Siteng User Manual V5A

1

Site Engineering Programs

User Manual

CASIO fx-7400G PLUS POWER GRAPHIC

www.simukai.com

Valentine Shambira © 2004

Phone 07960986483

[email protected]

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






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:


• 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


Plus Calculator.

2. Select programs by pressing 6

or scrolling to highlight the

programs option on the screen

and then pressing exe.


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).




(NB. E2 and N2 should be the

coordinates for the point whose whole

circle bearing and distance from point

1 is required.)


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.


• 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)


Plus Calculator.

11. Select programs by pressing

6 or scrolling to highlight the

programs option on the

screen and then pressing

exe.


SETOUT by scrolling to it


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.


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.


• 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

+=

+=


Plus Calculator.






COOR-CAL by scrolling to it


exe.




(NB. Point 1 must be located at a

known distance from the point 3

whose coordinates are required ).




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).


easting and northing of the

point whose coordinates were

required.

9. If the coordinates of another

point are needed press exe,


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.


• 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




LINEST by scrolling to it on the











(NB Point 3 must be point for which

you wish check that it lies on the same

line as points 1 and 3.)


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.


• 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.


Calculator.


scrolling to highlight the programs

option on the screen and then

pressing exe.


LINEST3D by scrolling to it on the


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.





exe.





exe.

(NB Point 3 must be point for which you

wish check that it lies on the same line as

points 1 and 2.)


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.


• 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.


Calculator.




pressing exe.


TURNRAD by scrolling to it on the


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.


• 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

+=

+=


Calculator.






LOCALCOO by scrolling to it


exe.

4. Enter the global easting

E1(Global) and northing

N1(Global) for point 1.


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.


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,


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.


• 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


Calculator.




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.


• 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


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).


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.


• 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


Calculator.




pressing exe.


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


• 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


Calculator.




pressing exe.


OFFLINE by scrolling to it on the


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


• 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


Calculator.




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


• 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)


Calculator.




pressing exe.


INTERSCT by scrolling to it on the



(E1,N1) and (E2,N2) which lie on

the first line.


(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


• 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.


Calculator.




pressing exe.


CAMBER by scrolling to it on the


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.


returns the level of the top profile

adjacent the left channel.


returns the level of the bottom

profile adjacent the right channel.


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.


Calculator.




pressing exe.

3. Choose the program called EMB

BATT by scrolling to it on the


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)


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.


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.


Calculator.




pressing exe.

3. Choose the program called CUT

BATT by scrolling to it on the


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)


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.


returns the batter rail level at the

specified offset distance.


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.


Calculator.




pressing exe.


TRAVERSE by scrolling to it on the


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


• 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.


Calculator.




pressing exe.


CENTRECT by scrolling to it on the


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).


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.


Calculator.




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

Documents

Siteng User Manual V5A