AREA COMPUTATION
Double Meridian Distance
Double Parallel Distance
Area By DPD Method
Example Problems
*Double Meridian Distance*
- The meridian distance from the midpoint of the line to
the references meridian.
Sample figure.
F
G
C
Based on the illustrative example, the following three rules
should provides a means of computing the DMD for each
course of a traverse.
Rule 1: The DMD of the first course is equal to the departure
of the course.
Rule 2: The DMD of any other course is equal to the DMD of
the preceding course, plus the departure
of the course itself.
Rule 3: The DMD of the last course is numerically equal to the
departure of that course, but with the opposite sign.
*DOUBLE PARALLEL DISTANCE*
By using the latitudes of the successive courses
instead of the departures, parallel distances can also be
computed in a manner similar to meridian distances.
Correspondingly, the following rules also provide a
means of computing the DPD for each course of a traverse.
Rule 1: The DPD of the first course is equal to the latitude of
the course.
Rule 2: The DPD of any course is equal to the DPD of the
preceding course, plus the latitude of the preceding course,
plus the latitude of the course itself.
Rule 3: The DPD of the last course is numerically equal to the
latitude of that course but with the opposite sign.
*AREA BY DMD METHOD*
The use of the double meridian distance (DMD) is to
determine the area of closed traverse. This method is at
adaption of the method of determining areas by coordinates.
FORMULAS:
DOUBLE AREA = DMD (adjusted Latitude)
AREA = (1/2)( NDA + SDA)
*AREA BY DPD METHOD*
The double parallel distance method of area
computation is the similar to the double meridian distance
method.
FORMULAS:
DOUBLED AREA = DPD(Adjusted Departure)
AREA = (1/2)(EDA + WDA)
EXAMPLE PROBLEMS:
+47.27
(Dep of +1661.26
AB) mof East
(Sum
+608.89 +786.78 +218.32
Departure)
(Dep of BC) C
(Dep of CD) (Dep of DE)
-327.41
D (Lat of
CD)
-1492.64m
B (Sum of south Latitudes)
+375.01
(Lat of FA)
-544.64 -1,116.62
(Dep of FA) ( Dep of
-1661.26m EF )
(Sum of West
Departures)
AREA BY DOUBLE MERIDIAN DISTANCE
LINE Adjusted latitude Adjusted Departure
(+N) (+E)
(-S) (-W)
AB 490.71 47.27
BC 587.12 608.89
CD 327.41 786.78
DE 1002.76 218.32
EF 122.67 1116.62
FA 375.01 544.64
SUM 1452.64 -1452.84 1661.26 -1661.26
Computation of DMD (Refer to the rules of the computing DMD)
DMD ab = 47.27
DMD bc = 47.27 + 47.27 + 608.89 = 703.43
DMD cd = 703.43 + 608.89 + 786.78 = 2099.10
DMD de = 2099.10 + 786.78 + 218.32 = 3104.20
DMS ef = 3104 + 218.32 -1116.62 = 2205.90
DMD fa = 2205.90 1116.62 -544.64 = 544.64
Computation of double areas DOUBLE AREA = DMD X Adj Lat.
DA ab = 47.27 x 490.71 = 23 195.86
DA bc = 703.43 x 587.12 = 412997.82
DA cd = 2099.10 x (-327.41) = -687266.33
DA de = 4104.20 x (-1002.76) = -3112767.59
DA ef = 2205.90 x (-122.67) = -270597.75
DA fa = 544.64 x 375.01 = 204245.45
DA = -3430192.54
THEREFORE:
2 X AREA = -3430192.54
AREA = -1715096.27 SQ M(negative sign is disregarded)
AREA BY DOUBLE PARALLEL DISTANCE
Computation of DPDs (Refer to rules for computing DPD)
DPD ab = 490.71
DPD bc = 490.71 + 490.71 + 587.12 = 1568.54
DPD cd = 15668.54 + 587.12 -327.41 = 1828.25
DPD de = 1828.25 327.41 -1002.76 = 498.08
DPD ef = 498.08 -1002.72-122.67 = -627.35
DPD fa = -627.35 122.67 + 375.01 = -375.01
Computation of Double Areas (DOUBLE AREA = DPD X ADJ.
LATITUDE)
DA ab = 490.71 x 47.27 = 2395.86
DA bc = 1568.54 x 608.89 = 955068.32
DA cd = 1828.25 x 786.78 = 1438430.54
DA de = 498.08 x 218.32 = 108740.83
DA ef = 627.35 x (-1116.62) = 700511.56
DA fa = 375.01 x (-544.64) = 204245.45
DA = 3430192.56
THEREFORE:
2 X AREA = 3430192.56
AREA = 1715096.28 SQ.M.
