Introduction to Theodolite THEODOLITE An instrument used for the measurement of angles is called a theodolite, horizontal and vertical angles are fundamental measurements in surveying. The horizontal angle is used primarily to obtain direction to a survey control point,, or to points to be set out. The vertical angle, is used in obtaining the elevation of points (trigonometric leveling) and in the reduction of slope distance to the horizontal. many types of theodolites are used to measure angles are available to meet varying requirements of accuracy ranging from 1 minutes to precision instruments which read direct to 0.1 second . Measuring a horizontal angle : • The horizontal angle between two lines is the angle between the projections of the lines on to a horizontal plane . • Line of sight of the instrument is directed toward the FROM or back sight station and the circle reading is observed as 00⁰ 00´ and it is recorded as the initial circle reading . • The final reading is obtained by loosing the upper clamp , rotating the alidade about the vertical axis , and directing the line of sight toward the TO or foresight station . • If the alidade has been turned in a clockwise direction , the reading will increase by the angle of rotation . • The difference between the initial reading and the final reading is the angle through which the line of sight was turned in going from the back sight station to the foresight station . M o Line of sight P 90 270 122⁰ 43´ 180 Horizontal circle Back sight M M 0 270 P Line of sight 90 180 Foresight Initial reading=122 43 Final reading =176 13 The angle from M to P =53 30 176⁰ 13´ Angle Observation tools • Transit and Theodolite used in making angle observations in near past. • Today, the total station instrument has replaced transits and theodolites. • Theodolite is more accurate than compass, accuracy of compass is not better than 30’. • Theodolites are in three types: – Vernier Transit (vernier reading system for the horizontal and vertical circle) – Optical (Micrometer system) – Digital or Electronic • Accuracy ranging from 1‘ to very precise instruments which read to up 0.1 second. Angle Observation tools Venire Transit Optical Electronic Vernier Circle readings Viewing through reading microscope (optical system) Measurement of a vertical angle • A vertical angle is the difference of direction between two intersecting lines measured in a vertical plane . • And it is the angle above or below a horizontal plane through the point of observation . • Angles above the horizontal plane of observation are called plus angles or angles of elevation or positive angles . • Those below the horizontal plane are minus angles or angles of depression . • Vertical angles are measured in trigonometric leveling and in stadia work as an important part of the field procedure . Electronic readings Optical Theodolite Parts 1-Telescope , 2- horizontal and vertical circles , 3- focusing ring or screw , 4- eyepiece ring or screw , 5- micrometer drum or screw , 6- horizontal clamp screw , 7- horizontal slow motion , 8- vertical clamp screw , 9- vertical slow motion , 10- reflecting mirror (illumination) , 11- optical plummet or centering rod , 12three leveling head screws , 13- circular and tubular bubbles , 14- fixing screw and more. Sources of Errors (Theodolite) Errors in theodolite results from : Instrument Natural Personal Usually it is impossible to determine the exact value of an angle , so, measured value contain an error. Sources of errors in Theodolite work : • • • • • • • • • Errors in theod. Surveys results from : - instrumental - natural - personal Normally it is impossible to determine the exact value of an angle , and therefore the error in this measured value . Precise results can be obtained by : A- following specified field procedure . B-manipulating the instrument carefully . C-checking measurements . Instruments Errors 1. 2. 3. 4. 5. Plate bubble out of adjustment . Axis of sight not perpendicular to the horizontal axis . Horizontal axis not perpendicular to the vertical axis . Axis of the telescope bubble not parallel to the axis of sight . 5- Eccentricity of centers . Vertical Horizontal Natural errors : • • • • Wind Temperature changes Refraction Setting of the tripod Personal errors : • • • • • • • Instrument not set up exactly over the point . Level bubble not centered perfectly . Improper use of clamps and tangent screws . Poor focusing . Parallax . Unsteady tripod . Careless plumbing and placement of the rod . Mistakes : • • • • • Sighting on , or setting up over the wrong point . Recording an incorrect value . Reading the wrong circle . Turning the wrong tangent screw . Using haphazard field procedure . Sights and Marks Double centering : • In a well adjusted theodolite , the line of sight is normal to the horizontal axis , horizontal axis must be perpendicular to the vertical axis , line of sight must be parallel to the axis of the telescope bubble tube , horizontal circle and verniers must be concentric , ---• A maladjustment of the theodolite in one or more of these respects is to be expected . In fact , a theodolite is never in perfect adjustment . • Errors due to maladjustment can be eliminated by DOUBLE CENTERING or double sighting .(making a measurements of a horizontal or a vertical angle once with the telescope in the direct position , face left , and once with the telescope in the reversed or face right ). • Double centering eliminates blunders and instrumental errors , and increase accuracy of the measured angle . Measuring FL and FR Double Face Observations Sta. face Circle reading mean B L 122⁰ 20´ 26" 122⁰ 20’ 29” R 302⁰ 20’ 32” L 165⁰ 46’ 11” R 345⁰ 46’ 15” L 182⁰ 06’ 14” R 02⁰ 06’ 16” DL 222⁰ 15’ 42” R 42⁰ 15’ 48” C D B E D C E 165⁰ 46’ 13” 182⁰ 06’ 15” 222⁰ 15’ 45” Trigonometric Levelling • Used where difficult terrain, such as mountainous areas. • May used where the height difference is large but the horizontal distance is short such as heighten up a cliff or a tall building. • Δh can be determined by measuring – The inclined or Horizontal distance – The zenith or altitude angle. • Slope distance is measured using electromagnetic distance measurers (EDM) and the vertical (or zenith) angle using a theodolite. • When these two instruments are integrated into a single instrument it is called a ‘total station’. • Total stations contain algorithms that calculate and display the horizontal distance and vertical height. Calculations • If S distance measured • If (H) horizontal distance measured Calculations • The difference in elevation can be calculated – hi= height of the instrument above an occupied point. – r = the reading on the rod . • The above figure applied where lengths are shorter than about 300 m. • For lengths longer than 300 m, the earth curvature and refraction that must be considered. E B α D C F A G DATUM CE DE sin DC tan CF total effect of curvature and refraction EF CE CF hAB AD CF CE EB CF=effect of curvature And refraction • To eliminate the uncertainty in the curvature and refraction correction , reciprocal vertical angle observation procedure must be applied . • The correct difference in elevation between the two ends of the line is then the mean of the two values computed both ways with out taking into account curvature and refraction . Reciprocal measurement • The combined effect of curvature and refraction over 100 m =0.7 mm, over 200 m = 3 mm, over 300 m = 6 mm, over 400 m = 11 mm and over 500 m = 17 mm. • For uphill sights curvature and refraction is added to a positive V to increase the elevation difference. • For downhill sights, it is again added, but to a negative V, which decreases the elevation difference. • If reciprocal applied, the combined effect is canceled.