MEASUREMENTS IN SURVEYING

Lecture 21

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MEASUREMENTS IN SURVEYING

There are five major types of measurements in

surveying:

Horizontal distances

Horizontal angles

Vertical distances

Vertical angles

Slope distances

The magnitudes measured must always be

reported in terms of specific units2

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MEASUREMENTS IN SURVEYING

When reporting the measurements, it is very

important to maintain the following:

Integrity

Legibility

Arrangement

Clarity

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SIGNIFICANT FIGURES

The accuracy of the measurement could be

indicated by the number of significant figures

(SF) recorded.

SF of any observed value is the number of

certain digits plus one digit that is estimated or

rounded off.

If a measuring tape smallest division is 0.001 m

and the reported measurement is 3.523 then it

has 4 SF (3 certain and 1 estimated). 4

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SIGNIFICANT FIGURES

Decimal Places may be used to maintain the

correct number of SF.

Two SF: 32, 3.2, 0.32, 0.032, 0.00030

Three SF: 324. 32.4, 0.000324, 0.0320

Four SF: 3245, 32.45, 0.003245, 0.03240, 32.00

32000-------------- ??????

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SIGNIFICANT FIGURES

Zeroes at the end of an integer may be expressed in terms of power of 10 to eliminate any uncertainty about SF

3.2000 x 104 --------------- 5 SF

3.200 x 104 --------------- 4 SF

3.20 x 104 --------------- 3 SF

Or

32000 --------------- 5 SF

32000 --------------- 4 SF

32000 --------------- 3 SF6

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SIGNIFICANT FIGURES

In mathematical operations it is important that

the number of SF reported is consistent with the

data used

(+, -) ------------- rightmost significant digit

(x, /) ------------- least number of SF

45.356 + 2.06 – 5.0 = ??

45.356 / 5.0 = ??

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ROUNDING OFF NUMBERS

Rounding off numbers is usually performed to

have only the SF in a number

Less than 5

Greater than 5

Equals five (nearest even number)

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PRECISION AND ACCURACY

Precision is an indication of the consistency of a

group of readings

Accuracy indicates the absolute nearness of the

readings to their true value

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PRECISION AND ACCURACY

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PRECISION AND ACCURACY

If two teams measured a horizontal 90o angle five

times in the field and the following results were

obtained:

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PRECISION AND ACCURACY

Max difference in readings:

Team 1: 00 00 50

Team 2: 00 00 05 (more precise)

Deviation from the true value:

Team 1: (more accurate)

Team 2:

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ERRORS IN SURVEYING

All types of measurements entail some degree of

error (± ε)

When dealing with errors, surveyors must

understand:

The different kinds of errors

The sources of errors

Estimate the magnitudes of the error

Error propagation

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ERRORS IN SURVEYING

There are three general sources of error:

Natural errors caused by variation in or adverse

weather conditions, refraction….

Instrumental errors caused by imperfect construction

and adjustment of the surveying instruments used

Personal errors caused by the inability of the

individual to make exact observations

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ERRORS IN SURVEYING

Classes of errors:

Blunders

Systematic errors (constant or variable)

Random errors

Constant errors

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ERRORS IN SURVEYING

Weights:

The are expressed numerically and an indication of

the relative precision of quantities within a set

The greater the weight, the greater the precision of

the observation to which it relates

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MEASURING DISTANCES

Frequently measured as a spatial distance in

three-dimensional space, however, it is usually

the horizontal component which is required

There are three basic methods of measuring

distances:

Direct (tape)

Indirect (stadia or tacheometry)

Electronic

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MEASURING DISTANCES

Methods of measurement:

Pacing:

a rapid means of estimating a distance

distance = individual pace distance x number of paces

Odometer:

Distance = number of revolutions of the wheel x

circumference of the wheel

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MEASURING DISTANCES

Stadia (or Tacheometry)

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MEASURING DISTANCES

Stadia (or Tacheometry)

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MEASURING DISTANCES

Chains

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MEASURING DISTANCES

EDM

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MEASURING DISTANCES

Tapes:

Four kinds of tapes are used:

Synthetic/Fibre-Glass Reinforced tape

Synthetic/ Steel - Plastic tapes

Steel tapes

Invar tapes

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MEASURING DISTANCES

Synthetic/Fibre-Glass Reinforced tape

hard-wearing, durable and water proof

materials can easily be stretched

used for measurements that

do not need to be highly precise

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MEASURING DISTANCES

Steel/Plastic Composite Tape

more precise than the fiber-glass tape

temperature and tension variations

can be corrected

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MEASURING DISTANCES

Steel Tapes

more precise and more stable

nominal length:

temperature = 20°C and

applied tension between 50 N to 80 N

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MEASURING DISTANCES

Invar tapes

most precise tape

made from an alloy of 36% nickel and 64% iron

low coefficient of expansion (only 1/13 that of steel

tape)

Disadvantages:

soft and weak

price is more expensive than steel tape

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MEASURING DISTANCES

Tape ancillary tools:

Chaining pins

Ranging poles

Thermometer

Plump bob

Tripod

Tension gauge

Bubble

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MEASURING DISTANCES

Sloping distances

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MEASURING DISTANCES

Errors in taping

Instrumental error

Human error

Natural error

To express the precision, the numerator should

be set to 1 while the denominator should be as

large as possible.

Precision =

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MEASURING DISTANCES

Tape calibration

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MEASURING DISTANCES

Correction for measurement:

Correction = L * α * (tm - ts)

where

L = measured length

α = coefficient of expansion, (0.000 012 per C for

steel)

tm = temperature at measurement

ts = temperature at standardization

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MEASURING DISTANCES

Correction for slope

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MEASURING DISTANCES

Correction for sag:

correction =

Where,

w = unit weight of tape

p = tension applied to the tape

L = length measured

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MEASURING DISTANCES

Examples

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MEASURING DISTANCES

Ranging

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