How To Find The Difference In Elevation Between Two Points

8. TOPOGRAPHICAL SURVEYS - DIRECT LEVELLING

eight.0 Introduction
one. In Capacity 5 and half dozen, y'all learned about various devices for measuring height differences. Yous also learned how to use these devices to solve 3 types of bug in measuring height differences, which you lot may confront when you lot plan and develop a fish-farm (see Department 5.0). Now, yous will learn how to plan surveys to solve these problems, how to tape the measurements yous brand in your field-volume, and how to discover the information you need from these measurements.
What are acme and distance?
2. Y'all have learned what the acme of a ground bespeak is. At present, notwithstanding, you lot will need to know a more than authentic definition of this term. When the superlative of a point is its vertical distance to a higher place or below the surface of a reference plane* you lot have selected, it is called the elevation* of that indicate. When the height of a point is its vertical distance above or below mean ocean level (as the reference plane), it is called the altitude* of the point. Example Summit of a point above a selected ground marking A Altitude of the same point above mean sea level (amsl) 1.83 m 345 m 3. The vertical altitude between 2 points is called the difference in top , which is like to what you lot accept learned as the deviation in height (run across Section 5.0). The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.
What are the main levelling methods?
4. You can level past using unlike methods, such as: straight levelling , where you measure out differences in peak directly. This is the virtually commonly used method; indirect levelling, where you calculate differences in elevation from measured slopes and horizontal distances.		Directly levelling
You lot accept already learned about indirect levelling in Section five.0, when you learned to calculate differences in elevation from slopes or from vertical angles. At present you will learn about directly levelling.		Indirect levelling

What are the kinds of directly levelling?

5. By direct levelling, you can measure both the acme of points and the differences in elevation between points, using a level and a levelling staff (run into Chapter 5). There are two kinds of straight levelling:

• differential levelling; and
• profile levelling.

six. In differential levelling , you find the divergence in acme of points which are some distance autonomously (see Section 8.1). In the simplest kind of direct levelling, you would survey merely ii points A and B from one key station LS. But you may demand to observe the difference in top betwixt:

• either several points A, B, ... E, surveyed from a single levelling station LS; or
• several points A ... F, surveyed from a serial of levelling stations LS1 ... LS6, for instance:

7. In profile levelling , you observe the elevations of points placed at short measured intervals forth a known line, such as the centre-line of a water supply canal or the lengthwise centrality of a valley. You lot find elevations for cross-sections with a similar kind of survey (see Section 8.2).

viii. You can also use direct levelling to determine elevations for contour surveying (come across Department 8.iii), and for setting graded lines of slope(run into Department 6.9), where you need to combine both differential levelling and contour levelling.

Differential levelling

Contour levelling

9. There are several simple ways to decide the elevations of ground points and the differences in meridian between basis points. You volition utilize a level and a levelling staff with these methods. In the following sections, each method is fully described to help you lot choose between them. Tabular array 10 will also assist you to compare the diverse methods and to select the one best suited to your needs in each type of state of affairs you may encounter.

 Tabular array x
Direct levelling methods

Section	Type	Method	Suitability	Remarks
8.1	Differential levelling	Open traverse	Long, narrow stretch of country	Cheque for closing fault
8.1	Differential levelling	Airtight traverse	Perimeter of land area and base of operations line for radiation	Check for closing error. Combine with radiating
8.1	Differential levelling	Square-filigree	Minor surface area with little vegetation	Squares x to 20 one thousand and 30 to 50 k
8.one	Differential levelling	Radiating	Large surface area with visibility	Combined with closed traverse
8.2	Longitudinal contour levelling	Open traverse	Non-sighting and sighting level	Check for endmost fault
8.2	Cantankerous-section profile levelling	Radiating	Sighting level with visibility
eight.iii	Contouring	Direct	Detailed mapping of small area with a sighting or a non-sighting level and target levelling staff	Slow and accurate. Progress uphill
8.3	Contouring	Square-filigree	Small-scale area with little vegetation Especially if perimeter has been surveyed. Modest to medium scale mapping	Terrain, scale and accuracy depend on contour interval. Progress uphill. Suitable for plane-tabling
8.3	Contouring	Radiating	Small to medium scale mapping of large area	Fast and fairly inaccurate. Progress uphill. Suitable for airplane-tabling
8.three	Contouring	Cross-sections	Preliminary survey of a long and narrow stretch of land	Fast, fairly inaccurate. Progress uphill. Suitable for plane-tabling

eight.1 How to level by differential
What is differential levelling?
1. You can all-time understand differential levelling by first considering but two points, A and B , both of which you tin can meet from one fundamental levelling station, LS . Sight with a level from LS at the levelling staff on betoken A. The point where the line of sight meets the levelling staff is point Ten. Measure AX. This is called a backsight (BS).		Find AX with a backsight
Turn around and sight from LS at the levelling staff on indicate B. The point where the line of sight meets the levelling staff is point Y. Mensurate BY. This is called a foresight (FS).		Find Past with a foresight
The difference in summit between signal A and indicate B equals BC or (AX- BY) or (backsight BS - foresight FS).		The divergence in elevation between points A and B equals AX minus Past
If yous know the acme of A, called Due east(A), you can calculate the elevation of B, called Eastward(B), as BS -FS + East(A). But BS + E(A) = Howdy, the height of the instrument or the elevation of the line of sight directed from the level.
Therefore, (the pinnacle at indicate B beingness equal to the elevation of the levelling instrument, minus the foresight).

What are backsights and foresights?
It is of import for you to understand exactly what "backsight" and "foresight" are in direct levelling. 2. A backsight (BS) is a sight taken with the level to a bespeak X of known acme E(X), then that the height of the instrument HI tin can be institute. A backsight in directly levelling is usually taken in a backward direction, simply non always. Backsights are too called plus sights (+ South), considering y'all must ever add them to a known superlative to observe HI.
three. A foresight FS is also a sight taken with the level, just information technology tin can be on any signal Y of the sight line where you have to decide the elevation Due east(Y). Yous will usually take it in a forward direction, but not e'er. Foresights are as well called minus sights (-South) , because they are always subtracted from Hullo to obtain the height E of the betoken. Think:
Surveying two points with i turning point
4. Often you will not be able to encounter at the same fourth dimension the two points y'all are surveying, or they might be far apart. In such cases, y'all will demand to do a serial of differential levellings . These are similar to the type explained above, except that you will utilize intermediate temporary points called turning points (TP).
5. Yous know the top of point A, E(A) = 100 k, and you want to find the elevation of point B, E(B), which is non visible from a central levelling station. Choose a turning indicate C nigh halfway between A and B. And so, ready up the level at LS1, about halfway between A and C.
6. Measure a backsight on A (for example, BS = i.89 1000). Mensurate on C a foresight FS = 0.72 m. Calculate HI = BS + E(A) = 1.89 m + 100 1000 = 101.89 k. Notice the elevation of turning indicate C as E(C) = How-do-you-do-FS = 101.89 chiliad - 0.72 m = 101.17 m.

7. Move to a second levelling station, LS2, nigh halfway between C and B. Prepare the level and measure out BS = 1.96 m, and then FS = 0.87 g. Calculate How-do-you-do = BS + E(C) = 1.96 m + 101.17 m = 103.13 m. 0btain E(B) = How-do-you-do- FS = 103.13 m - 0.87 m = 102.26 m. 8. You can make the calculations more than easily if yous tape the field measurements in a tabular array , as shown in the instance. You will not make any intermediate calculations. All BS's and all FS's must be added separately. The sum FS is subtracted from the sum BS to find the difference in elevation from point A to point B. A positive difference ways that B is at a higher elevation than A. A negative divergence means that B is at a lower elevation than A.
Knowing the tiptop of A, yous can now easily calculate the elevation of B. In this case, E(B) = 100 g + 2.26 m = 102.26 chiliad; this is the same as the result in footstep 7, which required more complicated calculations. This kind of calculation is called an arithmetic check. Example Table form for differential levelling with 1 turning betoken.

Surveying two points using several turning points

9. Oft you volition need to use more than one turning indicate between a signal of known meridian and another bespeak of unknown elevation. To practise this, you can use the procedure you have but learned, but you will need to tape the field measurements in a table to make calculating the results easier.

10. Knowing the peak of betoken A, you lot demand to discover the height of B. To do this, you need for example  5 turning points , TP1 ... TP5, and vi levelling stations, LS1 ... LS6.

Notation : the turning points and the levelling stations do not have to be on a straight line, but endeavor to place each levelling station about halfway between the two points you need to survey from it.

11. From each levelling station, measure a backsight (BS) and a foresight (FS) , except:

• at starting indicate A, where you have only a backsight measurement.
• at catastrophe point B, where y'all have merely a foresight measurement.

Example Tabular array class for differential levelling with several turning points.

Using pace 8 every bit a guideline, enter all measurements in a tabular array and calculate the results equally shown in the example beneath. You volition notice that point B is 2.82 m higher than betoken A and, therefore, that its pinnacle is E(B) = 100 thou + 2.82 one thousand = 102.82 k.

12. Fifty-fifty if yous are careful, you lot may still brand mistakes when you make your arithmetic calculations from the table. To reduce this kind of error, add together two additional columns to your tabular array that will make checking your calculations piece of cake. In these columns, enter the deviation (BS- FS), either positive (+ ) or negative (-), between the measurements you took at each levelling station. For instance, from LS1 you measure BS (A) = 1.50 grand and FS (TP1) = 1.00 g. The deviation 1.l m- 1.00 grand = 0.l m is positive, and you lot enter it in the (+) column on the TP1 line.

The arithmetic sum of these differences should be equal to the calculated difference in elevation D(E) = +2.82 k. These columns volition also help y'all to calculate the superlative of each turning point , and to check on the top of bespeak B more than carefully.

Case
Differential levelling with several turning points

Making topographical surveys by straight open up traverses
13. By now, you have learned enough to brand a topographical survey of two afar points by measuring the horizontal distance between them and the difference in their superlative. When you survey a future fish-farm site, you lot will use a very similar method. You lot tin can then ready a topographic map of the site (come across Chapter 9), which will become a useful guide for designing the fish-subcontract. 14. This is a survey method using straight open up traverses , that is, several intermediate stations forth 1 straight line. You know for case the elevation of starting point A, Due east(A) = 63.55 m. Y'all desire to know the distance of point B from point A, and its meridian. Because of the type of terrain on which you are surveying, y'all cannot see bespeak B from bespeak A, and yous need two turning points , TP1 and TP2 , for levelling. Measure horizontal distances as y'all move forward with the level, from point A toward indicate B; try to progress forth a direct line. If yous cannot, you will need to use the broken open traverse survey method, which involves measuring the azimuths of the traverse sections as you move forward and alter direction (run into step 17).

15. Set out a table like the one in step 12, and add together ii columns to it for horizontal distances. Enter all your distance and height measurements in the main part of the tabular array. So, in the beginning additional column, tape each fractional distance you measure out from one point to the next one. In the 2d column, note the cumulated distance , which is the altitude calculated from the starting indicate A to the point where you are measuring. The last number in the second column will be full altitude AB.

Example
Topographical survey of a direct open traverse by differential levelling

sixteen. Conclusions . Indicate B is 1.55 1000 higher than A and its elevation is 65.10 m. It is 156.5 m afar from point A. The arithmetic check from the (BS- FS) differences agrees with the calculated difference in elevation.

Making topographical surveys past broken open traverses
17. Call back, that if you survey past broken open up traverses (or zigzags), you volition too have to measure out the azimuth of each traverse section as you lot continue, in addition to distances and elevations.
18. You demand for example to survey open up traverse ABCDE from known point A. Y'all crave iv turning points, TP1, TP2, TP3 and TP4. You want to know: the elevations of points B, C, D and E; the horizontal distances betwixt these points; the position of each signal in relation to the others, which will assistance y'all in mapping them.

Go on with the differential levelling as described earlier, measuring foresights and backsights from each levelling station. Measure azimuths and horizontal distances as you progress from the known bespeak A toward the end point East. All the azimuths of the turning points of a single line should be the aforementioned. This will help yous check your work.
19. Make a tabular array similar to the ane shown in step 15, and add together three actress columns to it for recording and checking the azimuth values. Enter all your measurements in this table. At the lesser of the tabular array, make all the checks on the elevation calculations, as yous take learned to do them in the preceding steps.
Case Topographical survey of a broken open up traverse by differential levelling

Checking on levelling errors
xx. Checking on the arithmetic calculations does non tell you lot how accurate your survey has been. To fully check on your accuracy, level in the opposite direction , from the terminal signal to the starting bespeak, using the aforementioned procedure every bit before. Y'all will probably notice that the elevation of point A you obtain from this second levelling differs from the known acme. This deviation is the closing fault .
Example From signal A of a known elevation, survey by traversing through five turning points, TP1 ... TP5, and find the tiptop of point B. To check on the levelling error, survey by traversing BA through four other turning points, TP6 ... TP9; then summate the elevation of A. If the known elevation of starting point A is 153 g, and the calculated pinnacle of A at the end of the survey is 153.2 m, the endmost error is 153.2 one thousand - 153 m = 0.ii m.

21. The closing fault must be less than the permissible mistake, which is the limit of error you can have in a survey for it to be considered accurate. The size of the permissible error depends on the type of survey (reconnaissance, preliminary, detailed, etc.) and on the total altitude travelled during the survey. To help you discover out how accurate your survey has been, calculate the maximum permissible fault (MPE) expressed in centimetres , as follows:

Source: https://www.fao.org/fishery/docs/CDrom/FAO_Training/FAO_Training/General/x6707e/.!54083!x6707e08.htm

Posted by: greensupoed.blogspot.com

Share this post