Volume 10 | Number 1 | 217 

Methodological issues of metrological analysis of planned 
medieval towns and villages 

Maria Legut-Pintal1, Anna Kubicka2 

1 University of Wrocław, Institute of Archaeology, ul. Szewska 48, 50-137 Wrocław, Poland 
2 Warsaw University of Technology, Department of Geodesy and Cartography, Plac Politechniki 1, 00-661 Warszawa, Poland 

 

 

Section: RESEARCH PAPER  

Keywords: modular analysis; unit of measurement; Lower Silesia; parcellation; cosine quantogram 

Citation: Anna Maria Kubicka, Maria Legut-Pintal, Methodological issues of metrological analysis of planned medieval towns and villages, Acta IMEKO, 
vol. 10, no. 1, article 29, March 2021, identifier: IMEKO-ACTA-10 (2021)-01-29 

Editor: Ioan Tudosa, University of Sannio, Italy 

Received May 15, 2020; In final form November 13, 2020; Published March 2021 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Funding: The paper presents the preliminary results of a project funded by the Polish National Science Centre, No. 2020/39/D/HS3/01549. 

Corresponding author: Maria Legut-Pintal, e-mail: maria.legut-pintal@uwr.edu.pl  

 

1. INTRODUCTION 

Imagine you are a surveyor, hired to plan a new town in the 
middle of nowhere using only a rope and a stick. Is it possible 
that the effects of your work will still be visible after hundreds of 
years? 

The issue of surveying and dividing the area inside the walls 
of a medieval town has been the subject of academic debate [1]-
[4]. Research on the reconstruction of the primary layout of 
medieval towns in Central Europe has a long tradition [5]-[7]. 
This debate has mainly been stimulated by historians, architects 
and urban planners; however, a few archaeologists have also 
influenced the discussion. Central Europe from the 12th to the 
16th century was a place of urban and rural revolution. As a result 
of colonisation, hundreds of towns and thousands of villages 
were newly established. The ‘regular’ town was a result of the 
implementation of German law on spatial dimensions [8]. Towns 
with market squares and an orthogonal grid of streets appeared 

at the beginning of the 13th Century in Silesia, a region in today's 
Poland. These Silesian towns had a regular gridded urban pattern, 
which made them very distinct in the cultural setting of Central 
Europe. Urban pattern analysis, using the modular method, has 
been conducted for numerous Silesian towns. These studies have 
resulted in a better understanding of the medieval cityscape; for 
example, the exact sizes of primary plots have been estimated. 
During this period, some improvements in the layout of towns 
were made. The main observed tendency was that, in the 13th 
century, the city grid was ‘optimised’. The layout of the town 
centre evolved from a wide market street to a rectangular or 
square market - the width of the plot decreased, the blocks of 
buildings were shortened, and the size and proportions of market 
squares became standardised [9]. The developed model of a 
Silesian regular town spread further, to be used in neighbouring 
lands. 

In addition, the findings of archaeological excavations have 
extended the knowledge of the planning of medieval towns [10], 
[11]. It is worth noting that, in many cases, archaeological 

ABSTRACT 
In this paper, we illustrate problems related to the application of two methods used for the reconstruction of the parcellation of medieval 
towns: modular analysis and the cosine quantogram. We propose the usage of the cosine quantogram, which is rarely used to study 
urban layout, for the identification of units of measurement in regular medieval towns. Based on two examples from the region of Silesia, 
Poland, Namysłów and Dzierżoniów, we discuss the usefulness of both methods in the reconstruction of the original measuring system 
and town layout. For the first time, we have applied these two methods to the study of the layout of a regular village. Despite the 
limitations, such as the level of precision in the construction of a medieval town’s layout at the time of its foundation, later changes to 
the division of plots and the known inaccuracy of modern maps, it seems that combining both methods allows the determination of the 
module used for the planning of the original urban layout. The application of the cosine quantogram can be useful for improving the 
results of modular analysis. Nevertheless, the results of both methods should be verified against archaeological results and historical 
research. 

mailto:maria.legut-pintal@uwr.edu.pl


 

ACTA IMEKO | www.imeko.org March 2021 | Volume 10 | Number 1 | 218 

discoveries have confirmed the theoretical consideration of 
metrological analysis. 

Metrological analyses related to urban and rural planning are 
based on the assumption that in the case of regular settlements 
founded on previously uninhabited areas (lat. in cruda radice), the 
arranged space was specified in the contract between the locator 
and the founder (territorial lord - king, duke, knight, bishop, etc.); 
the area, the number of plots and their sizes were measured in 
the field applying algorithms. Despite subsequent changes, in 
many cases, in the division of plots and their development, it is 
possible to reconstruct the original ‘ideal’ plan. Decoding the 
original intention of the planner is the starting point for analysing 
subsequent changes in urban or rural space and studying their 
causes. 

In this paper, we will discuss the potential of metrological 
methods and their limitations in the study of regular towns and 
villages based on selected examples from the Silesian region. We 
aim to address the following questions: were medieval towns 
planned with mathematical precision? And if so, is it possible 
after all these years, to reconstruct the idea of medieval urban 
planning based on modern cadastral plans and terrain surveys? Is 
it then possible to apply the methodology of urban analysis to 
regular villages? 

2. METHODS 

In this paper we combine two methods of analysis, the 
modular analysis of a town layout and the cosine quantogram 
algorithm, which are applied to a series of measurements of a 
town. These methods represent two different approaches. In the 
first, the base unit of measurement is considered as known, from 
written sources, for example, and is well established. In the 
second method, the base unit is unknown and determined using 
statistical methods. 

2.1. Modular analysis 

The method used for the spatial analysis of an historic town’s 
plan consists of applying information from historical, 
iconographic, archaeological and architectural sources to the 
modern geodetic plan to reconstruct the transformation of the 
original city morphology [12]. This approach also includes the 
use of metrological methods. 

Modular analysis or the meteorological–geometric analysis 
method assumes the existence of a module that can be found in 
the city structure (e.g. dimensions of the market square and 
blocks of buildings or the width of streets). Among the lengths 
of measurement of basic objects in a town’s plan, a pattern of 
‘round’ multiplications (50, 100, 150) of the base-unit (foot) 
length is sought to establish which measurement system was used 
by medieval surveyors for planning. Having established a base 
measurement system, the whole plan is fitted into a rope-length 
grid, recalculating the lengths according to the multiplication of 
the rope lengths. 

However, grid adjustments are heavily burdened with errors 
in approximations related to the irregularity of the city and the 
fact that the original starting point from which it was measured 
is unknown. It is uncertain whether rope-length grid was 
commonly used as a too. While in some cases the rope-length 
grid was certainly used to determine the city's area and mark out 
the market square, in other cases the determination of the main 
axes of the town might have be sufficient. 

To reconstruct the original width of urban plots, a simple 
method is used. It consists of summing up the length of facades 
of neighbouring plots converted to the basic foot unit. Its 

advantage is in enabling the partial elimination of border shifts 
between neighbours resulting, for instance, from the possibility 
of erecting a firewall on the neighbour’s plot or hereditary 
divisions. However, the main problem is often an arbitrary 
determination of the size of the basic unit. 

The modular analysis method has been widely criticised for 
its susceptibility to errors resulting from inaccurate 
measurements made on historical plans and a dependence on the 
arbitrarily selected basic length unit. Thanks to new methods of 
analysis, in particular the possibility of measuring using geodetic 
ground plans or the use of GIS software to apply information 
from various sources, the modular analysis method has returned 
to favour. Nevertheless, the allegation that the underlying units 
of measurement are arbitrary has still not been resolved. 

2.2. Cosine quantogram 

The cosine quantogram is a method for reconstructing the 
smallest basic unit used in the design and construction process. 
The cosine quantogram algorithm was developed by D. G. 
Kendall to detect a quantum of unknown size from a set of data 
[13]. A statistical model of a cosine quantogram has successfully 
been implemented for the analysis of architectural sites of 
Mediterranean culture, studies on the layout of early medieval 
Anglo-Saxon settlements [14] and even in the meteorological 
analysis of architectural units in the Incan architecture of Machu 
Picchu [15]. Known examples of the method's use suggest that it 
could also be applied to the analyses of medieval regular cities. 

In the case of medieval town planning, a data set for 
metrological analysis is composed of parcel dimensions. Each 
parcel dimension can be described as an integer M, multiplied by 

the basic unit q plus an error ɛ (epsilon); the error might be the 
result of inaccuracy in the layout of the medieval city as well as 
modern methods of measurement: 

𝑋𝑖 = 𝑀𝑖𝑞 + ɛ𝑖  . (1) 

In the equation, ɛ, which is significantly smaller than q, is 
analysed and then the formula is applied to calculate an amount 
that clusters around q (2). The value of q, which maximises the 
formula within a given range, is the one with the highest 
probability of being a quantum:  

𝑓(𝑞) = √
2

𝑁
∙ ∑ cos (

2 π ɛ𝑖
𝑞

)

𝑛

𝑖=1

 , (2) 

where N is the sample size and the set of building dimensions. 

The term √2 𝑁⁄  adds the dependence of the cosine quantogram 
result to the sample size. The main problem of the application of 
the cosine quantogram to urban studies is the small size of the 
sample. We can usually obtain only a dozen, sometimes a few 
dozen, measurements. To ensure that the estimated quantum is 
neither evaluated by chance nor dominated by outlier 
measurements, we have applied the Monte Carlo bootstrap 
method, used to construct confidence intervals, to estimate the 
most likely quantum value range. Assuming a 5% significance 
level, if the quantum estimation for the original data falls within 
the confidence interval, the risk that the quantum is the product 
of chance can be interpreted as very low. 

3. CASE STUDIES 

For an evaluation of the described methods, we selected two 
regular towns from Silesia, Namysłów and Dzierżoniów, 



 

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founded in the advanced phase of colonisation. Both towns were 
founded in cruda radice, so no previous settlements affected their 
shape. In both towns, architectural and archaeological excavation 
confirmed the existence of medieval masonry from buildings, 
whose presence can provide information on the position of 
medieval plot boundaries. 

To check whether the methods used for town studies can also 
be applied to village research, we chose for our analysis one of 
the most regular Silesian villages, Mnichowice. The main 
question was, if the boundaries between the plots had never been 
fixed by walls, but only by wooden fences, would it be possible 
to decipher the original division units? 

3.1. Namysłów 

Namysłów was founded, according to written sources, 
around 1250 [16]. The layout of the town is quite well preserved. 
Small changes to block layouts are connected with the existence 
of wooden construction and arcades around the market square 
as well as the introduction of some new developments after the 
damage caused by World War II. Nevertheless, the northern 
frontage of the market square was fully built from bricks in the 
14th – 15th century, which froze the medieval boundaries of plots. 
This allows the measurements determined using the cadastral 
plans of the town in the field and their accuracy to be verified by 
measuring the façades of the tenement houses. 

First, we verified the results of previous studies on Namysłów 
parcellation [15]. The quantum was estimated based on the series 
of archive data on plot dimensions that had previously been 
analysed using the neighbouring plot method. The cosine 
quantogram function provides clear results in relation to the 
estimated quantum from the archive data set, 0.25 m (Figure 1a), 
which does not match the results of the neighbouring plot 

method, proposed by [17], in which the module of 0.31 m was 
re-established in the urban reconstruction of Namysłów. This 
first step in the study of Namysłów reveals that the two different 
methods of measurement analysis of the same data achieve two 
different results. Therefore, in the next step of the module search 
in relation to regular town planning, we applied cosine 
quantogram analysis to the set of measurements collected for this 
study in the field from Namysłów’s main square. 

The estimated value of the quantum from 16 field 
measurements was 0.155 m (Figure 1b), which is half of the foot 
standard established from written sources - 0.313 m, the so-
called Renish foot. The maximum of the function shows the 
smallest unit present in the set of measurements; therefore, we 
should interpret the Renish foot standard as the module used in 
Namysłów’s medieval parcellation of tenant houses in the main 
square. 

The final results of both methods of measurement analysis 
showed the same results in the search for modules in 
Namysłów’s main square. However, the results of the first 
method could not be confirmed by the second method, the 
cosine quantogram. The difference in results from the same data 
was influenced by the accuracy to which the actual measurement 
values were rounded, which made it impossible to obtain the 
same results with different methods. Nevertheless, the 
application of the cosine quantogram proved that, in the case of 
Namysłów’s buildings, the division of the medieval plot is still 
preserved. 

In the second step, with an already confirmed unit of 
measurement, the 0.31 m Renish foot, we applied modular 
analysis to the town's plan (Figure 2). We built the modular grids 
based on three different units used in medieval Poland: 44.5 m, 
based on a 0.296 m foot (green lines); 43.2 m, based on a foot of 

 

Figure 1. a) Quantum estimation from the archive data set for Namysłów; b) Quantum estimation from the data set collected during a field survey in Namysłów. 



 

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0.288 m (Kulm/Flemish foot; blue lines); and 46.5 m, based on 
a foot of 0.31 m (Renish foot, red lines). We then compared the 
results. The third step was to fit a grid to the crucial elements of 
the medieval town. Our reference for fitting the grid included the 
location and orientation of the most important elements of the 
town, such as the main frontage of the blocks (the west frontage) 
and the very well-preserved north frontage of the main square. 
The grid borders should finish within the line of fortification and 
be adjusted to the main elements of the town. The differences 
between the matching of the individual grids were not large, and 
it was possible to say that most elements from the preserved 
layout of the city fit into a rope grid with a side of 46.5 m (foot 
of 0.31 m). Using the standard unit of the Renish foot, the market 
has dimensions of 3 × 1.5 ropes, and the area of the whole 
regularly planned town probably fit into a grid 6 × 9 ropes. 

The results from applying three different methods of town 
planning analysis demonstrate the uniformity of the urban space 
in which the same unit of measurement (the Renish foot) was 
used to divide housing and plan the grid of the whole medieval 
town. However, the internal divisions of the blocks seem to be 
independent of the rope grid, which marks the main elements 
and the city border. 

3.2. Dzierżoniów 

The founding of Dzierżoniów (ger. Reichenbach), took place 
around 1260 [17]. The organisation of the city centre is based on 
the model of a cross, with a centrally located market square and 
streets intersecting in the centre. The course of the walls 
surrounding the city is almost round.  

As with the previous case, we started the analysis of 
Dzierżoniów’s plan with a metrological analysis of block 
parcellation. In this case, there are no similar studies with which 
to compare the results. The data set for the parcellation 
measurement came from the cadastral plans of the eastern wing 
of the market square. However, archaeological surveys 
conducted on the eastern block document the significant 
transformation of the earlier buildings. For this reason, we used 
a reconstruction of the width of each parcel for analysis, which 
is still visible in the modern town plan. The reconstruction of the 
potential medieval plot division is based on the results of the 
modular analysis and archaeological survey as well as an analysis 
of the preserved boundaries. We verified the existence of a 
potential quantum in a reconstructed model of the town (without 
later divisions of plots). The maximum value of the quantum was 
0.272 m (Figure 3). The bootstrap simulation also confirmed the 

 

Figure 2. Namysłów: matching different grid sizes to the town plan. Green lines - module 44.5 m, blues lines - module 43.2 m, red lines - module 46.5 m, red 
dots - location of town gates. 

 

Figure 3. Quantum estimation for Dzierżoniów’s data. Data set was based on a reconstructed plot division of the eastern frontage.  



 

ACTA IMEKO | www.imeko.org March 2021 | Volume 10 | Number 1 | 221 

results of 0.272 m as the best candidate for the basic unit of 
measurement (Figure 4).  

However, the value differed from that expected by 0.016 m.  
This error does not seem large if we consider that the 

measurements were taken from a plan with an accuracy of about 
0.10 m on the plot borders. Even if the quantum value obtained 
as a result of the distorted measurements is not identical to that 
expected, the quantum can be considered an indication of the 
unit used at a specific time period. In this example, the value of 
the quantum of 0.272 m is closer to the Polish foot (0.288 m) 
than the Renish (0.313 m). We presume that more precise 
measurements made in the field can bring the quantum value 
closer to the original unit of measurement. 

In the second step in the study of medieval town planning 
based on modular analysis and calculating the width of 
neighbouring plots, we tried fitting the rope-length grids into the 
town plan, in the same way as with Namysłów (Figure 5). 

The most regular part of the town was the market, with 
dimensions of around 2 × 3 ropes. Although the western and 
eastern fronts fit into the grid well, the southern and northern 
frontages did not. Seemingly regular streets appeared to diverge 
after the imposition of the grid, which is to a certain extent the 
result of uneven terrain and the town's location on a hill. It seems 
that the area of the medieval town fit into a square of 10 × 10 
ropes. The most probable rope length used was that of 43.2 m 
(blue lines), which corresponds to a foot of 0.288 m.  

3.3. Mnichowice 

Mnichowice is a small village in the district of Bralin, in 
Kępno County, Greater Poland Province. This area historically 
belonged to Silesia. The first mention of the village dates to 1220, 
at which time it was the property of the Augustinian monastery 
in Wrocław. The reorganisation of village according to German-
law is confirmed in a document from Duke Henry IV dated 25 
February 1276, and it is probably after this date that the village 
was transformed into a regular Angerdorf shape. The Angerdorf-
type villages, with oblong village greens and two rectangular 
blocks of farmsteads on either side, are typical for German-law 
villages in the lowlands, especially in Saxony, Silesia, Bohemia 
and Pomerania [18]. 

The ground plan of Mnichowice’s intravilan (built-up area) is 
very regular, almost rectangular, and its border has been 
strengthened along the roads. The village green was affected by 
transformations in the modern period; it was partially built up, 
and plot owners have attached part of the square to their 
farmsteads. The original border of the village green has partly 
been preserved by the location of rural houses, which have 
generally been built in the same place since the Middle Ages. 

The ideal concept of Mnichowice village consisted of a 
rectangular village green with a width of one rope (approx. 43.2 
m) and two rows of farmsteads (a 2.5 rope width - approx. 106 

 

Figure 4. Dzierżoniów: the bootstrap confidence interval for the quantum is 
0.272 m.  

 

Figure 5. Dzierżoniów: matching different rope-length grids to the town plan. Green lines - module 44.5 m, blues lines - module 43.2 m, red lines - module 46.5 
m, blue dots - location of town gates. 



 

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m). The reconstructed area of the intravilan was 6 × 18 ropes, 
which is 0.75 of a lesser lan (ger. kleine Hube - an old unit of area 
used in lands of German colonisation). Although it is not proven 
that the blocks of buildings were to be divided into equal plots, 
it seems that in this case a certain module was used (Figure 6). 
The width of the plots ranged between 34 m and 37 m. In one 
case, the width of the plot was double and was 72.59 m.  

The maximum value of the quantum from the measurements 
of the plot widths was 36.29 m (Figure 7). 
On this basis, we can conclude that the division into plots was 
independent of the distribution of the general layout of the 
village, and a rope of 43.2 m was not used. Instead, the length of 
the whole intravilan was measured using a different module to 
plot division. For the plot division, the value of about 36 m was 
equal to the so-called ‘small’ rope; 125 feet was used to delineate 
the parcellation. Small ropes are not confirmed in written sources 
from Silesia, but they were in use in neighbouring Lesser Poland 
[19]. In order to measure the integer number of equal plots in the 
whole length of the village, it is necessary to find the least 
common multiple of both moduli. If we consider the use of two 
types of rope, 150 feet and 125 feet, the common multiple would 
be 750 feet. Mnichowice’s intravilan is about 2,690 feet, and this 
length is not an integer multiplication of this module. This caused 
irregularities in plot division, visible at both ends of the village. 
The usage of different modules of division may also be explained 
by the idea that the designation of internal roads shortened the 
road from the centre of the village to the fields. 

4. DISCUSSION 

Studies on the reconstruction of the layout of medieval towns 
face many limitations related to the subject of research and the 
methods used. 

The first group of limitations is caused by inaccuracies made 
at the time the settlement was founded, resulting from, for 
example, human error, terrain conditions and the imperfection 
of tools used during delineation, such as ropes and rods. Even in 
the most regular towns, only the central area, near the market 
square, is regular, and the further from the market, the more 
irregularities there are. This is caused by the gradual process of 
the building of towns, which took decades. 

The second group of limitations is the result of numerous 
transformations in the original layout. In many cases, Central 
European small towns were developed primarily with wooden 
buildings, which did not perpetuate the original boundaries, 
including the arcades that occupied space in the streets or the 
market square. Even the early introduction of masonry buildings 
did not preserve the original boundaries, as the law allowed the 
construction of frontier walls using a neighbour’s plot. 
Numerous distortions in the original arrangement of blocks of 
buildings have also been lost as a result of divisions and the 
linking of neighbouring plots. In addition, fortifications built 
even a hundred years after the town's founding usually enclosed 
the town within an oval border, cutting off the rope-length grid 
and intersecting adjacent plots. 

The third group of limitations is connected with inaccuracies 
in the modern plans used for analysis. The accuracy of large-scale 
maps is about 0.10 m. This value is rather large when we think 
of determining units of length of 0.27–0.35 m. Even taking 
accurate measurements in the field does not guarantee that the 
original boundaries of the plot will be captured because the 
boundaries of the façades of individual objects are not the same 
as the plot boundary. Only in a few examples of Silesian towns 
are the boundaries of plots confirmed by archaeological 
excavation (e.g. Wrocław). 

The fourth group of limitations is related to the specification 
of methods. One of the aims of the research is to establish 
relatively small differences between the basic measurements of 
each system of town planning. In the case of the cosine 
quantogram method, the main risks and disadvantages are related 
to having a sufficient quantity of measurements with credible 
values. 

It is only in the towns of Silesia and Lesser Poland that known 
systems of measurement exist in which basic values varied. 
Depending on the time period, location, role and foundation of 

 

Figure 6. Mnichowice: current plot division (blue line) and reconstruction of 
an ideal plan of the village core (grey). 

 

Figure 7. Quantum estimation from the data set of block parcellation in Mnichowice village. 



 

ACTA IMEKO | www.imeko.org March 2021 | Volume 10 | Number 1 | 223 

the town, we can expect differences in the module value. In some 
cases, we have written sources in which the standard 
measurements were mentioned, but in the vast majority of cases, 
only analysis can provide information about the measurement 
used to plan the layout of the town. 

5. CONCLUSION 

The results presented above indicate that the application of 
metrological methods in urban history studies has many 
limitations and requires a holistic and interdisciplinary approach. 
Despite these limitations, it seems that the use of the cosine 
quantogram method in combination with traditional modular 
analysis may provide some new opportunities. In some cases, as 
in Namysłów, confirmation of the basic unit may be possible. In 
others, it may indicate the most likely basic unit. The example of 
the village of Mnichowice confirms that the cosine quantogram 
may also be used to establish larger modules (rope), not only 
small units (foot). 

In further studies, we also aim to apply the methodology we 
have adopted to regular settlements founded in cruda radice in 
Western Europe, for example, in France and Italy. The 
appearance of stone houses there, built shortly after the founding 
process, should affect the stabilisation of the measured 
boundaries in the city structure; therefore, the results obtained in 
the measurement analysis should be more accurate. 

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http://dx.doi.org/10.21014/acta_imeko.v6i3.460