## 2 Materials and Methods  
### Sources of the Required Data for Modeling the Modified Horizontal Force via the ANN Method  
In this study, two sources were considered in order to acquire the necessary information for modeling, via the ANN method and the modified horizontal force. The main source was from actual tillage field experiments using a chisel plow. These tillage experiments were run in three soil textures (three sites). The soil in the first experimental field (site) had a silty clay loam with 52% sand, 18% silt, and 30% clay, and was situated in an agricultural soil. The soil in the second field (site) experiment had a clay texture of 44.4% clay, 15% sand, and 40.6% silt. Finally, the soil in the third field (site) experiment had a clay texture with 17.7% silt, 28.5% sand, and 53.7% clay. The analysis of each soil texture was performed according to the standard procedure, which is the generally the best used process in agricultural machinery investigation [20]. For each soil texture, undisturbed soil samples from five random spots, obtained through the topsoil layer at a soil depth of 30 cm, were hand-selected by means of a soil sampling apparatus. The soil samples were weighed via a digital balance, and the weight of each soil sample was recorded and put in polythene bags. The samples of the soil were dried in an electric oven, and was kept at 105 \({}^{\circ}\)C for 24 h. The dried samples of the soil were re-weighed, and the weight was again noted in order to calculate the levels of the initial soil moisture content based on a dry weight and initial soil bulk density. Two agricultural tractors were used in the tillage experiments for measuring the horizontal force (draft) of the chisel plow, as is described in [6; 43; 44; 45; 46; 47; 48]. In the first and second experimental sites, the chisel plow under study was mounted at the rear of Ford tractor (main tractor) model TW15 with a diesel engine of 110 kW at 2300 rpm with help of three-point hitch of the tractor. A hydraulic dynamometer (pull type) was attached to the front of Ford tractor. An auxiliary tractor Lamborghini tractor model 1106 with a diesel engine of 110 kW at 2500 rpm was used to pull the chisel plow mounted through dynamometer. The auxiliary tractor pulled the chisel plow mounted tractor in neutral gear with the implement in operating condition. The idle draft force was also recorded in the same field when chisel plow was in lifted position. The difference draft at operating and idle condition gave the draft required to pull the chisel plow. The tillage operation was repeated for all the investigated runs and draft data for each run were recorded. A Kubota M1 tractor (70 kW) and Belarus (67 kW) were used as main and auxiliary tractors, respectively, at the first experimental site. A chisel plow, with seven shanks arranged in two rows, weighed 460 kg (4.51 kN), had a total width of 175 cm, and was employed in field experiments. The typical tillage speeds were changed by choosing different gears in the tractor manual transmission, and the plowing depth was fixed by using the hand located on the tractor. The tillage depth controller and the tillage depth data were recorded in three replications. The tillage depths were recorded using a steel measuring tape and by using the undisturbed surface as a reference. A straight distance of 25 m was used as a practice distance prior to the beginning of the experimental runs to permit the tractor and the chisel plow to reach the desired tillage speed and depth. The tillage time was recorded for each run of 20 m. To obtain the tillage speed, the distance was separated by the time taken to complete the run. The tillage experiments for the continuous measurement of variables were conducted on a 100 m straight section. The horizontal force was determined under different levels of tillage speeds, dissimilar tillage depths, and different levels of initial soil moisture content; all of the levels of variables were under different tractor power settings (Table 1).