Horizontal Distance Methods ApproachesPacingOptical rangefindersOdometersTacheometry (stadia or subtense)TapingElectronic Distance Measurement (EDM)Global Positioning System (GPS)IssuesOften measure surface or slope distancePotential error or need to reduce to horizontal

Incorrect Length of TapeConcept

Solution

Correction Example

Variations in Tape TemperatureConcept

For steel coefficient of thermal expansion (k)CorrectionIssues

Incorrect TensionConcept

For steelCorrection

SagConcept

Correction

Tape Not HorizontalConceptOccurs when tape is not kept levelSolutionCorrected using Pythagorean TheoremOr by approximate correction

How Far Off Can You Be?ProblemNo matter how hard you try, never have a horizontal tapeQuestionWhen does departure from horizontal cause significant error in result? In fieldTry to keep tape horizontal within this limit Or compute a correction

Incorrect Alignment/Tape Not StraightConcept

Correction

Incorrect alignmentTape not straight

Taping Correction ProblemBackgroundSteel tape calibrated at 68F (supported throughout) at 5 kg tension is found 30.006m between 0 m and 30 m marksTape has cross-sectional area of 0.003 in2 and weighs 0.7 kgProblemCrew is taping by laying tape along ground down a uniform grade from point A to point BPoint A is 190.45m AMSL and point B is 175.68m AMSLTemperature is 88F and tension is 7 kgFinal recorded distance is 148.47mWhat is corrected length of tape?

TacheometryConcept

MethodsStadia

Tacheometry: StadiaL1

Stadia PrinciplesNeed simple method for establishing

Method

Stadia Readings

Stadia PrinciplesA,B rod interceptsa, b stadia hairsS = rod intercept F = principal focus of objective lensCdDicfC = stadia constantK = f/i = stadia interval factord = distance from focal point to rodD = distance from instrument center to rodbaa'b'FBASf = focal lengthi = stadia hair spacing c = distance from instrument center to objective lens center

Stadia EquationsHorizontal sightsInclined sightsFrom similar triangles

Issues with Stadia MeasurementsStadia common for map data collection

Accuracy of stadia

Current situation

TacheometryConceptDetermine distances indirectly using triangle geometryMethodsStadiaEstablish constant angle and measure length of opposite sideLength increases with distance from angle vertex

Subtense

Tacheometry: Subtense

Subtense PrinciplesNeed simple method for establishing

Issues

Subtense EquationDerive equation for computing distance by subtense LWhat value would you choose for L?

Issues with Subtense MeasurementPrinciples still useful in many situationsAccuracy of subtense

Current situation

ReadingsChapter 6 sections 6.6, 6.7, 6.14 6.16Chapter 16 section 16.9.2