doc. Ing. Hana Staňková, Ph.D

One of the most fundamental surveying operations is the measurement of distance between two points on the surface of the earth.

Distance between points can be also be determined using geometric or trigonometric computations working with related distance and angle measurements.

Methods of measurementIn surveying there are several methods for measurement of distance. These are:

1. Direct methods (distance are actually measured on the ground with a tape or a chain or any another instruments;

2. Optical methods ( indirect, several parameters are measured directly and then the value is determined bymathematical relationship);

3. Electro- magnetic method ( distances are measured with instruments that rely on propagation, reflection and subsequent reception of either radio waves, light waves or infrared waves.

Approximate Methods Pacing,

taping,

passometer,

pedometer,

odometer,

speedometer.

Practical measure of distance

Consists in counting the number ofpace between 2 points of a line

The length of the line can then becomputed by knowing the averagelength of the pace

A pace is defined as one step

Varies with the individual, the nature ofthe ground, the slope of the countryand the speed of pacing

Low accuracy(1:100)

No equipment needed

Pacing

Passometer is an instrumentshaped like a watch and is carried inpocket or attached to one leg. Themechanism of instrument is operated bymotion of the body and automaticallycounts the number of paces. Distance iscalculated by multiplying number of paces& length of one pace.

Passometer

Pedometer is a device similar to Passometer. But pedometer counts the total distance when adjusted to the length of one pace.

Pedometer

Odometer is a device which registers the number of revolutionsof a wheel. Odometer is fitted to a wheel which is rolled along thelength to be measured. Distance between two points is given byproduct of number of revolution & circumference of wheel.Odometer is note so accurate while using on an undulatedground.

Odometer/measuring wheel

The name is carried over from theearly days when the Gunter’s chainand the engineer’s chain were inuse.

Chain is applied to measurement witha steel tape or synthetic tape (plasticor fiberglass). All standard in lengths100 m, 50m, 30 m, 20 m.

Observation of horizontal distances by taping consists of applying theknown length of a graduated tape directly to line a number of times.

It is fairly quick, easy and cheap, and hence is the most commonform of distance measurement.

Chain is prone to errors and mistakes.

Taping

Accurate surveyors tapes made of steel or a steel alloy with atypical lenght of 100meters were used for surveying distances.

For every accurate measurements , the temperature of the tapemust be taken into account, as well as the tension of the pull.

Each Steel Tape had its own temperature and tension coefficient,which was used to corrct each measurement.

A preliminary investigation of the field site is undertaken to map outa measutement strategy, and to identify and locate initial startingand fixed points

Range poles may be placed to help define the measurement line Field noted should be taken for later reference (e.g. date , weather,

temperature , potential obstructions , topography etc.)

Taping

Direct measurement involves applying a standard distance, which is theruler (tape) of known length "L" to the measured side and read its length.If side is measured longer, then its length consists of the number oftouchdowns tape "n" and ends residue "r„

d=nL+r45,35m = 2 ∗ 20m + 5,35m

ALL MEASUREMENTS TO BE CARRIED OUT IN TWO DIRECTIONS !!!

To increase the accuracy and control of determination of thedistance direct measurement of the distance is performed in twomain : directions and return

The difference „dl” for twice the measurement does not exceed

𝑑𝑑𝑑𝑑 = 𝑢𝑢 𝑑𝑑

u - coefficient of linear measurement of random errors u = 0,0059 d - side length in meters

𝑑𝑑𝑑𝑑 = 0,0059 56,45𝑚𝑚 = 0,044𝑚𝑚 = 4,4𝑐𝑐𝑚𝑚

OTHER ERRORSAmendment length at sea level

∆𝑑𝑑𝑚𝑚 = −𝐻𝐻 ∗ 𝑑𝑑𝑅𝑅

R - Average radius of the Earth, R = 6 367 650mH - Average height endpoint measured section

Amendment comparator with a comparison measure of length∆𝑑𝑑𝑘𝑘 = 𝑑𝑑𝑙𝑙𝑙𝑙 − 𝑑𝑑n

lrz- Actual length𝑑𝑑n- Nominal length(Information in certificate comparation the tape )

AMENDMENT TEMPERATURE∆𝑑𝑑𝑡𝑡 = 𝑑𝑑𝑙𝑙𝑙𝑙 ∗ 𝛼𝛼(𝑡𝑡p-tk)

𝛼𝛼 − 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑙𝑙 𝐿𝐿𝑒𝑒𝑒𝑒𝐿𝐿𝐿𝐿𝑒𝑒𝐿𝐿𝑒𝑒𝐿𝐿 𝑐𝑐𝑒𝑒𝐿𝐿𝑐𝑐𝑐𝑐𝐿𝐿𝑐𝑐𝐿𝐿𝐿𝐿𝐿𝐿𝑡𝑡 𝑒𝑒𝑐𝑐 𝑒𝑒𝑡𝑡𝐿𝐿𝐿𝐿𝑑𝑑𝑡𝑡p −𝑇𝑇𝐿𝐿𝑚𝑚𝑒𝑒𝐿𝐿𝑙𝑙𝐿𝐿𝑡𝑡𝑢𝑢𝑙𝑙𝐿𝐿 𝑚𝑚𝐿𝐿𝐿𝐿𝑒𝑒𝑢𝑢𝑙𝑙𝐿𝐿𝑚𝑚𝐿𝐿𝐿𝐿𝑡𝑡𝑒𝑒𝑡𝑡𝑘𝑘 −𝑇𝑇𝐿𝐿𝑚𝑚𝑒𝑒𝐿𝐿𝑙𝑙𝐿𝐿𝑡𝑡𝑢𝑢𝑙𝑙𝐿𝐿 𝑐𝑐𝑒𝑒𝑚𝑚𝑒𝑒𝐿𝐿𝑙𝑙𝐿𝐿𝑡𝑡𝐿𝐿𝑒𝑒𝐿𝐿

To compensate for errors of measurement with tape introduce thefollowing corrections:

1. ranging rods set up between points A and B2. from A to B, set zero of tape at A3. tape unwound towards B4. A third range rod is “ranged” in at C5. Tape straightened, held tight and read at rod C6. C marked with a pin7. for next bay, tape moved from A and zero set at8. C and so on

Taping Procedures

Taping Procedures

If the ground is not level, one or both surveyors must use aplumb bob. Normally, the only occasion when both surveyors have to use plumb bobs is when the ground rises or obstacles exist between two surveyors.

Use of a steel tape and plumb bob

Taping on the slope ground

There are 2 methods:

Chaining on sloping ground

1) Direct method (stepping)• In this method the sloping

ground is divided into a number of horizontal and vertical strips

• The lengths of horizontal portions are measured and added to get the total horizontal distance

The horizontal distance for each section may be found out by any of the following indirect methods:

2) Indirect method

a) The distance along the slope is measured and then the angle of slope and the horizontal surface is found with the help of Abney’s level.

The horizontal distance D can be calculated by the relation

D = L*cos α

By applying hypotenusalallowance In this method the slope of the ground is found by clinometer .Hypotenusal allowance is made for each step .Then hypotenusal allowance is applied on each step until the end of line is reached.

b) Hypotenusal allowance method

AD = AB = 1 ChainAC = sec α *1 chain BC = AC – AB = 1chain (Sec α- 1).

c) Knowing the difference of level

If the elevation difference between 2 terminals points and the sloping distance between 2 terminal points is known the horizontal distance D can be calculated as

Taping equipment and accessories

Plump bobs are used in taping to permit the surveyor to hold thetape horizontal when the ground is sloping. Used to transfer points on ground. Used for fixing instrument exactly over the stations.

Plump bobs

Arrows are made of tempered steel wire of diameter 4mm.One end of the arrow is bent into a ring of diameter 50mm and the other end is pointed.Its overall length is 400mm.An arrow is inserted into the ground after every chain measured on the ground

Arrows

Ranging rods made of wood, steel or aluminum. Ranging rods are 2 to 3 m in length.The main utility of range poles is to mark the line being measured so that the tape’s alignment can be maintained.Painted with alternate bands of black and white or red and white colors.

Made of timber or steel.Used to mark the position of stations.Pegs are in length of 15 cm.

Ranging rods

Pegs

Sources of error Systematic errors Faulty alignment. Taping pins must be ser in proper position. Sag, difficult to evaluate when wind blows. Tape no is nominal length. Temperature of tape during measurement is not that at which it was

standardized. Tension applied to the tape is not the same as that when standardized. Measure were made along slopes instead of in a horizontal plane. Several mistakes Faulty tallying. Misreading the tape graduations. Improper plumbing. Reversing or misunderstanding the calls in recording numbers. Mistaking the end mark.

EDM is very useful in measuring distances that are difficult to access or long distances.

It measures the time required for a wave to be sentto a target and reflect back.

Electronic Distance Measurement

These devices measure lengths by indirectly determining the number offull and partial waves of transmitted, electromagnetic energy required intraveling between the two ends of a line. In practice, the energy istransmitted from one end of the line to the other and returned to startingpoint; thus it travels the double path distance.

Multiplying the total number of cycles by its wavelength and dividing by 2, yields theunknown distance.

Sources of errors in chainingSources of errors:a) Instrumental errors : A tape may differ in actual

length from its nominal graduates length because of adefect in manufacture or repair, or as a result of kinks.

b) Natural errors: The horizontal distance between endgraduations of tape varies because of the effects oftemperature, wind, and weight of tape itself.

c) Personal errors: Tape person setting pins, reading thetape, or manipulating the equipment.

Once a line is being measured, it is necessary to convert themeasured length into a horizontal length. Series correctionshave to be applied. Five possible corrections have to beconsidered.These are:

• Erroneous Tape Length

• Slope

• Tension

• Temperature

• Sag

Corrections

Tape has a nominal length under certain conditions, atape stretches with time.Standardization needs to be carried out frequently byusing reference tape or baseline.

Erroneous Tape Length

All plan distances are always quoted as horizontal distancesL, therefore any distance not measured on the horizontal willneed to be corrected for slope. Slope correction must alwaysbe considered, and either eliminated in the field ormathematically compensated.

Slope Correction

A tape has a given lengthwhen pulled with a certaintension. If the tensionchanges then so does thetape length.

Tension Correction

Most materials expand and contract withtemperature change, and this effects tapeddistances. If a tape has stretched due to heat it willread shorter than it would at its normal (or standard)temperature.

Temperature Correction

If the tape cannot be supported for its length thenit will hang freely under the influence of gravity.The shape of the tape will take is known as (sag)and can be determined mathematically.

Sag Correction

Types of Electronic Distance Measurement Instrument

EDM instruments are classified based on the type ofcarrier wave as

1. Microwave instruments2. Infrared wave instruments3. Light wave instruments

Microwave Instruments

These instruments make use of microwaves. The most popular isTellurometers. These instrument needs only 12 to 24 V batteries. Therange of these instruments is up to 100 km. It consists of two identicalunits. One unit is used as master unit and the other as remote unit.Just by pressing a button, a master unit can be converted into aremote unit and a remote unit into a master unit.

It needs two skilled persons to operate. A speech facility is providedto each operator to interact during measurements.

Tellurometers

Infrared Wave Instruments

In this instrument amplitude modulated infrared waves are used.Prism reflectors are used at the end of line to be measured.These instruments are light and economical and can be mountedon theodolite. With these instruments accuracy achieved is ± 10mm. The range of these instruments is up to 3 km.

These instruments are useful for most of the civil engineeringworks. These instruments are available in the trade namesDISTOMAT DI 1000 and DISTOMAT DI 55.

The Distomat Di1000

Visible Light Wave Instruments

These instruments rely on propagation of modulated light waves.This type of instrument was first developed in Sweden and wasnamed as Geodimeter. During night its range is up to 2.5 km whilein day its range is up to 3 km. Accuracy of these instruments variesfrom 0.5 mm to 5 mm/km distance. These instruments are alsovery useful for civil engineering projects.

Tachemeter GEODIMETER series 600

Error in Electronic Distance Measurement Instruments

Personal Errors Inaccuracy in initial setups of EDMs and the reflectors over the preferred

stations Instrument and reflector measurements going wrong Atmospheric pressures and temperature determination errorsInstrumental Errors Calibration errors Chances of getting maladjusted time to time generating frequent errors Errors shown by the reflectorsNatural Errors Atmospheric variations in temperature, pressure as well as humidity. Micro

wave EDM instruments are more susceptible to these. Multiple refraction of the signals.

The advantage of using EDM instruments is the speed and accuracy inmeasurement. Several obstacles to chaining are automaticallyovercome when these instruments are used.

RANGEFINDERS

For linear measurement in geodetic matrices with detailedmeasuring the length of several hundred meters to severalkilometers, used rangefinders.

The principle of operation of rangefinders

Measuring the distance D is reduced to the measurement of time∆𝜏𝜏 , during which the measuring signal emitted from point Atravels a 2D equal 2AB

𝑑𝑑 =12𝑉𝑉 ∗ ∆𝜏𝜏