7_UELSurveyingMeasurement.pdf

basic concepts in surveying

1. Surveying & Measurement

Traverse

2. Introduction

* Almost all surveying requires some
calculations to reduce measurements into
a more useful form for determining
distance, earthwork volumes, land areas,
etc.

+ A traverse is a chain of straight lines to be
used as a basis for the measurement of
detail.

3. Type of Traverse

* A traverse is developed by measuring the
distance and angles between points that
found the boundary of a site

There are two types : ; F

4. Graphical Method

° A simple method that is useful for rough
area estimates is a graphical method.

In this method, the
traverse is plotted
to scale on graph
paper, and the
number of squares
inside the traverse
are counted.

oo

5. * Before the areas of a piece of land can be
computed, it is necessary to have a
closed traverse.

° The interior angles of a closed traverse
should total:

(n - 2)(180°)

* where n is the number of sides of the

traverse.

6. How to Calculate

* At least the coordinates of one point must
be given or chosen arbitrarily.

* At least the azimuth of one side (leg) must
be given or chosen arbitrarily.

° The horizontal distances between
successive points must be measured.

° The horizontal angles between successive
legs must be measured.

7. Error of Closure

A

tee
thay

Error of closure

Angle containing mistake

8. Surveying Heuristic

° A surveying heuristic is that the total angle
should not vary from the correct value by
more than the square root of the number
of angles measured times the precision of
the instrument

* For example an eight-sided traverse using
a 1’ transit, the maximum error is:

+11 8 = +2.83' = +3'

9. Surveying Heuristic

If the angles do not close by a reasonable
amount, mistakes in measuring have been made
If an error of 1’ is made, the surveyor may
correct one angle by 1’

If an error of 2’ is made, the surveyor may
correct two angles by 1’ each

If an error of 3’ is made in a 12 sided traverse,
the surveyor may correct each angle by 37/12 or
15”

10. Latitudes and Departures

° The closure of a traverse is checked by
computing the latitudes and departures of
each of it sides.

N N
Latitude ag [Y |
w y | E w BEN Departure cy, E
Bearing Z “A Departure ¿e cp

Latitude ¿y

S E

11. Latitude

° The latitude of a line is its projection on
the north — south meridian.

° The departure of a
line is its projection or
the east — west line. Latitude as

* A northeasterly w
bearing has a + En FR
latitude and +
departure. 5

N

12. * Consider the following statement:

“If start at one corner of a closed traverse and
walk its lines until you return to your starting
point, you will have walked as far north as you
walked south and as far east as you have
walked west”

* Therefore,
= > latitudes = 0
= > departures = 0

13. Error in Latitudes and Departures

° When latitudes are added together, the
resulting error is called the error in
latitudes (E, )

* The error resulting from adding departures
together is called the error in departures

(E,)

14. Error in Latitudes and Departures

* If the measured bearings and distances
are plotted on a sheet of paper, the figure
will not close because of E, and E,

Error of closure

(E) +(&)

closure —

er E,
€ Precision = “ese _
perimeter

+ Typical precision: 1/5,000 for rural land, 1/7,500
for suburban land, and 1/10,000 for urban land

15. Latitudes and Departures
Example

A
o

N 42° 59' E S 6° 15 W
234.58 189.53'
B
o
Es
5 29° 38' E
142.39
N 12° 24 W 175.18'
. 175.18

DN 81° 18° W E

16. Latitudes and Departures

Example
on
-W = (189.53 ft) sin(6°15') = -20.63 fr
w A E

S 6° 15'W
189.53'

Latitude ae

| -5 = (189.53 F+)cos(6'15") = -188.40 ft

17. Latitudes and Departures
Example

+E =(175.18 ft) sin(29°38') = 86.62 fr
w B E

175.18' -

-5 = (175.18 Ff)cos(29'38") = 152.27 fr

C
Ss

18. Latitudes and Departures
Example

Side Bearing
degree minutes

Length (ft)] Latitude | Departure

E

closure

= VE) +(6) = (0.079) + (-0.163 =0.182 fr

Precision Ensure _ 0.181 Ft 1
“perimeter 939.46ft 5,176

19. e. 577° I0"E

Compute the |

. N 29° 16' E 651.2
latitudes, B

60.5 »
departures,
E eiosure» and the S 38° 43° W
= = o

precision for the DOS 410 nu
following N64 09 Wg
traverse. c

Bearing Length (ft)| Latitude | Departure
degree minutes

20. Bearing Length (ft)| Latitude | Departure
degree minutes

Esso = V(E,2 +Ep?) = V((0.601} + (-1.110)2) = 1.262ft
Precision = Edtosure + Perimeter

= 1.262 + 2629.4

= 4.800x10-4= 1/2083

21. Compass and Bowditch Rule

* Balancing the latitudes and departures of
a traverse is to attempt to obtain more
probable values for the locations of the
corners of the traverse

* A popular method for balancing errors is
called the Compass or the Bowditch rule

22. Compass and Bowditch Rule

* The Compass method assumes:
1.angles and distances have same error
2. errors are accidental

° The Bowditch rule states:

“The error in latitude (departure) of a line is to
the total error in latitude (departure) as the
length of the line is the perimeter of the
traverse”

23. A

o
N 42* 59' E S 6° 15 W
234.58' 189.53"
B
o
Es
S 29° 38'E
142.39
N 12° 24 W 175.18
e 175.18
Dnsrisw %
Side Bearing Length (ft)| Latitude | Departure

degree minutes

24. WwW

S 6° 15' W
189.53"

B

“MS

S|

Latitude ¿e

-5 = (189.53 ff) cos(6'15') = 188.40

CorrectioninLat,, L,,
Es perimeter
E, ( Le )

Correction in Lat,, = ——
perimeter

Correction in Lat,, = wre +0.016 fr

25. W

S 6° 15' W
189.53

Y =(189.53 Ff) sin(6°15') = -20.63 fr

Correction in Dep _ has
Ex perimeter
E, ( Le)

Correction in Dep,, = ——
perimeter

Correction in Dep,, = u +0.033 fr

939.46 ft

26. -5 = (175.18 Ff)cos(2938') = -152.27 ft

B E
. Correction in Lat, _ Le
ER £, perimeter
S 29° 38' E E, E,
— Correction in Lat,. = Fille)
perimeter
€
S

0.079 fr(175.18 fr
Correction in Lat,. = or) +0.015 ft

939.46 ft

27. +E =(175.18 ft)sin(29°38') = 86.62 ff

B
| Correction in Dep. _ La
EW Es perimeter
S2938E| „7 : E, (be)

Correction in Dep, = |
Cc perimeter

S

+0.163 fr(175.18 fr
Correction in Dep,. = AAA +0.030 fr

939.46 ft

28. Length (ft) | Latitude | Departure | Latitude Latitude

0.079 | 0163 | 0.000 0.000

Bearing Length (ft)] Latitude | Departure | Latitude | Departure | Latitude | Departure
ES minutes

452 253
29.933
139.080
171.627

29. Q1

* Balance the latitudes and departures for
the following traverse.

Corrections Balanced

Length (ft)| Latitude | Departure Latitude

30. Q2

* Balance the data collected in the following
form:
op?! B
a NENE
N Mrs 713.93: 105° 39%,

\ eee

, \
781.18 7811 pa
TT €

124° 47
ll 391.27"

31. Calculating Traverse Area

* The best-known procedure for calculating
land areas is the double meridian
distance (DMD) method

° The meridian distance of a line is the
east-west distance from the midpoint of
the line to the reference meridian

° The meridian distance is positive (+) to
the east and negative (-) to the west

32. N 42° 59' E
234.58'
Es
142.39
N 12° 24 W
Reference |
Meridian o 175.18'

A
®

S 6” 15'W
189.53"
B
S 29° 38' E

175.18'

Onerisw ®

C N A
L 2
Reference N 42° 59'E eet
Meridian 23458" 189.53"
B
e
E
142.39 eeesee
N 12° 24 W 175.18:
> 17518

Dnarıisw ©

33. Calculating Traverse Area

* The most westerly and easterly points of a
traverse may be found using the
departures of the traverse

* Begin by establishing a arbitrary reference
line and using the departure values of
each point in the traverse to determine
the far westerly point

34. Calculating Traverse Area

bene [ess nt

-20,601 Be— A
| 86.648
| C
D «195.470 c
-30.551 E <— D
159.974 . .
E =" _, A Point E is the

farthest to the west

35. Calculating Traverse Area
DMD Calculation

Meridian distance of line EA

DMD of line EA is the
departure of line

36. Calculating Traverse Area
DMD Calculation

* The meridian distance of
line AB is equal to:
= the meridian distance of EA
" + % the departure of line EA
" + % departure of AB
* The DMD of line AB is twice
the meridian distance of
line AB

eridian
distance of
line AB

37. Calculating Traverse Area
DMD Calculation
* The DMD of any side is equal to the DMD
of the last side plus the departure of the
last side plus the departure of the present
side

38. Calculating Traverse Area
DMD Calculation

Balanced

Latitude

* The DMD of line AB is departure of line AB

* The DMD of line BC is DMD of line AB +
departure of line AB + the departure of line BC

39. Calculating Traverse Area
DMD Calculation

| Balanced |
Latitude | Departure
DMD

* The DMD of line CD is DMD of line BC +
departure of line BC + the departure of line CD

40. Calculating Traverse Area
DMD Calculation

Latitude | Departure
DMD

41. Calculating Traverse Area
Double Area

* The sum of the products of each points DMD
and latitude equal twice the area, or the double
area.

Balanced

Latitude | Departure
Y Double Areas

-188.388]|

* The double area for line AB equals DMD of line
AB times the latitude of line AB

42. Calculating Traverse Area
Double Area

Balanced

Latitude | Departure
Double Areas

| -152.253]|
= -
139.080
171.627

° The double area for line BC equals DMD
of line BC times the latitude of line BC

43. Calculating Traverse Area
Double Area

* The sum of the products of each points DMD
and latitude equal twice the area, or the double
area

Balanced

Latitude | Departure
Double Areas
k 0.601

-72,641
1 ft? = 0.09290304 m? Area= 36320.5 ft?

e 3374.285 m?

44. Q3

° Find the area enclosed by the following
traverse

Balanced

Latitude | Departure
Double Areas.