3.2 Differential Leveling Equipment, Rods, Targets, and Rod Reading

3.2 Differential Leveling Equipment, Rods, Targets, and Rod Reading

1. Differential Leveling Instruments

Differential leveling is the process of measuring vertical distances relative to a horizontal line of sight to determine elevation differences between points. NSPS CST Level I technicians must master optical automatic levels, digital electronic levels, and standard leveling rods.

Automatic Levels

An automatic level utilizes a precision wire-hung pendulum compensator with air or magnetic damping. Once the instrument operator manually centers the circular bullseye bubble (within approximately $\pm 10'$ to $\pm 15'$ of true plumb), the internal compensator automatically levels the line of sight through gravity.

• Internal Telescope Reticle: Contains a main horizontal crosshair and two shorter horizontal stadia hairs located symmetrically above and below the main crosshair.
• Stadia Distance Principle: The distance between the top and bottom stadia hairs subtends 1 foot on the rod per 100 feet of sight distance (stadia interval factor $K = 100$).

Digital Electronic Levels

Digital levels read electronic bar-code leveling rods using an internal solid-state CCD camera array. The instrument processes the bar-code pattern to calculate both elevation reading and horizontal distance automatically. Digital levels eliminate human reading errors, transposing blunders, and manual field book entry.

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2. Leveling Rod Types and Design

Leveling rods are graduated wooden, fiberglass, or aluminum staves held vertically on ground points.

The Philadelphia Rod

The Philadelphia rod is the standard two-section sliding rod used in U.S. surveying practice.

• Graduations: Graduated in feet, tenths, and hundredths of a foot ($0.01\text{ ft}$).
• Color Schemes: Major foot numbers are large red figures. Tenth-of-a-foot numbers are black figures.
• Bar Widths: Each individual black bar and white space is exactly $0.01\text{ ft}$ ($1/100\text{ ft}$) thick. The top of a black bar represents an even hundredth ($0.02, 0.04, 0.06, 0.08$), and the bottom represents an odd hundredth ($0.01, 0.03, 0.05, 0.07, 0.09$).

Direct-Reading (Lenker) Rods

A direct-reading rod features a continuous moving fabric tape graduated in reverse numbers running over top and bottom rollers. The tape is manually adjusted to match a known benchmark elevation. Once set, all subsequent rod readings yield the actual ground elevations directly without requiring mental subtraction from HI.

Rod Targets

When sights exceed 300 feet, or under poor atmospheric visibility, a metal rod target with a vernier scale is attached to the rod. The rodperson slides the target up or down until instructed by the instrument operator. Using the vernier scale, rod readings can be recorded to $0.001\text{ ft}$.

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3. Field Reading Protocols and Rod Plumbing

Accurate rod reading requires strict adherence to sight procedures:

Parallax Elimination

Before reading the rod, the instrument operator must focus the eyepiece on the crosshairs against a light background until they appear sharp and black. Next, focus the objective lens on the rod. Move the eye slightly up and down; if the crosshair appears to move relative to the rod graduations, parallax exists. Eliminate parallax by fine-tuning the objective focus.

Rocking the Rod (Plumbing Protocol)

If a leveling rod is held out of plumb (tilted toward or away from the level), the horizontal line of sight intersects the tilted rod at a higher reading than the true vertical distance.

• Procedure: The rodperson slowly sways the top of the rod forward toward the instrument and backward past vertical in an arc.
• Reading Criterion: As the rod passes through the vertical position, the reticle reading decreases to a minimum and then increases again. The lowest reading observed by the operator during the arc is the true vertical reading.

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4. Leveling Terminology and Turning Point Procedures

Differential level lines progress through a series of setup stations connecting benchmarks ($BM$) and turning points ($TP$).

[BM 1] --(BS)--> (Level Setup 1) --(FS)--> [TP 1] --(BS)--> (Level Setup 2) --(FS)--> [BM 2]

Key Definitions

1. Backsight (BS): A rod reading taken on a point of known elevation ($BM$ or $TP$) to determine the Height of Instrument ($HI$). Also referred to as a plus sight (+S). $\text{HI} = \text{Elevation} + \text{BS}$
2. Height of Instrument (HI): The vertical elevation of the telescope's horizontal line of sight above the vertical reference datum.
3. Foresight (FS): A rod reading taken on a point of unknown elevation ($TP$ or destination $BM$) to determine its elevation. Also referred to as a minus sight (-S). $\text{Elevation}_{\text{new}} = \text{HI} - \text{FS}$
4. Turning Point (TP): A solid, temporary stable point (such as a steel turning turtle, wooden stake, or concrete lug) used to advance the level line.
5. Page Check (Arithmetic Check): Verified at the bottom of every field book page: $\sum \text{BS} - \sum \text{FS} = \text{Ending Elevation} - \text{Starting Elevation}$

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5. Leveling Rod Comparison & Systematic Errors

[!TIP] Equalizing Backsight and Foresight Distances: Instrument line of sight tilt (collimation error $e$) and combined earth curvature and refraction ($h_{cr}$) introduce systematic errors proportional to sight distance squared. By keeping Backsight distance ($d_{BS}$) equal to Foresight distance ($d_{FS}$) for every setup, the errors in BS and FS are identical ($e_{BS} = e_{FS}$) and completely cancel out during subtraction!