Distance Measurement

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Florence A. GaleonAssistant Professor

U.P. College of Engineering

Outline

I. IntroductionII. Unit of MeasurementsIII. Significant FiguresIII. Significant FiguresIV. Methods of Distance Measurement

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Introduction

Distance measurement is the basis of all surveying.

In plane surveying, the distance between two

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In plane surveying, the distance between two points is understood to mean horizontal distance, regardless of the relative elevation of the points.

Lengths of lines is generally expressed in meters.

Unit of Measurement for Length

• Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the meter, second or degree Celsius.

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Fractions of a meterMillimeter, 1/1000Centimeter, 1/100

Multiples of a meterKilometer, x 1000

Unit of Measurement for Length

MeterIt is 1/10,000,000of one

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meridionalquadrant.

Origin of the Meter

• The origins of the meter go back to 18th century when in 1791, soon after the French Revolution, the French Academy of Sciences set the meter to equal 10-7 or one ten-millionth of the length of the meridian through Paris from pole to the equator.

• In 1889, a new international prototype was made of an alloy of platinum with 10 percent iridium, to within 0.0001, that was to be measured at the melting point of ice.

• In 1927, the meter was more precisely defined as the distance, at 0°, between the axes of the two central lines marked on the bar of platinum-iridium.

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Origin of the Meter

• In 1960, the meter was redefined based upon the wavelength of krypton-86 radiation.

• In 1983 this definition was replaced by the following definition:

The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

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Significant Figures

• Every measurement has a degree of uncertainty associated with it. The uncertainty derives from the measuring device and from the skill of the the measuring device and from the skill of the person doing the measuring.

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Rules for Identifying Significant Digits

• All non-zero digits are considered significant. Example: 91 has two significant digits (9 and 1).

• Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has zero digits are significant. Example: 101.12 has five significant digits: 1, 0, 1, 1 and 2.

• Leading zeros are not significant. Example: 0.00052 has two significant digits: 5 and 2.

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Rules for Identifying Significant Digits

• Trailing zeros in a number containing a decimal point are significant. Example: 12.2300 has six significant digits: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has 2, 3, 0 and 0. The number 0.000122300 still has only six significant digits (the zeros before the 1 are not significant). In addition, 120.00 has five significant digits.

• The significance of trailing zeros in a number not containing a decimal point can be ambiguous. Example: 1300

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Measurements can be Made Either Directly or Indirectly

Direct measurementIt is made by applying a graduated

instrument directly to the quantity to be measured.

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measured.

Indirect measurementThe value of a quantity is determined by

its relationship to some other measurable quantity or quantities.

Methods of Distance Measurement

1. Pacing

It consists of counting the number of steps or

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It consists of counting the number of steps or paces in a required distance. It is used to approximate measurement of distances.

Pace – defined as the length of a step in walkingStride – equivalent to 2 paces or a double step

2 Methods to Calibrate One’s Pace

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2 Methods to Calibrate One’s Pace

1. To determine the average length of an individual’s normal step

2. To adjust one’s pace to some predetermined lengthtiring and will only give less accurate results

Factors Affecting Length of Pace

Speed of pacingRoughness of the groundWeight of clothing and shoesFatigue on the part of the pacer

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Fatigue on the part of the pacerSlope of the terrainAge and sex/gender of the individual

Relative Precision: 1/200 to 1/100seldom less than 1/300

Methods of Distance Measurement

2. 2. TapingTapingIt involves direct measurement of the It involves direct measurement of the

distance with graduated tapes. This is the distance with graduated tapes. This is the most common method of determining most common method of determining distances.distances.

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distances.distances.

Types of Measuring Tapes

1. Steel tape2. Metallic tape3. Non-metallic tape4. Invar tape5. Lovar tape

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5. Lovar tape6. Fiberglass tape7. Wires8. Builder’s tape9. Phosphor-bronze tape10. Nylon-coated steel tape

Taping Accessories

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Wooden Stake

Plumb BobTension Handle

Range Pole Chaining Pins

Methods of Distance Measurement

3. TacheometryIt is used to quickly determine the horizontal

distance to, and elevation of, a point.

Two Common Methods of this Type of Measurement

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Two Common Methods of this Type of Measurement

a) Stadia Methods

In this method the distance is obtained by sighting the telescope of an instrument on a graduated rod (called stadia rod) held at the other end of the line, and observing the interval on the rod included between two special horizontal cross hairs (called stadia hairs) set in the telescope.

Stadia Method Illustration

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Stadia Method

ratio

rod interval: H

1: 100

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H

rodinterval

Methods of Distance Measurement

b) Subtense Bar Method

The Invar subtense bar is set on a tripod and aligned

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The Invar subtense bar is set on a tripod and aligned perpendicular to the survey line by means of a sighting device on top of the bar. 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 and the horizontal distance is computed.

Subtense Bar

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Subtense Bar Method Illustration

H

2m

H

1m

tan α/2 = 1H

H = 1

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αα/2

H = 1tan α/2

H = cot α/2

Relative Precision: 1/3000 with sights of about 150 m or less using a 1” theodolite

Methods of Distance Measurement

4. Electronic Distance Measurement or EDMIt includes electro-optic and electromagnetic

instruments. The basic principle of electro-optical devices is the indirect determination of the time required for an

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is the indirect determination of the time required for an electromagnetic radiation to travel between two stations.

Advantages:

speed and accuracylightweight and portablelow power requirementeasy to operateease in measurement over inaccessible terrainapplicable to measurement of both short and long

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applicable to measurement of both short and long lengthsautomatically measures, displays and records needed dataslope measurements are internally reduced to horizontal and vertical componentsautomatically accumulates and averages reading for slope range, horizontal and vertical angles.

Methods of Distance Measurement

5. Graphical/Mathematical MethodIt relates known and unknown

distances geometrically.

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Methods of Distance Measurement

6. Use of Mechanical Devices

a) Odometer

It is an instrument attached to the wheel of a

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attached to the wheel of a vehicle to measure its revolutions, which, when multiplied by the circumference gives the surface distance covered roughly.

Uses: Route Location Surveys

Preliminary SurveysSmall-scale Mapping

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Relative Precision:

1/200 on fairly level ground

b.) Measuring Wheel

It is very similar to odometer except that it is a more portable and self-contained device.

Uses: Determining distances along irregular or curved lines and boundaries.

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curved lines and boundaries.

Use of Mechanical Devices

c) c) PedometerPedometerIt is a small pagerIt is a small pager--size device worn on size device worn on

the belt that simply records the number of the belt that simply records the number of steps taken based on the body’s movement.steps taken based on the body’s movement.

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Use of Mechanical Devices

d.) Passometer

It registers a pace by impact each time a foot touches the ground.

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e.) Optical Rangefinder

It determines distances approximately by focusing.

Uses: Field SketchingPlane Table WorkReconnaissance Surveys

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Methods of Distance Measurement

7. Total StationIt is an incorporated digital

transit and electronic distance measuring device.

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Trimble DTM-302LEICA TCA2003 TPS1200

Methods of Distance Measurement

8. Global Positioning System or GPS

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Sample GPS Survey

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Methods of Distance Measurement

9. Smart Station It is an incorporated total station and GPS

36Leica TPS1200 Series

Methods of Distance Measurement

10. TellurometerIt is a surveying

instrument that measures distance by measuring the roundtrip travel time of

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roundtrip travel time of reflected microwaves.

prototype tellurometer

Sample Modern Tellurometers

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Methods of Distance Measurement

11. Laser Range Finders

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