The incurred ridger machinery cost per hectare was N7,147.54, N6,674.28, N6,609.31 and N6,652.93 for the widths predicted with the H- model for the listed prior capacities in the same order. The cost per hectare was N6,764.97 based on the L- model and N9,126.67 based on the Z- model for the 0.2673 ha/hr prior capacity and remained unchanged for the other capacities.
Figure 4.12: Selected minimum-cost ridger width (A) and annual ridger machinery cost per hectare (B) for varying chosen capacities
Generally the obtained results showed that the chosen prior tillage capacity affected the predicted tillage width for the H- model and that the choice of a proper prior capacity is needed to realize cost minimization with this model. The choice of a prior tillage capacity input was not needed for the L- and Z- models developed in the study. This shows that the developed models were more objective and less dependent on the user’s experience.
seen that a plough width (w) of 0.5481 m, 0.9740 m, 2.1009 m and 2.5997 m was derived from the minimum-cost plough capacity selected with the L- model for pool farm sizes (A) of 45, 145, 420 and 675 hectares respectively. Plough widths of 0.2251 m, 0.4242 m, 1.5880 m and 2.0579 m were obtained for the listed farm sizes in that order with the Z- model. The least-cost plough widths selected by the H- model are shown in Table 4.12 and plotted on Figure 4.13. They were 0.8186 m, 1.0201m, 1.5896 m and 1.7587 m for the same listed farm sizes in that order.
0 200 400 600 800
0 1 2
3 wL
Polynomial (wL) wZ
Polynomial (wZ) wH
Polynomial (wH)
Farm Size A (ha)
Minimum-cost Plough Width w (m)
Figure 4.13: Plough width predictions by the various models for different farm sizes
Table 4.12: The disc plough sizes and minimum cost predictions of the various models under the different pool farm sizes
Farm Area
A (ha)
Cum.
Transp t Distnc
e D (km)
Minimum-cost Plough Width
Width w (m) Width to Farm Size Ratio
wL wZ wH wRL wRZ wRH
45 32 0.5481 0.2251 0.8186 0.0126 0.0052 0.0188
82 56 0.7343 0.3013 0.9071 0.0090 0.0037 0.0111
145 122 0.9740 0.4242 1.0201 0.0067 0.0029 0.0071
200 148 1.2491 0.7022 1.2081 0.0062 0.0035 0.0060
295 208 1.5733 0.9826 1.3539 0.0053 0.0033 0.0046
420 268 2.1009 1.5880 1.5896 0.0050 0.0038 0.0038
453 358 2.1582 1.6367 1.6124 0.0048 0.0036 0.0036
588 434 2.4411 1.8797 1.6943 0.0041 0.0032 0.0029
620 506 2.4825 1.9204 1.7133 0.0040 0.0031 0.0028
675 596 2.5997 2.0579 1.7587 0.0039 0.0031 0.0026
Farm Area
A (ha)
Cum.
Transp t Distnc
e D (km)
Annual Plough Machinery Cost per Hectare
Machinery Alone Machinery and Transport
ACL ACZ ACH ACTL ACTZ ACTH
45 32 12485.44 16470.60 12378.38 14631.99 18572.06 15266.59 82 56 10002.47 12994.49 9884.03 11775.47 14712.39 12352.44 145 122 8480.44 10452.75 8471.28 10477.10 12364.81 11338.81 200 148 8344.88 9062.20 8385.45 10064.84 10710.40 10882.50 295 208 7621.26 7981.46 7710.79 9228.29 9516.68 10070.45 420 268 7611.25 7650.97 7708.13 9053.37 9039.01 9850.51 453 358 7489.00 7523.10 7585.63 9253.16 9219.65 10217.12 588 434 7028.27 7051.76 7154.24 8667.58 8624.65 9610.63 620 506 6974.23 6991.91 7095.78 8780.49 8724.89 9807.31 675 596 6892.56 6891.91 7010.44 8844.86 8768.33 9948.93 Selection of higher plough widths was favoured for bigger pool farm sizes by the 3 models. It can be seen that the least-cost plough width selected by the H- model was higher than the widths obtained from the developed models for farm sizes lower than 145 ha. Also the plough width obtained for the L- model was higher than those of the H- model for each of the given farm sizes. It must be noted that the choice of the prior capacity affected the least-cost width selected by the H- model. The 1.2738 m obtained with the 0.3101 prior capacity used will become 1.7923 if a 0.5168 ha/hr capacity is used as previously shown in Table 4.9. The dependence of the selected width on the user’s arbitrary capacity choice has been cited as a weakness in the H- model that this study is addressing.
The prediction of the plough width obtained for the 3 models with the farm size followed a 2nd order polynomial trend. The L- model trendline equation was as shown in Equation 4.2, and had an R2 value of 0.998.
wL=−3×10−6A2+0.0054A+0.2985 (4.2)
For the Z- model trendline was as shown in Equation 4.3, and had an R2 value of 0.9876.
wZ=−2×10−6A2+0.0044A+0.057 (4.3)
The H- model trendline equation was as shown in Equation 4.4, and had an R2 value of 0.996.
wH=−2×10−6A2+0.003A+0.6755 (4.4)
112
Prediction of the plough width from a 2nd order polynomial expression of the farm size was most precise (99.8 % accuracy) for the L- model least precise (98.76 % accuracy) with the Z-model. The prediction accuracy for the H- model was 99.6 %.
The ratio of the minimum-cost plough width to their respective farm sizes for the 3 models are shown in Table 4.12. The ratio varied from 0.0039 to 0.0126, 0.0031 to 0.0031 and 0.0026 to 0.0188 for the L- model, the Z- model and the H- model respectively. For the 3 models, the ratio was highest for the smallest farm size and reduced as the farm size increased. Table 4.13 shows the ANOVA table of the statistical analysis of width-to-farm Table 4.13: ANOVA table for statistical test on the developed models’ and Hunt-Wilson model’s plough widths-to-farm size ratio
Source of Variation SS df MS F P-value F crit
Between Groups 4.89E-05 2 2.45E-05
2.16162 7
0.13465 1
3.35413 1 Within Groups
0.00030
6 27 1.13E-05
Total
0.00035
4 29
size ratio for the 3 models at the 0.05 level of significance. The test F value of 2.1616 was lower than the F-critical of 3.3541, showing that the widths predicted by the developed models were not significantly different from the H- model widths for the farm sizes in question. Also the 0.1346 value obtained in the ANOVA test is greater than the 0.05 p-value for 95 % confidence level. This shows that the developed models predicted plough widths acceptably as does the H- model for the given farm sizes.
The annual plough machinery costs per hectare for varying farm sizes for the 3 models are also shown in Table 4.12, and plotted against varying farm sizes in Figure 4.14. The cost was N16,578.54, N10,670.67, N9,238.50 and N8,145.70 for the farm sizes (A) of 45 ha, 145 ha, 420 ha and 675 ha respectively for the L- model width. The annual plough machinery cost per hectare corresponding to the Z- model width was N18,151.45, N11,406.64, N8,880.93 and N7,883.90 for the same the listed farm sizes in that same order. For the H-model width it was N12,378.38, N8,471.28, N7,708.13 and N7,010.44 for the same the listed farm sizes in