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Land topography surveys and maps are used to measure and describe how the elevation of an area of land varies over distance. If the elevation of Pike's Peak Mountain in Colorado is 4,300 meters, the reader knows that as one moves from the sea coast to Pike's Peak, the elevation will increase from 0 to 4,300; the total distance traveled is not known because the horizontal distance between the sea and the mountain is not stated.
If a house lot is 80 meters long from the street to the back of the lot and the back is 4 meters below the street, then a more adequate description is given and the possibilities of having a "walk-out" basement become evident.
Knowing in great detail the topography of an area to be irrigated becomes very important:
· Water does not flow uphill or even on the level.
· Water flows rapidly down a steep slope so erosion or soil washing may result.
When water is to be moved from one point to another over a land area by gravity, there must be enough slope to cause flow over the surface but not enough slope to cause severe erosion.
The slope of the land along a line may be defined in two ways:
Sloppe = Vertical distance in meters lone / Horizontal distance in meters
Slope, % = [ Vertical distance in meters / Horizontal distance in meters ] x 100
If a field has a 6 percent slope in the direction where elevation changes most rapidly, there will be a difference in elevation of 6 meters vertically to 100 meters horizontally. Note that the longer distance is horizontal, not inclined parallel to the surface of the land. On moderate slopes, it would make little practical difference whether distance were measured horizontally or parallel to the land surface. Figure 7-1 shows the distances and relationships on a slope of 6 percent. With a horizontal distance of 100 m and a vertical distance of 6 m, the inclined distance is the hypotenuse of a right triangle. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, hence
Figure 7-1. Illustration of vertical,
horizontal, and inclined distances (not to scale)
There is little inaccuracy involved whether the horizontal distance or sloping distance is used. On the other hand, on a steep slope such as 45 percent, the horizontal distance would be 100 m, the vertical distance 45 m and the sloping distance would be:
(hypotenuse)² = 100² + 45² = 12,025
hypotenuse
= 109.6 m
or there would be about a 10 percent error from using the sloping distance.
If an irrigation ditch is designed for a 1 percent slope in the channel' the horizontal distance need not lie on a straight line, it might be curved.
A contour, or contour line, is a real, or an imaginary, line on an area with zero slope. That is, all points on the line are at the same elevation. If water is allowed to flow naturally over a land surface, as from rainfall, it will always flow in a direction perpendicular to the contour lines.
Although it is standard practice to refer elevations back to sea level, from a practical standpoint it is difficult and unnecessary to do that when making surveys over small areas such as a small irrigation project. For surveys and mapping of small areas, it is acceptable to select same point whose elevation is not likely to change during a limited future time period.
Such a point might include the top of a large rock, a mark on a large tree or a hole might be dug and filled with concrete. In any case, the map should indicate the location of this "bench mark" and describe it. Once a suitable bench mark has been selected, it is given an arbitrary elevation, such as 100.00 meters, all other elevations would then be in relation to the bench mark elevation (rather than to sea level).
To prepare a topographic map, it is customary and convenient to lay out a grid on the area to be mapped by placing markers at each corner of a group of that will cover the area of interest. The corners of the squares normally will be designated by driving short stakes as the squares are measured.
Figure 7-2 is a topographic map of a rectangular map of a rectangular field. The bench mark on the map was located at the approximate center of the field and assigned an elevation of 100.0 m. After two coordinate lines were constructed at right angles through the bench marks, the corners of the squares were located from the two coordinates.
Figure 7-2. Topographic map showing
elevations and contour lines
The size of the squares is arbitrary; the sides might be 5 m, 25 m or 100 m. The shorter the sides, the more accurately the contours may be drawn but more work will be involved in surveying. It is always best to err on the side of more detail.
After locating the corners, the elevation of each corner is determined in relation to the benchmark. When the map is complete with elevations, then contours may be drawn. Again contours might be drawn corresponding to 0.5, 1, 2, etc. meters. If in doubt, use reduced intervals.
On the map shown, contours were constructed as follows:
The 99.0 m contour started at the top of the map at a point "1" where the elevation was exactly 99.0 m.
Point "2" has an elevation of 98.2 m and point "3" has an elevation of 99.4, so there is a point at 99.0 between "2" and "3". By interpolation, the 99.0 m elevation should be nearer 99.4 than 98.2.
The proportion is found by:
L/100 = (99.4-99.0) / (99.4-98.2)
L = 100 (.4) / 1.2 = 33.3 m
Point 4 is then plotted at 33.3 m above the 99.4 elevation. Similar interpolation are made where contours cross coordinate lines.
Normally land surveyors use steel tapes when measuring
distances. The tapes are available in various lengths but a length of about 30 m
is common. If extreme accuracy is desired, the tape is leveled with a small
level hung on the tape. To locate the point on the ground where
the elevation
is lowest, a "plumb-bob", or plummet, is suspended from the end of the tape to
locate the point on the
ground.
The measurement "rod", is still used sometimes in measuring land. One rod equals 16½ ft. in the English system.
The land measuring rod (spelled "rood" in German ) was brought to England from Germany centuries ago. In Germany, it was 16½ (German ) feet long. Since the German "foot " was slightly longer than the English "foot", the rod became 16 (English) feet long.
When measuring distances on land, using a short measuring tool ( a meter stick or yardstick) is inconvenient. A longer measuring tool, such as a rod or a surveyor's "chain" (4 rods), is more convenient, and simple to construct.
The metric equivalent of a rod is about 5 meters. To construct a rod, take a board 2 to 4 cm square and perhaps 5 m 20 cm long. The extra length is so meter marks do not have to be made at the end of the rod. If boards that size are not available, substitute a strong, straight bamboo pole or other material.
Make marks with a knife at one meter intervals along the rod, beginning about 10 cm from one end. If you label the marks to avoid counting from one end, Roman numerals, etc. are easier to carve than Arabic numerals.
To give a finer measurement at the end of the course, the last meter, between IV and V, might be divided into decimeters (10 cm).
It would be customary to make the fifth decimeter mark a little longer than the others but shorter than the meter marks. Again, the decimeters could be counted or labeled. Centimeters could be estimated fairly accurately between the decimeters marks.
To measure a distance, place the rod on the ground successively making marks in the earth at 5-meter intervals or place markers such as a short piece of wire or nail to mark the end of the rod. Two rods could also be used successively.
Very accurate land surveys would normally use a level with a telescope and cross hairs to sight on a leveling rod resting on the surface of the ground. The surveying level essentially establishes a horizontal plane. Since the telescope is mounted on a base so it can be rotated, the level plane runs in all directions from the centers of the telescope
Figure 7-5 shows a tripod mounted surveying level and a rod to measure the vertical distance between the level plane. If one point is a benchmark with an assumed elevation of 100.00 m, then the level plane is 100.00 + 1.76 or 101.76 m. The other point is 2.42 m below the level plane and its elevation would be 101.76 -2.42 = 99.34 m.
Figure 7-5. Using a surveyor's level
to determine elevation at a point
Figure 7-6 shows a survey that covers a longer distance where the elevations at several points between the benchmark, "BM" and a final point "A" are determined. A survey made in steps is required if there is a visual obstruction between the beginning and end points or when the difference in elevation is great.
Figure 7-6. Differential survey
The intermediate points are commonly called "turning points." The sight back is called a "backlight" and the sight forward is called a "foresight." The elevation of the instrument is called "height of instrument."
Figure 7-7 shows a typical set of surveying notes for the survey in Figure 7-6. (Note, this example is in feet rather than meters.)
The field note calculations are as follows:
The backlight on the benchmark is 1.78 and this is added to the elevation of the benchmark, 100.00 to give an instrument (horizontal plane) height of 101.78 which is entered under height of instrument, HI on the second row of the notes. The foresight on turning point "1" TP, is 9.23. This is subtracted from the height of instrument to give an elevation of 101.78 - 9.23 = 92.55. The level is then moved ahead and the process is repeated.
Surveyiny levels are relatively expensive, and fragile instruments that may not be available in remote rural areas where PCV's are likely to work. Two much simpler and cheaper leveling devices are described below: the "chorobates" and plastic tube.
When a chorobates is used as a sighting instrument, it must be used with a leveling rod to measure the vertical distance from the line of sight to the ground.
Figure 7-7. Field notes on
differential survey in Figure
7-6
Chorobates. Most surveyors now use levels or transits that consist of a telescope with a cross hair to determine the elevation of the "target" Since these instruments are costly and rarely available in rural communities of developing countries, other alternatives may be useful.
The Roman surveyors used a "chorobates" shown in Figure 7-8.*
This level-transit can be made using locally available materials, wood. It can be used as a line-of-sight instrument, similar to a surveyor's level, or as a level, similar to a carpenter's level.
The illustration should be laryely self explanatory and sufficient to build the instrument. The "sights" might be small screw eyes or a piece of sheet metal with a hole bored through for sighting.
Figure 7-8. Reconstruction of
chorobates, levelling instrument (not from Vitruvius' measurements). No examples
survived. A: sights; B: water channel) C: plumb line; D: plummet
* Copied from The Roman Land Surveyors, O. A. W. Dilke, Barnes & Noble, Inc., New York, 1971.
The water trough would be about 1½ to 2 cm deep and about the same width. It could be cut with a wood chisel. To avoid water soaking into the wood and causing it to warp, the trough should be "waterproofed" with varnish, shellac, oil, wax, pitch, or some other suitable material. Also, do not leave water in the trough when the instrument (chorobates) is not in use.
To see that the instrument is working properly and built right, drive two stakes into the ground until the chorobates indicate the stakes are "level." Then turn the chorobates end-for-end; the water should still be level. If not, look for warpage, unequal leg length, or other factors that might be causing the difficulty.
To use the chorobates as a line-of-sight instrument, drive two stakes into the ground until the instrument is level, then sight ahead to the target on the leveling rod. The difference in elevation between the two points will be the difference in height above the ground of the sights on the chorobates and the target on the rod.
It is always more convenient to survey downhill than uphill.
To use the chorobates as a level, raise the leg on the downhill side until the chorobate's body is level. Then measure the distance from the raised leg to the ground. The distance between the raised leg and the ground is the difference in elevation between the ground at the two legs. A wedge under the raised leg may make leveling convenient.
If a long course is being run and the chorobates is used as a level, it is probably best to drive stakes in the ground for each leg to rest on.
At the end of the course, the distance between the next-to-last and last stake normally will be shorter than the distance between the legs. Set an intermediate stake to the side equidistant from the next-tolast and last stake as shown in Figure 7-9 where ''l'' is the distance between the legs of the chorobates.
Figure 7-9. Chorobates used as a
level
A leveling rod can be constructed much as a land-measuring rod is constructed, but the "O" must be the end of the rod, as shown in Figure 7-10. The overall length could be about 3 m with the rod marked in meters, decimeters, and centimeters. But you may mark in meters and use a meter stick to measure shorter distances.
Figure 7-10. A leveling rod with
marks at one-meter intervals (Distances of less than one meter are measured with
a meter stick)
Attach a moveable target to the rod. It might be a small board held against the rod with a short piece of rubber (from an old inner tube) to hold it in place after the height is adjusted.
When the surveying instrument is sighted on the rod, the target is moved up or down until it is centered on the line-of-sight. The vertical distance is then read.
If plastic tube is available, it will be faster than a chorobates. Tubing about 6 mm diameter is probably best and it normally is available, in the U.S., in 100 ft. lengths (30.48m). Hence, the difference in elevation between two points about 25 to 30m apart can be measured. When longer courses are to be measured, successive elevations are determined.
To establish the elevation of one point with respect to another for plastic, you calculate as shown in Figure 7-11. For convenience, two stakes are shown; actual ground level will be slightly lower.
Figure 7-11. Leveling with plastic
tubing
The level of the top of the upper stake is assumed to be at 100.00 m, a benchmark elevat on.
The distance from the water level is 9.6 cm or.096m. Hence the elevation of the water level is 100.096 (in actual practice, it is usually not necessary to measure elevations so accurately. The 9.6 cm would probably be read as 10 cm).
The top of the lower stake is 84.4 cm (.844m) below the water level, hence the elevation is 100.096.844 = 99.252.
If surveying notes similar to the ones shown in Figure 7-7 were being made, the notes would be as follows.
|
STA |
BS(+) |
HI |
FS(-) |
Elev. |
|
BM |
.096 | | |
100.000 |
|
INST. | |
100.096 | |
|
|
TPI | | |
.874 | |
ln standard surveying notes HI (height of instrument) corresponds to the term "water level."
Plastic tube usually can be found in chemical laboratories or at chemical supply houses. In the U S., it is available in hardware stores at approximately $0.75 per m.
Rubber tubing could be substituted by inserting a piece of glass tubing in each end.
Filling a tube by pouring in water is possible but slow. Alternatives are to straighten the tube and then coil it in the bottom of a container of water. The tube will fill as it is inserted into the water. Another method is to place a container of water at some elevation, i.e., 1 m above the ground and insert one end of the tube into the water; start siphoning to fill the hose by sucking on the other end and keeping it below the water container. When filling by siphoning, remember to use potable water.
Forming Right Angles. It is frequently necessary to form accurate right angles when surveying land or making instruments. Two practical methods for field use are:
a. The 3-4-5 triangle
A right triangle is formed when the dimensions of the three sides of a triangle are in the ratio of 3:4:5 (ratios of 6:8:10, etc. are also useful). To form the right triangle, form a base of say 4 units of length (Step 1) (Figure 7-12). Then find the intersection of the other two sides, one of three units (at a 90° angle) and one of five units (Step 2). The resulting triangle will contain the desired right angle.
b. Perpendicular to a straight line
Mark off a straight line and locate d point from which a perpendicular will be marked off (Step 1) (Figure 7-13). Mark off equal distances from the selected point (Step 2). For Step 3, draw an arc from each of the two points marked in Step 2, which is a greater distance than one unit of the baseline. In this example, twice the distance of one unit of the baseline is used. The perpendicular drawn through the original center point and the intersection of the two arcs will be perpendicular to the first line.
Locating a North-South Line. Draw a circle on a level surface and mark the center accurately (Figure 7-14). Erect d pole at the center with the top of the pole exactly above the center of the circle. This can easily be done with a plummet. Guy the pole with three guys to hold it accurately in position.
Figure 7-12. Forming a right
triangle
Figure 7-13. Erecting a
perpendicular to a lien
Figure 7-14. Locating east-west and
north-south coordinates
At some time during the morning, the shadow of the top of the pole will just touch the circle, mark this point. At some time in the afternoon, the shadow of the top of the pole will again just touch the circle, mark this point. Now connect the two points to give an east-west line. Draw a perpendicular to the east-west line to obtain a north-south line.
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