2. MEASURING HORIZONTAL DISTANCES

Expressing distances as horizontal measurements

Measuring distances along lines that run through obstacles

      TABLE 1

Distance measurement methods

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

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.

Note: to determine a more accurate pace factor:

• walk over a longer distance (at least 250 paces);
• repeat the measurements at least three times and calculate the average PF.

Example

For 250 paces, you measure successively 185 m, 190 m and 188 m; in total, for 3 x 250 = 750 paces, you have walked 185 + 190 + 188 m = 563 m; your average pace factor, PF = 563 m � 750 = 0.75 m.

• your pace will be shorter in tall vegetation than in short vegetation;
• your pace will be shorter walking uphill than walking downhill;
• your pace will be shorter walking on sloping ground than on flat ground;
• your pace will be shorter walking on soft ground than on hard ground.

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:

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.

Pacing with a passometer or a pedometer

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.

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.

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.

2.5 How to chain 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.

Example

If each link is 0.20 m long, there should be five links per metre of chain.

• 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.

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.

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...

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.

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.

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.

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.

Maximum permissible difference between two consecutive
distance measurements, per 100 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

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.

• 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).

2.7 How to measure distances with a clisimeter

• 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.

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.

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.

23. Carefully note this reading in your field-book.

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.

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).

Example

• Upper stadia hair reading: 1.62 m;
• Lower stadia hair reading: 0.52 m;
• Stadia interval = 1.62 m - 0.52 m = 1.10 m;
• Stadia factor = 100;
• Distance AB = 1.10 m x 100 = 110 m.