Geomatics : Levelling
Topic 2: Levelling Aims -Heights, datums and bench marks -Levelling equipment -Field procedure for levelling -Calculating reduced levels -Sources of error in levelling -Other levelling methods Levelling – how heights are defined Engineering surveying involves the measurement of three quantities; heights, angles and distances. Levelling it the process of measuring heights. It is possible when levelling to measure heights with an accuracy of millimetres Heights can also be measured using total stations, handheld lasers and GPS devices.
However, levelling offers an inexpensive, simple and accurate method for measuring heights, and it is widely used in construction sites. Any method of measuring the heights of points above or below the ground using an agreed datum. These datum’s or reference points are present in all construction sites and has an arbitrary height assigned to the point. Most construction sites will have several of these benchmarks, and if they have heights based on an arbitrary datum, they are known as Temporary Bench Marks. Heights Heights are defined using horizontal and vertical lines.
The figure below shows a plumbbob suspended at point P, the direction of gravity along the plumb-line defines the vertical at point P. A horizontal or level line is any line at right angles to this For site work, any horizontal line can be chosen as a datum for heights and for levelling. The height of a point is measured along the vertical above or below the chosen datum. The height of a point relative to a datum is known as its reduced level (RL). On most construction sites there is a permanent datum. The horizontal line or surface passing through this, with its height, becomes the levelling datum.
The height of the datum can be arbitrary, a value often used for this is 100. 000m. This is chosen to avoid any negative heights occurring. Any reference point on site which has had a height assigned to it is known as a bench mark. For most surveys and construction work, several bench marks would normally be established by levelling from the datum. If heights are based on an arbitrary datum these are known as Temporary Bench Marks or TBMs. Curved Surfaces Level (or horizontal) lines are always at right angles to the direction of gravity. The direction of gravity is generally towards the centre of the earth.
Over large areas, as the Earth is curved, level surfaces will also be curved. For these, a height difference is measured along a vertical between two curved level surfaces. When surveying over a large area, a curved level surface of zero height has to be defined. This has been established by the Ordnance Survey, this is called the Ordnance Datum (OD). This corresponds to the average sea level measured Poolbeg or Malin Head. Heights based on these are know as OD heights. The levelling staff Levelling involves measuring vertical distances with reference to a horizontal plane or surface.
To do this, a levelling staff is needed to measure vertical distances and an instrument known as a level is required to define the horizontal plane. Many types of staff are used with varying lengths and different markings. The E-type face is commonly used in the UK and Ireland. This can be read directly to 0. 01m and by estimation to the nearest mm. The staff must be held vertically – a circular bubble is sometimes fitted to help this. Automatic Level 1. Focusing screw 2. Eyepiece 3. Foot screw 6. Tangent screw 7. Circular bubble Automatic Level 4. Horizontal circle 5. Base plate 8. Collimator (sight) 9. Object lens
The main features of the telescope 1. Object lens 2. Focusing screw 3. Focusing lens 4. Diaphragm 5. Eyepiece The object lens, focusing lens, diaphragm and eye piece are all mounted on an optical axis called the line of collimation or the line of sight. This is an imaginary line which joins the optical centre of the object lens to the centre of the cross hairs. When looking through the eye piece of the surveying telescope, a set of lines called the cross hairs can be seen. These are used for taking measurements from the staff. These cross hairs are etched on a small sheet of glass known as the diaphragm.
To make the telescope work, the image of the staff is brought to a focus in the plane of the diaphragm using the focusing screw. The eyepiece is rotated so that the cross hairs are in focus and its focal point is also in the plane of the diaphragm. When looking into the telescope an observer will now see a magnified image of the levelling staff focused against the cross hairs. Parallax Parallax occurs when the focusing screw and the eyepiece is done incorrectly. This condition can be detected by moving the eye to different parts of the eyepiece when reading the staff. If different readings are obtained then parallax is present.
To remove parallax, hold a sheet of paper in front of the object and adjust the eyepiece so that the cross hairs are in focus. Then remove the sheet of paper and bring the staff into focus using the focusing screw. Once again check for parallax by moving your eye around the eyepiece. If parallax is still occurring repeat the adjustment procedure. The compensator In an automatic level, the compensator is mounted on the telescope next to the eyepiece. It will only work when the instrument has been levelled to within about 15’ of the vertical using the foot screws and circular bubble.
The function of the compensator is to ensure that the line of sight viewed through the telescope is horizontal even if the telescope is tilted Tilting levels Tilting levels use a spirit level instead of a compensator to establish a horizontal line of sight. When the bubble is centred the sprit level will be horizontal. When the bubble is off centre the axis will be tilted. By attaching a sprit level to the telescope such that its axis is parallel to the line of sight a horizontal line can be set. This is done by using a tilting screw, when this is rotated the telescope is tilted a small amount in the vertical plane.
The tilting screw is adjusted until the bubble is centred. Digital levels Digital levels are similar in appearance to automatic levels, a horizontal line is established by a compensator and this is done by centralising a circular bubble with the foot screws. The main difference between this and other levels is that the staff readings are taken and recorded automatically. When levelling, a special bar-coded staff is sighted, and there is no need to sight this staff as the level will do this automatically and display the measurement. It can also display the horizontal distance to the staff.
The advantages of digital levels are that observations are taken without the need to read a staff or record anything by hand. Introducing this automation removes two of the most common errors when levelling, reading the staff incorrectly and writing down the wrong value in the field book. The on-board computer also calculates the heights required so that the possibility of making a mistake is removed. This makes the digital level much faster to use. Laser levels Laser levels contain a rotating laser which defines a visible horizontal plane from which distance to the ground can be made and then the height can be determined.
Using a level The following steps are taken when using a level to measure heights 1. Set up the tripod 2. Ensure the top is level 3. Push legs firmly into the ground 4. Attach level 5. Use foot screws to centralise the circular bubble 6. Test to see if the compensator is working 7. Remove parallax Once the level is set up its important that the line of sight is horizontal. When the foot screws have been used to centralise the circular bubble, it is assumed that the compensator has set the line of sight to be horizontal.
However, most levels are not in perfect adjustment and when levelled their line of sight is never exactly horizontal. If the line of sight is not horizontal when the instrument has been levelled, the level has a collimation error. As most levels will have some level of collimation error, a method is required to check if the error is within acceptable limits. This is known as a two-peg test. This needs to be conducted when using a new or different level for the first time and at regular intervals thereafter. Two peg test Stage 1 On fairly level ground, two points A and B are marked a distance of Lm apart.
In soft ground, two pegs are used, on hard surfaces nails or paint may be used. The level is set up midway between the points at C and carefully levelled. A levelling staff is placed at A and B and staff readings S1 (at B) and S2 (at A) are taken. The two readings are: S1 = (S1‘ + x) and S2 = (S2‘ + x) S1‘ and S2‘ are the staff readings that would have been obtained if the line of collimation was horizontal, x is the error in each reading due to the collimation error, the effect of which is to tilt the line of sight by angle ?.
Since AC = CB, the error x in the readings S1 and S2 will be the same. The difference between readings S1 and S2 gives: S1 – S2 = (S1‘ + x) – (S2‘ + x) = S1‘ – S2‘ This gives the true difference in height between A and B. This demonstrates that if a collimation error is present in a level, the effect of this cancels out when height differences are computed provided readings are taken over equal sighting distances. Stage 2 The level is then moved so that it is L/10m from point B at D and readings S3 and S4 are taken.
The difference between readings S3 and S4 gives the apparent difference in height between A and B. If the level is in perfect adjustment then: S1 – S2 = S3 – S4 However this is not always the case and that an error term (e) needs to be estimates e = (S1 – S2) – (S3 – S4) per Lm If the results of these tests show that the collimation error is less than 1mm per 20m (or some specified value). If the collimation error is greater than this specified value then the level has to be adjusted. This is normally done by the manufacturer or a trained technician.
Example Readings obtained from a two peg test carried out on an automatic level with a staff placed on two pegs A and B 50m apart are: Staff reading at A = 1. 283m Staff reading at B = 0. 860m With the level position 5m from peg B (L/10): Staff reading at A = 1. 612m Staff reading at B =1. 219m Calculate the collimation error of the level per 50m of sighting distance Solution S1= 0. 860M S2 = 1. 283M S3 = 1. 219M S4 = 1. 612M e = (0. 860 – 1. 283) – (1. 219 – 1. 612) per 50M = (-0. 423 – (-0. 393)) = -0. 030M per 50M Exam Question 2007 (5 marks)
