SUBTOPIC:
SIMPLE SURVEYING COMPUTATIONS
SUBTOPIC CONTENTS:
1. Computing Bearing and Distance from coordinates.
2. Computing coordinates of a point by ‘single bearing and distance’ method.
3. Computing a bearing of a line from observed angle.
4. Quadrants in surveying – for computing bearing.
5. Computing coordinates of a point by On-line method.
6. Computing an Area of a parcel of land by cross-coordinates method.
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1. COMPUTING BEARING AND DISTANCE FROM COORDINATES
Consider the following surveying axes below.
X1
X
xb
M
Y
B
L
X
X
xa
β
Y1
A
ya
Y
yb
Distance computation
From a right-angled triangle AMB we have;
L2 =
X2 +
Y2
X2 +
L=
Y2
= distance between control points A and B
Bearing computation
From a right-angled triangle AMB we get;
Tan 𝛽 =
Y/
β = tan-1 (
X
Y/
X)
= bearing from point A to point B.
2
Y
2. COMPUTING COORDINATES BY ‘SINGLE BEARING AND DISTANCE’ METHOD.
In coordinating a point by bearing and distance method, the following should be
available:
 Coordinates of initial point
 The bearing of a line
 The distance of a line
Refer the following axes,
X1
X
xb
M
Y
B
L
X
β
X
xa
Y1
A
ya
Then, X2 = X1 +
but cos β =
Y
yb
X ----------------------------------- (I)
X/L
X = Lcosβ -------------------------------------- (2)
Substituting eqn 2 in eqn 1 we get
X2 = X1 + Lcosβ
Y ------------------------------------------ (3)
and Y2 = Y1 +
but sin β =
Y/L
Y = Lsinβ ------------------------------------------- (4)
Substituting eqn 4 in eqn 3 we get
Y2 = Y1 + Lsinβ
3
Y
3. COMPUTING A BEARING OF A LINE FROM OBSERVED ANGLE.
Consider the following figure below.
B (xb, yb)
C (xc, yc)
Θ
L
A (xa, ya)
To compute the coordinates of point C, the following procedure should be done.
 Compute the bearing from point A to point B (Back Bearing = BB)
 Compute the bearing from point A to point C (Forward Bearing = FB)
Then, BB + angle (θ) = FB = β
If FB > 3600 00’ 00’’, subtract one complete circle (3600 00’ 00’’) to get the correct
required Forward bearing.
XC = XA + Lcosβ
Hence,
And
YC = YA + Lsinβ
4. QUADRANTS IN SURVEYING – FOR COMPUTING BEARING
N
4th quadrant
1st quadrant
2700 < β ≤ 3600 00’ 00’’
000 < β ≤ 900 00’ 00’’
Add 3600 00’ 00‘’
Don’t add/subtract.
3rd quadrant
2nd quadrant
1800 < β ≤ 2700 00’ 00’’
900 < β ≤ 1800 00’ 00’’
Add 1800 00’ 00’’
Add 1800 00’ 00’’
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5. COMPUTING COORDINATES OF A POINT BY ON-LINE METHOD.
On-line coordination means computing the coordinates of a point, which is on the line
between two points which have the coordinates. In this case, let us compute the
coordinates of a point by applying bearing and distance method.
d1
A (xa, ya)
d2
G (xg, yg)
d3
H (xh,yh)
B (xb, yb)
 Make a datum check between the control points A and B, where the difference
between computed and measured distance should not exceed 3 cm.
 Measure line segments d1,d2,d3
 Compute the bearing from A to B ( brgAB )
Then:
XG = XA + d1 x cos brgAB
YG = YA + d1 x sin brgAB
and
XH = XA + (d1+d2) x cos brgAB
YH = YA + (d1+d2) x sin brgAB
Hence, the coordinates of point B can be checked using coordinates of A, G or H.
6. COMPUTING AN AREA OF A PARCEL OF LAND BY CROSS-COORDINATES.
The area of a parcel of land can be calculated using coordinates by cross-coordinates
method. Consider the following triangular piece of land, which is representing any
piece of land with any number of corners.
N
B (N2, E2)
A (N1, E1)
C (N3, E3)
E
2 x Area = { ( N1E2 + N2E3 + N3E1) - (E1N2 + E2N3 + E3N1) }
𝟏
Area = 𝟐 { ( N1E2 + N2E3 + N3E1) - (E1N2 + E2N3 + E3N1) }
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