Distance & Angle Measurement

What is horizontal distance?

Distance between two points measured in horizontal plane. Computed from slope distance using vertical angle or elevation difference.

What is slope distance?

Straight-line distance between points regardless of vertical angle. Must be corrected to horizontal for mapping.

What corrections apply to steel tape measurements?

1. Temperature 2. Tension 3. Sag 4. Slope 5. Standardization

What is the temperature correction formula?

Ct = α × L × (T - Ts) where α = 0.00000645/°F for steel L = measured length T = field temperature Ts = standard temperature (68°F)

What is tension correction?

Adjustment for difference between applied and standard tape tension. Positive when applied tension exceeds standard.

What is sag correction?

Adjustment for tape catenary when suspended. Always negative because sag increases measured distance.

What is breaking tape?

Measuring horizontal distance on slope by measuring in short, level increments and summing results.

What is stadia?

Optical distance measurement using telescope stadia hairs and graduated rod. Distance = 100 × rod interval.

What is direct reading angle measurement?

Method where full angle value is read directly from horizontal circle graduations.

What is angle by repetition?

Accumulating multiple angular measurements on horizontal circle to increase precision by averaging.

What is the direction method?

Reading directions to multiple targets from single setup, then computing angles by difference.

What is collimation error?

Angular error when line of sight is not perpendicular to vertical axis. Eliminated by equal BS/FS distances.

How do you convert slope to horizontal distance?

HD = SD × cos(α) or HD = SD × cos(ZA) or HD = √(SD² - VD²)

What is three-wire leveling?

Precise leveling reading upper, middle, and lower stadia hairs to check for rod movement and improve accuracy.

What is reciprocal leveling?

Technique for leveling across obstacles by taking readings in both directions to eliminate systematic errors.

What is trigonometric leveling?

Determining elevation differences using vertical angles and slope distances from a total station.

What affects EDM accuracy?

• Atmospheric conditions • Prism constant • Centering errors • Signal strength • Instrument calibration

How does elevation affect EDM?

High elevations have lower air pressure, reducing refractive index. EDM measures longer because light travels faster.

What is curvature and refraction correction?

Combined correction for level observations: C&R = 0.0206 × M² (feet) where M = distance in thousands of feet.

When is curvature and refraction significant?

Becomes significant for sight distances over 300 feet. At 1000 feet, correction is about 0.02 feet.

What is the effect of centering error?

1mm centering error at short distance (10m) causes much larger angular error than at long distance (100m).

What is standard tension for a 100-foot tape?

Typically 10-15 pounds, depending on tape type. Must match calibration conditions for accurate results.

What is the sag correction formula?

Cs = -w²L³/(24P²) where w = tape weight per unit length L = unsupported length P = applied tension

What is pacing accuracy?

Experienced pacer: 1:50 to 1:100 Useful for reconnaissance and checking taped measurements.