Transcript Surveying and Geometry

Surveying and Geometry
Brittany Crawford-Purcell
What is Surveying?
► Science
of accurately determining the
terrestrial or three-dimensional position of
points and the distances and angles
between them.
Prolong a Straight Line Forward from
an Existing Point
Prolong a Straight Line Forward from
an Existing Point
Line Needs to Extending Through an
Obstruction
►
1. Find appropriate
point C at angle α
from AB direction.
►
2. Turn angle -2α at
C and locate point D
such that CD = BC.
►
3. Turn angle α at D
to locate E and
extension of original
line.
The Collinearity of A, B, D and E
The line AB extended through B must meet CD say at some point D'.
The Collinearity of A, B, D and E
In a triangle each exterior angle is equal to the sum of the other two interior
angles.
Therefore <CBD’ and <CD’B are equal = α
The Collinearity of A, B, D and E
Becasuse <CBD’ and <CD’B are equal = α
CD= BC = CD’, D=D’
A, B, D are collinear
Horizontal Distance of a Surface
A map is flat and shows all the points on
the same level
► But the surface of the earth is rarely flat due
to all the local ups and downs
► How do you calculate the distance between
two objects of different height?
►
 Use the distance between two objects (on the
slope) and the correction term Ch
Horizontal Distance of a Surface
Ch= L- d
=L - √(L2-h2) Using the Pythagorean Theorem
=L - L(1 - (h/L)2)1/2
Newton's binomial expansion
(1 -x)1/2 = 1 - x/2 - x2/8 + ... with x = (h/L)2
Ch = h2/2L + h 4/ 8L3
Horizontal Distance of a Surface
cos α = d/L
d=L* cos α
Ch= L- d = L- (L* cos α)
Ch= L (1- cos α)