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NDS & NZDE
Land
Surveying 2
(DE6207 & ENGG6207)
Lecture 6
Land Surveying 2
Lecture Content
• Survey Computations
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Resection / intersection
Total station resection methods / calc’ns
Free Station
Various Area calculations
• Using coordinate method
• using a Planimeter
• using handheld programmable calculator (e.g.
Hewlett Packard HP50)
• Digitising methods
Resection & Free Station Calcs
Resection
• Resection (and its related method, intersection) are used
in surveying as well as in general land navigation.
• Both methods involve taking azimuths or bearings to two
or more objects, then drawing lines of position along
those recorded bearings or azimuths.
• In surveying work, the most common methods of
computing the coordinates of a point by resection are
Cassini's Method, Collins Point, & the Tienstra formula.
• Measuring the angles subtended by lines of sight to a
minimum of three mapped (coordinated) points.
• In geodetic operations the observations are adjusted for
spherical excess and projection variations.
Resection
Determining the position of a point by observing horizontal
directions from it to at least three points of known position.
• Depending upon the disposition of control
points, the unknown point can lie either inside
or outside the triangle formed by the control
points.
• Calculate the coordinates of the unknown point
using Collin’s Point methodology.
• Work through the example.
Collin’s Point - Arrangement 1
Q
B
A
C
P
Collin’s Point - Arrangement 2
Q
A
C
B
P
Collin’s Point - Arrangement 3
B
P
A
Q
C
Resection & Free Station Calcs
Resection
• Precise angular measurements using theodolites provides
most accurate results.
• trig beacons on high points & hills enable quick &
unambiguous sights to known (coordinated) points.
• Caution: first plot the locations of the known points along
with the approximate unknown point of observation.
• If all points, incl. unknown point, lie close to a circle that can
be placed on all four points, then there is no solution or the
high risk of an erroneous solution. This is known as
observing on the “danger circle”.
• Total Station functionality allows for calculation of resected
position.
Area Calculation using coordinate method
• Determining the area for an irregular polygon can be
found when you know the coordinates of the vertices.
• Create an array.
• List X & Y coordinates of each vertex of the polygon in
counter-clockwise order. Repeat the coordinates of the
first point at the bottom of the list.
• Multiply the X coordinate of each vertex by the Y
coordinate of the next vertex. Add the results.
• Multiply the Y coordinate of each vertex by the X
coordinate of the next vertex. Add these results.
• Subtract the sum of the products.
• Divide this difference by 2 to get area.
Area Calculation using coordinate method
Exercise
Calculate the area of the irregular polygon
figure using the coordinate method.
Area Calculation using coordinate method
Exercise
Calculate the area of the irregular polygon
figure using the coordinate method.
Area Calculation using a Planimeter
• A planimeter (also known as a platometer) is a
measuring instrument used to determine the area of
an arbitrary (often irregular) 2-D figure or shape,
usually one which is too complex for manual
measurement.
• It is typically a mechanical device, but digital versions
(e.g. Tamaya Planix 7) do exist.
Area Calculation using a Planimeter
• In its most common form, a polar planimeter, it
resembles a human arm from shoulder to wrist. The
“shoulder” is usually a metal cylinder which fixed in
position but can rotate. The “wrist” is a movable
pointer used to trace around the area. The “elbow” is
a hinge which can move in both directions.
Area Calculation using a Planimeter
• Device mechanises the process of calculating the
area using a formula known as Green’s theorem.
• Most commonly used on a scale representation such
as a map, or a plan.
How does it work?
• It is a combination of planimeter arm movement &
wheel rotations that measures direction & distance
that the pointer travels.
• Movement of the measuring wheel(s) consist of a
combination of sliding and turning on its axis.
• Precision of map & tracing skills are main sources of
error.
Area Calculation using a Planimeter
How do you use it?
• To use a mechanical planimeter,
the user sets up the device in
an approp position over the
area to be measured.
• Zero the recording wheels.
• Trace the pointer all the way around a closed shape (typ. in
a clockwise direction). Repeat process twice for accuracy.
• Area then read directly off the dials if scale set correctly.
Some models allow adjustments to read in various units &
scales.
Area Calculation using a Planimeter
How do you use it?
• Digital version (e.g. Planix 7) more flexible, not restricted by
limits of the planimeter arm length.
• Allows specific map or plan scales to be entered.
• Allows for different units (i.e. m² or km²)
Area Calculation using a Planimeter
How do you use it?
• Brief demo of two models
Practical exercise
• Calc area of uniform figure
• Calc area of irregular figure
• Calc volume from contours