Download 2011 Lecture 6 Measuring Distance

Measuring Distance
©2010 Dr. B. C. Paul
Note – 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.
How do We Know Distance?

Physically Measure It


Counting off paces (only good for very loose
surveys)
Tape Measures


For a line a mile long this gets fun fast
Optical Techniques


Things appear larger or smaller depending on
distance
Rate that things get smaller is function of focal
length of lens

If know focal length of lens can determine distance
optically by how big an object of know size is
More Knowing Distances

Wavelengths of Electromagnetic radiation

Send out a light beam and reflect it off of
something at point



Reflected beam will be out of phase unless the
distance is an integer multiple of the light
wavelength
Amount out of phase is the non-integer part of the
distance relative to the length of light wavelength
Send out more than one wavelength –
distance is the same but that distance will
only through several wave lengths out by a
certain amount for a unique distance

Technique is basis of Electronic Distance
Measurement
And More Knowing of Distance

If know the coordinates of two points


Pythagorean theorem will give you the distance
Getting coordinates of points


Grid of Global Positioning Satellites above the earth
Read the angel and distance to a satellite from an
electronic signal it sends down


Solve coordinates of any point from satellite position
If set up two points, a base point and a point being
measured can use ground based stations to compare
signals and get mm accuracy


Can hit within feet with single back-pack mounted units
May know this technology is being put in cars now
Surveyor’s Chains Were Robust
Wilderness Ready Tape Measures
A link is one of those wire lengths with a loop at each end
Chain Characteristics



Chains had 100 links with brass holding
handles at the ends.
Chains had brass tags every 10 links to
speed counting of links on partial chains
Two Basic Kinds of Chains

Surveyors Chain (also called Gunter’s
Chain)


Was 66 feet long
Engineers Chain

Was 100 feet long
Why a Profound Number Like 66
ft

Turns out a mile (5280 feet) is 80
chains long


Divides nicely for quarter sections or
common land divisions
Surveyors were laying out blocks of
land

Also helps explain why no little fractions for
inches etc.
The Class Chain

Is a reproduction 10 meters long

We’ll use it to measure out a baseline on
first lab just for nostalgia
Measurement by Tacheometry

Surveying Instruments have very
precise optics – focal length is very well
known


You can tell how far away something is by
how big it appears in the lens (provided
you know the size of the something)
That something is the rod used to mark
your foresight point
Stadia Measurements
That’s what those two funny
Short horizontal lines are
for
6.0
5.0
4.0
Take the upper and
Lower rod reading –
Now you have an object
Of known size in an
Interval the instrument
Was designed to measure
Reading the Rod
Rods are marked in 10ths and 100ths of
Feet. (not in inches)
This is 6.2 ft.
Reading the Finer Points
6.25
6.22
6.23
6.2
6.24
6.21
Getting the Hang of it!
Notice that both
The black mark
And the white
Space between
Are 1/100th of a
foot
Eyeball limitations – even with a telescope usually limit you to shots
Of 300 feet or less.
For Instruments Other Than Very
Old Ones


Ratio between the
stadia intercept
distance (which you
read from the rod) is
100
Can get distance by
H  100 * (U  L) * cos (verticalangle )
2
V  50 * (U  L) * sin( 2 * verticalangle )
You Think I Blew the Formula
Don’t forget the rod you read is inclined with respect
To the perpendicular measurement plane
(which is where the funny squared and double
Angle stuff came in)
α
α
Ground Level
I’m not going to do a trig
Proof in a 1 hours hands
On course
(entertain yourself with your
Own proof if your going nuts)
Vertical Control with Stadia


V in the formula is the vertical change
in distance from the height of
instrument to the center reading on the
rod
To get change in ground elevation
ΔV = V + Height of Instrument – Center Rod
Reading
An Example
The upper rod reads 6.5
The lower rod reads 6.1
The intercept is 6.5 – 6.1 = 0.4ft
Using a stadia constant of 100
0.4 * 100 = 40 feet
Measuring By EDM
EDM shoots a lazer
Beam into a reflector
Reflects back Out of Phase
You remember from physics that out of phase light beams
Cancel part of intensity. You can tell how far out of phase by
Measuring light intensity.
To Do it.
Turn the instrument on using the
Switch on the side
Our totally digital stations have
To be turned on to work at
All.
Take aim at your target using the telescope
Set Your Units for Distance
Measure
The ft and
M indictor tells
You what units
Its it.
Push the enter button to change it
The Real Tuff Part.
Push the Measure
Button
I Lied – This is Even Harder
Read the Distance
Proficiency #5



Task #1 chain the distance between 2
stakes – use instrument to keep people
on line
Task #2 measure a distance by stadia
Task #3 measure a distance by EDM