Most efficient path in transfering soil with bulldozer is selected by skilled operater. In cutting and banking the soil to make a flat paddy field, a soil transfering programm for most efficient path is desired. The efficiency of soil transfer could be evaluated in terms of:(1) minimum total path length;(2) minimum energy for transfer work; or (3) minimum operation time. One-dimensional model for the determination of minimum path length is illustrated in
Fig. 1. Table 1 shows a matrix of soil transfer, in which each figure indicates a distance between starting point and terminal point. In this matrix, if any pair of two rows is exchanged with each other, total of principal values remains unchanged. Therefore, there is no optimum value in a sense of minimum path length.
Problem of energy minimum can be treated as Hich-Kocks type of transportation. Energy of soil transfer
Z1, is supposed to be the sum of products of soil volume
xij and distance
Dij, that is
Z1=ε
xijDij. Minimum of
Z1 is obtained by assuming two conditions:(1) The weight of cutting soil equals to that of banking (coefficient of volume change ε);(2) Each transfered soil is limited to pass once across the borderline between cutting and banking areas.
Fig. 4 shows a paddy field which is divided into thirty coordiriate blocks
Si. Let
ci=
Si (
h-
h0),
bj=ε
xij,
ci=ε
xij, ε
ci=εβ
bj, where
h0 is the elevation of rearranged field,
ci is the total volume of soil transfered from the cutting area,
bj is the total volume transfered to the banking area.
The efficiency of earth works
Vij depens on operation distance
Dij of bulldozer as is shown in the previous paper (VIII)
Vij=
AQ0 (1-exp (
Dij/ph))
f 3600 log (1+
Dij/100)/(1+
a) From the inverse of
Vij, and
xij, the operation time
Z2 is obtained, that is Σ
xij/
Vij. Target function
Z1,
Z2 vary with the combination of feasible solution of {(
xij)}. Maximum and minimum values of function
Z are shown in
Table 5. Paths caluculated under the condition are illustrated in
Fig. 5, 6. Paths observed at the field are shown in
Fig. 7.
The results are summerized as follows:(a) From
Fig. 5, 6 and
Table 5, the combination of {(
xij)} in two cases of min
Z1 and min
Z2 are nearly equal to each other;(b) There are some differences between the operation time caluclated by computer and observed time. This is because the soil tranfer with bulldozer is performed by pushing with blade, not by carring, and besides is made by relay operation;(c) In view of time efficiency, the use of two types of machine in combination always fitted is more advantageous for the earth works in paddy field than that of single type like bulldozers. An example of combination may be backetozers suitable for soil tranfer and land graders suitable for levelling paddy field.
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