Reading Angles with Instruments

©2010 Dr. B. C. PaulNote – The techniques shown in these slides are considered common

knowledge to surveyors. Figures in the slides may be the authors own work or extracted from Instrument Users Manuals, Surveying by

Bouchard, Mine Surveying, or various internet image sources.

The Issue of Angles Angles are measured by 4 major scales

Radian Measure Great for math – rarely used in surveying

Degrees, Minutes and Seconds Common in surveying in the US Circle has 360 degrees Each Degree is divided into 60 minutes Each Minute is divided into 60 seconds 58º 47’ 30” - 58 degrees 47 minutes and 30 seconds Units finer than the second revert to decimal form (ie 22.7

seconds) Grads or Gons

Circle is divided in 400 grad Grads are a decimal system 359.5352g Can express in 100ths and 10000ths

359 g 53 c 52 cc

More Angle Measurements

Military Angle Measurement Mils – circle divided into 6400 mils Also was a convention that used 4000

mils Have moved somewhat away from

that

Controlling Angles Marks that line up form basis for reading angles in

pre-digital instruments On a Transit the marks are etched into

metal plates Windows you look through to view the

marks are called Verniers Most Transits have two windows on

opposite sides (A window and B window) Not surprisingly they read 180 degrees apart

Reading a Vernier

Pay Attention to the Outer Ring First

Note the innerNumbers getBigger as youGo clockwise

Note the Letter A and a zero on theInner ring

The A Tells you you are lookingThrough the A vernier(helps dumb a_ _ from readingAngles 180 degrees off)

Reading the Vernier

First Count the Marks Over to Where the A reads

OneTwoThree

Four

Five

SixSevenEight

We know this angle is 58 degrees

Increasing Precision

Note that Each Degree is SubdividedIn this case into 30 minute halves, butSome divide into 20 minute thirds

Note the A is past the 30Minute mark

This tells us we have30 minutes more thanThe 58 degrees weKnew about

Now our angle is58º 30’

Now for the Inner RingNote we are reading ourAngle clockwise

To pick up the rest of the angleWe look forward clockwise toFind inner and outer ring marksThat line up.

Read the inner ring scaleTo decide what the numberIs where the marks areLined up - Looks like 17

Add the 17 to the reading from the outer ring 58º 30’ plus 17 minutes is

58º 47’

Note that we are pastThe 30 minute mark

Get Out A Piece of Paper for Part I of Your First Proficiency

Read this angle in a clockwise direction – Write Your Answer on a piece ofPaper with your name

Tell me whether you are reading the A or B vernier window

Now Read This

Read the Angle Clockwise and write the answer on your paper

Vertical Angles

Since we assume that all surveys project onto a level plane And since we know that a projection of

a line onto a level plane is shorter than the physical length of an inclined line

We need to know vertical angle Transits have a similar scale for

measuring the tilt of the telescope

Confusing You With Vertical Angles

Where is 0 Its level bozo!

Old instruments this way Can be hard in reading slight positive and

slight negative How about straight up?

Called Zenith angle Common choice of newer instruments

Few measure 0 straight down

Reading- The Vertical Vernier

Step 1 – FindThe 0 on theBottom andSee what itPoints to.

Read up from themark

Reading the Inside WheelEight Seven Six Five Four

One Two Three

Looks Like We Are Almost to the30 minute mark beyond 8

Note We Read the Inner Vernier Moving Clockwise

Keep on Reading in this DirectionLooking for marks to line upOn the inside and out

We find theLined upMarkings.

Now Read the Outer Vernier

OuterVernierReads 26

Conclusion8◦ 26’

This resultedFrom turningThe scope up-Hill so we areGoing up at8◦ 26’

Lets Try AgainThe 0 on theOuter wheel pointsTo 22 andSomething veryClose to 30’

Read up fromThe zero

Note This Time We Advanced Up the Wheel Counterclockwise

Thus we will look for our matchingLines on this side of 0

Check the Line-UpLine up on 28’

Thus Angle is22◦ 28’

This time theScope was pointedDown so thisAngle is downFrom horizontal

Note this instrument uses the 0 is level convention.

Proficiency – Now Its Your Turn to Read!

Take out your paper and write down how you read this angle

Theodolites How are they different from Transits

Angle scales on a theodolite are etched into glass Light is brought in and to illuminate the scale from behind You read the scales through a scope rather than opening a

vernier window View in the telescope is usually either the horizontal or

vertical angle – optics are switched to determine what you see

Most use a dual scale – a coarse scale and a fine scale Dual scales allow most theodilites to read to 3 or 4 times

the accuracy of a transit Actually have to turn a knob (micrometer) to fine tune the

second window on your target. Many features – including the plumb bob are optical Usually do not have compasses on them Generally a little less rugged than the transit

Typical Theodolite

Note the instrumentHas two scopes toLook through

Larger one looksThrough telescopeOut into the field

Smaller one readsThe optical scalesFor angle measurement

Window and backlit scale

Has an opticalPlumb bob

A knob to switch viewFrom horizontal toVertical angle

Reading a Wild T2After sighting pointFirst have to useAn adjustment screwTo bring things intoalignment

`Note that the center line is pointingBetween 265 and 266.

We know the angle is >265º

The Next StepNote that 265 is toThe left of theCenter line

That means theNext reading willBe to the right sinceThe center line isTelling us we haveMore than 265º

We note the center line matches with the second of 3 lines or 40 minutes

Thus we now know our angle is 265º 40’

Note that 265 to 266 is divided into3 or 20 minutes per division

Now for the Exciting Lower Scale

` Scale reads 7All over

We thus know weHave 7 moreminutes

Now we have265º 47’

Read the upper part of the scale – 23.6Upper part of the lower scale gives us our seconds

The Angle is 265º 47’ 23.6”

Newer T2 are a little less Polish

We read 94º 10’

We read 2’ 44.3 “

We Add

94º 12’ 44.3”

Note there is still a coincidence window forLines to line up with the micrometer

Proficiency – Read This Angle

Put your answer on a piece of paper.

The Bracket – it Method

Turn theMicrometer untilYou get a majorScale numberNicely centeredThen go for theFiner scale

Now Read This

Put down whetherYou are reading theHorizontal orVertical Scale(or both) and giveThe reading.

Life the Easy Way – The Digital Transit

The On-Off Button The Angle Left or Right Button

We always measure angles right Sets Zero with a 0 button Chooses Vertical or Horizontal with

the V/H button

Watch Out Warnings There are European Theodolites out there that read

in Grads (Poland is in Europe) Usually find a “g” after number to clue you in you’ve been

had You Switch between vertical and horizontal angles to

view in most instruments Some show both at the same time If your really dumb you might get your vertical and

horizontal readings mixed up Vertical Angle Mix Up

Most transits call a horizontal telescope a 0 vertical angle Most theodolites call 0 angle either straight up or straight

down They are not even consistent with which one

Zero is straight up is called a Zenith Angle If you switch instruments you need to note which one you

are using or you won’t know whether you are going up hill or down

Lets Read This OneWe Check for Coincidence

We’ve got it on the horizontal

Must be 56 degrees

And 50 or five secondsAnd

WAIT!How the Heck Can WeHave 90 seconds?

Holy Crud – This Must be One of those Gon instruments (for peoples whose minds are gone)

Read it 56 g

Next read 50 + 3

53c

Finally read the lowest scale which say 34

56g 53c 34cc

Proficiency – Get Out That Paper

AB

C

Do any ofTheseInstrumentsAppear toHave anUnusualMeasurementSystem?

Read This And Write Down Your Answer on the Paper.

More Warnings

What if you see something like this?

637 638 639

1 1 1 1

30 35 40 45

Double Yipes! Someone has slipped aMil Instrument on you.

Read from the top 638.4

Read from the bottom 1.37

Put them together 638.4 + 0.137 = 638.537

Now adjust for 6400 mil scale 6385.37 mils

Measuring Direction of a Line Line Directions can be measured with

bearings or azimuths Azimuth is the angle clockwise from

north Number can be 0 to 360 degrees

N

Azimuth 45º

Azimuth 180º

Azimuth300º

Bearings

Bearings are done in quadrants Line runs North East 20 degrees

North East

South East

North West

South West

N

S

North 60º East

South 20º East

South 85º West

Contrasts Between Azimuth and Bearing

Bearings can be relative to any grid direction and grid direction should be noted

Azimuth is always measured relative to north Can get ambiguity of true north or

magnetic north

Proficiency #3 Measuring Direction

Get Out a Piece of Paper Put your name on itN

Write down the approximate azimuth and BearingOf this arrowed line.