Surveying: Distance Measurement and Units

Introduction

• Distance measurement serves as the basis for all surveying.
• In plane surveying, the distance signifies the horizontal distance between two points, irrespective of their relative elevations.
• Line lengths are typically expressed in meters.

Unit of Measurement for Length

• Measurement is the process of determining the ratio of a physical quantity to a unit of measurement.
• Examples of physical quantities include length, time, and temperature.
• Units of measurement include the meter, second, and degree Celsius.

Fractions of a Meter

• Millimeter equals 1/1000.
• Centimeter equals 1/100

Multiples of a Meter

• Kilometer equals x 1000

Origin of the Meter

• Initially defined in 1791 by the French Academy of Sciences as 10^-7 or one ten-millionth of the meridian length through Paris from the pole to the equator.
• In 1889, a new international prototype was created from platinum with 10% iridium, measured to within 0.0001 at ice's melting point.
• In 1927, the meter was more precisely defined as the distance at 0° between the axes of two central lines on a platinum-iridium bar.
• In 1960, the meter was redefined based on krypton-86 radiation's wavelength.
• In 1983, the meter became the length of the path traveled by light in a vacuum in 1/299792458 of a second.

Significant Figures

• Every measurement has a degree of uncertainty coming from the measuring device and the measurer's skill.

Rules for Identifying Significant Digits

• All non-zero digits are considered significant (e.g., 91 has two significant digits: 9 and 1).
• Zeros between non-zero digits are significant (e.g., 101.12 has five significant digits: 1, 0, 1, 1, and 2).
• Leading zeros are not significant (e.g., 0.00052 has two significant digits: 5 and 2).
• Trailing zeros in a number with a decimal point are significant (e.g., 12.2300 has six significant digits: 1, 2, 2, 3, 0, and 0). 0.000122300 still has only six significant digits (the zeros before the 1 are not significant).
• The significance of trailing zeros in a number without a decimal point can be ambiguous (e.g., 1300).

Direct vs Indirect measurement

• Direct measurement involves applying a graduated instrument directly to the quantity being measured
• Indirect measurement determines a quantity's value through its relationship to other measurable quantities.

Factors to Consider in Choosing Measurement Methods

• Purpose of the measurement
• Required Accuracy
• Cost

Pacing - Methods of Distance Measurement

• Pacing consists of counting steps or paces to measure a required distance, used for approximate measurements.
• A pace is defined as the length of a step in walking.
• Two paces equal a stride or double step.
• Relative precision achieved through pacing: 1/200 to 1/100, rarely less than 1/300

How to Calibrate One's Pace?

• Walk at a uniform step along a line of known length on level ground.
• Count the number of paces taken to cover the stretch.
• Compute the pace length factor (in meters/pace).
• Factors affecting pace: Speed of pacing, roughness of the ground, weight of clothing and shoes, fatigue of the pacer, slope of the terrain, age and sex of the individual.

Taping - Methods of Distance Measurement

• The method of direct measurement with graduated tapes, and the most common for determining distances.
• Examples of Tapes: Steel tape, metallic tape, non-metallic tape, invar tape, lovar tape, fiberglass tape, wires, builder's tape, phosphor-bronze tape, nylon-coated steel tape.
• Accessories: Range pole, chaining pins, wooden stake, tension handle, clinometer, and plumb bob.

Tacheometry Methods

• Tacheometry can quickly determine the horizontal distance to and elevation of a point.
• The two common methods of tacheometry: Stadia Methods or Subtense bar method

Stadia Methods

• Distance is obtained by sighting the telescope of an instrument on a graduated rod (stadia rod).
• Observing the interval on the rod included between two special horizontal cross hairs (stadia hairs) set in the telescope.

Subtense Bar Method

• An Invar subtense bar is set on a tripod and aligned perpendicular to the survey line using a sighting device.
• Fixed targets near the bar ends are precisely two meters apart.
• The horizontal angle between targets is measured with a theodolite reading to one second or smaller.
• The horizontal distance is computed using: H = cot (α/2)
• Relative precision is 1/3000 with sights of about 150 m or less using a 1" theodolite.

Electronic Distance Measurement (EDM)

• Involves electro-optic and electromagnetic instruments.
• The principle is the determination of the time needed for electromagnetic radiation to travel between two stations.

EDM advantages include:

• Speed and accuracy
• Lightweight and portable
• Low power requirement
• Easy to operate
• Ease in measurement over inaccessible terrain
• Applicable to both short and long lengths
• Automatic measuring, displaying, and recording of needed data
• Slope measurements are internally reduced to horizontal and vertical components
• Automatic accumulation and averaging for slope range, horizontal and vertical angles.

Graphical/Mathematical Method

• Relates known and unknown distances geometrically.

Use of Mechanical Devices

• Includes various tools for approximate distance measurement.

Odometer

• An instrument attached to a vehicle's wheel to measure revolutions, which, multiplied by the circumference, gives the surface distance covered.
• Uses include route location surveys, preliminary surveys, and small-scale mapping.
• Relative precision on fairly level ground is 1/200.

Measuring Wheel

• Similar to an odometer but is more portable and self-contained.
• Determines distances along irregular or curved lines and boundaries.

Pedometer

• Small, pager-sized device worn on the belt that records the number of steps taken based on body movement.

Passometer

• Registers a pace by impact each time a foot touches the ground.

Optical Rangefinder

• Determines distances approximately by focusing.
• Useful for Field Sketching, Plane Table Work, and Reconnaissance Surveys.

Total Station

• Integrated digital transit and electronic distance measuring device.

Global Positioning System (GPS)

• A system for determining position and distance using satellite signals.

Smart Station

• Integrated total station and GPS.

Tellurometer

• A surveying instrument that measures distance by measuring the roundtrip travel time of reflected microwaves.

Laser Range Finders

• Instruments that use lasers to measure distance.
• LASER means "Light Amplification by Stimulated Emission of Radiation".

LIDAR

• LiDAR stands for Light Detection and Ranging is a remote sensing technology that measures distance by illuminating a target with a laser and analyzing the reflected light.

This section covers the basics of distance measurement in surveying. It includes the definition of distance in plane surveying and commonly used units. It also details the origins and evolution of the meter as a standard unit of length.