LANDTECHNIK 71(5), 2016, 168–174
New regression model for predicting horizontal
forces of single tines using a dummy variable
and tine geometric parameters
Amer Khalid Ahmed Al-Neama, Thomas Herlitzius
This paper discusses three different equations of a regression model to predict the horizontal
force for single tines. Four standard single chisel plow tines were used (heavy duty, double
heart, double heart with wings and duck-foot). The first model is based on the effect of the op-
erational conditions speed and depth for each tine, the second model is employing a statistic
dummy variable, also representing each tine. The geometry of tines is base for the third model.
A stepwise selection with a multi-linear regression at significance level 5% was used to evaluate
these regression models. Experiments were carried out in a sandy loam soil at soil moisture
content of 10.3% ± 0.8 (based on dry matter) and soil bulk density of 1.38 g/cm³ ± 0.01 under
controlled soil bin conditions featuring varying speeds between 1.1 and 3.6 m/s and varying
depth from 5 to 20 cm. Field testing was done in order to validate the regression model obtained
from the soil bin. The results show that the horizontal force increases linearly with the speed-
depth interaction term and quadratically with the depth for each tine in all regression models.
The depth is effecting the force more significantly in comparison to speed (p < 0.05). Eventually
it can be stated that there is a good general accordance of observed and predicted values of the
horizontal force for all tines by using the dummy and the geometric regression models.
Keywords
Standard single tines, horizontal tine force, soil bin
For the purpose of reducing the energy required to process tillage, it is important to know typical
draft force (horizontal force) requirements and their range of variation in any given condition and
machine configuration. Many analytical models for predicting draft forces on tillage tools have been
developed. The analytical models are mainly focused on the soil failure zone ahead of tines, which
is described in Terzaghi’s passive earth pressure theory (TERZAGHI 1943) for a two-dimensional soil
failure for wide blade tools, which was further developed by HETTIARATCHI et. al. (1966) later. A three
dimensional soil failure model was initially proposed for a narrow blade by PAYNE (1956) and later
specified and improved by many other researches (HETTIARATCHI and REECE 1967, GODWIN and SPOOR
1977, MCKYES and ALI 1977, PERUMPRAL et al. 1983).
WHEELER and GODWIN (1996) have proven that a speed below was not significant on draft
force for single and multiple tines and speed becomes critical at , where g is the grav-
itational acceleration, w the tine width, and d the working depth. Many researches were finding a
linear or second order polynomial, parabolic or exponential relationship between the draft force and
the speed (ROWE and BARNES 1961, SIEMENS et al. 1965, GODWIN et al. 1984, MCKYES 1985, SWICK and PE-
RUMPRAL 1988, GUPTA et al. 1989). It can be seen that dynamic models for predicting draft force rely on
received 5 April 2016 | accepted 13 September 2016| published 21 October 2016
© 2016 by the authors. This is an open access article distributed under the terms and conditions of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/4.0).
DOI:10.15150/lt.2016.3138