An example problem

Booher (FAO, 1974) devotes a chapter in his manual on surface irrigation to land levelling. Included is an example problem around which useful suggestions are made regarding the methods and equipment for levelling the field into a workable surface irrigated field. The problem that is developed utilizes a different approach to that suggested herein so it will be partially repeated for purposes of both illustration and comparison.

The first six columns and the first eight rows of Booher's example field have been extracted and are shown in Figures 64 and 65. The locations of the field boundaries have been changed relative to the grid system to illustrate the importance of weighing grid point elevations based on the areas they represent. In the following example the standard grid spacing is 20 m by 20

m and begins one-half spacing from the upper left corner of the field (represented by the grid point [i, A] in Figure 65). The standard grid area is 400 m₂, but one will note that grid points adjacent to the right field boundary represent 500 m2. One point, the lower right grid

represents an area of 375 m2.

Figure 64. Example problem field layout

The first step in the calculation of the revised field plane is to determine the grid point weighing factors using Eq. 118. Using the standard area per point as 400 m2, the weighing coefficients, q _ij, are shown in Figure 66. The row and column weights are the sum of the grid point weights and are shown to the left and at the bottom of Figure 66.

Using the column and row weights, Eqs. 119 and 120 are used to calculate the average elevation of the respective rows and columns. These data are included along the left and bottom of Figure 65.

The field centroid is calculated with Eqs. 121 to 124 using the distances from the origin and the row and column weights. For the X coordinate of the centroid, this calculation is:

and for the Y coordinate:

Note that the origin is 10 m to the right and 10 m above the stake at grid position [i, A]. The next step is to run a linear regression through the average row and column elevations using Equations 125 and 126. These procedures are fairly standard on hand-held calculators and microcomputers so the calculations will not be shown here. The slope of the field from right to left is 0.000373 (A) and that from top to bottom is -0.002247 (B). It can also be mentioned that standard regression techniques will also yield an intercept value representing the elevation with which the best fit line through the average elevations will intercept the X and Y axis running through the origin. These intercepts can be ignored.

The final calculations involving the revised field plane involve the calculation of the C value in Eq. 117 as outlined in the paragraph preceding Eq. 127. The average elevation at the centroid of the field is determined by summing the average row or column elevations. This value is also

shown in Figure 65 as 1.557 m. From Eq. 127, then:

C = 1.577 - 0.000373 * 72 - (-.002746 * 87.743) = 1.7911 m

The resulting equation of the field plane defined by the procedure so far is: E(X, Y) = .000373 * X - .002746 * Y + 1.7911

If this relationship is used to recompute the elevations at each grid point, the cuts and fills are identified as the positive (fills) or negative (cuts) differences between the computed elevations and the original topography. Figure 67 shows these results as the upper number near the grid points.

Figure 67. First determination of cuts and fills for the example problem

In order for the earthwork to balance in the field after levelling, the volume of cuts should exceed the fills by 10 to 30 percent. For the 6th row shown below, Eqs. 128 and 129 are evaluated as follows:

| +.11 +.03 -.01 -.01 -.02 0 |

vi | * * * * * * |

Volume of Cuts for Row vi = (-.01) * 400 + (-.01) * 400 + (-.02) * 400 = -16 m3 or since the sign is irrelevant, the cut volume along row 6 is 16 m3, and for the fills: Volume of Fills for Row vi = 400 * (.11 + .03 + .000) = 56 m3

Determining the cuts and fills of each row and then summing yields a total cut volume of 627 m3 and a total fill volume of 1007 m3. Dividing the cut volume by the fill volume gives a cut/fill ratio of about 0.62, which of course is not satisfactory.

Assuming the cut/fill ratio should be about 1.3, Equation 131 can be used to recompute the elevation of the field centroid, C. The change in centroid elevation is determined by summing the area of each cut station times the depth of cut. There are 17 cut points in which the grid area is 400 m2, 2 involving the 500 m2 left boundary points, and 4 cuts along the 300 m grid points along the lower field boundary. Thus the area summation in the denominator of

Equation 124 is 9000 m2. The remainder of Equation 124 is then:

This calculation assumes that none of the previous fill locations become cut locations. To test this assumption, 0.033 m is subtracted from each cut and fill depth in Figure 67 and the results are shown in Figure 68. It is noted that 2 fill locations have become cut points.

Recomputing the volume of cuts from Eq. 128 and the fills from Eq. 129 yields the following cut/fill ratio (Eq. 130):

This value is slightly more than the 1.3 assumed in adjusting the C value in Eq. 117 and reflects the problem of grid points changing from cuts to fills (or vice versa in other cases). If the error had been greater, another iteration would be suggested. Not in this case, however, and the final field plane is as shown in Figure 68 with the subscript cuts and fills.

If the field is intended for borders and basins, the procedure is the same except that the A and/or B slopes in Eq. 117 would be zero. Similarly, if the field is to be terraced, the procedure is applied separately to the grid points in each terrace area.

purposes. This is illustrated for the evaluation of Eq. 132 for the area between rows v and vi. The final cut/fill depths for rows vii and viii are shown below.

v | * * * * * * | | +.28 +.18 +.05 +.01 0 +.05 | | | | | vi | * * * * * * | | +.08 -.01 -.04 -.04 -.05 -.04 |

It is assumed that the depth of fill at the left boundary is .28 m at row v and .08 m at row vi. Similarly, the fill and cut at the right boundary are .05 m at row v and -.04 at row vi

respectively. Equation 132 is evaluated as follows:

Grid Points Computations Total

| * +.28 +.28 = 0 m3 | * +.08 +.08 * * +.28 +.18 = .02 m3 * * +.08 -.01 * * +.018 +.05 = .89 m3 * * -.01 -.04 * * +.05 +.01 = 4.57 m3 * * -.04 -.04 * * +.01 +.0 = 8.10 m3 * * -.04 -.05 * * 0 +.05 = 5.79 m3

* * -.05 -.04 * | +.05 +.05 = 4.44 m3 * | -.04 -.04 Total 23.81 m3

Repeating these calculations for each grid area yields a total cut volume of 946.02 m3 which is very close to the 959 m3 estimated with Eq. 128.

It is perhaps worthwhile mentioning at this point that microcomputer programmes have been written to perform land levelling computations as illustrated above. Some of these are commercially available, some can be acquired by tracking down the programmer.

6.4 Laser land levelling

The advent of the laser-controlled land levelling equipment has marked one of the most significant advances in surface irrigation technology. One such system is shown in Figure 69. It has four essential elements: (1) the laser emitter; (2) the laser sensor; (3) the electronic and hydraulic control system; and (4) the tractor and grading implement.

Figure 69. Two views of land levelling equipment using laser control systems

The laser emission device, like that pictured in Figure 70, involves a battery operated laser beam generator which rotates at relatively high speed on an axis normal to the field plane. This rotating beam thereby effectively creates a plane of laser light above the field which can be used as the levelling reference rather than the elevation survey at discrete grid points in conventional land levelling techniques. Various beam generators are equipped with self- adjustment mechanisms that allow the plane of the beam to be aligned in any longitudinal or latitudinal slope desired. This reference plane of laser light is an extremely advantageous factor in the levelling operation because it is not affected by the earth movement, does not require a field survey to establish the high and low spots, and does not require the operator to judge the magnitude of cuts and fills. The distance between the laser beam and the earth surface is defined such that deviations from this distance become the cuts and fills. With laser systems, there is little or no need for the exhaustive engineering calculations of the

conventional approach. The cost of levelling is usually contracted on the basis of money per equipment hour. The laser emitter is generally located on a tripod or other tower-like structure on or near the field and at an elevation such that the laser beam rotates above any

obstructions on the field as well as the levelling equipment itself. The beam is targeted and received by a light sensor mounted on a mast attached to the land grading implement. The sensor is actually a series of detectors situated vertically so that as the grading implement moves up or down, the light is detected above or below the centre detector. This information is transmitted to the control system which actuates the hydraulic system to raise or lower the implement until the light again strikes the centre detector. It is in this manner that the sensor on the mast is continually aligned with the plane on the laser beam and thereby references the moving equipment with the beam. It is important to note that the sensitivity of the laser sensor system is at least 10 to 50 times more precise than the visual judgement and manual

hydraulic control of an operator on the tractor. Consequently, the land levelling operation is correspondingly more accurate. The skill of the operator is substantially less critical to the levelling which allows farmers and other personnel access to the land grading equipment.

Figure 70. Close up view of laser beam emmitter

The electronic and hydraulic control systems generally have two operating modes. In the first, or observation mode, the mast itself moves up or down according to the undulations in the field as the operator drives the equipment over the field in a grid-like fashion. The monitor in the tractor yields elevation data from which the operator can determine average field

elevations and slopes. In other words, the system operates as a self-contained surveying system. In this mode, the blade of the grading implement is fixed in place and only the sensor mast moves. In the second mode, or planing mode, the mast position is fixed relative to the implement blade which is then raised or lowered in response to the land topography. The beam plane is located the appropriate distance above the field centroid and at the desired slopes. By adjusting the height of the mast sensor relative to this plane and the centroid, the cutting and filling is accomplished simply by driving the tractor over the field. However, in many cases, the depth of cuts will exceed the depth which can be cut with the power of the tractor and the operator must override the automatic controls in order to keep the equipment operating.

The fourth element of the levelling system is the tractor - grading implement combination. This equipment is generally standard agricultural tractors and land graders in which the hydraulic and control systems have been modified to operate under the supervision of the electronic controller supplied with the laser emitter and sensor devices. The tractor needs to be carefully selected so that it is not under-powered and its hydraulic system is strong enough to work with the laser-imposed frequency of movements and adjustments. The grading implement can be as simple as a land plane which scrapes the earth and moves only as much as can be pushed in front of the blade or a complex piece of equipment which loads and carries earth. The former is used primarily for small levelling jobs, smoothing and repeat grading. The latter is usually better for initial levelling where cuts are larger and in the preparation of level basins where the cuts are also larger than in bordered or furrowed fields.

As a final note on levelling in general and laser levelling is particular, it is probable that the importance of accurate field grading has been under estimated. The precision improves irrigation uniformity and efficiency and as a result the productivity of water and land. On large fields, the improved productivity has been shown to pay economic dividends that easily

exceed the cost of the levelling. However, the equipment is expensive and quite beyond all but the largest of farmers. In the developing countries, laser-guided equipment is being

demonstrated and tested. There remains the solution as to how such equipment can be made useful for the small farmer.

Produced by: Natural Resources Management and Environment Department

Title: Guidelines for designing and evaluatin surface irrigation systems...

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7. Future developments