Vector Offset

1
Vector Offset Traverse Survey

• GPS for GIS
• Jerry Davis, Instructor

2
Locations where GPS works well

• Clear view of sky
• Meadows
• Not too many tall buildings
• Ridge tops
• Not too forested

3
Locations where GPS doesnt work as well

• Forest
• Deep canyons
• River riparian corridors
• Caves (well, duh!)
• Urban canyons

4
Simple offset

• Situation
• Cant read GPS at desired point (e.g. in the
  forest)
• But can read from a nearby location (a clearing)
• Solution
• Get a GPS location in the clearing (well call it
  a benchmark GPS)
• Survey the vector offset (D, Azimuth, Vertical
  Angle)to the target point
• Calculate the offset ?X, ?Y and ?Z from the
  vector offset
• Calculate the target point XYZ from the benchmark
  XYZ by adding the ?X, ?Y, and ?Z

5
Relative Position XY or XYZ offset

• The basic idea
• If you know where one point is, you can sight to
  another point to get its location
• We need direction and distance (polar
  coordinates)
• Add vertical angle for XYZ
• Well use cartesian coordinates, like UTM

6
Longer Traverse

• Sometimes you cant get to the target from the
  benchmark in one shot.
• Solution traverse
• Each point is derived as an offset from the last
  point
• Your whole area may be a mapped as a Traverse
  Survey
• Before we get into these methods, well take an
  aside to look at controlling a sketch
• Method of making a planimetric map from a sketch
• Applicable to GPS Alone, GPS with Offsets,
  Traverse Survey
• Well later look at georeferencing a sketch
  similar to georeferencing an image

7
Harrelson et al (1994)
8
Controlling a Sketch

• Using a set of locations you are actually
  measuring
• Called control points
• Might be points along a traverse or GPS points
• A means to turn a sketch into a map or profile
• the sketch has other details, with locations
  known less accurately
• by referencing them to control points they are
  more accurately known.

9
Going from sketch to planimetric map

• Sketches must be controlled to use as a
  planimetric map
• Fieldworkers vary in ability to accurately sketch
  a landscape
• Accuracy is needed to measure features and detect
  change
• Horizontal control
• Absolute XY position
• Relative distance and direction
• Or difference in X, difference in Y
• Vertical control
• Absolute elevation (Z)
• Relative vertical distance (difference in Z)
• both horizontal and vertical
• Absolute XYZ position
• Relative distance, direction, and vertical angle
• Or difference in X, difference in Y, difference
  in Z

10
Converting Absolute to Relative Position

• If we could always determine absolute position
  accurately, we could determine distances from
  these by either
• Measuring from a map
• Deriving using Pythagorean Theorem
• In practice
• Direct measurement may be easier,depending on
  what youre measuring
• GPS may not be sufficiently accurate,or may not
  work where you need it.

11
Horizontal and Vertical Distance

• Distances on a map are horizontal.
• Elevations are vertical distances relative to
  mean sea level.
• How do we measure horizontal distances?
• Hold the tape horizontal -- not always possible
• Trigonometry provides a solution (well see
  later)
• How do we measure vertical distance?
• There are various methods of measuring elevation
  -- altimeters, for instance -- but well see that
  it is one of the most difficult measures.

12
Angles on the planet

• Well come back to lengths, but we need to look
  at angles
• horizontal angles
• vertical angles e.g. slopes

13
Measuring horizontal angles

• Direct measurement
• Transits and some other surveying equipment
• Trilateration
• If the lengths of all three sides are known, the
  angles can be predicted
• Is the method used by GPS receivers
• Actually there are two possible shapes, one a
  mirror image of the other. Sketch can be used to
  determine which.
• Azimuth
• horizontal angle between a direction and magnetic
  north

14
Measuring azimuth

• Azimuth
• horizontal angle between a direction and magnetic
  north
• must take magnetic declination into account
• transits and theodolites have compasses built in
• Brunton and Suunto compasses good for field
  survey

Bruntonpocket transit
15
Vertical Angles

• Measured in degrees or percent
• percent is rise over run
• simplifies tree-height computation
• related by trigonometry
• percent tan(angle) 100
• Why measure vertical angles?
• By itself, slope angle is an important property
  for plants, soils, landforms, slope stability,
  and land use.
• To determine relative height, or elevation of one
  point in relation to another
• To determine horizontal distance from a direct
  along-slope measurement (see Deriving Horizontal
  Distance later)

16
Vertical angle instruments

• Transits can be used
• for highest accuracy needs
• Suunto clinometer
• used widely by foresters to measure tree heights
• accurate to 1/2 degree if calibration used
• Brunton pocket transit
• tricky to use for sighting, but makes a versatile
  combination with compass

17
Deriving Horizontal Distance

• Direct slope measurements must be converted to
  horizontal to be portrayed on a map
• b L cos(S)
• where S is the slope angle, L is the slope length
• and b is the horizontal distance

18
Deriving Vertical Distance (Relative Height)

• As with horizontal distances, height of land
  features is defined as a vertical distance
• elevation is the vertical distance from mean sea
  level to the feature
• Can also be derived with trigonometry
• ? Z L sin(S)

elevation vertical distance from sea level ?z
19
Simple 2-D compass traverse

• 2D
• Most traverses are 2D in that measurements are
  made horizontally.
• as if the area being mapped was a horizontal
  plane
• For a 2-dimensional map, need only azimuths and
  distances
• basic method
• Sight from A to B, get an azimuth, measure the
  distance
• Then go to B, and sight to C, measure the azimuth
  and distance, etc.
• To greatly improve accuracy, make backsights as
  well
• backsight from B to A should be 180º away from
  foresight from A to B

20
Preparation for Surveying

• Prepare field notebook First Page
• Choose Personnel book, instrument, chain, and
  record names on first page of book
• Record instrument number, date/time, location,
  starting reference information (e.g. benchmark
  id) if exists
• If leveling and a constant instrument height is
  used (e.g. eye height), record height.
• Subsequent Pages
• Data Recording Area (left pages)
• Sketch Map Area (right pages)
• If possible, estimate outer boundary or other
  known limits

21
Recording 3D compass traverse data
Data Recording Control Points
Sketch Area
Sta
D (ft)
bs
A
vert
Az(fs)
15.2
224.0
0.0
B
45.0
110.0
C
14.0
290.5
12.0
14.8
D
181.0
1.0
0.0
E
-12
B
20.0
300
121
Dirt road
A
C
A
maple
tree
D
Red alder
22
(No Transcript)
23
Compiling the map -- protractor method

• 1. Decide on a scale, and work out units with
  engineer's scale.
• 2. Mount your sheet on a drafting table.
• 3. Use a T-square and triangle to mark a North
  arrow.
• 4. Place your first point (A).
• 5. Use a protractor and T-square to determine the
  first direction, with point A at the origin, and
  the angle determined by the azimuth.
• 6. Measure the distance with the scale, place the
  point and draw the line with a straight edge.
• 7. Continue by plotting from B to C, etc.

(N) 0º
B
40º
90
A
50
A
0
24
Cartesian Coordinates method

• The problem with the protractor method
• depends on drafting accuracy -- each minor error
  is compounded
• tiny angle errors especially can create big
  position errors
• never used professionally
• Cartesian coordinates method
• use graph paper, or CAD/GIS
• determine XY offsets by trigonometry
• very suited to a spreadsheet or computer program
• COGO (Cooordinate Geometry) programs (as with
  Arc/Info) allow data entry of distances and
  azimuths, computes coordinates -- also closes
  closed traverses.

25
3D survey -- extra computations

• vertical angle is similar to measuring slope S
• direct measured distance measurement is
  hypotenuse
• Dz is opposite side, so sine works
• Dz L sin(S)
• horizontal distance is adjacent side, so cosine
  works
• Dh L cos(S)

L
Dz
S
Horizontal and vertical distance determinations
Dh
in 3D survey from control point A to B
26
(No Transcript)