Distance Measurement (Kavanagh)

Gunter's Chain Specifications

Length: 66 feet Subdivided: 100 links 1 link = 0.66 ft 80 chains = 1 mile 10 square chains = 1 acre Used for original surveys of most of North America. — Kavanagh Ch. 3, p. 63

Converting Chains/Links to Feet

Step 1: Combine chains and links as a decimal Example: 5 chains, 32 links = 5.32 Step 2: Multiply by 66 5.32 × 66 = 351.12 ft For meters: multiply result by 0.3048 — Kavanagh Ch. 3, p. 63

Standard Conditions for Steel Tapes (Foot)

1. Temperature = 68°F 2. Tape fully supported throughout 3. Tape under tension of 10 lb Field conditions rarely match these standards, requiring corrections. — Kavanagh Ch. 3, p. 75

Standard Conditions for Steel Tapes (Metric)

1. Temperature = 20°C 2. Tape fully supported throughout 3. Tape under tension of 50 N (≈11.24 lbs) 30-m tapes are most popular (similar to 100-ft tapes). — Kavanagh Ch. 3, p. 75

Slope Distance to Horizontal Formula (Angle Known)

H = S × cos θ Where: • H = horizontal distance • S = slope distance • θ = slope angle (or use 90° - zenith angle) — Kavanagh Ch. 3, p. 76

Slope Distance to Horizontal Formula (Elevation Known)

H = √(S² - V²) Where: • H = horizontal distance • S = slope distance • V = vertical distance (elevation difference) Derived from Pythagorean theorem. — Kavanagh Ch. 3, p. 76

Gradient (Percent Grade) Calculation

Gradient = (V/H) × 100% Where: • V = vertical rise • H = horizontal distance Example: 2 ft rise in 100 ft = 2% gradient — Kavanagh Ch. 3, p. 76

Systematic Taping Errors

1. Slope 2. Erroneous tape length 3. Temperature 4. Tension and sag These can be calculated and corrected because magnitude and sign are determinable. — Kavanagh Ch. 3, p. 75

Random Taping Errors

1. Slope estimation 2. Temperature estimation 3. Tension and sag estimation 4. Alignment 5. Marking and plumbing These vary unpredictably and tend to cancel (except alignment which is cumulative). — Kavanagh Ch. 3, p. 75, 79

Alignment Errors are Cumulative

Unlike most random errors, alignment errors always make measurements TOO LONG. Misalignment left or right both result in measuring a longer path than the true distance. Eliminate with theodolite alignment on precise surveys. — Kavanagh Ch. 3, p. 79

Definition: Normal Tension

The tension applied to a tape that eliminates sag errors. • 100-ft tapes: approximately 24 lb • 30-m lightweight tapes: approximately 90 N (20 lb) Can be determined experimentally for each tape. — Kavanagh Ch. 3, p. 78-79

Breaking Tape Technique

Used when slope is too steep for full tape horizontal. 1. Take shorter measurements, each horizontal 2. Use plumb bobs at intermediate points 3. Mark at even-foot graduations 4. Total all partial measurements Introduces more random errors due to extra marking/plumbing. — Kavanagh Ch. 3, p. 73

EDM Operating Principles

Most EDM instruments: 1. Send modulated light wave to target 2. Light reflects from prism back to EDM 3. Measure phase difference between sent and received waves 4. Calculate distance from wavelength and phase Pulse lasers measure time of flight instead. — Kavanagh Ch. 3, p. 61-62, 86

EDM Distance Formula

L = (nλ + φ) / 2 Where: • L = one-way distance • n = number of full wavelengths • λ = wavelength • φ = partial wavelength (phase) Divide by 2 because light travels there and back. — Kavanagh Ch. 3, p. 86

EDM Accuracy Statement

Format: ±(constant + ppm) Example: ±(5 mm + 5 ppm) • 5 mm = constant error (instrument) • 5 ppm = 5 mm per km (proportional) At 1,000 m: 5 + 5 = 10 mm total potential error — Kavanagh Ch. 3, p. 90

EDM Short Distance Concerns

At short distances (<100 m): • Constant (mm) error dominates • Centering errors significant • Prism centering adds 2+ mm • May be faster to use steel tape Example: 5 mm at 10 m = only 1:2,000 accuracy — Kavanagh Ch. 3, p. 64-65, 90

Atmospheric Effects on EDM

Factors affecting light velocity: 1. Temperature (±1°C = ∓1.0 ppm light wave) 2. Atmospheric pressure (±1 mm Hg = ±0.4 ppm) 3. Water vapor (minimal for light wave) For short distances, centering errors > atmospheric errors. — Kavanagh Ch. 3, Table 3.2, p. 88

Cube Corner Prism

Retro-direct capability: reflects light back precisely in same direction received. Allows prism to be somewhat misaligned and still function. Prism constant (−30 to −40 mm) must be accounted for. — Kavanagh Ch. 3, p. 89

EDM/Prism Constant Check

Field method: 1. Layout line A-B-C (>1 km) 2. Measure AC, AB, and BC 3. Constant = AC − AB − BC The constant appears in all measurements, so the difference reveals it. — Kavanagh Ch. 3, p. 91

Reflectorless EDM

Measures without prism—reflects off surfaces directly. Range: 100-2,000 m depending on: • Equipment type • Light conditions (cloudy/dark = better) • Surface reflectivity • Angle of incidence Standard reference: Kodak Gray Card (18% reflective) — Kavanagh Ch. 3, p. 91-92

Specifications for 1/5,000 Taping Accuracy

• Temperature: estimate to ±7°F (4°C) • Tension: known to ±5 lb (20 N) • Slope errors: ≤1 ft/100 ft • Alignment errors: ≤0.5 ft/100 ft • Plumbing/marking: ≤0.015 ft • Tape length known: ±0.005 ft — Kavanagh Ch. 3, Table 3.1, p. 80

Rear Surveyor Responsibilities

1. Align head surveyor by sighting range pole 2. Hold tape on mark (direct or plumb bob) 3. Call "Mark" when plumb bob is on point 4. Call out station and tape reading 5. Count full tape lengths 6. Maintain equipment — Kavanagh Ch. 3, p. 74

Head Surveyor Responsibilities

1. Carry tape forward (no loops/kinks) 2. Prepare ground for marks 3. Apply proper tension 4. Place marks (pins, stakes, etc.) 5. Take and record measurements 6. Supervise taping work — Kavanagh Ch. 3, p. 74

Common Taping Mistakes

1. Measuring to/from wrong marker 2. Reading tape incorrectly or transposing (56↔65) 3. Losing count of tape lengths 4. Recording values incorrectly 5. Calling out figures ambiguously 6. Wrong zero point on unfamiliar tape 7. Arithmetic mistakes — Kavanagh Ch. 3, p. 81