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ARDUINO DIY approximate value can be found in special
Let’s Cook Arrosticini Using tables).
In mathematics, the error function (also
Open-Source Hardware called the Gauss error function) is a particular
function encountered in probability, statistics,
and partial derivative differential equations. It
By Maurizio Di Paolo Emilio is defined as

rrosticini — sheep or lamb skewers —
are a staple of the cuisine of Italy’s
Abruzzo region. A typical dish of the and is valid for each real number x. The values
Apastoral tradition, they are said to in the erfc table can be obtained by developing
have been invented early in the last century the Taylor series error function and integrat-
by hungry shepherds stuck in the fields during ing for the whole real axis.
the seasonal movement of their flocks to fresh The aim is to prepare the coals by keep-
pastures. The shepherds would butcher an old ing the temperature under control so that it
sheep, cut the meat into small pieces, slide remains constant in time. The distribution
the pieces onto sticks, and cook the skewers that we should obtain is of the type shown
over a flame. in Figure 1.
Cooking an arrosticino to perfection Thermal diffusivity (unit of measurement
requires careful control of the cooking tem- mm s) is a specific property of the material
2
perature and cooking time as well as even that characterizes the non-stationary heat
heat distribution. The traditional method is to conduction. This quantity describes how
grill the skewers on a fornacella charcoal grill. Figure 1: Variation of temperature with quickly a material reacts to a temperature
According to purists, electric cookers compro- time for different sensors. The tempera- change. Thermal diffusivity is a prerequisite
mise the traditional flavor of an arrosticino ture starts from an initial value and then in solving the Fourier equation for non-
(and the self-respect of the chef). reaches its maximum and remains within a stationary heat transfer.
Grilling arrosticini the traditional way, how- certain tolerance. 1 The model equation can be solved to deter-
ever, is a labor-intensive, exacting process. Is mine the time required for the meat to reach
it possible to achieve grilling perfection using while maintaining a constant cooking process. the desired temperature, T(z,t)
a motorized setup? Suppose you have a plate piled high with
The following schematic project proposes meat at the initial temperature T o . At the start
a way to automate the process with a sensor of cooking, the surface of the meat is placed
system and motor control to yield perfect in contact with the surface of the grill at
arrosticini. The simplicity of the feedback temperature T g . For this simple condition, the
system allows for implementing any solution. temperature of the meat for any time, t, and
The components used include temperature any depth, z, can be modeled by the formula The only tricky part of this equation is to
sensors, a display to view the temperature, find the values for erfc. Surely, we would be
and a motor control solution. dealing with values of <1. Table 1 shows some
possible values of the temperature difference.
INTRODUCTION The typical arrosticino consists of meat
The first concern when grilling meat is to where D is the thermal diffusivity (or heat that is cut to a thickness of roughly 1 cm
bring the interior to the desired temperature diffusion coefficient) of the meat and erfc is (depending on the type) and is inserted onto
the complementary error function (whose a skewer measuring about 25 cm long. The

Figure 2: Each arrosticino is positioned on the fornacella at a distance of 7 to 15 cm
(adjustable) from the coals. The basic setup will vary depending on the number of
Table 1: Values for erfc arrosticini to be cooked.

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