Journal of Archaeological Science 38 (2011) 1080e1089
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Journal of Archaeological Science
journal homepage: http://www.elsevier.com/locate/jas
A proxy of potters’ throwing skill: ceramic vessels considered in terms
of mechanical stress
Enora Gandon a, *, Rémy Casanova a, Patrick Sainton a, Thelma Coyle a, Valentine Roux b, Blandine Bril c,
Reinoud J. Bootsma a
a
b
c
Institut des Sciences du Mouvement E.J. Marey (UMR 6233), Université de la Méditerranée, 163 avenue de LuminyeCP 910, 13009 Marseille, France
CNRS, Maison de l’Archéologie et de l’Ethnologie, Préhistoire et Technologie (UMR 7055), 21 Allée de l’Université, 92023 Nanterre cedex, France
Ecole des Hautes Etudes en Sciences Sociales, 54 bd Raspail, 75006 Paris, France
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 6 April 2010
Received in revised form
7 December 2010
Accepted 10 December 2010
This study is aimed at evaluating potters’ skills according to the mechanical characteristics of the vessels
they produced. It focuses on wheel thrown vessels. In a first stage, considering that the difficulty of
throwing ceramic vessels is to a significant extent determined by the risk of collapse of the thrown
structure, we applied the method of finite element modelling to derive an index of mechanical stresses
operating within a vessel. Validated via compression tests, the so-called Von Mises stress index was
employed as a global index of mechanical difficulty. Because this index allows comparisons between
vessels of different form, mass, and clay properties, it provides a more powerful tool than existing
techno-morphological taxonomies. In a second stage, in order to relate the Von Mises stress index to
throwing difficulty, we analysed the geometrical and mechanical characteristics of vessels thrown by
eleven expert potters invited to reproduce four different model forms with two different masses of clay.
The results demonstrated that reproductions revealed subtle but systematic deviations from the model
forms that allowed a decrease in the mechanical difficulty. More difficult forms showed larger degrees of
mechanical optimisation. These results, in combination with a new analysis of data from Roux’s (1990)
study with potters of different skill levels, indicate that skill resides, at least to a certain extent, in the
capacity to marshal the operative mechanical constraints. In other words, the latter, measured by the Von
Mises index, provides a useful signature of a potter’s skills.
! 2010 Elsevier Ltd. All rights reserved.
Keywords:
Pottery
Ceramic
Skill
Constraint
Mechanical stress
Expertise
Craft
Technique
1. Introduction
Classifying ceramics by form is a classic exercise in archaeology,
mainly used to characterise chrono-cultural periods or to identify
functions (e.g., Rice, 1987; Orton et al., 1993). Morphological
typologies can, however, also be used for other purposes, such as
evaluating the skills that potters acquired (e.g., Balfet, 1984; Berg,
2007). In the present framework, a skill is defined as “a form of
behaviour acquired through learning” (Bril, 2002: 115), and its
development regarded as determined by the social context in
which it develops. Evaluating the skills of the potters who produced
archaeological assemblages paves the way to rich fields of
* Corresponding author. Tel.: þ33 0491 17 22 55; fax: þ33 0491 17 22 52.
E-mail addresses: [email protected] (E. Gandon), remy.casanova@
univmed.fr (R. Casanova), [email protected] (P. Sainton), thelma.coyle@
univmed.fr (T. Coyle), [email protected] (V. Roux), blandine.bril@
ehess.fr (B. Bril), [email protected] (R.J. Bootsma).
0305-4403/$ e see front matter ! 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jas.2010.12.003
interpretation, including the ways production and transmission
were organised (e.g., Roux and Corbetta, 1990; Vitelli, 1993; Crown,
2001, 2007; Budden, 2008) and the mechanisms underlying
changes in ceramics (e.g., Gelbert, 1997, 2003; Gosselain, 2000).
Analysing ceramic forms from a skills point of view entails
describing the vessels not as abstract and purely geometric shapes,
but, in line with Gibson’s (1979) arguments, concretely as objects. In
other words, the description must be linked to the shaping process
and to the physical properties of the object the potter produced.
According to Ingold (2001: 22), “it is the activity itself e of regular,
controlled movement e that generates the form, not the design
that precedes it. Making, in short, arises within the process of use,
rather than use disclosing what is, ideally if not materially, readymade”.
Evaluating potters’ skills from ceramic vessels presupposes e
mutatis mutandis e recognising that a vessel is subject to physical
constraints and, in line with Bernstein’s (1967) suggestion,
considering that the skill level is reflected in the extent to which
these physical constraints have been marshalled. This hypothesis
E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
was the starting point for a preliminary study by Roux (1990), who
proposed a classification of wheel thrown ceramic forms according
to how difficult they are to produce. Within the framework of this
techno-morphological taxonomy, forms are described in terms of
absolute and relative dimensions, and classed successively
according to the size, the morphological category (open or closed),
and the relevant proportions (Fig. 1).
Field studies with Indian and French potters, examining their
appreciation of the difficulty encountered in producing specific
vessels, have validated the taxonomy in two different cultures
(Roux, 1990). Describing the vessel’s form by means of its absolute
and relative dimensions, the taxonomy pragmatically incorporates
the mechanical constraints underlying the risk of collapse.
However, it does not provide a unified global measure of the latter,
not only because geometry is reduced to the major proportions only,
but also because mass is considered separately from geometry.
In this paper we explore the part played by mechanical
constraints in the difficulties encountered by expert potters in
throwing different types of vessels on a wheel. The first part of this
paper presents a mechanical analysis of ceramic vessels, using the
well-established method of finite element modelling. The aim of
this analysis is to offer an index that expresses the level of difficulty
of throwing a vessel. This index should summarise the combined
influences of relevant characteristics of the vessel, such as form,
mass, and clay properties. The analysis culminates in a global index
of mechanical stresses known as the Von Mises stress index. We
then present an experiment aimed at testing the relevance of this
index for assessing the difficulties involved in the throwing of
vessels of different shapes and sizes. Rather than asking potters to
classify vessels according to their difficulty, in the present framework we evaluated the vessels they actually threw in terms of
1081
reproducibility and deviation from prescribed model forms. For
simple forms we expected potters to reliably and consistently
reproduce the models proposed. For more difficult forms we
expected potters to adapt the vessels’ form so as to alleviate the
operative mechanical stress, perhaps accompanied by a larger
variability over repeated productions.
Results are discussed in terms of the operative relations
between geometry and mechanical stress. We conclude that the
Von Mises stress index provides a useful global index for the classification of ceramic vessels in terms of difficulty, paving the road
towards an assessment of potters’ skills.
2. Materials and methods
2.1. Mechanical modelling
The mathematical method of finite element modelling is
commonly used in mechanics to predict collapsing risk in material
structures. The method integrates three elements: the geometry of
the object, the material characteristics of the object’s matter, and
the (mechanical) behaviour law relating stresses operating in and
on the object to the object’s deformations. It is widely used in civil
and aeronautical engineering, for instance to evaluate whether
material structures, such as dams, bridges and boats can resist
irreversible deformations under varying loading conditions, and to
identify the weak points where bending or twisting may occur. In
the present framework, we examined vessels in their immediate
post-throwing state, when the clay was still wet. In the course of
throwing, mechanical stresses increase as the vessel evolves
towards its final form, with the walls becoming thinner and the clay
wetter. Thus, for the purposes of interpreting skill from existing
Fig. 1. The techno-morphological taxonomy proposed by Roux (1990) is based on the principle that vessels with more acute angles a, b, and g (see top panels) are more difficult to
produce. These angles are globally captured by proportions (see bottom panels) relating base diameter (B), maximal diameter (MD), aperture diameter (A), and height (H). For an
open vessel (left panel), the classification ratios used are A/H and A/B. For a closed vessel (right panel), the difficulty of execution is captured by MD/H, MD/B, and MD/A. The larger
these ratios, the greater the difficulty, due to the danger of the vessel collapsing. In addition to these ratios, the height of the maximum diameter (HMD) is considered as
a complementary principle of classification for closed vessels: the lower the maximum diameter height, the greater the difficulty. For each vessel, wall thickness was determined at
4 levels: middle of the base (T.1), bottom (T.2), middle (T.3) and top (T.4) of wall (see bottom panels).
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
vessels, this immediate post-throwing state is considered the most
pertinent. As at this stage neither the potter nor the (no longer
rotating) wheel exert time-varying forces on the structure, a static
model may be adopted. Because thrown vessels are theoretically
symmetrical, we used a symmetrical model allowing mechanical
stresses in the entire structure to be computed from its profile.
In a first step, we examined the vessel under the load of its own
weight. Because under the load of its own weight the noncollapsing vessel does not deform plastically (i.e., irreversibly), the
wet clay’s behaviour was modelled as an elastic material, with
classic parameters obtained from the literature for Poisson’s ratio
e the ratio of decrease in the thickness (lateral contraction) to its
increase in length (longitudinal extension) when stretched e and
Young’s modulus e the modulus of elasticity characterising stiffness. Poisson’s ratio (n) was set to a value of 0.3 (Yin, 2006) and
Young’s modulus (E) to a value of 3.0 MPa (Gagou et al., 2008). The
density (r) of the sandstone clay used was experimentally determined by weighing controlled volumes as 1.95 g/cm3. The digitised face of the vessel was imported into the modelling software
(CASTEM 2000"), together with the thickness of the wall,
measured at four different levels (see Fig. 1). From these latter
data, the vessel’s geometry was reconstructed as a surface in 3D
and summarised by a distribution of quadrilateral elements. On
each element the software computes local stresses with three
components: the radial traction-compression stress srr, the axial
traction-compression stress szz, and the shear stress srz. To
summarise the three components, we used a global norm traditionally used in clay studies (Lemaitre and Chaboche, 2004), the
Von Mises norm, computed as:
sVonMises
sffiffiffiffiffi"
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
¼
$ ðsrr $ szz Þ2 þðsrr Þ2 þðszz Þ2 þ 3$srz2
2
With this method, we obtained a Von Mises stress distribution
map of the vessel under the load of its own weight (Fig. 2). Because
the location and magnitude of the maximum Von Mises stress
value determines where and when the structure risks collapse, this
value provides a pertinent index of mechanical stresses in the
vessel. The error associated with the derivation of the Von Mises
values was less than 5%. In future work, this error could be further
decreased by replacing the estimation of wall thickness along the
surface through interpolation of discrete measurements with
complete data from digitised walls.
The model was validated by comparing observed deformation
under the influence of an external force to vessel deformation
predicted by the behaviour law 3 ¼ Ss, where 3 is the local deformation, S the operator of flexibility which integrates the material’s
parameters E and n (Lemaitre and Chaboche, 2004), and s the
internal stresses. An expert potter threw six vessels of each of three
different forms (cylinder, bowl and open-necked vase1). Using
a classic mechanical testing protocol, three specimens of each form
were compressed with a controlled force applied by means of
a penetrometer. To this end, a perforated plastic plate was centred
on top of the vessel, covering its aperture. The penetrometer was
positioned in the middle of the plate so as to apply an evenlydistributed pressure. The tests were filmed to capture each vessel’s
profile before and after deformation and to detect the exact
moment of onset of irreversible deformation. Pressures exerted at
this moment were 159.2 & 15.8 kPa for the cylinder, 117.5 & 8.7 kPa
for the bowl, and 75.2 & 4.5 kPa for the open-necked vase. The
1
The three forms used for the mechanical tests during the validation stage were
drawn from the personal repertoire of the expert. They do not correspond to the
forms tested in the experiment, which were chosen to be impersonal.
Fig. 2. Von Mises stress distribution map for an open-necked vase under the load of its
own weight. The legend presents a correspondence between colour coding and Von
Mises stress expressed in Pa. The vessel is modelled as a finite element structure, with
individual elements forming a chain of volumes. Constituent stresses are computed in
each element taking into account its place in the structure. Under the load of its own
weight, the collapse zone (zone with the highest Von Mises stress values) of this vessel
is situated in its base.
remaining three specimens of each form were vertically cut and
photographed. From the photographs, the mean (between-specimen) wall thickness at four different locations (see Fig. 1) was
calculated for each form and integrated into the model. For each
form, the threshold pressures were then incorporated into the
software as load acting on the top of the vessels and we calculated
the deformation resulting from its application (see Fig. 3, second
panel, for an example). For all three forms, the model reliably
reproduced the experimentally observed zones of deformation (see
Fig. 3, third panel, for an example).
Finally, the modelling results revealed that the threshold stress
level, defined as the local maximal Von Mises stress value in the
vessel under the pressure exerted at the moment of deformation,
was equivalent for the three different forms (18 kPa & 15%). Given
that both the location of deformation zones and the threshold local
stress levels rendered consistent results, the model was deemed
suitable for analysing experimental vessels. Note that while
compression via external forces was used to validate the model, in
the remainder of this paper we focused on the mechanical stress
(represented by the maximal Von Mises stress index) operating in
the vessel under the load of its own weight (as in Fig. 2).
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
Fig. 3. Deformation of a vessel under the influence of an external pressure exerted on the top (compression test). The photographs show an experimental vessel before and after
deformation occurring at the level of the neck. As can be seen (right panel) from the Von Mises stress distribution map of the (not yet deformed) vessel under the influence of the
external pressure, the maximal stress values (indicative of the future collapse zone) are located at the level of the neck. The panel between the two photographs shows the model
before (red) and after (blue) deformation, under the same conditions. As for the experimental vessel, the model deforms at the level of the neck. (For interpretation of the references
to colour in this figure legend, the reader is referred to the web version of this article.)
2.2. Experiment
Selected on the basis of responses to a questionnaire evaluating
their experience in wheel-throwing and use of sandstone clay,
eleven expert right-handed French potters, nine men and two
women, agreed to participate in the experiment. With a wheelthrowing experience of 15e40 years (mean & sd: 29 & 7.7 years),
the participants’ age varied from 36 to 59 years (51 & 6.5 years). The
experiment took place in a large room of a dedicated pottery centre
in the Bourgogne area. All throwing was performed on the same
electrical wheel (Brent) using sandstone clay.
Participants were asked to reproduce four different model forms
using two different quantities of clay, for a total of eight experimental conditions (Table 1). The forms (referred to as cylinder,
bowl, sphere and conical vase, respectively) were presented on (2D)
drawings without any indication of dimension. The quantity of clay
provided for each trial corresponded to a mass of 0.75 kg or 2.25 kg.
The choice of the model forms was based on Roux’s (1990)
taxonomy, which suggests that for open forms the bowl is more
difficult to produce than the cylinder, while for closed forms the
conical vase is more difficult to produce than the sphere. In contrast
to the other three forms, the conical vase proposed was not typical
of classic ceramic forms. In the framework of our objectives, it was
included as a particularly difficult form, due to the very small height
of maximal diameter. As detailed in Table 1, the combination of
model forms and masses gave rise to a range of (maximal) Von
Mises stress indices varying between 2.6 and 18.8 kPa.
Table 1
The eight experimental conditions were defined by combining four different forms
(cylinder, bowl, sphere and vase) with two clay masses (0.75 and 2.25 kg), giving rise
to maximal Von Mises stress indices varying from 2.6 to 18.8 kPa.
Form
Cylinder
Bowl
Sphere
Vase
2D drawing
For the purposes of the present experiment, the participants
were instructed to accurately reproduce the proportions of the
models, to throw vessels with the thinnest walls possible, and to
refrain from embellishment operations once the vessel was thrown.
Participants practiced the task the day before the experiment,
producing at least one vessel under each of the eight experimental
conditions. During the experiment proper, the order of the different
conditions was randomised within each block of eight trials so as to
avoid systematic learning effects. With an experimental session
comprising five blocks e potters thus producing five specimens in
each experimental condition e each participant produced a total of
40 vessels.
2.3. Methods
2.3.1. Data recording
Experimental sessions were videotaped using a Panasonic
NV-GS320 camcorder and the image of each vessel immediately
after throwing was extracted from the films for further analysis. In
order to determine the wall thickness, throwing vessels were
transversely cut the following day using a fine cord and photographed using a Canon A720 camera. From the post-throwing
images extracted from the video recordings we recovered for all
vessels the absolute dimensions (in mm) of base (B), height (H) and
aperture (A), complemented with maximal diameter (MD) and
height of maximal diameter (HMD) for the closed forms. As for the
mechanical tests, wall thickness was measured from the photographs of cut vessels at four levels (see Fig. 1). Values of thicknesses
are presented in Table 2.
Table 2
Between-participants average wall thicknesses of thrown vessels measured at 4
levels: middle of the base (T.1), bottom (T.2), middle (T.3) and top (T.4) of wall.
Form
Mass (kg)
T.1 (mm)
T.2 (mm)
T.3 (mm)
T.4 (mm)
Cylinder
0.75
2.25
0.75
2.25
0.75
2.25
0.75
2.25
7.3
9.7
9.7
12.3
6.4
9.1
6.6
8.9
10.5
14.7
18.2
27.3
15.4
21.8
14.2
20.5
6.5
8.9
8.5
11.7
6.5
8.0
9.0
11.1
5.2
6.4
6.4
7.8
6.8
8.9
6.9
8.8
Bowl
Sphere
Mass of clay (kg)
0.75
2.25
0.75
2.25
0.75
2.25
0.75
2.25
Von Mises (kPa)
2.6
4.1
6.9
12.4
6.5
9.9
12.5
18.8
Vase
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
2.3.2. Data analysis
The analysis was focused on three sets of dependent variables: (i)
absolute dimensions (H, B, and A for open forms, complemented
with MD, and HMD for closed forms; see Fig. 1), (ii) proportions (A/B
and A/H for open forms; MD/B, MD/H, and MD/A for closed forms;
see Fig. 1) and (iii) Von Mises indices obtained via modelling.
Our goal was to compare model and thrown vessels in terms of
each of these sets of dependent variables. In order to allow such
a comparison on the absolute dimensions, the model vessels e defined
as geometric forms (proportions) without intrinsic scale e were
homeomorphously transformed to match the mean between-participant height of the vessels thrown in each condition (see Table 3).
Combining these absolute model dimensions with local extrapolations of the measured wall thicknesses of the thrown vessels in each
condition (see Table 2) allowed the derivation of the models’ maximal
Von Mises stress indices reported in Table 1.
Accuracy of reproduction was assessed via comparisons
between model and thrown vessels according to the means of the
absolute dimensions, except, of course, for the vessel height H,
which served to scale the models’ absolute dimensions in the
different experimental conditions. Using the between-trial variabilities over the five specimens thrown by each participant in each
condition, reproducibility was assessed via the coefficients of variation (CV ¼ 100% * standard deviation/mean). From the measured
absolute dimensions we then calculated the thrown vessels’
proportions, identified in Roux’s taxonomy. Deviations from the
model forms were calculated as the percentage difference between
the proportions of the thrown vessels and model forms. Differences
in mechanical stress between the model and thrown vessels were
characterised using the maximal Von Mises stress indices.
The effects of Form (cylinder, bowl, sphere, and conical vase)
and Mass (0.75 and 2.25 kg of clay) were evaluated using analyses
of variance (ANOVA) with repeated measures on both factors.
Significant (a ¼ .05) main effects and interactions were further
explored using NewmaneKeuls post-hoc test procedures.
vessels and average thrown vessels. As can be seen from Fig. 4,
deviations from the model forms were largest for aperture in the
open forms and for maximal diameter in the closed forms.
The five reproductions of each experimental condition allowed
quantification of the (intra-individual) between-trial variability in
absolute dimensions, captured by the coefficient of variation (CV).
The mean CVs of the absolute dimensions are reported in Table 4.
Inspection of the CVs revealed that the geometrical deviations
from the model forms, depicted in Fig. 4, were produced in
a systematic fashion. Indeed, CVs of the absolute dimensions were
overall small, between 2 and 6% for the open forms (cylinder and
bowl) and between 2 and 11% for the closed forms (sphere and
vase). Repeated-measures ANOVAs on the CVs averaged over
different absolute dimensions demonstrated that the factor Mass
did not significantly influence the intra-individual variability (F(1,
10) ¼ 1.23, ns), while the factor Form did (F(3, 10) ¼ 21.83,
p < .001). Post-hoc analysis (p < .05) of the latter effect revealed
that the CV of the vase (7.4%) was larger than the CV of the sphere
(5.6%), which in turn was larger than the CVs of the bowl (4.6%)
and the cylinder (3.8%).
The absolute dimension with the least intra-individual variability was the base for the cylinder (3.3%), the aperture for the
bowl (3.4%), and the maximal diameter for the sphere and vase
(3.2% for each). Interestingly, these lowest-variability absolute
dimensions also showed the largest deviation from the model
forms (Fig. 4).
Overall, the analysis of the absolute dimensions revealed that
potters did not faithfully reproduce the model forms, deviating
from them in a (form-specific) systematic manner. Although the
more difficult forms e according to Roux’s (1990) taxonomy e
revealed a larger variability in absolute dimensions, in general
between-specimen variability was low. The level of standardisation
of the experimental vessels as measured by the CVs (5.5% on
average) was close to the 6% reported by Roux (2003).
3.2. Proportions
3. Results
3.1. Absolute dimensions
Table 3 summarises the absolute dimensions of the model and
thrown vessels. For the thrown vessels, both form and mass were
found to influence the absolute dimensions of H, B, A, MD, and HMD
(all main effects and interactions p < .001, except for the interaction
Form ' Mass for MD, ns). As was to be expected on the basis of
allometric scaling laws, the increase in size was not proportional to
the threefold increase in the amount of material available (as can be
observed in the percentage increase reported in Table 3).
In order to visualise the results summarised in Table 3, Fig. 4
graphically presents, for each form and mass, the scaled model
In order to better understand the observed systematic deviations from the model forms, we next analysed the proportions (i.e.,
relative dimensions) of the thrown vessels. To this end, we calculated the ratios A/H and A/B for the open forms (cylinder and bowl)
and the ratios MD/H, MD/B, and MD/A for the closed forms (sphere
and vase). Proportions of the model vessels and thrown vessels are
presented in Table 5.
According to the taxonomy proposed by Roux (1990), the larger
these ratios, the more difficult the task. Fig. 5 presents the ratios of
the thrown vessels as a function of the model ratios. We observe
that, except for the cylinder, all the other forms produced revealed
systematic negative deviations from the model ratios. Participants
consistently produced bowls, spheres and vases of smaller
Table 3
Absolute dimensions of model and thrown vessels. Only defined by their proportions, the model vessels were scaled to the average height of thrown vessels for comparison
purposes. H: Height, B: Base, A: Aperture, MD: Maximal Diameter, HMD: Height of Maximal Diameter. The increase in absolute dimensions between the 0.75 kg vessels and the
2.25 kg thrown vessels are expressed as percentage increase (% inc).
Model Vessels
Thrown Vessels
Form
Mass (kg)
H (mm)
B (mm)
A (mm)
Cylinder
0.75
2.25
0.75
2.25
0.75
2.25
0.75
2.25
177.2
286.5
92.3
138.1
120.7
186.9
99.9
150.8
101.9
164.6
73.7
110.5
84.4
130.4
91.8
138.7
98.5
159.2
272.5
408.8
83.9
129.7
64.5
97.4
Bowl
Sphere
Vase
MD (mm)
171.7
265.4
214.2
323.4
HMD (mm)
H (mm)
57.0
88.1
30.3
45.8
177.2
286.5
92.3
138.1
120.7
186.9
99.9
150.8
% inc
61.7
49.6
54.9
51.0
B (mm)
101.3
142.5
86.5
127.8
97.0
142.4
113.3
169.5
% inc
40.7
47.8
46.8
49.7
A (mm)
104.8
143.9
214.5
330.3
86.3
116.7
68.8
89.5
% inc
MD (mm)
% inc
HMD (mm)
% inc
37.2
54.0
35.3
30.2
158.8
234.0
164.9
242.6
47.4
47.1
59.5
91.0
37.4
52.4
52.8
40.4
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
0.3
0.25
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
-0.1
-0.05
0
0.05
0.1
0
-0.25
-0.2
-0.15
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0
-0.2
-0.1
-0.05
0
0.05
0.1
-0.15
-0.1
-0.05
0
0.05
0.15
0.1
0.2
0.15
0.25
0.2
Fig. 4. Graphical representation, with scale in m, of model (grey) and average thrown vessels (black) for each of the four forms and two clay masses.
proportions than the models presented, in line with the predictions
drawn from Roux’s taxonomy.
Average deviations of thrown vessels from model proportions
are presented in Table 6. A repeated-measures ANOVA on the
percentage deviation averaged over the different proportions
revealed that Mass influenced the deviations from the model
proportions to a certain extent (F(1, 10) ¼ 7.38, p < .05), with an
average deviation of $18.5% for the 0.75 kg masses and $16.8% for
the 2.25 kg masses. Form had a clear-cut effect (F(3, 30) ¼ 61.44,
p < .001), while the interaction Mass ' Form was not significant (F
(3, 30) ¼ 0.8, ns). Post-hoc analysis (p < .05) of the main effect of
Form indicated that deviations from the model ratios were larger
for the vase ($26.9%) and bowl ($25.2%) forms as compared to the
sphere ($10.7%). The latter in turn demonstrated larger deviations
from the model ratios than the cylinder (þ2.4%).
As can be seen from Fig. 5 and Table 6, for the bowl, the A/B ratio
decreased on average by 30.7% and the A/H one by 19.6%. These
effects were largely due to the decrease in A and, to a lesser degree,
the concomitant increase in B (see Fig. 4). Both closed forms also
revealed a decrease in ratios (Fig. 5). Mainly due to the decrease in
MD, MD/H and MD/A decreased respectively by 8.8% and 4.7% for
the sphere and 22.4% and 21.2% for the vase. The concomitant
Table 4
Mean coefficients of variation (CV) of the absolute dimensions of thrown vessels. H:
Height, B: Base, A: Aperture, MD: Maximal Diameter, HMD: Height of Maximal
Diameter.
Form
Mass (kg)
H (%)
B (%)
A (%)
MD (%)
HMD (%)
Cylinder
0.75
2.25
0.75
2.25
0.75
2.25
0.75
2.25
4.4
5.2
5.1
4.6
5.2
5.1
7.4
6.6
3.4
3.3
5.8
5.1
5.7
4.9
7.7
6.0
3.1
4.1
3.9
2.9
8.7
7.5
10.3
10.1
3.4
3.0
3.6
2.9
6.3
5.9
9.5
9.9
Bowl
Sphere
Vase
increase in B gave rise to a decrease in MD/B of 18.5% and 37.0% for
the sphere and vase, respectively.
3.3. Mechanical stresses
As can be seen from Table 1, the mechanical stress e indicated by
the maximal Von Mises index e of the model forms to be reproduced
varied as a function of both form and mass. Fig. 6 presents the
maximal Von Mises indices for the models and the thrown vessels.
As can be seen, compared to the models presented, levels of
mechanical stress were lower in all the thrown vessels, except for the
0.75 kg cylinder. For the three standard forms (cylinder, bowl, and
sphere), the mechanical stress in the thrown vessels (with both 0.75
and 2.25 kg of clay) covaried linearly (R2 ¼ 0.986) with the
mechanical difficulty indicated by the maximal Von Mises indices of
the models to be produced, according to VMthrown ¼ 0.53
VMmodel þ 1.74. This result is all the more interesting in light of the
fact that the maximal Von Mises index allows the inter-classification
of different forms and masses. These analyses in fact reveal two
concurrent phenomena. First e as indicated by the positive slope in
the VMthrown vs. VMmodel relation e more mechanically taxing
models systematically gave rise to thrown vessels being characterised by higher maximal Von Mises indices. Second, except for the
0.75 kg cylinder, all thrown vessels revealed a decrease in
mechanical stress relative to the models presented, as revealed by
the positive intercept and less-than-unity slope of the VMthrown vs.
VMmodel relation. Expert potters were thus capable of reproducing
vessels of varying mechanical difficulty, while adapting the vessel’s
form in order to diminish the operative mechanical stress.
For the (unfamiliar) conical vase shape, the vessels produced
revealed maximal Von Mises indices that were considerably lower
than expected on the basis of the linear relation described above.
While larger for the 2.25 kg than for the 0.75 kg clay masses, the
maximal Von Mises indices of the vases were, respectively, 68.2%
and 67.1%, smaller than prescribed by the models.
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
Table 5
Proportions of model vessels and average proportions of thrown vessels. For the open vessels: aperture/height (A/H) and aperture/base (A/B). For the closed vessels: maximal
diameter/height (MD/H), maximal diameter/base (MD/B) and maximal diameter/aperture (MD/A). Between-participants averages of the within-participant standard deviation
capturing the variability over repeated reproductions are presented in parentheses.
Model Vessels
Form
Mass (kg)
A/H
A/B
Cylinder
0.75
0.56
0.97
2.25
0.56
0.97
0.75
2.96
3.70
2.25
2.96
3.70
Bowl
Sphere
Vase
Thrown Vessels
MD/H
MD/B
MD/A
0.75
1.42
2.04
2.05
2.25
1.42
2.04
2.05
0.75
2.14
2.33
3.32
2.25
2.14
2.33
3.32
4. Discussion
Designed as a first step towards an assessment of potters’ skill as
derived from ceramic assemblages, in this study we examined the
geometrical and mechanical characteristics of vessels of different
difficulty thrown by expert potters. Difficulty was experimentally
varied by asking participants to reproduce (four) different model
forms using (two) different quantities of clay. Absolute size was not
prescribed: we solicited the largest possible form by asking
participants to throw vessels of the form prescribed with the
thinnest walls possible. Analysis of the absolute dimensions of the
vessels thrown revealed that for each form participants indeed
threw larger vessels when using the larger quantity of clay. They
did not however faithfully reproduce the model forms, as revealed
by differences in proportions (i.e., relative dimensions) between
thrown vessels and model forms. Except for the cylinder e the
simplest form e the deviations from the model forms invariably
showed a lowering of throwing difficulty as assessed by Roux’s
(1990) techno-morphological taxonomy. For the open forms,
A/H
A/B
0.60
(0.04)
0.51
(0.04)
2.34
(0.17)
2.42
(0.14)
1.03
(0.04)
1.01
(0.03)
2.50
(0.15)
2.62
(0.14)
MD/H
MD/B
MD/A
1.33
(0.09)
1.26
(0.06)
1.68
(0.15)
1.65
(0.13)
1.66
(0.10)
1.66
(0.09)
1.48
(0.10)
1.46
(0.08)
1.87
(0.17)
2.03
(0.17)
2.46
(0.23)
2.77
(0.27)
participants produced bowls that had smaller ratios of aperture
over base and height. For the closed forms, participants produced
spheres and vases that had smaller ratios of maximal diameter over
aperture, base and height. Corresponding to another way of
lowering throwing difficulty that can be derived from the
taxonomy, the height of the maximum diameter of the closed forms
also increased relative to the model forms, an effect especially
visible for the (conical) vase (see Fig. 4).
These deviations from the model forms were produced in
a reproducible, standardised manner, as revealed by the low level of
intra-individual between-specimen variation (5.5% on the average).
Hence, interpreted within the framework of Roux’s technomorphological taxonomy, the deviations observed suggest that
potters tend to reduce throwing difficulty for the more difficult
forms.
However, as Roux’s (1990) taxonomy of throwing difficulty is
based on proportions of archetypal forms, it cannot be used to
derive an absolute measure of throwing difficulty, nor to provide
a criterion for classifying forms of different size. To obtain a global
classification criterion, applicable to all vessel shapes and masses,
we hypothesised that throwing difficulty is, at least partially,
determined by mechanical constraints, notably those determining
the risk of collapse of a thrown vessel under the influence of its own
weight. Mechanical stress tests conducted in the first part of the
study on wheel thrown vessels allowed the Von Mises stress index,
derived via finite element modelling, to be validated in the present
context as a useful global descriptor of the operative mechanical
constraints.
Table 6
Average deviations (in percentages) of thrown vessels from model vessels’ proportions. For the open vessels: aperture/height (A/H) and aperture/base (A/B). For the
closed vessels: maximal diameter/height (MD/H), maximal diameter/base (MD/B)
and maximal diameter/aperture (MD/A).
Form
Mass (kg)
A/H (%)
A/B (%)
Cylinder
0.75
2.25
0.75
2.25
0.75
2.25
0.75
2.25
6.8
$8.6
$20.9
$18.4
7.1
4.4
$32.4
$29.1
Bowl
Sphere
Fig. 5. Average proportions (ratios) of thrown vessels as a function of the model ratios
for each condition for the two clay masses (0.75 kg in white and 2.25 kg in black) and
the four forms (C ¼ cylinder, B ¼ bowl, S ¼ sphere and V ¼ vase).
Vase
MD/H (%)
MD/B (%)
MD/A (%)
$6.6
$11.0
$21.7
$23.1
$18.6
$18.4
$36.7
$37.5
$8.6
$0.8
$25.8
$16.5
E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
1087
Fig. 6. Maximal Von Mises stress values for the models and thrown vessels. The eight experimental conditions are ordered (left-to-right) following increasing maximal Von Mises
values for the model vessels. The two masses are represented in grey (0.75 kg) and black (2.25 kg).
The results obtained with respect to the Von Mises stress criterion confirmed and substantially extended the analyses based on the
techno-morphological taxonomy, limited to comparing forms of the
same size. Integrating both form and mass, the Von Mises index
allowed inter-classification of vessels thrown under the eight
different experimental conditions. The mechanical analysis of the
models indicated that the larger cylinder was more difficult than the
smaller cylinder but less difficult than the small sphere. The small
sphere was approximately of the same difficulty as the small bowl.
The large sphere was more difficult than the small bowl but less
difficult than the large bowl, with the latter’s difficulty being
approximately equal to that of the small vase. The large vase was the
most difficult. For the cylinders, bowls, and spheres, potters threw
vessels that followed the same ordering. Thus, for these forms, the
difficulty of execution as captured by the level of mechanical stress
can be accurately predicted from the difficulty of the models that
potters were attempting to reproduce. An interesting result from
a complementary video-based observational analysis revealed that
the time spent in observing the model during throwing varied as
a linear function of the mechanical difficulty of the model (Observation time ¼ 0.28 VMmodel e 0.67; R2 ¼ 0.878).
While producing vessels of higher mechanical difficulty for
more taxing models, potters did not faithfully reproduce the model
forms. The mechanical analysis unambiguously revealed that the
observed systematic deviations from the model forms are to be
attributed to mechanical optimisation. Hence, notwithstanding the
organising character of the intended form, in the throwing process
potters adjusted the vessel’s form so as to alleviate the mechanical
stress within the vessel to a certain extent. This observation resonates well with Ingold’s (1993: 461) assertion that “it is precisely
because the practitioner’s engagement with the material is an
attentive engagement rather than a mere mechanical coupling e
because he watches, listens and feels as he works e that skilled
activity carries its own intrinsic intentionality, quite apart from any
designs or plans that it may be supposed to implement”.
The starting point of our research programme into the evaluation of potters’ skills according to the characteristics of ceramic
vessels is the hypothesis that the difficulty of throwing a vessel is to
a significant extent determined by the operative mechanical
constraints. This hypothesis was tested in the present contribution
by comparing the degree of mechanical stress e synthesised by
means of the Von Mises stress index e with the degree of task
difficulty derived from Roux’s techno-morphological taxonomy of
throwing difficulty. This taxonomy allows for several comparisons.
First, it states that, for a given form, larger-sized vessels are more
difficult to throw. For each tested form, clay masses of 2.25 kg
systematically gave rise to larger-sized vessels than clay masses of
0.75 kg. Because the larger-sized vessels were always characterised
by higher Von Mises stress indices, this first comparison corroborates our hypothesis. Second, the taxonomy states that open form
vessels with larger ratios of aperture over height and base are more
difficult to throw. Comparing the open forms experimentally tested
(i.e., cylinder and bowl), our results demonstrated that, relative to
the cylinder, the bowl revealed both larger A/H and A/B ratios and
higher Von Mises stress indices, again corroborating the hypothesis. Third, the taxonomy states that closed form vessels with larger
ratios of maximal diameter over height, base and aperture are more
difficult to throw. Comparing the closed forms experimentally
tested (i.e., sphere and vase), our results demonstrated that, relative
to the sphere, the conical vase revealed both larger MD/H, MD/B
and MD/A ratios and higher Von Mises stress indices, once again
corroborating the hypothesis. Integrating both mass and form into
a global measure, and thus going beyond the mere categorical
classifications allowed by Roux’s (1990) techno-morphological
taxonomy, the Von Mises stress indices allowed the different-sized
cylinders, bowls, spheres and vases to be arranged along the same
mechanical stress dimension (Fig. 6). Based on the foregoing
comparisons and the informal results on the duration of model
observation during the throwing process, we suggest that this
arrangement also corresponds to experienced task difficulty.
Participants in the present study were all expert potters. The
results discussed so far indicate that, even for these highly skilled
experts, more mechanically taxing forms were more difficult to
throw, as revealed on the one hand by the correspondence between
mechanical stress in the models proposed and in the vessels thrown,
and on the other hand by the systematic mechanical optimisation
produced, visible in the subtle yet methodical geometrical and
mechanical differences between models proposed and vessels
thrown. It is also noteworthy that even these expert potters were
found to encounter severe difficulties when asked to reproduce the
unfamiliar and mechanical strenuous conical vase form.
To further validate the merits of the Von Mises index for the
evaluation of potters’ skill, we analysed the productions of experts
and intermediate potters as they appear in a dataset reported by
Roux (1990). This dataset, including the relevant dimensions of
vessels thrown by a group of seven expert potters and by a group of
seven intermediate potters asked to reproduce four different forms
(with two specimens per condition), allowed calculation of the
degree of mechanical stress (i.e. Von Mises index) in the models
and vessels thrown by the two groups.
As can be seen from Fig. 7, while Roux’s expert potters revealed
the same type of mechanical optimisation reported in the present
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E. Gandon et al. / Journal of Archaeological Science 38 (2011) 1080e1089
Fig. 7. Maximal Von Mises stress values for models and vessels thrown by two groups of potters of different expertise levels (experts in grey and intermediates in black), calculated
on the basis of the data from Roux (1990). Intermediate and experts potters are adults, their skill levels differing with regard to the type of usual productions.
experiment, the vessels they produced nevertheless demonstrated
higher Von Mises indices than the vessels produced by the intermediate group. Thus, expertise is indeed visible in the degree to
which the mechanical constraints of the form to be produced are
marshalled.
5. Conclusion
In the present contribution, we examined the possibility to
characterise and classify ceramics in terms of throwing difficulty,
defined via a measure of the mechanical stresses operating within
the vessel under the influence of its own weight. In a first step, we
demonstrated the validity of the Von Mises stress index, which
incorporates the combined influences of form, mass, and clay
properties, for assessing the sturdiness of a given vessel. By having
potters attempt to reproduce different model forms with different
quantities of clay, in a second step we compared throwing difficulty
as measured by the Von Mises stress index to that derived from
Roux’s (1990) techno-morphological taxonomy, grounded in
geometrical proportions. These comparisons confirmed the
potential of the Von Mises stress index to provide a valuable scale
for evaluating throwing difficulty. Moreover, comparisons between
model and thrown vessels revealed that expert potters were
implicitly attuned to mechanical difficulty, with thrown vessels
systematically deviating from model forms so as to reduce the risk
of collapse. In a final step, we demonstrated that expert potters
were better able to marshal the mechanical constraints than less
experienced potters, demonstrating that this implicit attunement
develops as a result of learning the skill of throwing.
To conclude, we would like to insist on the importance of an
analysis of ceramics taking into account the skill point of view. As
a general rule, adoption of the wheel and its mastery has been
progressive (e.g., Knappett, 2005; Roux, 2010). By assessing the
skills developed in relation to the range of wheel-made ceramics, it
is now possible to interpret the evolution of this range in terms of
an evolution of the potters’ cultural perception of the properties of
the wheel. Cultural perception of technical tasks is transmitted in
the course of apprenticeship and defines ways of ‘doing’ of cultural
groups (e.g., Dobres, 2000). Change in perception will express
innovations, challenging the question of the dynamics underlying
evolution in both producers’ behaviour and consumers’ demand.
On this ground, variability within morphological types could be
questioned in terms of a potter’s ability to reproduce types
depending on its forming difficulties, which leads us to transmission studies and the genesis of new shapes in the course of
apprenticeship. In the end, characterising distribution of skills over
social groups will enable us to approach issues such as craft
specialisation and socio-economic structures of ancient groups, on
the one hand, and statuses of objects which may be unravelled
through the understanding of the skills required for their making,
on the other hand. Studying ceramic assemblages in terms of skills
corresponds first of all to an anthropological approach to artefacts.
In this regard, the analysis of the numerous technically heterogeneous ceramic assemblages, including wheel-made ceramics from
the 5th to the 1st millennium BC, should greatly benefit from it.
Because it allows interpretation of the time-frozen traces of
ancient dexterity, the Von Mises stress criterion would seem to
provide a useful window into the assessment of potters’ skills from
ceramic archaeological assemblages. Considering the possible
inferences on the socio-historic dimensions, this approach should
be complementary to the others. The present contribution suggests
that the assertion by Orton et al. (1993: 23) that “. every pot was
(i) made or used at a certain time; (ii) made at a certain place; (iii)
used for a certain purpose or purposes” may be usefully complemented with “(iv) made with a certain level of skill”.
Acknowledgements
We express our gratitude to the CNIFOP (Centre National de
Formation aux Métiers de la Céramique) for providing us with
access to facilities and material during the experiment.
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