5. MEASURING HEIGHT DIFFERENCES - PART 1

5.0 Introduction

Height differences in fish culture 

Making your own levelling staff

9. To make your own levelling staff, get a straight length of wood, 2 to 3 m long and 5 to 10 cm wide. Clearly mark graduations along it every 10 cm. It is best if you paint the levelling staff white and mark the graduations on it in red. Make these graduations fairly large (about 1 cm thick) so you will be able to read them easily and accurately from a long distance.

10. You can also make a levelling staff by gluing one or more graduated measuring tapes onto a straight piece of wood 2 to 3 m long. Glue the tapes on lengthwise, end to end. To read the small graduations accurately, you may have to decrease the distances over which you take the measurements, or rely on an assistant to make the reading.

11. Another model of levelling staff is described in Section 6.5. It is used for contouring and for setting graded lines of slope.

Choosing the best method for measuring height differences

Calculating height differences from vertical angles

14. If you have measured vertical angle ABC in degrees, you can calculate the height difference AC from:

• either the ground distance BC along the slope

obtaining sine ABC from Table 14

• or the horizontal distance BA

obtaining tangent ABC from Table 3.

Example

• Vertical angle ABC = 7 degrees. You need to calculate AC.
• If you have measured BC= 47 m: from Table 14, sin 7� = 0.12187; AC = 47 m x 0. 12187 = 5.72789 m = 5.73 m;
• If you have measured BA= 46.7 m: from Table 3, tan 7� = 0.1228; AC = 46.7 m x 0.1228 = 5.73476 = 5.73 m.

With the ground distance, calculate AC = BA x sine ABC

Using height differences to calculate horizontal distances

16. You also learned one way of correcting distance measurements, using slope (see Section 4.0, steps 10-13).

17. Another way of correcting distance measurements is to use measurements of height differences in the following formula:

Horizontal distance = � (G² - H²)

• You have measured AB = 45 m along the sloping ground;
• The height difference AC from point A to point B equals 9 m;
• The horizontal distance

CB = �((45 m)² - (9 m)²) = 
= �(2025 m - 81 m) = �1944 m = 44.1 m

5.1 How to use the straight-edge level

1. You can make a simple device for measuring height differences over a small distance out of a mason's level (see Section 6.1) and a wooden straight-edge.

Making a straight edge

2. Get a piece of wood that is heavy enough to resist warping, and 2.5 to 3 m long. This piece of wood must be cut very carefully so that the edges are straight and squared-off.

3. When you have cut the straight-edge, hold one end to your eye and sight along the top and bottom edges to find which is the straightest.

Making a straight-edge level

Measuring height differences using the straight-edge level

Making your own line level

3. Wrap the loose ends of the cords with string to reinforce them.  

Using the line level for levelling  

8. The rear person reads the height of that end of the cord on the levelling staff. The front person does the same. Be sure to double-check all measurements. Write down the measurements carefully, putting the rear measurements in one column and the front measurements in another column so you won't get them confused. (See the chart in step 10)

9. Then the front person removes the levelling staff from the ground and replaces it with a marking pin. The team progresses forward along the line, repeating the same procedure. The rear person should stop each time at the marking pin that the front person has placed for the previous measurement.

Finding height differences with the line level

Making a T-bone level

3. Lay the other piece of wood lengthwise on the ground, and centre the grooved piece, grooved side up, perpendicularly across it in a "T" shape. Make sure that their top sides are even and that they form an exact 90� angle. Nail the grooved piece in position to the other piece and add two support struts to hold it in place. The total height of the device should be 1 m.

Note: to improve the accuracy of the level, you can make the horizontal top piece 1.5 m long rather than 1 m.

Using a T-bone level for levelling

5. Have your assistant hold the levelling staff in a vertical position at the next point B of the line, about 10 m away.

6. Sight along the edge of the groove, as though you were sighting a gun, toward the graduation of the levelling staff.

8. Note these readings down in a table and calculate the height differences (see Section 5.2, step 10).

Note: since your T-bone level is exactly 1 m high, all you have to do to obtain the height difference between two points is to subtract 1 m from the reading on the levelling staff.

• the top piece forms a 90� angle with the support piece and is centred over it in a T-shape; and
• the widest face of the top piece is horizontal to provide a flat surface.

Using the improved T-bone level for levelling

4. You use the improved T-bone level the same way as the simple T-bone level (see Section 5.4), except that:

• first you drive it into the ground, down to the reference line;
• then you adjust the top board with the mason's level to make it horizontal;
• finally, you set the sighting line with the metal sights attached to the mason's level.

8. To allow the triangle to move freely, place small blocks of wood or short segments of bamboo between the wooden strips of the triangle where they cross at the top and between the back of the triangle at this point and the vertical staff.

9. Loosely bolt the triangle, through the wooden blocks or bamboo segments, to the hole in the vertical staff. The sighting line should be exactly 1.50 m from the ground. This height is convenient for both calculations and sighting. With the bamboo sighting tube perpendicular to the support staff, measure the vertical distance from the centre of the tube to the bottom of the staff. Mark a reference line 1.50 m below the line of sight.

5.7 How to use the hand level

1. The hand level is a ready-made tool for quickly finding differences in level. Its range in the field should not exceed 15m. You may be able to borrow a hand level from a local survey station or buy one from a hardware store. The hand level is made up of a sighting channel, a spirit level and a mirror. The mirror allows you to take a reading and, at the same time, check to see that the sighting line* is horizontal.

Using the hand level for levelling

2. The directions for using the hand level are the same as those given for the bamboo sighting level (see Section 5.6), except that:

• you can use it held in your hand;
• the height of the sighting line is the vertical distance from the ground to your eye level; and
• the bubble of the spirit level must be centred while you take the reading.

      5.8 How to use the surveyor's level and theodolite

1 . For very accurate levelling over long distance surveyors use modern instruments called surveyor's levels and theodolites. These instruments are expensive and can be damaged easily. Only skilled personnel should operate, adjust and repair them.

2. To level survey a small farm you will not usually need the high accuracy of these instruments, and you may use cheaper devices. You have learned about these in earlier sections. However, either a surveyor's level or a theodolite may be available for your survey. Both should be used with a modern levelling staff (see Section 5.0, step 8) to give the greatest accuracy. The levelling staff is set vertically on the ground so that its graduation marks are upside down, since the sighting devices on the surveyor's instruments invert the images, making them appear upside down.

3. A surveyor's level is basically a telescope, fitted with cross-wires for sighting, and attached to a levelling device which is mounted on a tripod (a support with three legs). In older instruments, the horizontality of the sighting line was adjusted with a sensitive spirit level and fine-threaded adjusting screws. In more recently made instruments (known as self-levelling or automatic levels), the line of sight is automatically brought to the horizontal, which makes surveying operations much easier. The telescope magnifies far-away objects, which means you can observe the graduation on a levelling staff at a much greater distance than you could with your ordinary eyesight.