doi:10.1016/j.biosystemseng.2006.01.015Biosystems Engineering (2006) 94 (2), 275284 doi:10.1016/j.biosystemseng.2006.01.015SWSoil and WaterDraught Prediction of Agricultural Implements using Reference Tillage Tools inSandy Clay Loam SoilR.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 eld 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 rst step, the draught requirements of three different reference tillage tools: (1) a plough with a width of cut of 0 1 m; (2) a tine with a width of cut of 0 075 m and (3) a disc with a diameter of 0 3 m were veried in the soil bin by operating in a reference soil condition (sandy clay loam soil with average cone penetration resistance of472 kPa and bulk density of 1170720 kg/m3) at three depths (0 05, 0 075 and 0 1 m) and four speeds (1 2, 2 2,3 2 and 4 2 km/h). In the second step, the draught requirements of six different scale-model implements: two mouldboard ploughs (0 15 and 0 25 m width); two cultivators (2 and 3 tine); and two disc gangs (0 34 and0 37 m width) were measured in the same soil with ve different soil conditions (average cone penetration resistance and the corresponding bulk density varied from 470 to 1420 kPa and 1170 to 1680 kg/m3, respectively) at particular depth (0 075 m) and speed of operation (3 2 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 veried in the laboratory as well as in the eld conditions. A good general agreement between observed and predicted draught values was found with the average absolute variations of 7 0%, 6 2% and 7 5% in the laboratory as compared to 10 6%, 10 2% and 13 2% in the eld for the mouldboard plough, cultivator and offset disc harrow respectively. This methodology produced sufciently 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 reservedPublished by Elsevier Ltd1. IntroductionThe 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 eld 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 avail- ability 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 specic 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, soil1537-5110/$32.00 275 r 2006 IAgrE. All rights reservedPublished by Elsevier LtdR.K. SAHU; H. RAHEMANDRAUGHT PREDICTION OF AGRICULTURAL IMPLEMENTSNotationa, b, c multiple regression exponentsC0, C1, C2, C3, orthogonal regression coefcientsC4, C5c0, c1, c2, c3, c4, multiple regression coefcientsc5D draught, Nd depth of tillage operation, md*, d** orthogonal depthf1, f2, f3 functions related to operating para- meters, implement geometry and soil conditionsg acceleration due to gravity, m/s2L set of characteristic lengths describ- ing implement geometry, mR2 coefcient of determination, decimalRc cone penetration resistance of soil, kPa V speed of implement, km/hV* and V** orthogonal speedW tool or implement width, ma set of characteristic angles describing implement geometry, degreesrw bulk density of soil, kg/m3Subscriptsi any tillage implementr reference tillage toolp prototype/scale-model implementSuperscripts reference soil conditiontexture and soil strength. The relationship between the draught of plane tillage tools and speed, has been dened as linear, second-order polynomial, parabolic From the studies conducted in cohesive and frictional soils, Wheeler and Godwin (1996) conrmed that inertia effects on draught of tine are not signicant belowand exponential (Rowe & Barnes, 1961; Siemens et al., speeds of p5gW and are limited up to speeds of1965; Luth & Wismer, 1971; Godwin & Spoor, 1977; 5gW06d where g is the acceleration due top Godwin et al., 1984; McKyes, 1985; Swick & Perumpral,1988; Gupta et al., 1989). These differences in the ndings 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 soilmetal friction, all of which vary with soil type and condition. In this context, the current analytical methods of draught prediction (God- win & 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 MohrCoulomb soil properties characterising a homogeneous and isotropic soil medium. These funda- mental soil properties vary in the real-eld environment, where soil structure, vegetation, spatial variations in soil density, soil water content and stone content greatly inuence soil strength (Desbiolles et al., 1997). However, departing from the simple idealised soiltool 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 follow- ing the approach taken by Stafford (1979) in modelling the effect of velocity upon the draught of a simple tine. gravity in m/s2, 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 signicant 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 eld 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 applic- ability 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 eld conditions with an instrumented mobile powersource such as tractor to measure draught at the desired depth and speed of operation. However, eld studies of draught measurement require enormous amounts of time, energy and cost for gathering agricultural machin- ery 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 scale- model is predicted using a reference tillage tool in a reference soil condition under laboratory conditions and prototype tests are conducted in the eld 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; Case I: For a given soil condition and implement, Eqn(2) can be expressed asDi f 1 d ; V (3) According to Glancey and Upadhyaya (1995), thegeneral relationship for the draught of a given imple-ment in a specic soil type and condition can be given asDi c0 c1 d c2 d 2 c3 V c4 V 2 c5 dV (4) These regression coefcients (c0, c1, c2, c3, c4 and c5) aretool and soil specic. The existence of multicollinearity between the term for d and d2 as well as V and V2 in Eqn(4) caused difculty in quantifying the coefcients. To overcome this problem, an orthogonal regression technique was adopted (Glancey & Upadhyaya, 1995) for correct determination of the coefcients. The transformed equation takes the form(2) to determine the scale factors related to soil proper-ties and implement geometry; and nDi C0 C1 d nn C2 d C3 V n C4 V nn n C5 d V n(3) to verify the applicability of the developed equations for predicting the draught of scale-model and prototype tillage implements in laboratory and eld conditions, respectively.The study was limited to sandy clay loam with average soil moisture content of 9 1% 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 (5)where: d* and d** and V* and V** are orthogonal depth and speed, respectively; and C0C5 are orthogonal regression coefcients.rQuantifying the coefcients and hence, knowing the signicant terms in the orthogonal regression equation [Eqn (5)] for an implement, the draught requirement of a reference tillage tool Ds in N in a reference soil condition can be expressed using Eqn (4) containing signicant terms only and neglecting the non-signicant terms.Case II: The draught requirements of different tillage implements in a given soil at same speed and depth can be expressed asThe draught requirement of any passive tillage implement Di in N was found to be function of working depth d in m, travel speed V in km/h, width of the implement Wi in m, tool geometry characterised by angle ai in degree and length Li in m, and soil propertiessuch as bulk density rw in kg/m3 and cone penetrationresistance Rc in kPa (Upadhyaya et al., 1984) and can beexpressed asDi f d ; V ; W i ; Li ; ai ; rw ; Rc (1) Equation (1) can also be written asDi f 1 d ; V f 2 W i ; Li ; ai f 3 rw ; Rc (2)where: f1, f2 and f3 are functions related to operating Di f 2 W i ; Li ; ai (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). Con- sidering 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 asparameters, implement geometry and soil conditionsrespectively. Dp W p a Lp b ap c (7)The contributions of a function towards the draught Dr W r Lr arof an implement can be found by keeping the other two function variables constant. These are discussed in the following three cases. where the subscripts p and r denote prototype and reference tillage tool, respectively; and a, b, c are multiple regression exponents.Assuming the set of characteristic lengths and angles to be same for both reference tool and prototype/scale- model implement, Eqn (7) can be reduced to Eqn (8). compacting the soil respectively to obtain the desired cone penetration resistance and a water sprayer for spraying water on the soil to maintain the desiredDpDr W p aW r (8) 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 theCase III: The draught of an implement in any soilcondition at same speed and depth can be given byDi f 3 rw ; Rc (9) Similar to Eqn (7), the ratio of draught requirements ofa reference tillage tool in any soil condition andreference soil condition at same speed and depth is given as b Rc c 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 move- ment 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 ofreference tillage tools and scale-model implements inDr rw DrRs s s r w c (10) laboratory condition consisted of an extended octagonalsring transducer and a four-channel thermal write-outMultiplying Eqn (8) and Eqn (10) gives chart recorder with universal amplier. The extended octagonal ring transducer was designed and fabricatedwDp W p a r b Rc c (11) for a maximum force of 3 kN following the design ofDrRrW rs s s w cTaking logarithms on both sides of Eqn (11) results in Godwin et al. (1993) and ODogherty (1996). The draught values were continuously recorded in the recorder after amplifying the signal coming from the Dp logDsrr a log W pb W r r wlogc log RcsRw c transducer.(12)where, a, b and c are regression exponents that are specic to reference tillage toolimplement combina- tions.Thus, the draught requirement of a prototypeimplement 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.3. Experimental procedureAll the experiments were conducted in the stationary soil bin to obtain the empirical regression coefcients in Eqns (4), (5) and (11).3.1. Soil binThe 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 15 0m long, 1 8 m wide and 0 6 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, Fig. 1. Detail of experimental arrangementTable 1Some physical properties of the experimental soilSoil order AlsolSoil texture Sandy clay loamSand 57 1% Silt 19 9%Clay 23% Particle density 2650 kg/m3Moisture content 10 3 % (d.b.) Cohesion 11 76 kPaAdhesion 7 66 kPaFrictional angle 221levelling blade and roller for tilling, levelling and 3.1.1. Soil description and soil bed preparationExperiments were conducted under laboratory condi- tions 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 hand- operated soil cone penetrometer was used for measuring the cone penetration resistance to a depth of 0 15 m at intervals of 0 025 m at six locations in the soil bin following the procedures outlined in the ASAE Stan- dards (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 (0 5m 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 penetration175 mmDirection of travel(a)(b) (c)Fig. 2. Reference tillage tools used in the experiments: (a) mouldboard plough, (b) cultivator time, (c) harrow discresistances and bulk densities were signicantly different from each other.3.2. Reference tillage tools and implementsThe mouldboard plough, tine and disc (Fig. 2) were selected as reference tillage tools to the prototype/scale- model 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 coefcients 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 regres- sion coefcients 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 eld conditions.3.3. Experiment layout3.3.1. Laboratory experimentsA 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 require- ments 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 9 1% d.b. with a maximum variation of 71 2% d.b. To nd the regression coefcients 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 (0 15 and 0 25 m width); two cultivators (2 and 3 tine); and two disc gangs (0 34 and 0 37 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/m3, depths of 0 05 and 0 10 m and forward speeds of 2 2 and3 2 km/h.The soil data were collected using core sample and hand-operated soil cone penetrometer before each tillage experiment. After xing 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 xed distance of 10 m was recorded using a mechanical stopwatch to calculate the speed of operation.Table 2Variable levels for all experimentsExperiment 1effect of speed and depth on draught of reference tillage toolsReference tillage tools mouldboard plough, cultivator tine and harrow discSoil condition soft (Rc of 472735 kPa, rw of 1170720 kg/m3)-reference soilSpeed 1 2, 2 2, 3 2 and 4 2 km/hDepth 0 05, 0 075 and 0 10 mExperiment 2effect of scale factors of soil condition and implement geometry on draughtModel implements two mouldboard ploughs (widths of cut of 0 15 and 0 25 m)two cultivators (2 and 3 tine, spacing between tines of 0 23 m)two disc gangs (widths of cut of 0 337 and 0 367 m, disc diameter of 0 30 and 0 40 m, three discs in each gang)Soil condition average Rc of 470, 720, 980, 1250 and 1420 kPa and the corresponding to rw of 1170, 1340, 1470, 1600, and1680 kg/m3Speed 3 2 km/hDepth 0 75 mRc, cone penetration resistance; rw, bulk density of soil.3.3.2. Field experimentsField 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 1 8 to 5 9 km/h and two depths of operation (0 135 and 0 185 m for the mouldboard plough, 0 05 and 0 095 m for the cultivator and 0 055 and 0 105 m for the offset disc harrow) with two replications. All eld tests were conducted in sandy clay loam soil. Fallow areas of approximately 0 6 ha each was selected after the rainy season as (1) hard soil condition (Rc of 1398 kPa, rw of 1600 kg/m3) and (2)soft soil condition (Rc of 699 kPa, rw of 1320 kg/m3).The soft soil condition was achieved by ploughingfollowed 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 eld 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 of450 kPa and average bulk density of 1170 kg/m3) andvery soft (average cone penetration resistance of 200 kPa and average bulk density of 600 kg/m3) 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 three- point 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 experi- mental data from the force measuring system andTable 3Mean and deviation of soil bulk density, moisture content and potentiometers were recorded in a data logger (HP34970 A, Hewlett Packard Company, USA). Simulta- neously, the time taken to cover a xed distance of 50 m was noted using a stopwatch to calculate the operating speed of the tractor and implement combination.4. Results and discussion4.1. Effect of speed and depth on draughtOrthogonal regression analyses were performed using a computer-based software (SPSS) package on the average draught data of reference tillage tools to determine the speeddepth response curves for each reference tillage tool in the reference soil condition and the results are summarised in Table 4. The regression coefcients determined (Table 4) from this analysis were the coefcients in Eqn (5). The high values for the coefcients of determination R2 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 coefcients that depth is the dominant factor inuencing 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 ofspeed and depth were found to be signicant for both tine and disc reference tillage tools; whereas the square of speed and depth were found to be non-signicant. However, for the mouldboard plough all other termsTable 4Regression coefcients (C0C5) from different regression analyses on draught of each reference tillage tool in the reference soil condition; R2, coefcient of determinationRegression coefficient Plough Tine DiscMultiplec0 0 0 0 0 0 0 c1 831 726 573 c2 0 0 0 0 0 0 c3 0 0 0 0 0 0 c4 0 0 0 0 0 0 c5 588 241 208R2 0 971 0 981 0 945 OrthogonalSoil condition Dry bulk density, kg/m3 Dry moisture content, % (d.b.) Cone penetration resistance, kPa c0 180 13 102 37 84 82 c1 65 66 38 04 29 60 c2 7 45 0 0 0 0 c3 21 90 8 89 7 95 c4 0 0 0 0 0 0Hard 1600790 12 570 8 1398765Soft 1320740 10 571 0 699752 c5 7 91 3 63 1 90R2 0 994 0 988 0 948were found to be signicant except the square of the speed. It is apparent from the orthogonal regression that V2 term was not an important factor in explaining the Table 5Multiple regression exponents of scale factors for each reference tillage toolimplement combination based on the reference soil condition; R2, coefcient of determinationdraught even though mouldboard plough draught is believed to have a predominant V2 effect (Kepner et al.,1982; ASAE, 2000a). This observation is due to negligible inertia effect on the draught due to lower Reference tillage toolimplement combination Multiple regression R2exponenta b cspeed of operation at which the laboratory experiments were conducted. Similar nding has been reported byGlancey and Upadhyaya (1995) while predicting the Ploughmouldboard plough 0 98 0 0 1 98 0 928draught of tillage implements using standard chisel and Tinecultivator 1 15 0 0 3 05 0 993Discdisc gang 0 94 0 0 1 66 0 978lister as reference tillage tools when operated at depths between 0 076 to 0 305 m and speeds between 0 8 and7 2 km/h. To predict the draught beyond the depth andspeed ranges of reference tillage tools, multiple regres- sion equation was developed with the real depth and speed variables considering the signicant terms com- mon 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 asDsr c1 c5 V d (13) The high values for coefcients of determination R2 in Table 4 indicate that the variables depth and theinteraction of speed and depth in the regression explainmost of the variability in the experimental data. Comparing the values of multiple regression coefcients 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 coefcients of Eqn (13) are soil and tool specic.4.2. Effect of scale factors on draughtrThe multiple regression analysis was carried out to obtain the regression coefcients in Eqn (12) for each reference tillage toolimplement 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 signicant. 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 R2 indicate a good prediction of draught ratio Dp =Ds for each reference tillage toolimplement combination. 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 equation4.3.1. Laboratory testsThe 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-tted lines (0 95 for mouldboard plough, 1 01 for cultivator and 0 96 for disc harrow) were close to unity and hence the equation developed was veried. The regression equation predicted the draught of the mould- board plough, cultivator and disc gang with an average absolute variation of 7 0%, 6 2% and 7 5%, respec- tively. These variations are considered acceptable considering the errors incurred while measuring the draught and variation in soil condition.4.3.2. Field testsThe 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 0 94, 1 07 and0 96 and the coefcient of determination 0 88, 0 97 and0 91 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 10 6%, 10 2% and 13 2% 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 de- sign, implement adjustment and soil conditions. Since the variations were less than 15%, the implement draught equation developed for sandy clay loam soil is15001250Predicted draught, N1000750500 condition and the scale factors related to soil properties and implement width. Orthogonal and multiple regres- sion techniques were used to develop the draught equations based on the laboratory data. The developed empirical equations were veried in the laboratory as well as in the eld conditions. This methodology produced sufciently accurate results to enable for predicting the draught requirement of prototype imple- ments in different soil conditions. Only the reference tillage tool needs to be tested in the desired soil type at reference soil conditions. The specic conclusions drawn from the study are given as:(a)(b) 25000 250 500 750 1000 1250 1500Observed draught, N100008000Predicted draught, N60004000200000 2000 4000 6000 8000 10000Observed draught, N (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 (1 24 2 km/h), when compared to the effects of depth.(3) The relationship between the draught ratio (draughtrequirements 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 7 0%, 6 2% and 7 5% in the laboratory as compared to 10 6%, 10 2% and13 2% in the eld for the mouldboard plough,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 harrowacceptable for gathering agricultural machinery man- agement data for selecting matching implements with tractors, estimating fuel consumption, simulating and comparing the performance of farming systems. How- ever, more tests are required for wider acceptability of the concept for developing the draught equation for different tillage implements in other soil types.5. ConclusionsThe draught prediction equation for tillage imple- ments was developed using the concept of the draught requirements of a reference tillage tool in a reference soil 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 proto- type implements in eld conditions with scale factors related to soil properties and implement width.ReferencesASAE Standard (2000a). ASAE D497.4. Agricultural Machin- ery Management Data. ASAE, St. Joseph, MI, USAASAE Standard (2000b). ASAE S313.3. Soil Cone Penetrom-eter. ASAE St. Joseph, MI, USABashford L L; Byerly D V; Grisso R D (1991). Draft and energy requirements of agricultural implements in semi-arid regionsof Morocco. Agricultural Mechanization in Asia, Africa andLatin America, 22(3), 7982Collins N E; Kemble L J; Williams T H (1978). Energy requirements for tillage on coastal plains soil. 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