Siteng User Manual V5A
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Transcript of Siteng User Manual V5A
1
Site Engineering Programs
User Manual
CASIO fx-7400G PLUS POWER GRAPHIC
www.simukai.com
Valentine Shambira © 2004
Phone 07960986483
2
Table of Contents
Cover Page 1
List of Contents 2
Calculating the distance between 2 points (Program DISTANCE) 3
Whole Circle Bearing Calculation (Program WCB+DIST) 4
Coordinates calculation 1 (Program SETOUT) 5
Coordinates calculation 2 (Program COOR-CAL) 6
Checking if three points are co-linear (Program LINEST) 7
Checking the three-dimensional co-linearity of three or more points (LINEST3D) 8
Checking if a point falls on the circumference of a circle (Program TURNRAD) 9
Local coordinate calculation (Program LOCALCOO) 10
Checking if three given points fall on the same straight line (Program ARC-X) 11
Calculating the coordinates of a new station (Program NEWSTATN) 12
Determining the coordinates of an offset from a circular curve (Program OFFCIRCLE) 13
Determining the coordinates of an offset from a straight baseline (Program OFFLINE) 14
Determining the area in side a polygon whose vertices are known (Program AREA) 15
Determining intersection point of two lines (INTERSECT) 16
Determining profile levels for a road with camber (CAMBER) 17
Calculation of embankment batter rail levels (EMB BATT) 18
Calculation of embankment cut rail levels (CUT BATT) 19
Calculation of traverse station coordinates (TRAVERSE) 20
Calculation of as-built column centre co-ordinates (CENTRECT) 21
Level book (LEVELS) 22
Calculation of levels along a slope (SLOPE) 23
3
N
Point 1
(E1,N1)
Point 2
(E2,N2)
Theory: Calculating the distance between 2 points
(DISTANCE)
Using the program DISTANCE
Fig 1
Problem.
Given the following:
• The coordinates of point 1 and point 2.
Calculate the distance between point 1 and point 2.
Solution
1. Use the given coordinates and Pythagora’s
theorem to calculate the distance, b, between the
two points as follows:
22 )21()21( NNEEb −+−= .
1. Switch on Casio FX7400G
Plus Calculator.
2. Select programs by pressing
6 or scrolling to highlight the
programs option on the
screen and then pressing
exe.
3. Choose the program called
DISTANCE by scrolling to it
on the screen, then pressing
exe.
4. Enter the easting E1 of the
point 1, then press exe.
5. Enter the northing N1of
point 1, then press exe.
6. Enter the easting E2 of the
point 2, then press exe.
7. Enter the northing N2of
point 2, then press exe.
8. The program returns the
distance between point 1 and
point 2.
9. If the distance of another
point, relative to point 1, is
needed press exe, then enter
new values for E2 and N2.
b
4
b
a
c
A Point 1
(E1,N1)
Point 2
(E2,N2)
N
E
Theory: Whole Circle Bearing Calculation (WCB) Using The Program WCB
Fig 2
Problem:
Given the following:
• The coordinates of point 1 and point 2
calculate the whole circle bearing, A, and distance
,b, between Point 1 and point 2.
Solution.
1. Using Pythagora’s theorem, the distance
between point 1 and 2 equals 22 )21()21( NNEEb −+−= .
2. The same formula is used to calculate distances
a & c.
3. The Whole Circle Bearing (WCB) of point 2
(E2,N2) from point 1 (E1,N1) is measured
clockwise positive from north (N), and is equal
to A.
4. If E1=E2 and N1 ≤N2 then WCB=360o , else:
5. Using the Cosine rule, If E1≤E2 then
−+=
−
bc
acbCosWCB
2
2221
6. If E1>E2 then
−+−=
−
bc
acbCosWCB
2360
2221
1. Switch on Casio FX7400G
Plus Calculator.
2. Select programs by pressing 6
or scrolling to highlight the
programs option on the screen
and then pressing exe.
3. Choose the program called
WCB by scrolling to it on the
screen, then pressing exe.
4. Enter the easting E1 for point 1
then press exe. Enter northing
N1 for point 1 then press exe.
(NB. E1 and N1 should be the
coordinates of the station from which
the whole circle bearing of other
points will be calculated and sighted).
5. Enter the easting E2 for point 2
then press exe. Enter northing
N2 for point 2 then press exe.
(NB. E2 and N2 should be the
coordinates for the point whose whole
circle bearing and distance from point
1 is required.)
6. The program returns the
whole circle the whole circle
bearing and distance between
point 1 and point 2.
7. If the whole circle bearing of
another point is needed press
exe, then enter new values for
E2 and E2.
5
N
Point 1
(E1,N1)
Point 2
(E2,N2)
Theory: Coordinates calculation 1 (SETOUT) Using the program SETOUT
Fig 3
Problem.
Given the following:
• The coordinates of point 1 (E1,N1), the whole
circle bearing (WCB) to point 2 form 1 and the
distance (d) from point 2 to 1,
Calculate the coordinates of point 2 (E2,N2).
Solution
1. E2 = E1 + d.Sin(WCB)
2. N2 = N1 + d. Cos(WCB)
10. Switch on Casio FX7400G
Plus Calculator.
11. Select programs by pressing
6 or scrolling to highlight the
programs option on the
screen and then pressing
exe.
12. Choose the program called
SETOUT by scrolling to it
on the screen, then pressing
exe.
13. Enter the easting E1 of the
point 1, then press exe.
14. Enter the northing N1of
point 1, then press exe.
15. Enter the distance from point
1 to point 2, then press exe.
16. Enter the whole circle
bearing from point 1 to point
2, then press exe.
17. The program returns the
coordinates of point 2.
18. If the coordinates of another
point are required press exe,
then enter new values for
distance and whole circle
bearing to that point.
d
WCB
6
Theory: Coordinates calculation 2 (COOR-CAL) Using The Program COOR-CAL
Fig 4
Problem.
Given the following:
• coordinates of point 1 and point 2
• the distance, e, between point 1 and point 3
(which has unknown coordinates)
• and the angle, D, (measured clockwise positive)
made by the lines between point 2, 1 & 3
(departing from point 2)
Calculate the coordinates of point 3.
Solution
1. The whole circle bearing A of point 2 relative
to point 1 is calculated as illustrated in fig 1.
2. The whole circle bearing of point 3 relative to
point 1 equals the sum of A and D.
DAWCB +=
3. The partial easting, f, of point 3 relative to point
1 equals the product of the distance, e, and the
sine of the whole circle bearing
)sin(. WCBef =
4. The partial northing, g, of point 3 relative to
point 1 equals the product of the distance, e,
and the cosine of the whole circle bearing
)cos(. WCBeg =
5. The easting and northing of point 3 equal the
sum of point 3’s partial easting and northing
and point 1’s easting and northing, respectively.
13
13
NgN
EfE
+=
+=
1. Switch on Casio FX7400G
Plus Calculator.
2. Select programs by pressing 6
or scrolling to highlight the
programs option on the screen
and then pressing exe.
3. Choose the program called
COOR-CAL by scrolling to it
on the screen, then pressing
exe.
4. Enter the easting E1 for point 1
then press exe. Enter northing
N1 for point 1 then press exe.
(NB. Point 1 must be located at a
known distance from the point 3
whose coordinates are required ).
5. Enter the easting E2 for point 2
then press exe. Enter northing
N2 for point 2 then press exe.
6. Enter the distance between
point 1 and the point whose
coordinates are needed, the n
press exe.
7. Enter the angle between point
2, point 1 and the point whose
coordinates are needed, then
press exe.
(NB. This angle is measured
clockwise positive starting from point
2 moving towards the point whose
coordinates are needed).
8. The program returns the
easting and northing of the
point whose coordinates were
required.
9. If the coordinates of another
point are needed press exe,
then enter new values for
distance and angle.
D
A f
e Point 1
(E1,N1)
Point 2
(E2,N2)
N
E
Point 3
(E3,N3)
b
c
c
a g
7
N
E
Theory: Checking if three points are co-linear
(LINEST)
Using the program LINEST
Figure 5
Problem.
Given the following:
• The coordinates of point 1, point 2 and point
3.
Check if point 3 forms a straight line with points
1 and 2.
Solution
1. Calculate distances a, b and c using the
coordinates of points 1, 2 and 3 and
Pythagora’s theorem.
2. Use the cosine rule to evaluate angle A as
follows:
−+=
−
bc
acbCosA
2
2221
3. Calculate distance d as follows:
If A>90, then d= c. Cos D, where D = 180 – A
If A≤90, then d = c.Cos A
4. If d=0, then points 1, 2 & 3 are colinear.
5. To determine which direction point 3 must
move to approach the straight line, calculate
the difference in whole circle bearings ∆wcb
between point 1&3 and points 1&2,
respectively.
6. If 0< ∆wcb<180, then point 3 must move right
of the vector measured from point 1 to point
2, if 180< ∆wcb<360 point 3 must move left.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the
programs option on the screen
and then pressing exe.
3. Choose the program called
LINEST by scrolling to it on the
screen, then pressing exe.
4. Enter the easting E1 for point 1
then press exe. Enter northing
N1 for point 1 then press exe.
5. Enter the easting E2 for point 2
then press exe. Enter northing
N2 for point 2 then press exe.
6. Enter the easting E3 for point 3
then press exe. Enter northing
N3 for point 3 then press exe.
(NB Point 3 must be point for which
you wish check that it lies on the same
line as points 1 and 3.)
7. The program returns the
perpendicular distance and
direction (left or right) between
point 3 and the straight line
defined by points 1 and 2. If this
perpendicular distance equals 0,
then points 1, 2 and 3 lie on a
straight line.
8. If you need to check if another
point lies on the same line as
points 1 and 2, press exe, then
enter new values for E3 and N3.
b
A D
Point 1
(E1,N1)
Point 2
(E2,N2)
Point 3
(E3,N3)
a c d
8
N
E
Theory: Checking if three points are co-linear
(LINEST3D)
Using the program LINEST3D
Figure 6
Problem.
Given the following:
• The coordinates and levels of point 1, point 2 and
point 3.
Check if point 3 forms a straight line with points 1 and
2.
Solution
7. Calculate distances a, b and c using the
coordinates of points 1, 2 and 3 and Pythagora’s
theorem.
8. Use the cosine rule to evaluate angle A as follows:
−+=
−
bc
acbCosA
2
2221
9. Calculate distance d as follows:
If A>90, then d= c. Cos D, where D = 180 – A
If A≤90, then d = c.Cos A
10. If d=0, then points 1, 2 & 3 are colinear.
11. To determine which direction point 3 must move
to approach the straight line, calculate the
difference in whole circle bearings ∆wcb between
point 1&3 and points 1&2, respectively.
12. If 0< ∆wcb<180, then point 3 must move right of
the vector measured from point 1 to point 2, if
180< ∆wcb<360 point 3 must move left.
13. Calculate slope per unit distance between points 1 and
2, then use linear interpolation to calculate the required
level at point 3. Compare this level to actual measured on
site and determine if the measured point should be raised
or lowered in order to be colinear with points 1 & 2.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
LINEST3D by scrolling to it on the
screen, then pressing exe.
4. Enter the easting E1 for point 1 then
press exe. Enter northing N1 for
point 1 then press exe. Enter the
level LVL1 for point 1 and press
exe.
5. Enter the easting E2 for point 2 then
press exe. Enter northing N2 for
point 2 then press exe. Enter the
level LVL2 for point 2 and press
exe.
6. Enter the easting E3 for point 3 then
press exe. Enter northing N3 for
point 3 then press exe. Enter the
level LVL3 for point 3 and press
exe.
(NB Point 3 must be point for which you
wish check that it lies on the same line as
points 1 and 2.)
7. The program returns the
perpendicular distance and direction
(left or right) between point 3 and
the straight line defined by points 1
and 2. If this perpendicular
distance equals 0, then points 1, 2
and 3 lie on a straight line.
8. Press exe again and the program
returns the vertical alignment of
point 3 relative to the vertical line
between points 1 and 2, and tells
you whether to move up or down if
there is a discrepancy.
9. If you need to check if another
point lies on the same line as points
1 and 2, press exe, then enter new
values for E3 and N3 and LVL3.
b
A D
Point 1
(E1,N1,LVL1)
Point 2
(E2,N2,LVL2)
Point 3 (E3,N3,LVL3)
a c d
9
N
Centre of radius
(E1,N1)
Point 1
(E2,N2)
Radius,R
Theory: Checking if a point falls on the
circumference of a circle (TURNRAD)
Using the program TURNRAD
Fig 7
Problem.
Given the following:
• Method (1) The radius and centre of a
circular curve and the coordinates of any
arbitrary point 1, or alternatively, Method (2) the radius, R, and 2 tangent points
along the curve, TP1 and TP2
Check if point 1 lies on the locus of the
circular curve.
Solution
1. Method (1) Calculate the distance between
the centre of the circle and point 1 using the
given coordinates and Pythagora’s theorem.
If this distance equals radius R, then point 1
lies on the circular curve defined by the
given radius and centre.
2. Method (2) Find the WCB and Distance from
TP1 to TP2. The line from TP1 to TP2 forms a
triangle with the 2 radii from the centre to s TP1
and TP2; from this the sine rule can be used to
find the angle at TP1. Add or subtract this angle
to the WCB between TP1 and TP2 to find the
WCB between TP1 and the centre. Hence
calculate the coordinates of the centre from the
new WCB and radius. Then follow stage 1,
above.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
TURNRAD by scrolling to it on the
screen, then pressing exe.
4. Enter the radius of the circular curve,
then pres exe.
5. Choose option [1] to define the curve
by centre and radius only or option [2]
to define the circle by 2 tangent points
and radius.
6. If using option [1], enter the easting
E1 for the centre of the radius, then
press exe. Enter northing N1 for the
centre of the radius,then press exe. Go
to stage 8 below.
7. If using option [2] enter coordinates
for TP1, then TP2, and then assuming
that you are standing at TP1 looking
towards TP2, choose option [1] if the
centre of the circle lies to the right,
and option [2] if the centre lies to the
left. Go to stage 8 below.
8. Enter the easting E2 for point 1, then
press exe. Enter northing N2 for point
1, then press exe.
9. The program returns the difference in
length between the given radius, and
the calculated distance between the
centre of radius and point 1. If this
difference equals 0, then point 1 lies
on the circular curve defined by
radius R, and the centre of radius.
10. If you need to check if another point
lies on the same curve, press exe,
then enter new values for E2 and N2.
TP2
TP1
10
Point 1
[E1(global),
N1(Global)]
[E1(local),
N1(local)]
f
e
c
E
Point 3 (E3,N3)
b
c
c
D a
g
A
Point 2
[E2(global), N2(Global)]
[E2(local), N2(local)]
N
Theory: Local coordinate calculation (LOCALCOO) Using The Program LOCALCOO
Figure 8
Problem.
Given the following:
• Both Global and Local Coordinates of point 1 and
point 2
• Global coordinates of point 3
Calculate the local coordinates of point 3.
Solution
1. The whole circle bearing of point 2 form point 1
(WCBGLOB2) is calculated using global coordinates.
2. The whole circle bearing (WCBLOC2) of point 2 from
point 1 is calculated using local coordinates.
3. The angle between the Global and Local axes, ∆θ, is
calculated as follows:
∆θ = WCBLOG2-WCBLOC2
4. The global whole circle bearing of point 3 from point
1 is calculated, and the local whole circle bearing of
point 3 from point 1 is determined from it by
substracting ∆θ from the global whole circle bearing.
WCBLOC3= WCBGLOB3- ∆θ
5. The distance between point 3 and point 1 is calculated
as follows, using Pythagora’s theorem:
22 )31()31( NNEEe −+−=
6. The local partial easting, f, of point 3 relative to point 1
equals the product of the distance, e, and the sine of the
whole circle bearing )WCBLOCsin(. 3ef =
7. The local partial northing, g, of point 3 relative to
point 1 equals the product of the distance, e, and the
cosine of the whole circle bearing
)WCBLOCcos(. 3eg =
8. The local eastings and northings are given by:
13
13
NgN
EfE
+=
+=
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6
or scrolling to highlight the
programs option on the screen
and then pressing exe.
3. Choose the program called
LOCALCOO by scrolling to it
on the screen, then pressing
exe.
4. Enter the global easting
E1(Global) and northing
N1(Global) for point 1.
5. Enter the global easting
E2(Global) and northing
N2(Global) for point 2.
6. Enter the local easting
E1(Local) and northing
N1(Local) for point 1.
7. Enter the local easting
E2(Local) and northing
N2(Local) for point.
8. The program checks if the
distances between points 1&2
are equal in the global and
local systems. If not a warning
is printed together with the
level of error. Press 2to accept
the error and continue, or 1 to
restart with new coordinates.
9. Enter the global easting
E3(Global) for point 3 then
press exe. Enter the global
northing N3(Global) for point 3
then press exe.
(NB: Point 3 is the point whose known
global coordinates need conversion to
local coordinates)
10. The program returns the local
easting E3(local) and northing
N3(local) for point 3.
11. If you need to convert another
point’s global coordinates to
local coordinates, press exe,
then enter new values for
E3(Global) and N3(Global).
11
Radius,R
Theory: Checking if three given points fall on
the same straight line. (ARC-X)
Using the program ARC-X
Fig 9
Problem.
Given the following:
• The length of a chord, ‘B’, which connects
end points of a circular arch.
• The radius of the circular arch.
• A horizontal distance, x, from the cenctre of
the arch along the chord B.
Calculate the corresponding distance (or height)
, ‘y’, between the chord and the arch.
Solution
1. The equation of a circle whose centre is at
the origin is given by X2+Y
2=R
2 , hence at a
horizontal offset ‘x’ from the centre of the
circle, the height of the arch above O is
given by, 22XRY −=
2. The distance between O and the chord
which defines the arch is found from
distance A (which equals radius R), and half
of the chord length 2
B, using Pythagora’s
theorem.
3. The distance between the chord and top of
the arch is given by, y = Yx-D
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called ARC-
X by scrolling to it on the screen,
then pressing exe.
4. Enter the radius of the arch.
5. Enter the length of the chord
between the two ends of the arch.
6. Enter the horizontal offset distance
from the centre of radius of the
arch to the point whose height is
desired.
7. The program returns the height of
the arch at the specified point.
A D
E
2
B
2
Bx
y
X
Y
O
Yx
12
N
New Station
(E3,N3)
Point 2
(E2,N2)
Point 1
(E1,N1)
a
b C
B c
Theory: Calculating the coordinates of a new station
(NEWSTATN)
Using the program
NEWSTATN
Fig 10
Problem.
Given the following:
• Two points, Point 1 and Point 2 whose coordinates
are known.
• Horizontal distance between point 1 and 2 and the
new station, ‘a’ and ‘b’ respectively.
Calculate the coordinates of the new station.
Solution
1. The whole circle bearing and distance of point 2
from point 1 is calculated.
2. Angle B is found from distances ‘a’, ‘b’ and ‘c’ using
the Cosine rule.
3. The whole circle bearing of the new station from
point 1 is the sum of angle ‘B’ and the whole circle
bearing of point 2 from point 1.
4. The partial easting and partial northing of the new
station relative to point 1 are, respectively, the
products of distance ‘a’ and the Sine and Cosine of
the whole circle bearing calculated in stage 3.
5. The easting ‘E3’ and northing ‘N3’ of the new
station are the sum of easting ‘N1’ and northing ‘N1’
of point 1 and the partial easting and partial northing
calculated in stage 4.
1. Switch on Casio
FX7400G Plus
Calculator.
2. Select programs by
pressing 6 or scrolling to
highlight the programs
option on the screen and
then pressing exe.
3. Choose the program
called NEWSTATN by
scrolling to it on the
screen, then pressing exe.
4. Enter the coordinates of
point 1, ie E1(Left) and
N1(Left) ,then press exe.
[Please note that point 1
must always be selected
as that point which falls
left of the new station
(see figure 8)]
5. Enter the coordinates of
point 2, ie E1(Right) and
N1(Right) ,then press
exe.
6. Enter the distance to
point 1 from the new
station, Dist(Left) ,then
press exe.
7. Enter the distance to
point 1 from the new
station, Dist(Right).
8. The program returns the
easting and northing of
the new station.
9. The program also returns
the angle C, between
point 1, the new station
and point 2 which can be
compared against
measured values on site.
13
Centre of radius
(E1,N1)
Theory: Determining the coordinates of an offset from a
circular curve (Offcircle)
Using the program OFFCIRCLE
Fig 11
Y
X
E Problem.
Given the following:
• Method (1) Centre of radius coordinates, [E1,N1] and the starting
point (TP1) of the curve, [E2,N2], or alternatively
Method (2) the radius, R, and 2 tangent points along the curve, TP1
and TP2
• A chainage, X, along the curve, measured from [E2,N2]
• A desired offset distance, Y, perpendicular to the tangent at the
chainage specified
Calculate the coordinates of the offset point [E4,N3]
Solution
1. Method (1) Calculate the radius R from coordinates, [E2,N2] and
[E1,N1].
2. Method (2) Find the WCB and Distance from TP1 to TP2. The line
from TP1 to TP2 forms a triangle with the 2 radii from the centre to
s TP1 and TP2; from this the sine rule can be used to find the angle
at TP1. Add or subtract this angle to the WCB between TP1 and TP2
to find the WCB between TP1 and the centre. Hence calculate the
coordinates of the centre from the new WCB and radius.
3. Calculate angle, θ, using the chainage and radius R
X
πθ
2
360.=
4. The whole circle bearing of [E2,N2] form [E1,N1] is found.
5. By turning through angle θ away from the line connecting [E1,N1]
& [E2,N2], the whole circle bearing of [E3,N3] from [E1,N1] is
found.
6. The partial easting and partial northing of [E2,N3] from [E1,N1] are
respectively given by the following expressions.
α
α
CosYRN
SinYRE
).(
).(
+=∆
+=∆
7. NNN
EEE
∆+=
∆+=
13
13
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
OFFCIRCLE by scrolling to it on
the screen, then pressing exe.
4. Choose option [1] to define the
curve by centre and one tangent
point only or option [2] to define the
circle by 2 tangent points and
radius.
5. If using option [1], enter the
coordinates of the centre followed
by the tangent point, ie E(CHNG
=0) and N(CHNG=0). Go to stage 7
below.
6. If using option [2] enter coordinates
for TP1, then TP2, and then
assuming that you are standing at
TP1 looking towards TP2, choose
option [1] if the centre of the circle
lies to the right, and option [2] if the
centre lies to the left. Then enter the
coordinates of zero chainage ie,
E(CHNG =0) and N(CHNG=0),
which could be TP1 or TP2 or
another point.. Go to stage 7 below.
7. Enter the chainage of the desired
offset along the curve. For the
clockwise direction enter a positive
figure, and a negative figure for a
chainage in the anti-clockwise
direction.
8. Enter an offset distance from the
curve. If the desired offset is inside
the circle defined by the curve, enter
a negative figure. If the desired
offset is outside the circle, enter a
positive figure.
9. The program, returns coordinates
for the offset point.
10. Press exe to enter a new chainage
and desired offset distance.
(E3,N3)
N
TP1
(E2,N2)
R θ
ά
TP2 E2a, N2a
14
N
Theory: Determining the coordinates of an offset
from a straight baseline (Offline)
Using the program OFFLINE
Fig 12
Problem
Given the following:
• Beginning of baseline [E1,N1]
• End of baseline, [E2,N2]
• A chainage, Y, along the curve, measured from
[E1,N1]
• A desired offset distance, X, perpendicular to
the baseline.
Calculate the coordinates of the offset point [E3,N3]
Solution.
1. Find angle, θ, from distances X and Y.
2. Calculate distance, Z, from distances X and Y.
3. Calculate the whole circle bearing of E2,N2
form E1, N1.
4. By turning through angle θ away from the
baseline, the whole circle bearing of [E3,N3]
from [E1,N1] is found.
5. The partial easting and partial northing of
[E2,N3] from [E1,N1] are respectively given by
the following expressions.
α
α
CosYRN
SinYRE
).(
).(
+=∆
+=∆
NNN
EEE
∆+=
∆+=
13
13
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
OFFLINE by scrolling to it on the
screen, then pressing exe.
4. Enter coordinates for the
beginning of the baseline
E1(baseline) and N1(baseline).
5. Enter coordinates for the end of
the baseline E2(baseline) and
N2(baseline)
6. Enter the desired chainage
distance from point 1. Enter a
positive distance if the chainage is
in the same direction coming
[E1,N1] to [E2,N2]. Enter a
negative figure for the opposite
direction. 7. Enter the desired offset distance.
Enter a positive number, if the
offset is on the right side of the
vector from [E1,N1] to [E2,N2].
Enter a negative number if the
offset is on the left side of the
vector from [E1,N1] to [E2,N2].
8. The program returns coordinates
for the offset point, E(offset) and
N(Offset)
9. Press exe to enter a new chainage
and desired offset distance.
(E1,N1)
(E3,N3)
(E2,N2)
Y Z
X
ά
15
N
Theory: Determining the area in side a polygon
whose vertices are known (AREA)
Using the program AREA
Fig 13
Problem
Given the following:
• The coordinates of all the vertices of a
polygon,
Calculate the area of the polygon.
Solution.
The area of the polygon is given by
−∑∑ ++
n
nn
n
nn ENNE1
)1(
1
)1(.5.0
Where n=number of vertices on the polygon, and
E1=En+1 and N1=Nn+1
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called AREA
by scrolling to it on the screen, then
pressing exe.
4. Enter the eastings and northings for
corner the first corner, second
corner, etc. These points must be
entered in the same sequence that
they are linked to form the polygon. 5. After entering the last point, either
enter the coordinates of the first
point or (more quickly) press
ALPHA then A, followed by
ALPHA then B.
6. The program returns a value for the
area bound by the lines that link the
corner coordinates entered.
(En,,Nn)
(E1,N1)
(E3,N3)
(E2,N2)
16
N
Theory: Determining intersection point of two
lines (INTERSECT)
Using the program INTERSCT
Fig 14
Problem
Given the following:
• Points (E1,N1) and (E2,N2) which lie on
one line, and points (E3,N3) and (E4,N4)
which lie on another line.
Calculate the intersection point (En,Nn) of the two
line..
Solution.
1. The equation of each of the two straight
lines is determined from the two coordinates
on each line using the formula (y-y1)=m(x-
x1) where the ‘y’ and ‘x’ axis are
respectively synonymous with the
‘northings’ and ‘eastings’, and ‘m’ is the
slope of each line.
2. The simultaneous equations determined
above are then solved using the substitution
method to evaluate the intersection point
(En,Nn)
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
INTERSCT by scrolling to it on the
screen, then pressing exe.
4. Enter the eastings and northings for
(E1,N1) and (E2,N2) which lie on
the first line.
5. Enter the eastings and northings for
(E3,N3) and (E4,N4) which lie on
the second line.
6. The program returns the eastings
and northings of the intersection
point (En,Nn)
(En,,Nn)
(E2,N2)
(E1,N1)
(E3,N3)
(E4,N4)
17
Theory: Determining profile levels for a road
with camber (CAMBER)
Using the program CAMBER
Fig 15
Problem
Given the following:
• The left channel, right channel and crown
levels and horizontal positions of a road,
Calculate the levels of the profiles which are
required to form the left and right cross-falls.
Solution.
1. The level difference between the crown and
channels, and the horizontal positions are
used to evaluate the left and right cross-
falls.
2. Linear interpolation and the traveler length
are used to determine the profile levels at
the desired stake positions.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
CAMBER by scrolling to it on the
screen, then pressing exe.
4. Enter the level of the left channel
and press exe.
5. Enter the level of the right channel
and press exe.
6. Enter the level of the crown and
press exe.
7. Enter the distance from the left
channel to the centre line and press
exe.
8. Enter the distance from the right
channel to the centre line and press
exe.
9. Enter the traveler length and press
exe.
10. Enter the offset distance of the
profile stake from the left channel
press exe.
11. Enter the offset distance of the
profile stake from the right channel
press exe.
12. The program returns the level of the
bottom profile adjacent the left
channel.
13. Press exe again and the program
returns the level of the top profile
adjacent the left channel.
14. Press exe again and the program
returns the level of the bottom
profile adjacent the right channel.
15. Press exe again and the program
returns the level of the top profile
adjacent the right channel.
16. Press exe to restart the program.
Left
Channel to
left stake
Right Channel
to right stake
Centre line to
left channel
Centre line to
right channel
Left channel
level Left channel
level
Left channel
top profile
Right channel
top profile
Crown
level
Left channel
bottom profile
Right channel
bottom profile
Traveller
18
Theory: Calculation of embankment batter rail
levels. (EMB BATT)
Using the program EMB BATT
Fig 16
Problem
Given the following features of an embankment :
• Top and bottom levels, slope, traveler length,
and offset position of batter rail stake from the
toe,
Calculate the levels of the batter rail at desired offset
positions from the toe.
Solution.
1. The bottom level plus the traveler length equals
the level of the cross-piece on the traveler when
the latter is positioned at the toe of the
embankment.
2. At a given offset from the toe, the level of the
batter rail is lower than the traveler level at the
toe by an amount equal to the offset distance
divided the slope specified, ie “1 in”.
3. The horizontal distance of the embankment
equals the difference between the bottom and
top levels multiplied by the slope specified, ie
“1 in”.
4. The slope distance is found by applying
Pythagora’s theorem to the horizontal and
vertical distances between the batter rail (at the
desired offset position ) and the top of the
traveler when placed at the top of the
embankment.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called EMB
BATT by scrolling to it on the
screen, then pressing exe.
4. Enter the bottom level and press exe.
5. Enter the top level and press exe.
6. Enter the slope “1 in” and pres exe.
(nb. This is the horizontal distance
corresponding to one unit in vertical
dimension along the slope)
7. Enter the traveler length and press
exe.
8. Enter the offset distance form the toe
and press exe.
9. The program returns the horizontal
distance between the top and bottom
of the embankment.
10. Press exe again and the program
returns the batter rail level at the
specified offset distance.
11. Press exe again program returns the
sloping distance between the batter
rail at the specified offset distance
and the top of the traveler when the
latter is positioned at the top of the
embankment.
12. Press exe again to enter a new offset
distance and obtain the
corresponding batter rail level
IN 1 Offsets from toe
Traveler
length
Slope
specification
Batter rail
levels
Top level
Bottom
level
19
Theory: Calculation of embankment cut rail
levels. (CUT BATT)
Using the program CUT BATT
Fig 17
Problem
Given the following features of a cut:
• Top and bottom levels, slope, traveler length,
and offset position of batter rail stake from the
top,
Calculate the levels of the batter rail at desired offset
positions from the top.
Solution.
5. The top level plus the traveler length equals the
level of the cross-piece on the traveler when the
latter is positioned at the top of the cut.
6. At a given offset from the top, the level of the
batter rail is higher than the traveler level at the
top by an amount equal to the offset distance
divided the slope specified, ie “1 in”.
7. The horizontal distance of the embankment
equals the difference between the bottom and
top levels multiplied by the slope specified, ie
“1 in”.
8. The slope distance is found by applying
Pythagora’s theorem to the horizontal and
vertical distances between the batter rail (at the
desired offset position ) and the top of the
traveler when placed at the bottom of the
embankment.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called CUT
BATT by scrolling to it on the
screen, then pressing exe.
4. Enter the bottom level and press exe.
5. Enter the top level and press exe.
6. Enter the slope “1 in” and pres exe.
(nb. This is the horizontal distance
corresponding to one unit in vertical
dimension along the slope)
7. Enter the traveler length and press
exe.
8. Enter the offset distance from the
top and press exe.
9. The program returns the horizontal
distance between the top and bottom
of the cut.
10. Press exe again and the program
returns the batter rail level at the
specified offset distance.
11. Press exe again and the program
returns the sloping distance between
the batter rail at the specified offset
distance and the top of the traveler
when the latter is positioned at the
bottom of the cut.
12. Press exe again to enter a new offset
distance and obtain the
corresponding batter rail level.
Bottom
level
Traveler
length
1 IN
Offsets from toe
Batter rail
levels
Slope specification
Top
level
20
Theory: Calculation of traverse station
coordinates (TRAVERSE)
Using the program TRAVERSE
Fig 18
Problem
Given the following features of a theodolite traverse:
• Coordinates of the starting station, coordinates
or a whole circle bearing (relative to the starting
station) of the reference object [RO], and a
series of horizontal angles and forward
distances for new stations along the traverse,
Calculate the co-ordinates of the new stations.
Solution.
1. The whole circle bearing of the reference point
relative to the starting station (ie the backsight)
is added to the horizontal angle of measured
after turning to the new station (ie the foresight),
to give the forward whole circle bearing of the
new station.
2. The forward whole circle bearing (from step 1)
and measured forward distance are used to
calculate coordinates for the new station.
3. Steps 1 and 2 are repeated, using STATION1 as
the backsight and the second new station as the
foresight. The process can be repeated for as
many new stations as is desired.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
TRAVERSE by scrolling to it on the
screen, then pressing exe.
4. Enter the easting for STATION1 and
pres exe
5. Enter the northing for STATION1 and
pres exe
6. Choose whether to specify reference
object coordinates by pressing 1 then
exe, or reference object whole circle
bearing by pressing 2 then exe
7. If you have chosen 1 form step 6,
enter E(RO), then press exe followed
by N(RO) then press exe again. If you
have chosen 2 from step 6, enter
WCB(RO) then press exe.
8. The program now displays the
sequence number of the point (or new
station) along the traverse whose
coordinates will be calculated next.
Press exe to progress program
execution.
9. Enter the measured horizontal angle
HZ, then press exe
10. Enter the forward distance, then press
exe.
11. The program returns the forward
whole circle bearing to the new
station.
12. Press exe again to display the easting
of the new station.
13. Press exe again to display the northing
of the new station.
14. Press exe again to begin data entry for
the next new station.
Reference
Object [RO]
Horizontal
angles [HZ]
North Forward
Bearing
[FWD WCB]
STARTING
STATION
E(STATION1)
N(STATON1) NEW STATION
E(NEW STN)
N(NEW STN FORWARD
DISTANCE
FWD DIST
21
Theory: Calculation of as-built column centre
co-ordinates (CENTRECT)
Using the program CENTRECT
Fig 19
Problem
Given the following:
• Coordinates for two adjacent corners of a
structural element such as a column, and the
perpendicular width of the structural element,
(relative to the baseline defined by the given
coordinates),
Calculate the coordinates of the centre of the
column.
Solution.
1. The distance and whole circle bearing between
the two corners that define the baseline is
calculated from the given co-ordinates.
2. The angle between the baseline and the centre
of the column is evaluated since the ratio of half
the column width to half the baseline distance
equals ‘tan’ of this angle.
3. The whole circle bearing of [E(centre),
N(centre)] from [E1(baseline), N1(baseline])
equals the sum of the angles calculated in stages
1 and 2.
4. Using the whole circle bearing from stage 3 and
the distance from E(centre), N(centre) to
E1(baseline), N1(baseline), the coordinates of
the centre are found.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called
CENTRECT by scrolling to it on the
screen, then pressing exe.
4. Enter E1(baseline) and press exe
5. Enter N1(baseline) and press exe 6. Enter E2(baseline) and press exe
7. Enter N2(baseline) and press exe 8. Enter the columns with and pres exe.
9. The program returns easting for the
centre of the column E(centre).
10. Press exe again and the program
returns northing for the centre of the
column N(centre).
11. Press exe to restart the program.
Width
E(centre)
N(Centre)
E2(Baseline)
N2(Baseline)
E1(Baseline)
N1(Baseline)
22
Theory: Level book (LEVELS) Using the program LEVELS
Fig 20 Date ...................................................................... ................... Levels taken for ....................................................................
From ...................................................................... ................... ...................... To ....................................................................
BACK
SIGHT
INTER-
MEDIATE
FORE-
SIGHT
COLLIMATION
or H.P.C REDUCED LEVEL DISTANCE REMARKS
Problem
• Given the reduced level of a bench mark, back sight staff
readings, intermediate staff readings, and foresight staff
readings
Record the figures mentioned above in the correct parts of the
Survey Book, and calculate the reduced levels of surveyed points
correctly, or calculate staff readings required for setting out.
Solution.
1. In your survey book, record the value of the bench mark
(where the staff is) in the column titled reduced level. Add a
name or description of the bench mark in the remarks column.
2. Record the staff reading in the back sight column.
3. Add the back sight to the reduced level of the benchmark and
record this in the Collimation or H.P.C column. The H.P.C is
the height of your instrument.
4. To find the reduced level at other locations, record the staff
readings at the points of interest in the intermediate column
and the corresponding descriptions of these locations in the
remarks column. Subtract each intermediate reading from the
Collimation to give the reduced level, and record this in the
reduced level.
5. When performing a level traverse, it may be necessary to
change the instrument’s position due to limited visibility. In
this case record the staff reading before moving the instrument
in the column titled foresight; keep the staff in the same
location while moving the instrument. Subtract the fore sight
from the collimation to give the reduced level at the staff’s
location. From the instrument’s new location record a second
staff reading in the back sight column. Add this to the
reduced level to give the new collimation of the instrument.
6. To calculate a staff reading which corresponds to a level
required for a structure which is yet to be built, subtract the
required level (which you read from the design drawings)
from the instrument’s height (ie the collimation or H.P.C)
Switch on Casio FX7400G Plus Calculator.
1. Select programs by pressing 6 or scrolling
to highlight the programs option on the
screen and then pressing exe.
2. Choose the program called LEVELS by
scrolling to it on the screen, then pressing
exe.
3. Enter the reduced level of the bench mark
or station where the staff is held.
4. Enter the backsight staff reading
5. The program calculates and displays the
collimation which should be written in the
survey book.
6. - To calculate reduced levels of surveyed
points, go to stage 7 below.
- To record a foresight and new
backsight and collimation at a change
point, go to stage 8 below.
- To calculate staff readings for levels to
be set out, go to stage 9below.
7. If carrying out a level survey, enter the
staff readings in the intermediate column
of your survey book, and choose option [1]
on the calculator. Enter the staff reading,
and the calculator will calculate and
display the reduced level of the surveyed
point.
8. If the staff location is the last point prior to
moving the instrument, enter the staff
reading into the foresight column of the
survey book, then choose option [2] on the
calculator then enter the staff reading. The
program calculates the reduced level. If
the staff’s location is a change point,
choose option [1] then enter a new value
of the backsight (from the instrument’s
new location). The program displays the
new collimation of the instrument, and is
ready to proceed as before. If the staff is
at a new station choose option 2 and
proceed as before.
9. Choose option [3] in order to enter levels
into the program and obtain staff readings
for setting out and control purposes.
23
Theory: Calculation of levels along a slope
(SLOPE)
Using the program SLOPE
Fig 21
Problem
• Given 2 points, ‘A’ and ‘B’, separated by a distance
‘y’ and with known levels, ‘a’ and ‘b’ respectively,
Calculate the level at point C which is at a distance of
‘x’ from point A.
Solution.
1. By linear interpolation, the level at point C is
given by the following formula.
−+=
y
abxac
- If b>a then the slope is uphill
- If b<a then the slope is downhill.
2. Note 100
−
y
ab gives % slope which is
used in drainage pipe lasers and sloping
rotating lasers.
1. Switch on Casio FX7400G Plus
Calculator.
2. Select programs by pressing 6 or
scrolling to highlight the programs
option on the screen and then
pressing exe.
3. Choose the program called SLOPE
by scrolling to it on the screen, then
pressing exe.
4. Enter the starting level, ie ‘a’ or ‘b’
in Fig 21.
5. Enter the total fall, ie (b-a) if your
starting point is ‘A’ or (a-b) if your
starting point is ‘B’
6. Enter the total distance, ie ‘y’, the
distance from ‘A’ to ‘B’.
7. The program calculates and displays
the slope as a percentage, which can
be used as input on pipe and rotating
lasers.
8. Enter the interim distance, ie the
distance from the starting point to
the point whose level is needed, ie
distance ‘x’ to point ‘C’ in Fig 21.
9. The program calculates and displays
the value of ‘c’, the level at point
‘C’.
10. Press exe to enter a new interim
distance..
Point A
Level = a
Point B
Level = b
Point C
Level = c
x
y