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CIV 205

Introduction to GeomaticsCourse InstructorSaidi Siuhi, Ph.D., EIT.Lecture 02-Leveling

12 Elevation or Height vertical distance above or below an arbitrary level surface

Datum: the level surface used for reference Geoid: a horizontal surface shaped by the gravity field of the earth Mean Sea Level (MSL): the average height of seas surface for all stages of the tide over 19 year period.

Horizontal Line: straight line tangent to a level surface

Bench Mark (BM): a relatively permanent object, natural or artificial, with its elevation above or below an adopted datum is known or assumed.

KEY DEFINITIONSLeveling terms23CURVATURE AND REFRACTION

Curvature Correction:Cc = 0.0785 K2(m)(approx. 7.9 cm/km)K = distance in km

Combining Refraction: Refraction diminishes the effect of curvature by 14%. BD is the combined effect of Curvature and Refraction: Ccr= 0.0675 K2 (m) (approx. 6.75 cm/km)

4LEVELING METHODS

Measuring vertical distances by taping or EDM.

Barometric Leveling.

Differential Leveling.

Trigonometric Leveling.

Reflectorless EDMDifferential levelingSurveying altimeter5DIRECT DIFFERENTIAL LEVELINGHI = known elevation + BSNew Elevation = HI - FS

Plus sight (Backsight) = 8.42 ft.Height of Instrument (HI) = 820 + 8.42 = 828.42 ft.Minus Sight (Foresight) = 1.20 ft.Elevation of point X = 828.42 1.20 = 827.22 ft.

6TRIGONOMETRIC LEVELING FOR SHORT LINESFor short lines (shorter than 300 m): Observe: Zenith or vertical angle Horizontal or slope distance Heights of instrument Height of target

Compute elevation differenceV = S cos(z)

V = S sin ()

V = H cot(z)

V = H tan()

elev = hi + V - r

7TRIGONOMETRIC LEVELING FOR LONG LINES Instrument is set up at C over point A. Sight D is made on a rod held at point B. Zm or m is measured.

elev = HG + GF + V ED r

elev = HI + V + (C R) r

8LEVELING: FIELD PROCEDURES AND COMPUTATIONS Setting up a level

Holding the rod

9DIFFERENTIAL LEVELINGKEY WORDS

Bench Mark (BM)

Turning Point (TP)

Backsight (BS)

foresight (FS)Height of Instrument (HI)

Figure 5.4: Differential leveling10DIFFERENTIAL LEVELINGProcedure and Arithmetic CheckFigure 5.4 illustrates the procedure followed in differential leveling. Elev. of new BM Oak is to be determined by originating a leveling circuit at established BM Mil. A plus sight (BS) is taken at the established benchmark.HI is computed using eqn 4.4FS is taken on the intermediate point (Turning Point-TP1) and its elev. is determined using eqn 4.5The process of taking a BS followed by FS is repeated until the circuit is completed.11DIFFERENTIAL LEVELINGProcedure and Arithmetic CheckHorizontal lengths for BS and FS should be approx. equal.Before leaving the field, all possible note checks must be made to detect any mistakes in arithmetic and verify achievement of acceptable closureThe algebraic sum of the BS and FS minus applied to the first elevation should give the last elevationThe difference between first and final elevation is the loop misclureIf closure is made to another benchmark, the section misclosure is difference between the closing benchmarks given elevation and elevation obtained after leveling through the section

12DIFFERENTIAL LEVELINGPrecisionPrecision in leveling is increased by:Repeating measurementsMaking frequent ties to established benchmarksUsing high-quality equipmentKeeping equipment in good adjustmentPerforming the measurements carefully

No matter how carefully the work is executed, errors will exist and will be evident in form of misclosures.

To determine whether or not work is acceptable, misclosure are compared with permissible values on the basis of number of setups or distance covered.13DIFFERENTIAL LEVELINGPrecisionFor a simple construction survey, an allowable misclosure given below may be used

Where n is the number of setups

The Federal Geodetic Control Subcommittee (FGCS) recommends the following formula to compute allowable misclosure:

Where:C = allowable loop or section misclosure, in mmm = constantK = total distance leveled, in km

14DIFFERENTIAL LEVELINGPrecision

For loops (circuits that begin and end on the same benchmark), FGCS specifies constants as follows:

Class of levelingmFirst-order class I4First-order class II5Second-order class I6Second-order class II8Third-order class I1215DIFFERENTIAL LEVELINGPrecision

Example

A differential leveling loop is run from an established BM A to a point 2 miles away and back, with a misclosure of 0.056 ft. what order of leveling does this represent?

See white board or page 111

16FIELD NOTES17EXAMPLEDifferential leveling notes and computationsStaBSHIFSElev.Adj. ElevBM Mil1.332053.18TP10.228.37TP20.967.91TP30.4611.72BM Oak11.958.71TP412.552.61TP512.770.68BM Mil18Adjustment Of Simple Level CircuitsPermissible misclosure are based on:Lengths of lines leveledNumber of instrument setups

Adjustment of elevations is made in proportion to these values

19Adjustment Of Simple Level CircuitsEXAMPLEObserved elevation differences d and lengths of sections L are shown for the circuit below. The misclosure found by algebraic summation of the elevation differences is 0.24 ft. Make adjustment of elevation differences. ADBC110.52107.35115.88100.00L=1.0 miL=0.8 miL = 0.7 miL=0.5 mi20RECIPROCAL LEVELING

Set up the instrument on point x Take several reading for point b Move the instrument to point y Take several readings for point aelev is the average of both settings 21PROFILE LEVELING

22PROFILE LEVELING FIELD NOTES

23EXAMPLE A profile leveling circuit starts at BM CURB (that has an elevation of 76.72 ft) and ends at BM STAIR (that has an elevation of 88.35 ft). The field readings for the circuit are as per the following (in the order of being observed):BS on BM CURB 7.98 ft;Intermediate foresight (IFS) on 11+00 is 3.57 ft;FS on TP1 is 6.35 ft;BS on TP1 is 9.91 ft;IFS on 12+00 is 5.34 ft;IFS on 13+00 is 4.75 ft;FS on TP2 is 4.44 ft;BS on TP2 is 8.54 ft;IFS on 14+00 is 3.82 ft; andFS on BM STAIR is 3.98 ft.Prepare, check and adjust a set of profile leveling field notes for the above observations.24PROFILE LEVELING OUTPUT