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last section, because of more complicated phenomena
occurring in boundary zones, we apply this method
along parallel and non parallel trajectories only in the
main field body and expose simulation results.
2 CENTRIFUGAL SPREADING
DRAWBACKS
According to the soil and crops characteristics, agri-
cultural engineers state the amounts to be applied
within the farmland. These desired doses often takes
the form of prescribed dose map. This map depicts the
field which is virtually gridded and where each mesh
corresponds to the previously specified doses. Fertil-
ization aims to distribute nutrients so that the actual
spread doses get close to the prescribed ones. This
spreading regularity is above all performed by cen-
trifugal spreaders with double spinning discs which
eject fertilizers along each tramline in the field. The
functioning principles of these applicators are very
simple. Indeed, while the tractor progresses, fertiliz-
ers granulars contained in the hopper pour onto each
disc and are ejected by centrifugal effect.
Nowadays, with precision farming technologies, in
order to apply inputs according to the machine lo-
cation and a prescribed dose map, tractor-implement
combination is equipped with a GPS antenna, a radar
speed sensor and an actuator. The two first tools en-
able to know the tractor position and speed. Con-
cerning the actuator, it permits to control the fertilizer
mass flow rate. The actual amount of applied fertiliz-
ers currently called spread pattern has an irregular dis-
tribution which is often underlined by the transverse
distribution curve obtained by summing the amounts
along each travel direction. An example of spread pat-
tern and its related transverse distribution for only one
disc are depicted in Figure 1. Thus, this spatial het-
eregeousness lead the tractor driver to follow outward
and return paths in order to have an uniform deposit
from transverse distribution summation for each suc-
cessive tramlines within the arable land. This strategy
is detailed in Figure 2. As we can notice, fertiliza-
tion strategy is essentially based on the best overlap-
pings of transverse distribution according to the dif-
ferent tractor trajectories. This method is applied for
experiments undertaken to evaluate fertilizer applica-
tion accuracy or to investigate device settings accord-
ing to tests procedures such as (ISO, 1985). So, these
procedures enable to select optimal machine settings
in order to obtain a regular deposit. Some studies re-
lying on these tests are also led to assess performance
of applicators like in (Yule et al., 2005). Deposits are
considered to be uniform when the distance between
two overlapping lines are equal to the distance sep-
arating two successive tramlines. Moreover, if this
Figure 1: Spread pattern (spatial distribution) and trans-
verse distribution (red curve).
condition is checked, overlapping lines are symmetry
axes which make two consecutive paths coincide. In
this case, the distance between two successive trajec-
tories, called working width, is said optimal. Unfortu-
nately, when applying this strategy in the field, the ac-
tual phenomenon occurring during spreading process
is ignored. Indeed, the deposit on the ground results
in fact from the accumulation of several amounts dis-
tributed for different spreader GPS positions. There-
fore, when geometrical singularities occur, like non
parallel paths or start and end of spreading, fertiliza-
tion application errors appear as illustrated in Figure
3(c) where results are obtained by simulating spread
patterns overlappings with settings imposed by manu-
facturers rules. To limit these issues, a solution could
be to look for optimal paths for the machine as in (Dil-
lon et al., 2003).
However, this kind of solution cannot be applied
when tramlines are already fixed by other agricultural
operations like sowing. So, it is clear that some ef-
forts must be done to achieve better spread patterns
arrangement according to geometrical constraints met
Figure 2: Fertilization strategy based upon transverse dis-
tribution summation.
ON THE USE OF OPTIMIZATION METHODS FOR THE MINIMIZATION OF FERTILIZER APPLICATION ERROR
WITH CENTRIFUGAL SPREADERS
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