Precision Agriculture, 3, 225–236, 2002
© 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
Measurements of Mouldboard Plow Draft: I.
Spectrum Analysis and Filtering
H. N. HAYHOE, D. R. LAPEN, AND N. B. McLAUGHLIN Hayhoeh@em.agr.ca
Eastern Cereal and Oilseed Research Centre, Agriculture and Agri-Food Canada,
Ottawa, Ontario, Canada K1A 0C6
W. E. CURNOE
University of Guelph, Kemptville, Ontario, Canada
Abstract. Measurements of mouldboard plow draft can potentially provide a useful tool for continuously
mapping, as a surrogate variable, crop limiting soil properties such as soil strength/compaction. Numerous
researchers have shown that loading on tillage tools can be periodic. One source of higher frequency periodic
loading has been related to failure modes in the soil. Lower frequency periodic loading on tillage tools, assum-
ing tillage depth is relatively constant, more often reﬂects local spatial variability in soil physical properties
such as soil moisture, soil texture, organic matter, and/or soil strength/compaction. This study presents a spec-
trum and cross-spectrum analysis of mouldboard draft recorded during normal fall plowing operations along
adjacent transects. One objective of this study was to determine the dominant periodic components in order to
elucidate meaningful frequencies which might be better related to variation in soil physical properties. Spectral
densities were generally dominated by signals with a few cycles per 300-m transect. The cross-amplitude and
squared coherency between draft recorded on adjacent transects provided further indication of the frequencies
which characterized the signals because they provide an indication of correlation as a function of frequency.
Spatial dependence in the data was quantiﬁed using spatial autocorrelation and cross-correlation. An additional
objective was to use the spectral information to help design more physically meaningful ﬁlters for the raw
draft data. Taking the Fast Fourier Transform of the raw draft data and ﬁltering in the frequency domain using
an optimal ﬁlter informed via the spectrum and cross-spectrum analysis, provided a convenient method for
isolating a more physically meaningful signal.
Keywords: spectrum and cross-spectrum analysis, optimal ﬁlter, plow draft, instrumented tractor
Measurements of plow implement draft provide a useful tool for assessing energy require-
ments of different tillage and management systems (Perfect and McLaughlin, 1996;
Perfect et al., 1997) and for continuously mapping, as a surrogate information, crop
limiting soil properties such as soil strength/compaction (Lapen et al., 2001a; Hayhoe
et al., 2000). These measurements can also lead to a better understanding of soil-tool
interaction (Upadhyaya et al., 1987; Owen et al., 1990).
Numerous researchers have shown that loading on tillage tools is periodic. One source
of higher frequency periodic loading resulting from soil/tool interaction has been related
to failure modes in the soil. Stafford (1984) identiﬁed brittle and ﬂow failure types.
Godwin and Spoor (1977) referred to these failure types as crescent and lateral failure.
Brittle failure involves the development of successive shear planes which lead to distinct