To determine the difference in level between points on the surface of
the ground a 'series' of levels will need to be carried out; this is called
a
The leveling or field procedure that should be followed is shown in Figure 1 below..
- Set up the leveling instrument at Level position 1.
- Hold the staff on the Datum (RL+50 m) and take a reading. This will be a backsight, because it is the first staff reading after the leveling instrument has been set up.
- Move the staff to
**A**and take a reading. This will be an intermediate sight. - Move the staff to
**B**and take a reading. This also will be an intermediate sight. - Move the staff to
**C**and take a reading. This will be another intermediate sight. - Move the staff to
**D**and take a reading. This will be a foresight; because after this reading the level will be moved. (A changeplate should be placed on the ground to maintain the same level.) - The distance between the stations should be measured and recorded in the fieldbook (see Table 1)
- Set up the level at Level position 2 and leave the staff at
**D**on the changeplate. Turn the staff so that it faces the level and take a reading. This will be a backsight. - Move the staff to
**E**and take a reading. This will be an intermediate sight. - Move the staff to
**F**and take a reading. This will be a foresight; because after taking this reading the level will be moved. - Now move the level to Leveling position 3 and leave the staff at
**F**on the changeplate.
Now repeat the steps describe 8 to 10 until you finished at point
All staff readings should be recorded in the fieldbook. To eliminate errors resulting from any line of sight (or collimation) backsights and foresights should be equal in distance. Length of sight should be kept less than 100 metres. Always commence and finish a level run on a known datum or benchmark and close the level traverse; this enables the level run to be checked. [ top of page ] There are two main methods of booking levels: - rise and fall method
- height of collimation method
The millimeter reading may be taken by estimation to
an accuracy of 0.005 metres or even less.
- Backsight, intermediate sight and forsight readings are entered in the appropriate columns on different lines. However, as shown in the table above backsights and foresights are place on the same line if you change the level instrument.
- The first reduced level is the height of the datum, benchmark or R.L.
- If an intermediate sight or foresight is
**smaller**than the immediately preceding staff reading then the difference between the two readings is place in the**rise**column. - If an intermediate sight or foresight is
**larger**than the immediately preceding staff reading then the difference between the two readings is place in the**fall**column. - A rise is added to the preceding reduced level (RL) and a fall is subtracted from the preceding RL
[ top of page ] Arithmetic checks
While all arithmetic calculations can be checked there is no assurance that
errors in the field procedure will be picked up. The arithmetic check poves only that the rise and fall is correctly recorded in the approriate rise & fall columns. To check the field procedure
for errors the level traverse If the arithmetic calculation are correct, the the difference between the sum of the backsights and the sum of the foresights will equal: -
the difference between the sum of the rises and the sum of the falls,
and
- the difference between the first and the final R.L. or vice versa.
(there are no arithmetic checks made on the intermediate sight calculations. Make sure you read them carefully)
[ top of page ]
- Booking is the same as the rise and fall method for back-, intermediate- and foresights. There are no rise or fall columns, but instead a height of collimation column.
- The first backsight reading (staff on datum, benchmark or RL) is added to the first RL giving the height of collimation.
- The next staff reading is entered in the appropriate column but on a new line. The RL for the station is found by subtracting the staff reading from the height of collimation
- The height of collimation changes only when the level is moved to a new position. The new height of collimation is found by adding the backsight to the RL at the change point.
- Please note there is no check on the accuracy of intermediate RL's and errors could go undetected.
The rise and fall method may take a bit longer to complete, but a check
on entries in all columns is carried out. The RL's are easier to calculate
with the height of collimation method, but errors of intermediate RL's
can go undetected. For this reason students should use the rise and fall
method for all leveling exercises.
[ top of page ]
Always
Misclosure in millimeter 24 x √km
back to the known
Datum or RL. Misclosure in millimeter 24 x √km
[ top of page ]
Area calculations refer usually to rectangular and triangular shapes. If you need the trigonometric function for calculations click here. There
are different ways to calculate the area of the opposite figure. Try to
minimise the amount of calculation. The figure could be divided in three
distinct areas =10.39x4.79c or the whole rectangle minus the hole (d) A =16.67x10.31-6.25x4.55. As you can see the 2nd method is easier. Look at the shape and try to shorten the calculations. If you know only the sides of a triangle then use the formula given in the figure below. An area can usually be divided it in triangles (rectangles, parallelograms, trapeziums etc). Parallelograms has opposite sides parallel and equal. Diagonals bisect the figure and opposite angles are equal..
The trapezium has one pair of opposite sides parallel.
An arc is a part of the circumference of a circle; a part proportional to the central angle. If 360° corresponds to the full circumference. i.e. 2 r then for a central angle of (see opposite figure) the corresponding arc length will be b = /180 x r . [ top of page ]
Volume calculations for rectangular prism and pyramid are shown below: A truncated pyramid is a pyramid which top has been cut off. If the A _{1} + A_{2}) / 2
A prismoid is as a solid whose end faces lie in parallel planes and consist of any two polygons, not necessarily of the same number of sides as shown opposite, the longitudinal faces may take the form of triangles, parallelograms, or trapeziums. [ top of page ] |