# 2. MEASURING HORIZONTAL DISTANCES

## 2.0 Introduction

### Measuring distances along straight lines

1. In topographical surveys, you measure distances along straight lines. These lines either join two fixed points or run in one direction starting from one fixed point. They are plotted in the field with pegs, pillars or ranging poles.

### Expressing distances as horizontal measurements

2. You should always measure distances as horizontal distances. You may have to measure on ground which has no slope, or only a very small slope that is less than or equal to 5 percent (see Section 4.0). The distance measured on this type of ground will be equal to or very close to the horizontal distance. When the slope of the terrain is greater than 5 percent, however, you will have to find the horizontal distance. To do this, you must either correct any measurements you made along the ground (see Section 4.0) or use another method of measurement (see following sections). Unlevelled ground also requires particular methods of measurement.

### Measuring distances along lines that run through obstacles

3. Usually, you will be able to reach all the points of the straight line you want to measure. But in some cases an obstacle such as a lake, a river or a cultivated field will be in the way, and you will have to take indirect measurements. This means that you will calculate horizontal distances along the original straight line (see Section 2.9).

Chaining with a rope

### Choosing the most suitable method

4. There are many good ways to measure distances. The method of measurement you use will depend on several factors:

• the accuracy of the result needed;
• the equipment you have available, to use;
• the type of terrain you need to measure.

In the following sections, you will learn how to use the various methods of measurement. Table 1 will also help you to compare these methods and to select the one best suited to your needs.

TABLE 1

Distance measurement methods

 Section1 Method Distance Error2 per 100 m2 Remarks Equipment3 22* Pace count Medium to long 1 to 2 m or more For quick, rough estimates None 22* Pacing with a passometer or podometer Long 1 to 2 m or more For quick, rough estimates Passometer or podometer 21* Ruler Short 0.05 to 0.10 m Especially useful for sloping ground Ruler (mason's level, plumb line) 23** Chaining using a rope Medium to long 0.5 to 1 m Cheap Liana or rope, string, marking line 24** Chaining using a band or tape Medium to long less than 0.05 m Best results with steel lines Steel band, measuring tape 25** Chaining using a chain Medium to long 0.02 to 0.10 m Stronger quality Surveying chain 27*** Clisimeter Medium 1 to 2 m For quick and rough estimates Clisimeter (lyra-) (2 m stadia staff) 28*** Stadia Medium to long 0.1 to 0.4 m For quick and accurate measures Telescope with stadia hairs, levelling staff

1 * Simple ** More difficult *** Most difficult.
2 Error increases as the terrain becomes more difficult (slope, vegetation, obstacles).
3 In addition to ranging poles (setting out the line), marking pegs (intermediate points), and notebook/pencil. In italics, equipment you can build yourself, as explained in text.

### Calculating perimeter lengths

5. The perimeter of an area is its outer boundary. The length of the perimeter of regular geometrical figures can be calculated from the mathematical formulas given in Annex 1, at the end of this manual.

AB + BC + CD + DE + EF + FA = Perimeter ABCDEFA

Perimeter WXYZW

## 2.1 How to measure short distances with a ruler

1. To measure short distances, use a measuring stick called a ruler, 4 to 5 m long. You can make your own by following the steps below. A ruler is particularly useful for measuring horizontal distances on sloping ground.

2. Get a piece of wood which is straight and flat. It should be about 5 cm wide, and a little more than 4 m long. You can also use a shorter length, if the distance you are going to measure is shorter.

3. It is best to use a planed piece of wood, but if you cannot get one you may use a straight wooden pole. If you use a pole, you should plane at least one of its surfaces.

 Measuring with a ruler A planed piece of wood is best... ... but you can also plane one side of a pole

4. You should now add graduations to it. Graduations are marks which show exact measurements, in centimetres, decimetres, metres, etc. To do this, you need to get two ready-made measuring tapes, such as the 2 m ribbon tapes that tailors use. Glue one of these measuring tapes onto the planed face of your piece of wood. Take care to align the zero mark of this tape with one of the ends of the piece of wood. Glue the second tape next to the end of the first tape; this should reach near the end of the piece of wood. Drive several small nails through the tapes to secure them better.

5. You can also make the graduations yourself. Using a measuring ruler or tape, mark the graduations on the piece of wood with a pencil. With a knife or saw, make a straight, shallow cut every 10 cm. A carpenter, with his tools, can help you to do this more accurately. Identify the graduations with numbers (for example, every 0.5 m) using paint or ink; or you can use a piece of hot wire to burn the graduations and their numbers into the wood.

 Use glue and nails to secure the tapes Mark your ruler accurately

### Measuring short distances with your ruler

6. When you have to measure a short distance on horizontal terrain, mark each end of the distance with ranging poles. Place your ruler on the ground with its end at the first ranging pole, making sure the ruler follows the straight line. Put a marking peg at the other end of the ruler. Then take the ruler and place its first end at this marking peg. Continue in this way until you reach near the end of the line, keeping an accurate count of the number of ruler lengths. You will usually need to use only part of the ruler's length to measure the last part of the line. Take care then to read the graduations on the ruler correctly.

 7. When you need to measure a distance on sloping terrain, your ruler will be very useful for finding horizontal distances. You proceed downhill, and for each measurement: make sure that the ruler is horizontal, using a mason's level (see Section 6.1); determine the point where you need to place the marking peg, using a plumb-line at the end of the ruler (see Section 4.8). A mason's level Note: when you measure a distance on sloping ground, remember that you should proceed downhill. A plumb-line

## 2.2 How to measure distances by pacing

1. You may measure distances roughly by pacing. This means you count the number of normal steps which will cover the distance between two points along a straight line. Pacing is particularly useful in reconnaissance surveys, for contouring using the grid method (see Section 8.3) and for quickly checking chaining measurements (see Sections 2.3 to 2.5).

2. To be accurate, you should know the average length of your step when you walk normally. This length is called your normal pace. Always measure your pace from the toes of the foot behind to the toes of the foot in front.

 Count your steps as you walk

### Finding your own pace factor

3. To measure the average length of your normal pace (the pace factor, or PF):

• take 100 normal steps on horizontal ground, starting with the toes of your back foot from a well-marked point, A, and walking along a straight line.
• mark the end of your last step with peg B, at the toes of your front foot.
• measure the distance AB (in metres) with, for example, a tape and calculate your pace factor PF (in metres) as follows:

Walk 100 paces

 PF = AB �100

Example

If for 100 paces, you measure a distance of 76 m, then your pace factor is calculated like this: PF = 76 m � 100 = 0.76 m.

Mark the distance

### Measuring horizontal distances by pacing

5. Clearly plot the straight lines you have to measure, using wooden pegs or ranging poles. If necessary, remove any high vegetation standing in the way.

6. Walk along the straight lines, carefully counting your steps.

7. Multiply the number of steps N by your pace factor PF (in metres) to get a rough estimate of the distance in metres, as follows:

 Distance (m) = N x PF

Plot the lines you want to measure

Example

To measure ABCD, pace distances AB = 127 steps; BC = 214 steps; and CD = 83 steps. ABCD = 127 + 214 + 83 = 424 steps.
If PF = 0.75 m, ABCD = 424 x 0.75 m = 318 m

Note: to avoid errors when counting your steps:

• count only double steps or strides, and multiply the total count by 2;
• take count of the hundreds with your fingers (using one finger for each hundred steps);
• take count of the thousands by ticking them off on paper;
• when crossing obstacles such as fences and small streams, estimate the number of steps, strides or half-steps it would take to cross them.

Estimate the size of obstacles

### Pacing with a passometer or a pedometer

8. You can register your paces mechanically by using a simple device called a passometer. The passometer is about the size of a watch. You should wear it on a point near the centre of your body, attached to a belt or waistband for example. At each pace you take, the jolt of your step makes a pointer in the passometer turn. This pointer shows the number of paces.

9. The pedometer is a similar device, but it registers distance. This is usually expressed in kilometres and fractions of kilometres.

10. You should check these two devices for accuracy before you use them. To check a passometer, walk a few hundred paces, counting them carefully. Then compare your total count of paces with the number of registered paces, and adjust the device as necessary. To check a pedometer, walk at a normal pace along a straight line over a known distance. Compare this distance with the registered distance, and adjust the device as necessary.

The pedometer measures distances

## 2.3 How to chain with a rope

1. For greater accuracy in measurement, especially over difficult terrain, you can use a measuring line made from rope. Depending on the distances you need to measure, you can make a measuring rope 10, 20 or 30 m long.

### Making your own measuring rope

2. Get a rope 1 to 1.5 cm thick, made of natural fibres. Ropes of man-made fibres, such as nylon, may change over time, but natural materials, such as jute, will shrink or stretch very little. A piece of used sisal rope is better to use than a new one. You can also use a piece of supple liana, which you can easily find in the forest.

3. Put the first mark- the zero mark- about 20 cm from one end of the rope. From this point, accurately measure the length you need one metre at a time. Leave about 20 cm at the other end of the rope. Mark each metre point with durable waterproof paint, dye, ink or coloured wax. Keep these metre marks as thin as possible to avoid inaccurate measurements. You can use thin string for the marks instead, threading the string through the rope so that it does not shift position.

4. Reinforce the two ends of your measuring rope. To do this, tightly wind some light string around the last 10 cm of each end of the rope.

Choose the right size rope

Make each mark easy to read

Reinforce the ends with string

### Measuring horizontal distances with a rope

5. Clearly plot the straight lines you want to measure, using wooden pegs, for example. On either side of each of these lines, clear a narrow strip of ground completely, removing vegetation and large stones.

6. If the distances are shorter than your rope, or about the same length, you can take their measurements directly. To do this, carefully stretch the rope from one peg to the next. If a distance fails between the metre marks on your rope, measure this shorter length with a ruler or a tape graduated in centimetres.

Clear the ground where you are working

7. If the distances are longer than your rope, you will need to use one of the chaining methods described later (see Section 2.6). These methods can be used with all measuring lines, including ropes, bands, tapes or chains.

Stretch the rope straight

Measure the difference with a ruler

## 2.4 How to chain with bands or tapes

1. You can buy bands and tapes in stores. A measuring band is made of a strip of steel, usually 6 mm wide and 30 or 50 m long. Metres, decimetres and centimetres are clearly marked on the band. Bands are wound onto an open frame, with a spindle and handle for rewinding.

A measuring band

2. Measuring tapes are made of steel, metallic cloth or fibreglass material. They come in lengths of 10 to 30 m or more. They are usually marked at 1 m intervals, with the first and last metres graduated in decimetres and centimetres. They are wound into a case, with a handle for rewinding. Tapes can present some problems. Steel tapes can easily become twisted and break. Cloth tapes are less precise than the others, since they often vary slightly in length.

A measuring tape

### Measuring horizontal distances with a steel band or a tape

3. Plot the straight lines you need to measure. If the lines are the same length as your measuring band or tape or shorter, you can measure the distances directly. To do this, stretch the band or tape from one peg to the next one.

Note: you should pull bands and tapes tight, so that they do not sag, especially when you are measuring long distances. But, you should avoid over-stretching them (especially fibreglass tapes), since this could lead to errors.

 Keep the band or tape straight and tight Read the measurement at the peg

## 2.5 How to chain with a surveyor's chain

1. Surveyor's chains are also sold in stores. They are made of a series of steel links; each link is the same length, usually 20 cm. The links are attached to each other by steel rings. The length of one link includes its straight portion, its two rounded ends, and the two half-rings that connect it to the links on either side. Each metre of the chain is usually marked by a brass ring. At each end of the chain, there is a metal handle which you should include in the measurements. The total length of the chain is usually 10 or 20 m. Chains are less accurate than bands and tapes, but they are much stronger.

Measuring with a surveyor's chain

2. When you use a surveyor's chain, you should be careful of the following:

• make sure that the rounded end of one length does not remain on top of the one next to it. This can make the chain shorter. At the start of each survey, check for this by sliding the entire length of the chain through your hand and straightening all the links;
• avoid leaving the chain in the sun since the heat may cause the chain to become longer;
• pull the chain tight enough for accurate measurement.

Make sure the links are straight

Measure the length of each link with a ruler

Check the length of the chain

 3. When using a chain for the first time, you should carefully measure the length of each link, using a ruler. Remember that this length includes the straight part and its two rounded ends, as well as the two connecting half- rings. At each end of the chain, the handle, one shorter link, and half the connecting ring make up the length of a link. After measuring the length of the links, check that 1 m of chain equals the expected number of links. Example If each link is 0.20 m long, there should be five links per metre of chain.

 4. You should always fold the surveyor's chain as follows: take the two handles together in your left hand, doubling the chain; collect two links at a time with your right hand, putting them slantwise. Take both handles in your left hand Collect the links two at a time 5. To unfold a surveyor's chain, hold the two handles in your left hand and throw the chain in the direction of the measurement you want to make. Throw the chain in the direction of the measurement

### Measuring horizontal distances with a chain

6. The chain is used for measuring the lengths of straight lines, which should be marked at each end with a ranging pole. You will need an assistant to help you. The method of chaining you use depends on the type of terrain you are measuring (see Section 2.6).

 When you measure with a chain, you will need an assistant Hold the chain tight against the marker

## 2.6 How to measure distances by chaining

1. As you have learned, measuring lines can be ropes, bands, tapes or surveyor's chains. When you measure long distances, the way you use the measuring line will depend on the slope of the terrain. When the terrain is flat or nearly flat (that is, with a slope of 5 percent or less - see Section 4.0), you can measure the horizontal distances by following the ground surface. This method is usually used in measuring fish culture sites, where steeper slopes must be avoided. When the slope of the terrain is steeper than 5 percent, you should be especially careful when you measure the horizontal distances because in this case the surface measurement is always greater than the horizontal measurement.

 On flat ground, measure directly   The horizontal distance is the true measurement... ... the surface measurement is longer

### Chaining over horizontal ground

2. Mark each straight line you need to measure with a ranging pole at each end. On lines longer than 50 m, place intermediate markers at regular intervals,

3. To measure long distances accurately, you will need marking pins. You can use thin wooden stakes about 25 cm long, which you can easily carry in a small basket. These marking pins will be driven vertically into the ground as you proceed with the chaining.

4. Chaining is carried out by two persons, a rear chainman and a head chainman. The rear chainman is responsible for the measurements. He notes the results. He also guides the head chainman to make sure that the consecutive measurements are made exactly along straight lines between the marked ground points.

5. Start the measurements at one end of the straight line. Remove the ranging pole and drive the first marking pin into the ground at exactly the same point.

6. The rear chainman places his end of the measuring line against this marking pin. The head chainman, taking with him a number of marking pins, walks away along the straight line with the other end of the measuring line.

The rear chainman stays at the first point...

7. The head chainman stops when the measuring line is stretched out tightly to its full length on the ground. He then looks towards the rear chainman. If the measuring line is not placed exactly along the straight line, the rear chainman then tells the head chainman how to correct the position of the measuring line.

... and helps the head chainman find the second point

 8. When the measuring line is correctly placed, the rear chainman signals to the head chainman to place a second marking pin at the end of the measuring line. 9. The rear chainman immediately notes down this measurement. 10. The rear chainman then removes the first marking pin, putting it in his basket, and replaces the ranging pole at the starting point. When the second pin is placed... ... the rear chainman notes the measurement ... and puts the first pin in his basket... 11. Still holding their ends of the measuring line, both chainmen move forward along the straight line, always keeping the measuring line well stretched. This is particularly important when using a surveyor's chain. 12. The rear chainman stops at the second marking pin and places his end of the measuring line against it. 13. The head chainman tightens the measuring line along the ground, corrects its position following any directions from the rear chainman, and places a third marking pin at the end of the measuring line when signalled to do so. Both chainman move forward... ... to measure the distance between the second and third pins 14. The rear chainman notes down this measurement. Then he puts the second marking pin in his basket before moving on. 15. The process in steps 10 to 14 should be repeated along each section of the straight line until the end is reached. The head chainman notes each distance

 Note 1: when the end of the line is reached, the number of marking pins in the basket of the rear chainman shows the number of complete measuring-line lengths measured. You can use this to check on the measurements noted down. Note 2: using a set of 11 marking pins makes it easier to keep track of the number of measurements completed. When the rear chainman has ten pins in his basket, ten complete measuring-line lengths have been measured. He notes this down and gives the ten pins back to the head chainman, leaving the eleventh pin in the ground; this is the starting point of a new series of measurements. The number of pins in the basket helps you keep count 10 chain lengths have been measured Example Using a chain 10 m long, the rear chainman has marked 4 x 10 pins in his notebook. He has 6 marking pins in his basket. At the marking pin still in the ground, he has measured a distance of (4 x 10) + 6 = 46 chain lengths or 46 x 10 m = 460 m.

### Chaining over sloping ground

16. When you are measuring on ground with a slope greater than 5 percent (see Section 4.0), you will need to use the measuring line differently to find the horizontal distances.

17. Proceed as described in the previous section. Mark the straight lines with ranging poles at each end and intermediate pegs. Remember to work downhill for greater accuracy.

18. The head chainman should hold the measuring line horizontal, above the ground, in this case.

19. When the measuring line is in the right place and is fully stretched, the head chainman finds the exact point on which to place the marking pin, using a plumb-line (see Section 4.8).

20. Keep proceeding in this way along the slope.

Note: on steep slopes, use a shorter measuring line (such as 5 m, rather than 10 m).

21. As you measure on sloping ground, remember these important requirements:

 horizontal measuring line; well-stretched measuring line; Horizontal measuring line Well-stretched measuring line exact placement of the marking pins. Exact placement of the marking pins Note: you may also measure along the ground on a slope. But to obtain horizontal distances, you will need to correct these ground measurements afterwards by using mathematical formulas .

### Chaining over irregular ground

22. You may need to measure distances over irregular ground that has ridges, mounds, rocks, trenches or streams in the way. In such cases, you need to lift the measuring line above the obstacle. Make sure that you do the following:

• keep the measuring line well stretched. The head chainman may shorten it by looping it in his hand if necessary;

 23. Instead of using a plumb-line, you can use longer marking pins, such as ranging poles, set vertically in the ground. Ranging poles are taller than marking pegs 24. In very hard or rocky soils, you will not be able to use marking pins. In such cases, mark t he points with objects you can see easily, such as painted rocks or blocks of wood. Make sure that your markers will not blow or roll away. Or, you can make a mark on the ground with a stick, or make a mark on a rock with chalk. Painted rock or block

### Improving the accuracy of your chaining

25. To make your chaining more accurate, you should repeat the measurements at least once; start measuring at the point where you finished, and continue back along the line. This second measurement should not differ too much from the first one (see Chart below).

26. If the two measurements agree, you can calculate their average value. The average value is taken as the true measured distance.

Measure twice for accuracy

AB + BA = Average
2

Maximum permissible difference between two consecutive
distance measurements, per 100 m

 Steel band or tape 0.1 m Other tape 0.2 m Surveyor's chain 0.2 m Home-made rope 1.0 m

 Example Using a surveyor's chain, you take the following measurements: first measurement: 312.6 m; second measurement: 313.2 m; real difference: 313.2 m - 312.6 m = 0.6 m; acceptable difference: 0.2 m x (312.6 m � 100) = 0.2 m x 3.12 m = 0.62 m which is larger than the real difference and therefore agrees; average distance: (312.6 m + 313.2 m) � 2 = 312.9 m First measurement Second measurement

 27. If the two measurements differ by too much, you should take a third measurement. Compare this with the first two measurements. Then calculate the average value from the two most similar values, as shown above. First measurement Example Chaining with a steel tape, you take the following measurements: first measurement: 754.4 m; second measurement: 753.2 m; real difference: 754.4 m - 753.2 m = 1.2 m; acceptable difference: 0.1 m x 7.54 m = 0.75 m, which is smaller than the real difference and therefore does not agree; third measurement: 753.9 m; difference 754.4 - 753.9 m = 0.5 m which is acceptable, being smaller than 0.75 m; average distance: (754.4 m + 753.9 m) � 2 = 754.15 m. Second measurement Third measurement

 28. If you find you have very different measurements of the same line, you may not have been measuring along the true straight line. To reduce such errors, put more ranging poles on the line between the endpoints. If you tie white or brightly coloured pieces of cloth to the poles, you will be able to see them better. Also, be sure to guide the head chainman carefully as you measure. A crooked line gives the wrong measurement More ranging poles increase your accuracy Flags make sighting easier 29. Further improve the accuracy of your measurements by: inspecting the full length of the measuring line before using it to measure a series of straight lines; keeping a uniform tension on the measuring line during each measurement; accurately marking each point of measurement; keeping an accurate count of these points; using the right device, such as a ruler, to measure distances less than the measuring-line length, and knowing how to read the graduations on it (see Section 2.1). Check your line before use Note: it is better if the head chainman holds the zero end of the measuring line. The rear chainman can then directly make and note down any intermediate readings. Always stretch it tight Mark and count points accurately

## 2.7 How to measure distances with a clisimeter

1. The lyra clisimeter is a simple instrument which can be used for measuring distances. It is also used for measuring ground slope (see Section 4.5). The clisimeter is not as accurate as a measuring line, but you can get a quick estimate of distances from it without having to walk the length of the line. The longer the distance you measure with it, however, the less accurate the measurement will be. For good estimates, do not exceed 30 m distances. For rough estimates, you may measure distances up to 150 m.

A folded clisimeter

2. The lyra clisimeter consists of a sighting device, a hanging ring, and a bottom weight to keep the instrument in a stable vertical position. The clisimeter folds into this weight so that it can be easily carried.

Sighting with a clisimeter

3. When you look through the sighting device, you will see three vertical scales. A scale is a series of marks along a line at regular intervals. You will use the central scale, the stadimetric scale, for measuring horizontal distances. Note that this central scale is made up of two parts:
• The top part, marked 150, 100 ... 7 m;
• The bottom part, marked 150, 100 ... 10 m.

4. To measure a distance with the clisimeter, you need an assistant to help you, and a reference height (called the base). The method you use with the clisimeter will depend on the kind of base you choose.

• You may use a 2 m base, clearly marked on a wooden stake called a stadia staff. In this case, you will use the top part of the distance scale, marked BASE 2.00 m.
• Or you may take the height of your assistant as the base; in this case, you will use the bottom part of the distance scale, marked BASE 1.70 m.

The scale inside a clisimeter

5. Get a straight piece of wood 2.50 m long. A rectangular stake with a cross-section of 8 x 4 cm is best, but you can use a round pole with a cross-section of 6 to 8 cm instead.

6. Get two wooden boards measuring 30 x 40 cm each.

7. Nail these boards along their centre lines 10 cm from each end of the stake, as shown in the figure.

Materials

8. Draw a horizontal line across the middle of one of these boards. This is called the median line.

9. From this line, measure exactly 2 m along the stake. You should reach a point near the middle of the second board. At this point draw a horizontal line across the board.

10. Using a pencil and ruler, divide the length of the stake between the two boards, which should be 1.70 m, into 10 cm sections.

11. Paint the two sections of the boards lying outside the 2 m length in bright red. Then paint, in red, the first 10 cm section next to each board and each alternate section in between.

12. Paint all the other sections of the boards and stake in white, including the 10 cm end sections of the stake. Your stadia staff is now ready to use for measuring distances.

Note: for short distances, you can use a simpler staff; get a pole or staff exactly 2 m long and paint it alternately in red and white, as described above.

### Measuring distances with a stadia staff

13. Send your assistant, carrying the stadia staff, out to the first point along the line you want to measure. There he places the staff as nearly vertical as possible and the painted side of the staff should face you.

14. Holding the clisimeter in one hand, look through its sighting device at the stadia staff. Align the zero line of the central scale with the median line of the bottom board.

15. Look at the top part of the central scale (BASE 2.00 m) of your clisimeter, and read the distance in metres at the graduation which lines up with the median line of the top board.

16. Carefully note this reading in a field-book.

17. Signal to your assistant to remove the stadia staff and replace it with a marking pin. He should then move on to the next point to be measured.

18. Move up to the marking pin left by your assistant, and repeat the procedure until you reach the end of the line.

Note: remember that for fairly accurate measurements, each distance you measure along the straight line should not exceed 30 m

Sighting at the stadia staff using the upper scale

### Measuring distances without a stadia staff

19. If you do not have a stadia staff, you can use the height of your assistant as a reference instead. The height you need for this method is 1.70 m. Measure your assistant's height. If this differs much from 1.70 m, do one of the following:

• if your assistant is taller than 1.70 m, measure the height of his eyes or mouth from the ground and choose the height nearest 1.70 m;
• if your assistant is shorter than 1.70 m, ask him to place an object on his head (such as a can, a bottle or a block of wood) which will increase his height up-to 1.70 m.

Find a reference point 1.70 m high

20. Send your assistant out along the line you want to measure and, at the selected point, ask him to stand as straight as possible, facing you.

21. Holding the clisimeter in one hand, look through the sighting device at your assistant. Align the zero line of the central scale with the 1.70 m mark you have chosen, such as the top of his head, his eyes or the top of a bottle carried on his head.

22. Look at the bottom part of the central scale (BASE 1.70 m), and read the distance in metres at the graduation which lines up with the ground level under his feet.

24. Signal to your assistant to drive a marking pin into the ground at the point where he was standing, and to move onto the next point to be measured.

25. Move up to the marking pin and repeat the procedure as many times as necessary. For the greatest accuracy, each distance you measure along the line should not exceed 30 m.

Sighting at your assistant using the lower scale

### Measuring distances on sloping ground

26. If you are taking a measurement on a slope greater than 5 percent, you must correct the clisimeter reading to get the true horizontal distance. To do this, you need to use a mathematical formula, as explained in Section 4.0.

## 2.8 How to measure distances by the stadia method

The stadia method is rapid and accurate for measuring long distances, but to apply this method, you need to get expensive surveying equipment and learn how to use it. Therefore, only a brief description of the method is given here so that you can understand its basic principles.

1. The equipment used with this method includes a highly technical sighting device called a telescope. To use it, you must sight through two crossed hairs; there are also two extra horizontal hairs called stadia hairs. Most surveyor's levels (see Section 5.8) have these stadia hairs at an equal distance above and below the horizontal cross-hair.

2. To measure a distance, you will also need a levelling staff which is clearly graduated in centimetres (see Section 5.0).

3. Set up the surveyor's level at the point from which you will measure the distance. Signal to your assistant to place the levelling staff vertically at the next point of the line. The distance between you and the staff may be several hundred metres.

4. Look through the telescope and read the graduations (in metres) on the levelling staff that line up with the upper stadia hair and the lower stadia hair. Note these measurements down in your field-book.

5. Subtract the smaller reading from the larger reading. This represents the interval between the two hairs, called the stadia interval.

6. To find the distance (in metres), multiply the stadia interval by a fixed value called the stadia factor. It is given for each telescope, but on most instruments this factor equals 100.

Note: if you are working on sloping ground, you must correct this figure to find the true horizontal distance (see Section 4.0).

Sighting at a levelling staff with the telescope

The scale inside a surveyor's telescope

Example

• Stadia interval = 1.62 m - 0.52 m = 1.10 m;
• Distance AB = 1.10 m x 100 = 110 m.

## 2.9 How to measure distances that run through obstacles

1. To use the preceding methods, you must be able to walkover the whole length of each straight line and take direct measurements. Sometimes, however, there is an obstacle on the line that makes measuring the distance directly impossible. Such a line could be across a body of water such as a lake, a lagoon or a river, or across agricultural fields with standing crops. In these cases, you must take indirect measurements of a segment of the line. You will use some of the methods you learned in Section 1.6 for setting out a line across an obstacle.

### Measuring a distance across a lake or an agricultural field

2. From point A on the line XY running through the obstacle, set out another straight line AZ, avoiding the obstacle.

3. On this new line, layout a perpendicular line CB joining the original line at point B behind the obstacle (see Section 3.6).

4. Measure the two new line sections AC and CB and calculate the unknown distance AB from a mathematical formula as follows:

 AB = �(AC2 + BC2)

Line XY crosses a lake

Set out line AZ

Lay out perpendicular CB

### Measuring a distance across a river

5. Here, the obstacle (a river) cannot be avoided, but you can see the points you need to measure from both sides of the river. There are several methods, based on geometry, which can be used. Two simple ones are described here.

6. Method 1. You need to measure distance GH across a river. Using ranging poles, prolong line GH back to point C. At G and C, lay out perpendiculars GZ and CX. On each of these lines, set out a point, E and F, so that they lie on a straight line FY passing through H, on the opposite bank. Measure accessible distances GE, GC and CF. Calculate the inaccessible distance GH as:

 GH = (GE x GC) �(CF - GE)

GH crosses a river

You can see point H from point G

Prolong the line back to point C

Lay out perpendiculars GZ and CX

Find points E and F on line FEHY

Calculate distance GH

Example

You wish to measure GH, across a river:

• prolong line GH back to C;
• lay out perpendiculars GZ and CX;
• select points F and E on line FEH;
• measure distances GE = 34 m; GC = 36 m; CF = 54 m;
• calculate GH = (34 m x 36 m) � (54 m - 34 m);
GH = 1 224 m � 20 m = 61.2 m.

 7. Method 2. You need to measure distance AB across a river. Layout line BX perpendicular to AB on one river bank. Determine the point C of this perpendicular from which you will be able to sight point A across the river, using a 45-degree angle (see, for example, Section 3.6, step 63). Measure distance CB, which is equal to inaccessible distance AB. Line AB crosses a river Lay out perpendicular BX Layout 45� angle BCA Calculate distance AB Example You need to measure distance AB: from B, lay out perpendicular BX; determine C, so that angle BCA = 45 degrees; measure BC = 67 m; distance AB = BC = 67 m.