Horizontal Distance

Horizontal Distance

Horizontal Distance

Measurement

Measurement

Tape

Tape

Odometer

Odometer

Subtense Bar

Subtense Bar

Stadia

Stadia

EDM

EDM

Distance Measurement 

Distance Measurement 

•

•  _{Older technologies “ quick  Older technologies “ quick look”look”} •

• _{Pacing  !"#Pacing  !"#}

•

• _{Optical range$inders ! "#Optical range$inders ! "#}

•

• _{Odometers !%##Odometers !%##}

•

• _{Tacheometr& ' stadia ! "##Tacheometr& ' stadia ! "##}

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• _{Subtense bar ! (###Subtense bar ! (###}

•

• _{Tapes ! !#)###Tapes ! !#)###}

•

• Modern Modern TTechnologyechnology::

 - Electronic Distance Measuring (EDM) devices: 2 +2 

 - Electronic Distance Measuring (EDM) devices: 2 +2 

Devices and accuracy:

Distance Measurement 

Distance Measurement 

•

•  _{Older technologies “ quick  Older technologies “ quick look”look”} •

• _{Pacing  !"#Pacing  !"#}

•

• _{Optical range$inders ! "#Optical range$inders ! "#}

•

• _{Odometers !%##Odometers !%##}

•

• _{Tacheometr& ' stadia ! "##Tacheometr& ' stadia ! "##}

•

• _{Subtense bar ! (###Subtense bar ! (###}

•

• _{Tapes ! !#)###Tapes ! !#)###}

•

• Modern Modern TTechnologyechnology::

 - Electronic Distance Measuring (EDM) devices: 2 +2 

 - Electronic Distance Measuring (EDM) devices: 2 +2 

Devices and accuracy:

Tape Measurement 

Tape Measurement 

•

•

_{*ccurac& and speed considerations $or}

_{*ccurac& and speed considerations $or}

ci+il engineers,

ci+il engineers,

•

•

_{Sources o$ Errors}

_{Sources o$ Errors}

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• -ncorrect length o$ the tape-ncorrect length o$ the tape

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• _{Temperature di$$erenceTemperature di$$erence}

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• SagSag

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• Poor alignmentPoor alignment

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• _{Tape not hori.ontalTape not hori.ontal}

•

Odometer and Subtense Bar 

 !"u#tense $ar 

Distance H % cot( &2) m'

   &2

&2

tan ( &2) % (&2) & H

H % (&2) & tan( &2) *  % 2 m, then

H %  & tan (&2) % cot (&2)

       H

Example:

.hat is the

horizontal distance #et.een  and $ i the angle  .as

Stadia

• _{3hapter 1!42}

• _{Principle o$ the Stadia}

• _{Horizontal Distance = 100 rod intercept $or a}

hori.ontal line o$ sight and a +ertical rod

• _S&mbols

•  1-2 rod intercept) or stadia inter+al •  1i2 spacing bet5een stadia hair

• _{1$'i2 0 k 0 !## stadia inter+al $actor}

Electronic Distance Measurement 

_{Earl& t&pes}

• _{Transmit light) measure up to %" miles} • _{Transmit micro5a+es) measure up to "#}

miles

•

_{3lassi$ication o$ EDM}

• _{Electro8optical laser or in$ra red re$lected}

$rom passi+e prism or sur$aces) the 9S has installed a prism on the moon,

• _{Micro5a+e t5o positi+e units) :PS}

replaced them $or most engineering

Distance Computation

• _{;e onl& measure the phase angle shi$t}

1change2 ) di$$erent signals o$ 5a+e length !# !## !### !#)### m are sent, Each $raction

pro+ides a digit1s2,

• _{(Phase shift / 360)*wave length = non coplete}

c!cle length"

 The Idea:

To measure the distance bet5een t5o points 1*2

and 1B2 the EDM on point 1*2 sends

electromagnetic 5a+es, The 5a+es recei+ed at

1B2 are re$lected back or resent to 1*2 b& a

de+ice on 1B2,

Electronic Distance Measurement  EDM 

•0no.ing the seed o electromagnetic .aves in

the air, the EDM comutes the distance #y

measuring the time dierence or the shit o the

.ave hase angle (.ill #e e1lained in details

later)'

hase ngle  3 43 53 263  ssume that  % 2 m

* _ % 53, it corresonds to a distance % (53&783) 9  % 3' m * ₂ % 7;, it corresonds to a distance % (7;&783) 9  % 3'6; m * ₇ % 23, it corresonds to a distance % (53&783) 9  % '77 m



Distance 0 >elocit& ? Time 0 11@ ?

2 6

2 ' %

;here

 _{is a $raction o$ 5a+e length 0}

1

_{'(4#2 ?}

@ is the number o$ $ull c&cles) ambiguit&A

Basic relationships

"ince  is divided #y 2, so is , .e call &2 “effective wave length”

EDM Mounted on a theodolite

The angle #et.een the rays  and < is

dou#le the angle #et.een the t.o mirrors %

2 943

 % 53

=otice that the o#>ects .ill loo? uside

do.n, notice the #o1 at the tail o the arro.

 

<

Aiming at a rism thro!gh th" t"l"sco" of a total station in a zoo#

Reflectors (Prisms)

$rism an% sighting targ"t

@ully rotating rism

• _{* re$lector might include a single}

prism or a group o$ prisms

• _{e$lectors can be a simple re$lecting}

paper8sticker) the& are called sheet8 prisms) paper prism) or re$lecti+e sheeting, >er& instrumental in

construction sites and de$ormation monitoring o$ structures,

EDM Accuracy

• _{(mm) and (ppm is the most common}

,

• _{Estimated error in distance 0}

E_i% _{6 e}

r % 6 ec% 6 1 pp C D2%

• ;here E_i and e_r are the centering errors o$ the

instrument and the re$lector) e_c is the constant error o$ the EDM) and PPM is the scalar error o$ the EDM

E7ample 48" page !"4 i$ the estimates errors o$ centering the instrument and target 5ere  (mm and  "mm respecti+el&) the EDM had a speci$ied error o$  1%mm 6%ppm2 5hat is the estimated error in measuring =%,(%F mA

•

_{Prism constant}

consideration,

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_{Total station >s EDM,}

_{Data collectors,}

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_{Prismless EDM up to}

!## m) can reach hard

places) $igure 48!<,