Transcript
ISTANBUL TECHNICAL UNIVERSITY DEPARTMENT OF GEOMATICS ENGINEERING SURVEYING – I
WEEK 8
CLASS PRESENTATIONS FOR SURVEYING I COURSE BY E.TARI, H. KARAMAN
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LEVELING Leveling is the procedure for determining differences in elevation between points.
An elevation is the vertical distance above or below a reference datum. Areas of Applications design highways, railroads, canals
lay out construction projects according to specific design calculate the volume of earthwork investigate drainage characteristics of an area map earth’s topography
monitor earth subsidence and crustal motion
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LEVELING Definitions: Vertical line is a line that follows the local direction of gravity as indicated by a plumb line. Level surface is a curved surface that every point is perpendicular to the local plumb line. Level line is a line in a level surface, therefore, a curved line.
Horizontal plane is a plane perpendicular to the local direction of gravity. In plane surveying, it is a plane perpendicular to the local vertical line. Horizontal line is a line in a horizontal plane. In plane surveying, it is a line perpendicular to the local vertical.
Vertical datum is any level surface to which elevations are referenced. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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LEVELING Definitions: Elevation is the distance measured along a vertical line from a vertical datum to a point or object. Geoid is a particular level surface that serves as a datum for elevations and astronomical observations. Mean Sea Level is the average height of the sea’s surface for all stages of the tide over a 19-year period. Benchmark is a relatively permanent object, natural or artificial, having a marked point whose elevation above or below a reference datum is known or assumed. Vertical control is a series of benchmarks or other points of known elevation established throughout an area.
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LEVELING
Figure1: Leveling Terms
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LEVELING CONCEPTS
Figure 2 : Leveling Concepts
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LEVELING
Figure:3
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LEVELING Benchmarks:
Figure 4: Benchmarks
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LEVELING Levelling Methods: Differential Leveling Trigonometric Leveling Barometric Leveling Stadia Leveling
Gravimetric Leveling Profile Leveling GPS Leveling
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LEVELING METHODS Differential Leveling:
Differential leveling is the operation of determining differences in elevation of points some distance apart or of establishing benchmarks. To measure the difference height of (ΔH) between two points A and B, vertical rods are set up at each of these two points and a level set up approximately halfway between them. The height of difference between A and B is the difference between the rod (staff) readings.
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Differential Leveling:
Figure: 5
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Differential Leveling: Rod Reading
Figure: 6
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Differential Leveling: Rod Reading:
Backsight reading (BS) is the first reading when the level has been set up. Foresight reading (FS) is the last staff reading. Intersight-intermediate (IS) is the other staff reading between the BS and FS.
Change point or turning point is the point at which the last staff reading has been performed.
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INTERMEDIATE STAFF READINGS backsight Intermediate sights
0.738
2.111
1.843
1.440
0.174
1.603
F D
A = 20.450
B
BS
IS
FS
0.738
H.P.C.
RL
21.188
20.450
COMMENTS OBM (=20.450) point A
2.111
19.077
Point B
1.843
19.345
Point C
1.440
19.748
Point C
1.603
19.585
Point E
0.174
21.014
Point F (last reading)
FS
Last First
0.174
0.564
BS 0.738
E
C
BS - FS 0.564
Check sums: arithmetic OK
Differential Leveling: Leveling Rods: They are manufactured from wood, metal, or fiberglass and are graduated in meters. The metric rod can usually be read directly to 0.01 m, with millimeters being estimated. Rod must be held vertically on a point. To ensure that the rod is plumb, a rod level is used.
Figure: 7 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Leveling Rods: Cross-hair readings; leveling instruments have three horizontal crosshair; the upper and the lower hair, the center hairs. The three wire leveling gives check on readings.
Figure: 8
Center = (Upper + Lower) / 2 Sight Distance = 100*(Upper – Lower) If Upper reading > lower reading ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Levelling Staff (rod) Check bottom of staff for
wear and cleanliness Hold staff Vertical Use spirit level attachment if necessary OR line up edge of staff with edge of a building For more accurate work “rock” staff towards and away from Instrument Be aware of hitting live overhead cables with aluminium staff
Reading Staff (rod) Alternate colours BLACK
/ RED every 1metre Leg of E and small blocks are 10mm i.e. 0.010m Learn to estimate to nearest 2mm i.e.0.002 If extension used, check catch fully engaged Use peg, foot plate or other easily retraced point for change points and mark its position with a temp. marker.
Reading Staff (rod)
For close up work numbers may not be visible – ask assistant to place pencil on staff and move it up/down until it is visible then look at staff with naked eye.
Leveling Rods: Suggestions for rod work: The rod should be properly extended and clamped. Take care to
ensure that the bottom of the sole plate does not become encrusted with mud, dirt, and so on, which can result in mistaken readings. If a rod target being used, ensure that it is properly positioned and that cannot slip. The rod should be held plumb for all rod readings. Either a rod
level is used, or the rod is waved gently to and from the instrument so that the lowest (indicating a plumb rod) reading can be determined. This practice is particularly important for all backsights and foresights. Ensure that all points used as turning points are suitable, in other
words, describable, identifiable, and capable of having the elevation determined to the closest 0.001m. The TP should be nearly equidistant from the two proposed instrument locations. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Leveling Rods: Suggestions for rod work: Make sure that the rod is held in precisely the same position for
the backsight as it was for the foresight for all turning points.
If the rod is held temporarily near, but not on, a required location,
the face of the rod should be turned away from the instrument so that the instrument operator cannot take a mistaken reading. This type of mistaken reading usually occurs when the distance between the two surveyors is too for to allow for voice communication and sometimes even for good visual contact.
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Differential Leveling: Theory of Differential Leveling
Figure: 9
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Differential Leveling: Theory of Differential Leveling -1 (Rise and Fall method) The basic procedure is illustrated in figure 9. An instrument set up approximately halfway between benchmark and point BM01. Also, make sure rod will be visible when instrument leveled at new position. Assume the elevation of on a rod held on BM gives a reading of 1.862 m . Backsight (BS) is the reading on a rod held on a point of known elevation.
If the telescope is then turned to bring into view a rod held on point BM01, called foresight (FS), is obtained. In this example it is 0.648 m. Difference elevation between two points; Δh = BS – FS ( 1.862m – 0.648m ) Elevation BM01 = Elevation BM + Δh = 950.495m + (1.862m0.648m) = 951.709 m. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Theory of Differential Leveling-1 ( Rise and Fall Method) Basic theory; Δh = BS – FS
Δh > 0
Δh < 0
HB = HA + ΔhAB
HB = Elevation (height) of point B HA = Elevation (height) of point A
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Differential Leveling: Theory of Differential Leveling-1 (Rise and Fall Method)
Figure: 10
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Differential Leveling: Theory of Differential Leveling-1 (Rise and Fall Method) Δh1 = BSA – FS1 Δh2 = BS1 – FS2 Δh3 = BS2 – FS3 Δh4 = BS3 – FSB
ΔH = Σ (BSA + BS1 + BS2 + BS3 ) – (FS1 + FS2 + FS3 + FSB ) ΔH = ΣBS - ΣFS HB = HA + Σ ΔhAB
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Differential Leveling: Theory of Differential Leveling-1
Figure:11
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Differential Leveling: Theory of Differential Leveling-1 (Rise and Fall Method)
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation Method)
Figure:12
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation Method) The optical line of sight forms a horizontal plane, which is at the same elevation as the telescope crosshair. By reading a graduated rod held vertically on a point of known elevation (Bench Mark) a difference in elevation can be measured and a collimation height (height of instrument (H.I)) calculated by adding the rod reading to the elevation of the bench mark. Collimation height: HA + BSA = 755.11m + 8.46 m Elevation of point which is set up a leveling rod on: Collimation Height - ( IS or FS )
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation method)
Figure:13 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation method)
Figure:14 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation Method)
Figure:15 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Theory of Differential Leveling-2 ( Collimation method) In the following example, the elevation at BM-A is known, and we need to know the elevation of BM-K. The level is set up at a point near BM-A, and a rod reading taken. Collimation height (HI) is calculated and a rod reading to a turning point (TP1) is taken. The reading of the foresight is subtracted from the collimation height to obtain the elevation at TP1. The rod stays at TP1, the level moves ahead and the rod at TP1 now becomes the backsight. This procedure is repeated until the final foresight to BM-K.
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Differential Leveling: Theory of Differential Leveling-2
Control :
Σ(H.I) +HBMA = Σ Elevation + Σ I.S + Σ F.S ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling: Theory of Differential Leveling-2
Σ(H.I) = 74.917m Control :
Σ Elevation = 76.633m
Σ(H.I) +HBMA = Σ Elevation + Σ I.S + Σ F.S
Control : 74.917 +10.00 = 76.633 + 6.680 + 1.604
84.917 = 84.917 *Collimation Height (H.I) = HA +BSA (for the first reading)... * Elevation of point 1 = (H.I)- I.S1 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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Differential Leveling:
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TYPES OF LEVELING NETS Open Leveling Nets
Closed – Loop Leveling Nets
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TYPES OF LEVELING NETS Closed Link - ClosedConnecting Leveling Nets
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TYPES OF LEVELLING NETS Leveling between two points is performed in two steps; forward (ΔHAB) , backward (ΔHBA) ;
Open Leveling Net Condition: In open leveling nets, the height differences between ΣhAB and ΣhBA should be theoretically zero. ΣhAB - ΣhBA = 0
Closed Loop Leveling Net Condition: Σ Δh = 0 ( the point of which height is known is the same point, both starting and ending point.) Closed-Link Leveling Net Condition:
Σ Δh = HB – HA ( elevations of two points A and B are known)
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TYPES OF LEVELLING NETS Misclosure error for open leveling nets fh = |ΣΔhforward|- Σhbackward | Loop misclosure for closed loop leveling nets fh= ΣΔh - 0.000
Loop misclosure for closed-link leveling nets fh = ΣΔh - (HB – HA)
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TYPES OF LEVELLING NETS Correction for leveling nets with proportion of leveling distances Vhi = - ( fh / Σl ) * li
Vhi = correction for elevation difference between two points l i = leveling distance between two points Σl = total leveling distance for leveling loop
Correction for leveling nets with proportion of elevation differences Vhi = - ( fh / |ΣΔh| ) * |Δh i | Vhi = correction for elevation difference between two points |Δh i | = absolute elevation distance between two points |Σ Δh|= absolute total elevation distance for leveling loop
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TYPES OF LEVELLING NETS Correction for leveling nets by calculating collimation method Vhi = - ( fh / Σl ) * Li
Vhi = correction for elevation without correction at a point L i = distance from starting point to point whose elevation is corrected
Limit of difference between forward and backward leveling and limit of loop misclosure : These values are checked in respect of Production Regulation of Large Scale Map standards.
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TYPES OF LEVELLING NETS Closed Loop Leveling Nets Computation
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TYPES OF LEVELLING NETS Closed Loop Leveling Nets Computation
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TYPES OF LEVELLING NETS Closed Loop Leveling Nets Computation
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TYPES OF LEVELLING NETS Closed -Link Leveling Nets Computation
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TRIGONOMETRIC LEVELING
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TRIGONOMETRIC LEVELING
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TRIGONOMETRIC LEVELING
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TRIGONOMETRIC LEVELING Curvature Effect
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TRIGONOMETRIC LEVELING Curvature Effect Horizontal line=line of collimation Effect of curvature
Level Line
MSL
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TRIGONOMETRIC LEVELING Refraction Effect The air has different optical properties everywhere. Air pressure, humidity etc. Have an impact on the refractivity. Thus the light does not propagate along a straight line, but along a curve:
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TRIGONOMETRIC LEVELING
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TRIGONOMETRIC LEVELING
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TRIGONOMETRIC LEVELING
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TYPES OF LEVEL Dumpy Levels Tilting Levels
Automatic Levels Digital Levels
Although each differs somewhat in design, all have two common components, a telescope to create a line of sight and enable a reading to be taken on a graduated rod, and a system to orient a line of sight in a horizontal plane. Dumpy and tilting level use the level vials to orient the lines of sight, while automatic levels employ automatic compensators. Digital levels also employ automatic compensators, but use bar-coded rods for automated digital readings.
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LEVEL
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TYPES OF LEVELS
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LEVELS Telescopes: Telescopes of leveling instruments define the line of sight and magnify the view of a graduated rod against a reference reticle, thereby enabling accurate readings to be obtained. The components of a telescope are mounted in a cylindrical tube. Its four main components are the objective lens, negative lens, reticle and eyepiece.
Objective lens: securely mounted in the tube’s object end, has its optical axis reasonably concentric with the tube axis. Its main function is to gather incoming light rays and direct them toward the negative focusing lens.
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LEVELS Telescopes: Negative lens: the negative lens is located between the objective lens and reticle, and mounted so its optical axis coincides with that of the objective lens. Its function is to focus rays of light that pass through the objective lens onto the reticle plane. During focusing, the negative lens slides back and forth along the axis of the tube. Reticle: it consists in a pair of perpendicular reference lines( usually called crosshairs) mounted at the principal focus of the objective optical system. The point of intersection of the crosshairs, together with the optical center of the objective system, forms the so-called line of sight, also sometimes called the line of collimation. Two additional lines parallel to and equidistant from the primary lines are commonly added to reticles for special purposes such as for three-wire leveling. Eyepiece: It is a microscope for viewing the image.
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LEVELS FOCUSING: Focusing the telescope of a level is a two stage process.
First the eyepiece lens must be focused. Since the position of the reticle in the telescope tube remains fixed, the distance between it and the eyepiece lens must be adjusted to suit the eye of an individual observer. This is done by bringing the crosshairs to a clear focus; that is; making them appear as black as possible when sighting at the sky or a distant, light-colored object. Once this has been accomplished, the adjustment need not be changed for the same observer, regardless of sight length, unless the eyes fatigue. The second stage of focusing occurs after the eyepiece has been adjusted. Objects at varying distances from the telescope are brought to sharp focus at the plane of the crosshairs by turning the focusing knob. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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LEVELS Parallax: After focusing, if the crosshairs appear to travel over the object sighted when the eye is shifted slightly in any direction, parallax exists. The objective lens, the eyepiece, or both must be refocused to eliminate this effect if accurate work is to be done. Elimination of Parallax: Focus the crosshair (using the eyepiece) Focus the object (using the focusing screw) Move eye up and down over the eyepiece Images appear to move
Parallax exists and must be removed by bettering focus The eyepiece and objective lens must be refocused to eliminate
this effect.
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LEVELS Level Vials: Level vials are used to orient many different surveying instruments with respect to the direction of gravity. There are two basic types; the tube vial and the circular or so-called “bull’s-eye” version. Tube vials are used on tilting levels to precisely orient the line of sight horizontal prior to making rod readings. Bull’s eye vials are also used on tilting levels, and on automatic levels for quick, rough leveling, after which precise final leveling occurs.
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TYPES OF LEVELS The coincidence-type tube level:
Figure illustrates the coincidence type tube level vial used on precise equipment. A prism splits the image of the bubble and makes the two ends visible simultaneously. Bringing the two ends together to form a smooth curve centers the bubble. This arrangement enables bubble centering to be done more accurately.
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TYPES OF LEVELS The coincidence-type tube level: Prism
Bubble tube
Bubble tube is tilted
Bubble tube is horizontal (leveled)
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TYPES OF LEVELS Tilting levels:
They are used for the most precise work. With these instruments, quick approximate leveling is achieved using a bull’s eye bubble and the leveling screws. On some tilting levels, a ball-and-socket arrangement (with no leveling screw) permits the head to be tilted and quickly locked nearly level. Precise level in preparation for readings is then obtained by carefully centering telescope bubble. This is done for each sight, after aiming at the rod,
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TYPES OF LEVELS Tilting levels:
Source: Engineering Surveying, Shofield & Breach, 2007 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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TYPES OF LEVELS Tilting levels:
The tilting feature saves time and increases accuracy, since only one screw need to be manipulated to keep the line of sight horizontal as the telescope is turned about a vertical axis. The telescope bubble is viewed through the a system of prisms form the observer’s normal position behind the eyepiece. A prism arrangement splits the bubble image into two parts. Centering the bubble is accomplished by making the images of the two ends coincide.
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TYPES OF LEVELS Automatic Levels:
Automatic levels incorporate a self-leveling feature. Most of these instruments have a three screw leveling head, which is used to quickly center a bull’s-eye bubble, Although some models have a ball-and-socket arrangement for this purpose. After the bull’s-eye bubble is manually centered, an automatic compensator takes over, levels line of sight, and keeps it level.
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TYPES OF LEVELS Automatic Levels:
Source: Engineering Surveying, Shofield & Breach, 2007 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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TYPES OF LEVELS Automatic Levels:
Source: Engineering Surveying, Shofield & Breach, 2007 ITU DEPARTMENT OF GEOMATICS ENGINEERING
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TYPES OF LEVELS Automatic Levels:
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TYPES OF LEVELS Automatic Levels:
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TYPES OF LEVELS Automatic Levels: The advantages of the automatic level over the tilting level are: (1) Much easier to use, as it gives an erect image of the staff. (2) Rapid operation, giving greater productivity. (3) No chance of reading the staff without setting the bubble central, as can occur with a tilting level. (4) No bubble setting error.
A disadvantage is that it is difficult to use where there is vibration caused by wind, traffic or, say, piling operations on site, resulting in oscillation of the compensator. Improved damping systems have, however, greatly reduced this defect. During periods of vibration it may be possible to reduce the effect by lightly touching a tripod leg. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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TYPES OF LEVELS Importance of Circular Levels:
Bubble
of Automatic
Although the circular bubble is relatively insensitive, it nevertheless plays an important part in the efficient functioning of the compensator: (1) The compensator has a limited working range. If the circular bubble is out of adjustment, thereby resulting in excessive tilt of the line of collimation (and the vertical axis), the compensator may not function efficiently or, as it attempts to compensate, the large swing of the pendulum system may cause it to stick in the telescope tube. (2) The compensator gives the most accurate results near the center of its movement, so even if the bubble is in adjustment, it should be carefully and accurately centered.
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TYPES OF LEVELS Importance of Circular Levels:
Bubble
of Automatic
(3) The plane of the pendulum swing of the freely suspended surfaces should be parallel to the line of sight, otherwise over- or under-compensation may occur. This would result if the circular bubble were in error transversely. Any residual error of adjustment can be eliminated by centering the bubble with the telescope pointing backwards, whilst at the next instrument set-up it is centered with the telescope pointing forward. This alternating process is continued throughout the leveling. (4) Inclination of the telescope can cause an error in automatic levels, which does not occur in tilting levels, known as ‘height shift’. Due to the inclination of the telescope the center of the object lens is displaced vertically above or below the center of the cross-hair, resulting in very small reading errors, but which cannot be tolerated in precise work. ITU DEPARTMENT OF GEOMATICS ENGINEERING
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TYPES OF LEVELS Digital Levels: The newest type of automatic level, the electronic digital level.
It uses a pendulum compensator to level itself, after an operator accomplishes rough leveling with a bull’s-eye bubble. With its telescope and crosshairs, the instrument could be used to obtain readings manually, just like any of the automatic levels. Also, it is designed to operate by employing electronic digital image bar-coded rod and focused. At the press button, the image of bar codes in the telescope’s field of view is captured and processed. This processing consists of an on-board computer comparing the captured image to the rod’s entire pattern, which is stored in memory. When a match is found, the rod reading is displayed digitally.
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TYPES OF LEVELS Digital Levels
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Instrument Set Up: Set the tripod Put the instrument on the table of the tripod and fixed it using
tightening screw.
Center circular level with using three foot screws for approximate
level.
Aim the telescope to the rod
Focus the rod using the focus screw Sharpen the image of crosshair using focusing ring on the eye
piece.
Bring the vertical crosshair exactly on the rod using tangent screw.
Center the bubble of spirit level using knob for coincidence setting. Read the rod in mm precision.
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SOURCES OF ERROR IN LEVELING Instrumental errors: Line of sight
Crosshair not exactly horizontal Rod not correct length Tripod legs loose
Natural errors: Curvature of the Earth Refraction Temperature Variations Wind Settlement of the Instrument Settlement of the turning point ITU DEPARTMENT OF GEOMATICS ENGINEERING
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SOURCES OF ERROR IN LEVELING Personal errors: Bubble not centered
Parallax Faulty Rod reading Rod handling Target setting
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MISTAKES IN LEVELING Improper use of a long rod
Holding the rod in different places for the foresight and backsights
on a turning point Recording notes
Touching tripod or instrument during reading process
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Adjusting the level The two-peg test
b1
a1 d1
A
d1
d2
P
d2
B
Collimation error - the line of collimation is not horizontal, when the level is levelled The effect of collimation error cancels, if d1=d2. Thus the height difference is:
H AB a1 b1
Adjusting the level The two-peg test
b2
a2 d1 d 2 d3
d3
A
d1+d2
B
d3
Q
H AB a2 d1 d 2 d3 b2 d3 H AB a2 b2 d1 d 2 From the previous configuration:
H AB a1 b1
a2 b2 a1 b1 d1 d 2
REFERENCES:
Basic Surveying -The Theory and Practice, Oregon Department of Transportation,
Geometronics Unit, Ninth Annual Seminar, February 2000,
Barry F. Kavanagh, Surveying Principles and Applications, Pearson Education International
Edition, Eighth Edition, 2009.
C.D. Ghilani, P.R. Wolf; Elementary Surveying , Pearson Education International Edition,
Twelfth Edition, 2008 .
Ü.Öğün , Topografya Ders Notları ,
U.Özerman, Topografya Ders Notları , Bahar 2010,
H. Özener, Lecture Notes, CE200 Surveying, Bogazici University Kandilli Observatory and
Earhquake Research Institute Department of Geodesy.
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