LABORATORY 45 · CIVIL ENGINEERING

Two-Peg Collimation Error Test & Line-of-Sight Calibration for Optical and Digital Levels

Detect and calibrate instrument collimation axis deviation from the true horizontal plane using the classic Two-Peg differential leveling method according to ISO 17123-2. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.

STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING

Your virtual civil engineering laboratory.

COLLIMATION ELEVATION ERROR ΔE—

CIVIL INFRASTRUCTURE TELEMETRY

Ready to sample with Distance Diff ΔD = 30.0 m.

Sight Distance Differential ΔD30.0 mSet Distance Diff ΔD (m)

Civil Engineering Material / Medium: Standard certified structural testing standard at 20.0 °C

Adjust Distance Diff ΔD, then execute civil engineering measurement.

Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.

Civil engineering assumptions and boundary condition limits

The civil engineering physical models apply within the specified calibrated operational window (10.0 to 60.0 m). Tested on an optical automatic level with intentional reticle collimation tilt. Linear model relates apparent elevation error Δe directly to sighting distance differential ΔD with inclination slope c = 0.00185 m/m.

Laboratory apparatus & testing equipment.

Automatic Optical Level with Magnetic Dampened Compensator

32x magnification precision surveyor's level with double-run accuracy 1.0 mm/km.

Two 5-Meter Telescopic Aluminum Invar Leveling Staffs

E-face and millimeter graduation leveling staves with bullseye leveling bubbles.

Two Solid Cast-Iron Leveling Change Plates (Turtles)

Heavy triangular steel plates with rounded top studs preventing staff settlement in soil.

50-Meter Heavy-Duty Steel Surveying Tape

Calibrated steel tape establishing exact 30 m and 60 m baseline peg spacings.

Heavy-Duty Aluminum Leveling Tripod

Torsional rigid tripod with wide base plate and clamping foot locks.

Reticle Crosshair Adjusting Pin

Standard tommy bar adjusting internal diaphragm screws to re-align collimation axis.

FOLLOW THE METHOD

A reason behind every step.

Detect and calibrate instrument collimation axis deviation from the true horizontal plane using the classic Two-Peg differential leveling method according to ISO 17123-2. Standardized parameter settings: 10.0, 20.0, 30.0, 40.0, 50.0, 60.0 m.

Baseline Peg Layout & Benchmark Driving

Select level ground; drive two rigid wooden pegs (Peg A and Peg B) spaced exactly 60.0 m apart; place cast-iron change plates over peg heads.

Instrument Setup at Midpoint (Position 1)

Set up level at exact midpoint M (30.0 m from Peg A, 30.0 m from Peg B); level circular bubble; verify compensator moves freely by lightly tapping tripod leg.

Midpoint Staff Readings & True Elevation Difference

Hold staff vertically on Peg A; record staff reading a_1; turn telescope to Peg B; record staff reading b_1; compute true elevation difference ΔH_true = a_1 - b_1 (collimation errors cancel exactly due to equal 30 m sight lengths).

Instrument Relocation Behind Peg A (Position 2)

Move level to Position 2, set up directly behind Peg A (e.g. 5.0 m from Peg A, 65.0 m from Peg B, differential ΔD = 60.0 m); level instrument carefully.

Near and Far Staff Readings

Record staff reading a_2 on Peg A (near sight, D_near = 5.0 m); record staff reading b_2 on Peg B (far sight, D_far = 65.0 m); compute apparent elevation difference ΔH_app = a_2 - b_2.

Collimation Error Calculation across Systematic Distances

Compute net collimation error Δe = ΔH_app - ΔH_true across six systematic distance differentials (ΔD = 10, 20, 30, 40, 50, and 60 m); plot Δe versus ΔD; compute collimation error factor c; adjust reticle screw to correct crosshairs.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into civil engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Two-Peg Level Collimation mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b

Δe = 0.00185 · ΔD

#	Sight Distance Differential ΔD (m)	Collimation Elevation Error Δe (m)	Sighting distance differential ΔD = (D_far - D_near) (m)	Apparent elevation difference collimation error Δe (m)	Remove

No readings yet. Execute a civil engineering trial and record it.

Calculate it yourself.

Your estimate of Collimation Axis Angular Error Factor (m/m)

CHECK YOUR UNDERSTANDING

Explain what the civil engineering metrics mean.

In differential leveling, collimation error is completely eliminated if:

In the Two-Peg test, the true elevation difference between Peg A and Peg B is determined when the level is positioned:

If an optical level has a collimation error of c = +0.002 m/m, a foresight sight length of 50 m will have an error of:

The mechanical adjustment to eliminate collimation error in an optical level moves the:

THEORY AND STRUCTURAL CONTEXT

Civil engineering background & physical principles.

In civil surveying engineering, optical automatic levels and electronic digital levels establish precise vertical elevations for road grading, drainage pipe invert slopes, foundation benchmarks, and structural settlement monitoring. An automatic level utilizes an optical telescope fitted with crosshairs and an internal wire-hung pendulum compensator (or magnetic damping prism) that automatically levels the line of sight when the circular bubble is roughly centered. However, mechanical shock during transit or thermal expansion can knock the reticle crosshair out of alignment, causing the optical collimation axis (line of sight) to tilt upward or downward at an angle α relative to the true local horizontal plane. When backsight (BS) and foresight (FS) distances are strictly equal, collimation errors cancel out completely: e_BS = e_FS. But on uneven terrain, steep grades, or river crossings where sight lengths are unequal, collimation error induces cumulative elevation errors: e = D · tan(α) ≈ D · α. Developed as the universal calibration procedure, the Two-Peg Test (ISO 17123-2) isolates and quantifies this collimation error factor c = tan(α). Two rigid benchmark pegs (A and B) are driven into firm ground separated by distance D (e.g. 30 to 60 m). The level is set up midway between pegs (Instrument Position 1, where equal sight lengths yield true elevation difference ΔH_true = a_1 - b_1) and then relocated immediately behind Peg A (Instrument Position 2, where sight lengths are heavily unequal, exposing collimation error: c = [(a_2 - b_2) - ΔH_true] / ΔD). In this laboratory investigation, apparent error Δe is monitored across sight distance differentials from 10.0 to 60.0 m to calibrate the collimation inclination factor c = 0.00185 m/m (1.85 mm per meter, or α = 381.6 arcseconds).

Δe = 0.00185 · ΔD

Tested on an optical automatic level with intentional reticle collimation tilt. Linear model relates apparent elevation error Δe directly to sighting distance differential ΔD with inclination slope c = 0.00185 m/m.