ARTICLE IN PRESS. Draught Prediction of Agricultural Implements using Reference Tillage Tools in Sandy Clay Loam Soil

Biosystems Engineering (2006) 94 (2), 275 284 doi:10.1016/j.biosystemseng.2006.01.015 SW Soil and Water ARTICLE IN PRESS Draught Prediction of Agricultural Implements using Reference Tillage Tools in Sandy Clay Loam Soil R.K. Sahu; H. Raheman Agricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur, India; e-mail of corresponding author: rohit@agfe.iitkgp.ernet.in, hifjur@agfe.iitkgp.ernet.in (Received 4 March 2005; accepted in revised form 20 January 2006; published online 18 April 2006) An investigation was carried out to predict the draught requirements of commonly used tillage implements in any field condition from the knowledge of : (i) the draught requirements of reference tillage tools in a reference soil condition; and (ii) the scale factors related to soil properties and implement geometry. In the first step, the draught requirements of three different reference tillage tools: (1) a plough with a width of cut of 01 m; (2) a tine with a width of cut of 0075 m and (3) a disc with a diameter of 03 m were verified in the soil bin by operating in a reference soil condition (sandy clay loam soil with average cone penetration resistance of 472 kpa and bulk density of 1170720 kg/m 3 ) at three depths (005, 0075 and 01 m) and four speeds (12, 22, 32 and 42 km/h). In the second step, the draught requirements of six different scale-model implements: two mouldboard ploughs (015 and 025 m width); two cultivators (2 and 3 tine); and two disc gangs (034 and 037 m width) were measured in the same soil with five different soil conditions (average cone penetration resistance and the corresponding bulk density varied from 470 to 1420 kpa and 1170 to 1680 kg/m 3, respectively) at particular depth (0075 m) and speed of operation (32 km/h). The empirical equations for draught requirements of reference tillage tools and hence, scale-model implements were developed using orthogonal and multiple regression techniques. The developed empirical equations were verified in the laboratory as well as in the field conditions. A good general agreement between observed and predicted draught values was found with the average absolute variations of 70%, 62% and 75% in the laboratory as compared to 106%, 102% and 132% in the field for the mouldboard plough, cultivator and offset disc harrow respectively. This methodology produced sufficiently accurate results to enable the draught prediction of tillage implements in different soil conditions by testing only the reference tillage tool in the desired soil type at reference soil condition. r 2006 IAgrE. All rights reserved Published by Elsevier Ltd 1. Introduction The mouldboard plough, cultivator and disc harrow are generally used to prepare the soil bed for growing crops in the least possible time by accomplishing maximum field capacity of tillage implements. For this, larger equipment at low speeds or smaller equipment at higher speeds is followed. However, the combination that enables the task to be completed in the shortest time with minimum operating cost and energy requirement is usually selected (Onwualu & Watts, 1998). The availability of data on the draught requirements of tillage implements is an important factor while selecting tillage implements for a particular farm situation. Farm managers and consultants use draught and power requirement data of tillage implements in specific soil types to determine the size of tractor required and to calculate the cost and energy requirement of different tillage implements. The draught requirement of any tillage implement was found to be a function of soil properties, tool geometry, working depth, travel speed, and width of the implement (Glancey et al., 1996). Soil properties that contribute to tillage energy are moisture content, bulk density, soil 1537-5110/$32.00 275 r 2006 IAgrE. All rights reserved Published by Elsevier Ltd

276 R.K. SAHU; H. RAHEMAN Notation a, b, c multiple regression exponents C 0, C 1, C 2, C 3, orthogonal regression coefficients C 4, C 5 c 0, c 1, c 2, c 3, c 4, multiple regression coefficients c 5 D draught, N d depth of tillage operation, m d *, d ** orthogonal depth f 1, f 2, f 3 functions related to operating parameters, implement geometry and soil conditions g acceleration due to gravity, m/s 2 L set of characteristic lengths describing implement geometry, m R 2 coefficient of determination, decimal R c cone penetration resistance of soil, kpa V speed of implement, km/h V * and V ** orthogonal speed W tool or implement width, m a set of characteristic angles describing implement geometry, degrees r w bulk density of soil, kg/m 3 Subscripts i r p Superscript s any tillage implement reference tillage tool prototype/scale-model implement reference soil condition texture and soil strength. The relationship between the draught of plane tillage tools and speed, has been defined as linear, second-order polynomial, parabolic and exponential (Rowe & Barnes, 1961; Siemens et al., 1965; Luth & Wismer, 1971; Godwin & Spoor, 1977; Godwin et al., 1984; McKyes, 1985; Swick & Perumpral, 1988; Gupta et al., 1989). These differences in the findings are the result of inertia required to accelerate the soil, the effect of shear rate on shear strength and the effect of shear rate on soil metal friction, all of which vary with soil type and condition. In this context, the current analytical methods of draught prediction (Godwin & Spoor, 1977; Godwin et al., 1984; McKyes, 1985; Swick & Perumpral, 1988) are inadequate as they have not, as yet, been successfully developed for complex tillage tool shapes. These methods predict the draught requirement at incipient soil failure, based upon failure mechanisms modelled from experimental observations, and follow the classical mechanics theories, which rely upon Mohr Coulomb soil properties characterising a homogeneous and isotropic soil medium. These fundamental soil properties vary in the real-field environment, where soil structure, vegetation, spatial variations in soil density, soil water content and stone content greatly influence soil strength (Desbiolles et al., 1997). However, departing from the simple idealised soil tool systems operating in quasi-static conditions, Owen (1989) adopted an existing three dimensional soil wedge model of soil failure to predict the effect of tool speed on the draught requirement of a winged sub-soiler tine following the approach taken by Stafford (1979) in modelling the effect of velocity upon the draught of a simple tine. From the studies conducted in cohesive and frictional soils, Wheeler and Godwin (1996) confirmed that inertia effects on p draught ffiffiffiffiffiffiffiffiffiffi of tine are not significant below pspeeds ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of 5gW and are limited up to speeds of 5gðW þ 06dÞ where g is the acceleration due to gravity in m/s 2, W is tool width in m and d is the depth of tillage operation in m, while Glancey et al. (1996) found the speed effects to be less significant as compared to the effect of depth. Many regression equations for the draught prediction of various tillage implements have been developed using the data collected from the field experiments to facilitate machinery selection, implement matching with tractor and estimation of fuel consumption (Larson et al., 1968; Wang et al., 1972; Collins et al., 1978; Gee-Clough et al., 1978; Eradat-Oskoui & Witney, 1982; Eradat-Oskoui et al., 1982; Kepner et al., 1982; Kydd et al., 1984; Nicholoson & Bashford, 1984; Upadhyaya et al., 1984; Summer et al., 1986; Gebresenbet, 1989; Bashford et al., 1991; Harrigan & Rotz, 1995; Grisso et al., 1996; ASAE, 2000a ; Kheiralla et al., 2004). However, the applicability of such regression equations is limited to those soil and implement conditions for which these equations were developed. Therefore, new regression equations are required to be developed empirically for other soil and implement conditions. Alternative approaches to the use of regression equations for predicting the draught of tillage implement have also been developed using standard tillage tools (Glancey & Upadhyaya, 1995; Glancey et al., 1996; Desbiolles et al., 1997). In these approaches, the standard tillage tools were tested in the field conditions with an instrumented mobile power

DRAUGHT PREDICTION OFAGRICULTURAL IMPLEMENTS 277 source such as tractor to measure draught at the desired depth and speed of operation. However, field studies of draught measurement require enormous amounts of time, energy and cost for gathering agricultural machinery management data to select matching implements with tractors, to estimate fuel consumption, and to simulate and compare the performance of different farming systems. In this study, the draught of any scalemodel is predicted using a reference tillage tool in a reference soil condition under laboratory conditions and prototype tests are conducted in the field conditions to verify the approach. The objectives of this study were as follows: (1) to develop the regression equations for predicting the draught of reference tillage tools in a reference soil condition in the laboratory; (2) to determine the scale factors related to soil properties and implement geometry; and (3) to verify the applicability of the developed equations for predicting the draught of scale-model and prototype tillage implements in laboratory and field conditions, respectively. The study was limited to sandy clay loam with average soil moisture content of 91% dry basis (d.b.). This moisture content was chosen to coincide with the normal moisture level at which tillage operations are carried out in this soil. 2. Draught prediction approach for tillage implement The draught requirement of any passive tillage implement D i in N was found to be function of working depth d in m, travel speed V in km/h, width of the implement W i in m, tool geometry characterised by angle a i in degree and length L i in m, and soil properties such as bulk density r w in kg/m 3 and cone penetration resistance R c in kpa (Upadhyaya et al., 1984) and can be expressed as D i ¼ f ðd; V; W i ; L i ; a i ; r w ; R c Þ (1) Equation (1) can also be written as D i ¼ f 1 ðd; VÞf 2 ðw i ; L i ; a i Þf 3 ðr w ; R c Þ (2) where: f 1, f 2 and f 3 are functions related to operating parameters, implement geometry and soil conditions respectively. The contributions of a function towards the draught of an implement can be found by keeping the other two function variables constant. These are discussed in the following three cases. Case I: For a given soil condition and implement, Eqn (2) can be expressed as D i ¼ f 1 ðd; VÞ (3) According to Glancey and Upadhyaya (1995), the general relationship for the draught of a given implement in a specific soil type and condition can be given as D i ¼ c 0 þ c 1 d þ c 2 d 2 þ c 3 V þ c 4 V 2 þ c 5 dv (4) These regression coefficients (c 0, c 1, c 2, c 3, c 4 and c 5 ) are tool and soil specific. The existence of multicollinearity between the term for d and d 2 as well as V and V 2 in Eqn (4) caused difficulty in quantifying the coefficients. To overcome this problem, an orthogonal regression technique was adopted (Glancey & Upadhyaya, 1995) for correct determination of the coefficients. The transformed equation takes the form D i ¼ C 0 þ C 1 d n þ C 2 d nn þ C 3 V n þ C 4 V nn þ C 5 d n V n (5) where: d * and d ** and V * and V ** are orthogonal depth and speed, respectively; and C 0 C 5 are orthogonal regression coefficients. Quantifying the coefficients and hence, knowing the significant terms in the orthogonal regression equation [Eqn (5)] for an implement, the draught requirement of a reference tillage tool D s r in N in a reference soil condition can be expressed using Eqn (4) containing significant terms only and neglecting the non-significant terms. Case II: The draught requirements of different tillage implements in a given soil at same speed and depth can be expressed as D i ¼ f 2 ðw i ; L i ; a i Þ (6) In essence the standard tool is an analogue of the implement. Schafer et al. (1969) found that the draught of scale-models varied logarithmically with the scale factor for several implements such as triangular chisels, bulldozer blades, mouldboard ploughs, sweeps and cone penetrometer tips and concave discs. Although the interaction of implement geometry and soil properties is highly complex, the relationship between the draught of an implement and a standard tool was found to be consistently logarithmic (Glancey et al., 1996). Considering this, the ratio of draught requirements of the prototype/scale-model implement and the reference tillage tool in a given soil at same speed and depth can be expressed as D p ¼ W a p L b p a c p (7) D r W r L r a r where the subscripts p and r denote prototype and reference tillage tool, respectively; and a, b, c are multiple regression exponents.

278 R.K. SAHU; H. RAHEMAN Assuming the set of characteristic lengths and angles to be same for both reference tool and prototype/scalemodel implement, Eqn (7) can be reduced to Eqn (8). a (8) D p ¼ W p D r W r Case III: The draught of an implement in any soil condition at same speed and depth can be given by D i ¼ f 3 ðr w ; R c Þ (9) Similar to Eqn (7), the ratio of draught requirements of a reference tillage tool in any soil condition and reference soil condition at same speed and depth is given as D r ¼ r b w R c c (10) D s r r s w Multiplying Eqn (8) and Eqn (10) gives D p D s ¼ W a p r b w R c c r W r r s w R s (11) c Taking logarithms on both sides of Eqn (11) results in log D p D s r ¼ a log W p W r R s c þ b log r w r s w þ c log R c R s c (12) where, a, b and c are regression exponents that are specific to reference tillage tool implement combinations. Thus, the draught requirement of a prototype implement in any soil condition can be predicted by knowing the scale factors for implement and soil conditions, and the draught of reference tillage tool in the reference soil condition at any speed and depth. compacting the soil respectively to obtain the desired cone penetration resistance and a water sprayer for spraying water on the soil to maintain the desired average moisture content. The different speeds of operation were obtained by choosing suitable gears of a gear reduction unit coupled to the input shaft of the revolving drum, which was attached to soil processing trolley with stainless-steel rope. A control unit, placed outside the soil bin, controlled the direction of movement of the soil processing trolley. The testing tool/ implement was mounted on the frame of the implement trolley, where screw jack arrangements were provided to vary the depth of operation. The instrumentation for measuring the draught of reference tillage tools and scale-model implements in laboratory condition consisted of an extended octagonal ring transducer and a four-channel thermal write-out chart recorder with universal amplifier. The extended octagonal ring transducer was designed and fabricated for a maximum force of 3 kn following the design of Godwin et al. (1993) and O Dogherty (1996). The draught values were continuously recorded in the recorder after amplifying the signal coming from the transducer. 3. Experimental procedure All the experiments were conducted in the stationary soil bin to obtain the empirical regression coefficients in Eqns (4), (5) and (11). 3.1. Soil bin The soil bin comprised a stationary bin, a carriage system, implement and soil processing trolleys, power transmission system, control unit and instrumentation for draught measurement (Fig. 1). The bin was 150m long, 18 m wide and 06 m deep. Two rails, one on top of each side of the bin wall, were used for supporting the soil processing and the implement trolleys. The soil processing trolley comprised a frame, rotary tiller, levelling blade and roller for tilling, levelling and Fig. 1. Detail of experimental arrangement Table 1 Some physical properties of the experimental soil Soil order Alfisol Soil texture Sandy clay loam Sand 571% Silt 199% Clay 23% Particle density 2650 kg/m 3 Moisture content 103 % (d.b.) Cohesion 1176 kpa Adhesion 766 kpa Frictional angle 221

DRAUGHT PREDICTION OFAGRICULTURAL IMPLEMENTS 279 3.1.1. Soil description and soil bed preparation Experiments were conducted under laboratory conditions in a remoulded sandy clay loam soil for which the physical properties are given in Table 1. Before starting the experiments, the soil bed was prepared to achieve the required levels of cone penetration resistance and bulk density. Firstly, the tiller was used to pulverise the soil after spraying water to achieve the required moisture content. Then, the soil was levelled with the levelling blade and compacted by the roller to achieve the required cone penetration resistance and bulk density in layers. At the end of each soil preparation, a handoperated soil cone penetrometer was used for measuring the cone penetration resistance to a depth of 015 m at intervals of 0025 m at six locations in the soil bin following the procedures outlined in the ASAE Standards (ASAE, 2000b). The locations were 2 m apart along the centre of the bin and were selected to check the soil condition near the starting of the soil bed, at the middle and towards the far end. At each of these locations, two samples were taken across the bin (05 m apart). The locations were chosen so as not to interfere with actual tillage tests. To get soil uniformity, the soil bed preparation was repeated if the cone penetration Direction of travel 30 (a) 45 15 100 mm 20 205 mm 175 mm Direction of travel 33 mm 300 mm Direction of travel 75 mm (b) (c) Fig. 2. Reference tillage tools used in the experiments: (a) mouldboard plough, (b) cultivator time, (c) harrow disc

280 R.K. SAHU; H. RAHEMAN resistances and bulk densities were significantly different from each other. 3.2. Reference tillage tools and implements The mouldboard plough, tine and disc (Fig. 2) were selected as reference tillage tools to the prototype/scalemodel mouldboard plough, cultivator and disc harrow implements widely used in primary and secondary tillage operations, respectively. These reference tillage tools were similar to prototype implements but of smaller sizes. The soil manipulation by reference tillage tools and prototype implement were similar. These reference tillage tools were operated in a reference soil condition at different depths and speeds (Table 2) to determine the regression coefficients of Eqns (4) and (5). In addition to these reference tillage tools, six scale-model implements (two scale-model implements from each category of reference tillage tool) were selected for conducting experiments in the laboratory to determine the regression coefficients of the scale factor related to implement geometry and to validate the developed regression equation [Eqn (11)]. Three prototype implements (mouldboard plough, cultivator and offset disc harrow) were also selected to validate the developed regression equation [Eqn (11)] in field conditions. 3.3. Experiment layout 3.3.1. Laboratory experiments A 3 by 4 by 3 by 3 factorial experiment (three reference tillage tools, four forward speeds, three depths, and three replications) was used to determine the effect of speed and depth of operation on draught requirements of reference tillage tools in a reference soil condition. The levels of these variables are given in Table 2. A soft soil condition that is easy to prepare was selected as reference soil condition. The average moisture content during the tests was 91% d.b. with a maximum variation of 712% d.b. To find the regression coefficients of the scale factors related to soil properties and implement width, the various levels used are also shown in Table 2. To verify the developed regression equation, a separate set of experiments was conducted using six scale-model implements: two mouldboard ploughs (015 and 025 m width); two cultivators (2 and 3 tine); and two disc gangs (034 and 037 m width). The experiments were conducted in the same soil at average cone penetration resistances of 813 and 1230 kpa, average bulk densities of 1390 and 1610 kg/m 3, depths of 005 and 010 m and forward speeds of 22 and 32 km/h. The soil data were collected using core sample and hand-operated soil cone penetrometer before each tillage experiment. After fixing the desired depth and selecting a gear for particular speed, the implement trolley along with reference tillage tool/scale-model implement was pulled by the soil processing trolley in the soil bin keeping the pulling arm horizontal to the soil bed. With the help of the calibrated extended octagonal ring transducer, the data for draught of reference tillage tool/model implement were continuously acquired by the measuring system. Simultaneously, the time taken to cover a fixed distance of 10 m was recorded using a mechanical stopwatch to calculate the speed of operation. Table 2 Variable levels for all experiments Experiment 1 effect of speed and depth on draught of reference tillage tools Reference tillage mouldboard plough, cultivator tine and harrow disc tools Soil condition soft (R c of 472735 kpa, r w of 1170720 kg/m 3 )-reference soil Speed 12, 22, 32 and 42 km/h Depth 005, 0075 and 010 m Experiment 2 effect of scale factors of soil condition and implement geometry on draught Model implements two mouldboard ploughs (widths of cut of 015 and 025 m) two cultivators (2 and 3 tine, spacing between tines of 023 m) two disc gangs (widths of cut of 0337 and 0367 m, disc diameter of 030 and 040 m, three discs in each gang) Soil condition average R c of 470, 720, 980, 1250 and 1420 kpa and the corresponding to r w of 1170, 1340, 1470, 1600, and 1680 kg/m 3 Speed 32 km/h Depth 075 m R c, cone penetration resistance; r w, bulk density of soil.

DRAUGHT PREDICTION OFAGRICULTURAL IMPLEMENTS 281 3.3.2. Field experiments Field experiments were conducted for three prototype tillage implements (two furrow mouldboard plough, nine tine cultivator and a double gang of seven disc offset disc harrow) with 37 kw two-wheel drive tractor in hard and soft soil conditions at two/different speeds in the range of 18 to 59 km/h and two depths of operation (0135 and 0185 m for the mouldboard plough, 005 and 0095 m for the cultivator and 0055 and 0105 m for the offset disc harrow) with two replications. All field tests were conducted in sandy clay loam soil. Fallow areas of approximately 06 ha each was selected after the rainy season as (1) hard soil condition (R c of 1398 kpa, r w of 1600 kg/m 3 ) and (2) soft soil condition (R c of 699 kpa, r w of 1320 kg/m 3 ). The soft soil condition was achieved by ploughing followed by twice discing and twice cultivating. Before starting the experiments, bulk density, moisture content and cone penetration resistance data for the plot were collected and are summarised in Table 3. To validate the developed regression equation, the draught values were measured during the field tests of mouldboard plough, cultivator and offset disc harrow. The predicted draught for offset disc harrow was the sum of predicted draught values of the front and rear disc gangs. The soil condition for rear disc gang was taken as soft (average cone penetration resistance of 450 kpa and average bulk density of 1170 kg/m 3 ) and very soft (average cone penetration resistance of 200 kpa and average bulk density of 600 kg/m 3 ) to predict the draught of offset disc harrow on hard and soft soil conditions respectively. The measurement for draught was carried out for the set of implements using a developed force measuring system employing electrical strain gauges on a threepoint linkage system of the tractor. The strain gauges were mounted on each of the two lower links and proving ring attached to the top link. The strain gauges were then connected in the Wheatstone bridge to measure the draught. The implement operating depth, horizontal and vertical angles of the lower and top links were measured using potentiometer circuits. The experimental data from the force measuring system and Table 3 Mean and deviation of soil bulk density, moisture content and cone penetration resistance data in the field before experiments Soil condition Dry bulk density, kg/m 3 Dry moisture content, % (d.b.) Cone penetration resistance, kpa Hard 1600790 125708 1398765 Soft 1320740 105710 699752 potentiometers were recorded in a data logger (HP 34970 A, Hewlett Packard Company, USA). Simultaneously, the time taken to cover a fixed distance of 50 m was noted using a stopwatch to calculate the operating speed of the tractor and implement combination. 4. Results and discussion 4.1. Effect of speed and depth on draught Orthogonal regression analyses were performed using a computer-based software (SPSS) package on the average draught data of reference tillage tools to determine the speed depth response curves for each reference tillage tool in the reference soil condition and the results are summarised in Table 4. The regression coefficients determined (Table 4) from this analysis were the coefficients in Eqn (5). The high values for the coefficients of determination R 2 in Table 4 indicate that the variables depth, speed and the interaction of speed and depth in the regression can explain most of the variability in the experimental data. In Table 4, it is noticeable from the values of orthogonal regression coefficients that depth is the dominant factor influencing the draught of all reference tillage tools tested in the reference soil condition. Within the range of speeds and depths used, the depth, speed and the interaction of speed and depth were found to be significant for both tine and disc reference tillage tools; whereas the square of speed and depth were found to be non-significant. However, for the mouldboard plough all other terms Table 4 Regression coefficients (C 0 C 5 ) from different regression analyses on draught of each reference tillage tool in the reference soil condition; R 2, coefficient of determination Regression coefficient Plough Tine Disc Multiple c 0 00 00 00 c 1 831 726 573 c 2 00 00 00 c 3 00 00 00 c 4 00 00 00 c 5 588 241 208 R 2 0971 0981 0945 Orthogonal c 0 18013 10237 8482 c 1 6566 3804 2960 c 2 745 00 00 c 3 2190 889 795 c 4 00 00 00 c 5 791 363 190 R 2 0994 0988 0948

282 R.K. SAHU; H. RAHEMAN were found to be significant except the square of the speed. It is apparent from the orthogonal regression that V 2 term was not an important factor in explaining the draught even though mouldboard plough draught is believed to have a predominant V 2 effect (Kepner et al., 1982; ASAE, 2000a). This observation is due to negligible inertia effect on the draught due to lower speed of operation at which the laboratory experiments were conducted. Similar finding has been reported by Glancey and Upadhyaya (1995) while predicting the draught of tillage implements using standard chisel and lister as reference tillage tools when operated at depths between 0076 to 0305 m and speeds between 08 and 72 km/h. To predict the draught beyond the depth and speed ranges of reference tillage tools, multiple regression equation was developed with the real depth and speed variables considering the significant terms common to all the three reference tillage tools and the regression results are also presented in Table 4. Considering the result of multiple regression analysis, the draught requirement of a reference tillage tool in a reference soil condition can be expressed as D s r ¼ðc 1 þ c 5 VÞd (13) The high values for coefficients of determination R 2 in Table 4 indicate that the variables depth and the interaction of speed and depth in the regression explain most of the variability in the experimental data. Comparing the values of multiple regression coefficients of Eqn (13) from Table 4, it can be stated that the depth of operation contributes more than the interaction of speed and depth towards the draught for all reference tillage tools. It is also noticeable from the Eqn (13) that the contribution of speed of operation on draught is less as compared to the effect of depth. The regression coefficients of Eqn (13) are soil and tool specific. 4.2. Effect of scale factors on draught The multiple regression analysis was carried out to obtain the regression coefficients in Eqn (12) for each reference tillage tool implement combination and the results are presented in Table 5. It is apparent from Table 5 that the variables such as scale factors of implement width and soil cone penetration resistance in the regression do explain most of the variability in the experimental data while the scale factor of soil bulk density is not significant. This is due to relatively low operating depth and speed of operation maintained during the laboratory tests carried out for mouldboard plough, cultivator and disc harrow. The high values of R 2 indicate a good prediction of draught ratio D p =D s r for each reference tillage tool implement combination. Table 5 Multiple regression exponents of scale factors for each reference tillage tool implement combination based on the reference soil condition; R 2, coefficient of determination Reference tillage tool implement combination Multiple regression exponent a b c Plough mouldboard 098 00 198 0928 plough Tine cultivator 115 00 305 0993 Disc disc gang 094 00 166 0978 From the regression results, it is stated that the scale factor of implement width contributes more than the scale factor of soil condition towards the draught ratio. Therefore, implement width has more effect on the draught than that of soil condition at given depth and speed of operation. 4.3. Validation of the developed draught equation 4.3.1. Laboratory tests The observed and predicted values of draught for all the tillage implements tested were compared [Fig. 3(a)]. From this graph, it can be seen that the slopes of the best-fitted lines (095 for mouldboard plough, 101 for cultivator and 096 for disc harrow) were close to unity and hence the equation developed was verified. The regression equation predicted the draught of the mouldboard plough, cultivator and disc gang with an average absolute variation of 70%, 62% and 75%, respectively. These variations are considered acceptable considering the errors incurred while measuring the draught and variation in soil condition. 4.3.2. Field tests The observed and predicted values of draught for all the tillage implements were compared [Fig. 3(b)]. A good general agreement between observed and predicted values of draught was found with slope 094, 107 and 096 and the coefficient of determination 088, 097 and 091 for mouldboard plough, cultivator and offset disc harrow respectively. The average absolute variations between the observed and predicted values of draught were found to be 106%, 102% and 132% for the mouldboard plough, cultivator and offset disc harrow respectively in both hard and soft soil conditions. These variations are due to differences in implement design, implement adjustment and soil conditions. Since the variations were less than 15%, the implement draught equation developed for sandy clay loam soil is R 2

Predicted draught, N 1500 1250 1000 750 500 ARTICLE IN PRESS DRAUGHT PREDICTION OFAGRICULTURAL IMPLEMENTS 283 condition and the scale factors related to soil properties and implement width. Orthogonal and multiple regression techniques were used to develop the draught equations based on the laboratory data. The developed empirical equations were verified in the laboratory as well as in the field conditions. This methodology produced sufficiently accurate results to enable for predicting the draught requirement of prototype implements in different soil conditions. Only the reference tillage tool needs to be tested in the desired soil type at reference soil conditions. The specific conclusions drawn from the study are given as: (a) Predicted draught, N (b) 250 10000 8000 6000 4000 2000 acceptable for gathering agricultural machinery management data for selecting matching implements with tractors, estimating fuel consumption, simulating and comparing the performance of farming systems. However, more tests are required for wider acceptability of the concept for developing the draught equation for different tillage implements in other soil types. 5. Conclusions 0 0 250 500 750 1000 1250 1500 Observed draught, N 0 0 2000 4000 6000 8000 10000 Observed draught, N Fig. 3. Comparison of observed and predicted draught values for all implements tested in (a) the laboratory (b) the field: n, mouldboard plough; &, cultivator;, disc harrow The draught prediction equation for tillage implements was developed using the concept of the draught requirements of a reference tillage tool in a reference soil (1) An orthogonal regression technique was used successfully to quantify the effects of speed and depth as well as the higher-order effects of speed and depth on the draught of the three reference tillage tools and hence, prototype implements. (2) The draught values of all reference tillage tools and hence, scale-model/prototype implements were found to be primarily dependent on depth of operation. The effects of speed were found to be less within the test range of speed (12 42 km/h), when compared to the effects of depth. (3) The relationship between the draught ratio (draught requirements of model/prototype implement in any soil condition divided by the draught requirements of reference tillage tool in reference soil condition) and scale factors of implement width and soil condition was logarithmic for all the reference implement tillage tool combination. (4) A good general agreement between observed and predicted draught values was found with the average absolute variations of 70%, 62% and 75% in the laboratory as compared to 106%, 102% and 132% in the field for the mouldboard plough, cultivator and offset disc harrow respectively. (5) The concept of the reference tillage tool and the reference soil condition was used successfully to predict the draught requirements of various prototype implements in field conditions with scale factors related to soil properties and implement width. References ASAE Standard (2000a). ASAE D497.4. Agricultural Machinery Management Data. ASAE, St. Joseph, MI, USA ASAE Standard (2000b). ASAE S313.3. Soil Cone Penetrometer. ASAE St. Joseph, MI, USA Bashford L L; Byerly D V; Grisso R D (1991). Draft and energy requirements of agricultural implements in semi-arid regions of Morocco. Agricultural Mechanization in Asia, Africa and Latin America, 22(3), 79 82

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