FW06 — Tacheometric Distance and Elevation Measurement Using a Transit/Theodolite

Learning Objectives

  • Obtain upper, middle, and lower stadia-hair readings on a vertical rod.
  • Measure the corresponding vertical angle for horizontal and inclined sights.
  • Determine horizontal distance from the stadia intercept.
  • Determine the vertical component from the instrument axis to the central-hair intercept.
  • Compute the ground elevation of observed points when station elevation and instrument height are known.
  • Compare tacheometric results with an independent reference measurement when available.

Stadia Intercept

The rod interval intercepted between the upper and lower stadia hairs, commonly written as s = U − L.

Stadia Interval Factor

The multiplying constant K of the telescope. A value near 100 is common, but the actual assigned or calibrated constant shall be used.

Activity Principle

Tacheometry determines distance and elevation indirectly from optical rod readings and a measured vertical angle. The middle-hair reading is not discarded: it is required when converting the vertical component of the line of sight to the elevation of the ground point carrying the rod.

Stadia Intercept

Difference between upper and lower stadia readings.

s=U−Ls=U-L

Variables

SymbolDescriptionUnit
ssstadia intercept-
UUupper stadia-hair rod reading-
LLlower stadia-hair rod reading-

Horizontal Distance for an Inclined Sight

Horizontal component for a vertical rod and inclined line of sight.

H=Kscos⁡2α+Ccos⁡αH=Ks\cos^2\alpha+C\cos\alpha

Variables

SymbolDescriptionUnit
HHhorizontal distance from instrument station to rod-
KKstadia interval factor-
ssstadia intercept-
CCadditive constant-
α\alphasigned vertical angle from horizontal-

Vertical Component to Central-Hair Intercept

Vertical distance from the instrument axis to the central-hair intercept on the rod.

V=Ks2sin⁡(2α)+Csin⁡αV=\frac{Ks}{2}\sin(2\alpha)+C\sin\alpha

Variables

SymbolDescriptionUnit
VVvertical component, positive upward-
KKstadia interval factor-
ssstadia intercept-
CCadditive constant-
α\alphasigned vertical angle-

Ground Elevation of Rod Point

Elevation of the ground point supporting a vertical rod.

EP=ES+hi+V−rE_P=E_S+h_i+V-r

Variables

SymbolDescriptionUnit
EPE_Pelevation of observed ground point-
ESE_Selevation of occupied station-
hih_iinstrument height above occupied station-
VVvertical component to central-hair intercept-
rrmiddle-hair rod reading-

Horizontal Sight

When α = 0 and C = 0, the equations reduce to H = Ks and V = 0.

Field Procedure

Tacheometric Observation Sequence

  1. Occupy the assigned station and complete centering, leveling, focusing, and parallax elimination.
  2. Measure and record the instrument height from the station mark to the instrument reference axis.
  3. Confirm the assigned values of K and C; do not assume them if instrument calibration information is provided.
  4. Hold the stadia rod vertical at the assigned point.
  5. Record upper, middle, and lower stadia-hair readings exactly as observed.
  6. Record the signed vertical angle or the raw vertical-circle reading with its instrument convention.
  7. Repeat the observation when required and retain all raw readings.
  8. Compute s, H, V, and point elevation after the observation set is complete.
  9. Compare at least one tacheometric distance or elevation with an independent taped, EDM, or leveling reference when assigned.

Rod Verticality

A leaning rod changes the stadia intercept and central-hair reading. Use a rod bubble when available or carefully plumb the rod before recording the observation.

Field Quality Check

Submission Timing

Fieldwork Data is due within the scheduled 3-hour class period. The Full Fieldwork Report is due on the next class meeting. FW00 remains authoritative for safety, raw-data integrity, station identification, and submission requirements.

FW06 — Required Data Tabulation

Use this structure as the minimum field or research data table. Add columns when the activity requires more detail.

StationTargetUpper hairMiddle hairLower hairStadia interceptVertical angleHD (m)Δh / Elevation
ST-01P-01RecordRecordRecordComputeRecordComputeCompute
ST-01P-02RecordRecordRecordComputeRecordComputeCompute

Record the stadia constant(s) used and instrument height. The middle-hair reading must remain in the elevation reduction; do not report only the stadia intercept.

FW06 — Grading Rubric

Award points according to the evidence shown for each criterion.

Total: 25 pts
CriterionFull-credit evidencePoints
Instrument setup and stadia observation techniqueInstrument and staff are properly set; all three hair readings and vertical angles are observed correctly.5
Raw tacheometric dataUpper/middle/lower hairs, constants, instrument height, target IDs, and angles are complete and internally consistent.5
Distance and elevation computationsStadia intercept, horizontal distance, vertical component/elevation difference, and target elevations are correctly reduced.7
Checks and engineering interpretationIndependent/reference checks are performed where assigned and discrepancies or unsuitable observations are explained.4
Report and technical presentationTables, sketch, formulas used, metadata, units, and final results are clear and traceable.4
Total25 / 25

Scoring guide: full credit for complete, technically correct, traceable evidence; reduce proportionally for minor errors, incomplete work, or weak documentation.

Key Takeaways
  • Tacheometry combines optical rod readings and vertical angles to obtain engineering distances and elevations.
  • The middle-hair reading is required for ground-elevation reduction.
  • Constants K and C are instrument parameters and must be documented.
  • Comparison against an independent measurement is a valuable accuracy check.