Insight Manual

InSight User Manual

InSight Land Surveying Utility Programs Library

For Casio FX-7400G+

User Manual

N

E

InSight User Manual

Support : insight4survey.wordpress.com

Distributor : Marco Corporation (M) Sdn. Bhd. www.marco-groups.com

This publication makes reference to Casio FX-7400G+, a registered trademark of

Casio Computer Inc.

© 2007 QED Education Scientific Sdn. Bhd.

InSight User Manual is published by

QED Education Scientific Sdn Bhd.

PO Box 3307, 47507,

Subang Jaya, Selangor,

Malaysia.

InSight User Manual

CONTENTS

Pages

PART 1 Getting Started With FX-7400G+ and InSight

1.1 Some Questions and Answers 1

1.2 Scientific Calculations 2

1.3 Entering Data 2

1.4 Error Messages 3

1.5 Overview of InSight 4

1.5.1 Program Listing and Free Memory Required 4

1.5.2 Input and Data Storage Limitations 5

1.5.3 Measurement Units and Data Input 5

1.5.4 Data Error and Fail-safe 6

1.5.5 Abbreviations and Symbols Used 6

PART 2 PROGRAM LIBRARY

2.1 START Interface Program 7

2.2 Using UTILITY 8

2.3 Using AREA 10

2.4 Using VOLUME 13

2.5 Using CIRCLE 15

2.6 Using TRISOLVE 17

2.7 Using LEVEL 19

2.8 COGO Interface Program 20

2.9 Using OFFSET 21

2.10 Using RADIAL 23

2.11 Using XSECT 26

2.12 Using TRAVRS 30

2.13 CURVE Interface Program 35

2.14 Using CIRCULAR 36

2.15 Using SPIRAL 40

InSight User Manual

END USER LICENSE AGREEMENT (EULA) Please read this EULA before using InSight Utility Program Library (UTILITY). By using the UTILITY, you are agreeing to be bound by the terms of this license. If you do not agree to the terms, please do not use the UTILITY. 1. License. The UTILITY is licensed to you by QED Education Scientific Sdn. Bhd. (QED) for use solely under the terms of this EULA. QED retains all intellectual property rights to the UTILITY. The rights granted to you include any upgrades that supplement the original UTILITY, unless such upgrade contains a separate license. You acknowledge and agree that the UTILITY is copyrighted and protected under the copyright laws. 2. Restriction & Transfer. This license allows you to install and use one copy of the UTILITY on a single FX-7400G+ at a time. You may not reverse engineer, decompile, disassemble, or create derivative works from the UTILITY. You may not market, distribute, rent, assign, loan, or transfer copies of the UTILITY or electronically transfer the UTILITY from one calculator to another, or over any computer network. 4. Disclaimer of Warranties. The UTILITY is furnished “as is”, without warranty of any kinds. QED does not warrant that the UTILITY is free from bugs, errors, defects, or other program limitations. 5. Limitation of Liability. To the extent not prohibited by law, QED will in no event be liable for direct, indirect, special, consequential, or incidental damages resulting from any bugs, errors, defect, or limitation in the UTILITY, including, without limitation, any interruption of service, loss of business, loss of profits or good will, legal action or any other consequential damages. You assume all responsibility arising from the use of the UTILITY.

SUPPORT If you need support on using InSight, please visit the InSight Support Weblog maintained by the programmers at insight4survey.wordpress.com. Current news about the program library and various resources of other Casio models are available at the weblog. You can also email for support to the address [email protected]. Support for FX-7400G+ is provided by Casio authorized distributor, Marco Corporation (M) Sdn. Bhd. You can contact them at No 2, 2

nd Floor, Jalan Segambut, 51200, Kuala Lumpur, Malaysia.

Tel: +603-4043 3111. This limited warranty support is only available if you bought your FX-7400G+ through Marco Corporation or its subsidiaries in Malaysia, Thailand, Singapore, Cambodia, Vietnam and Brunei.

ABOUT InSight is a library of utility programs which perform land surveying calculations. As of February 2007, the most current version is version 1.1. It is written using Basic available in the FX-7400G+. It takes up 15,835 bytes of memory in the FX-7400G+ and requires another 1,570 bytes of memory during execution. InSight is written by a team from QED Education Scientific.

InSight User Manual

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PART 1 Getting Started With FX-7400G+ and Insight

Firstly, we would strongly advice you to read up Chapter 1 and Chapter 2 of the FX-7400G+ User’s Guide to learn about using the calculator. You can find out about programming at Chapter 8, and on statistical calculation at Chapter 7. You should use this manual in tandem with the FX-7400G+ User’s Guide. If you cannot find answer to you query from both manuals, please contact us at [email protected].

◊ 1.1 SOME QUESTIONS AND ANSWERS Question 1: How to get my FX-7400G+ working after it is out of the box?

ANSWER: We have put in 2 additional batteries during installation. You can start using the calculator right out of the box. Just press the grey O key. We also recommend that you read up Chapter 1 of the User’s Guide to learn more.

Question 2: What is this icon menu that I see when I turn on my FX-7400G+?

ANSWER: All calculator functions are put into areas call modes. You can either access each mode by first selecting it using the 4-way navigation key, and then press l, or you can choose a number from 1 to 9.

For example, to do scientific calculations we scroll to the icon Q and press l, or we just tap 1 once. For programming, it is the icon S or the number 9. To access different modes we must return to the icon menu by tapping on p.

Question 3: Where can I do scientific calculation at this calculator?

ANSWER: Go to Q or RUN mode. It is the scientific calculator.

Question 4: How do I check my calculator memory status?

ANSWER: Turn on calculator, select the icon H and press l. Now you are in the MEM mode. You will see the calculator current memory status here. Please find out more about memory status in Chapter 2 of User’s Guide.

Be careful when selecting RESET or DEL here as you may unintentionally delete important data permanently. Question 5: How do I access the programs library of InSight?

Answer 1: Again, press O to turn on the calculator and then press 6. You should see the program list, which begins with the program START. More programs are down the list. You can scroll down with N.

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◊ 1.2 SCIENTIFIC CALCULATIONS

Example: Find )''33'1730sin( ° .

1. Turn on the calculator and select RUN mode. O1

2. Enter the expression and then calculate. h30i$w$q

17q33q

l

Example: Edit )''33'1730sin( ° to find )"33'4730sin( ° .

1. After the previous example, edit the expression then recalculate. !!!!!!!

2. Edit “1” to “4”, and then find the new value. 4l

Example: Find 73.0cos 1− and display answer in DMS form.

1. Enter the expression and find the said angle. Lj0.73l

2. Display the angle in DMS. i$w$w

◊ 1.3 ENTERING DATA We shall discuss about entering data at FX-7400G+ using the utility program AREA, in particular the function HERON. Now, go to PRGM mode, and with START selected, press ll to go to START home screen. Then, press 3l to run AREA.

.

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Example: Find the area of the triangle in Fig. 1 using HERON.

1. Choose HERON, and enter the sides’ lengths. For the sake of this example, suppose we

accidentally key in 40.57 for 48.57, but have not register the entry. 1ll

40.57

2. You could scroll back, make deletions, and key in the correct entry. !!!!PPPP

8.57l

46.35l

23.63ll

3. A quicker way is to clear the incorrect entry, and key in the right one. So after step (1), do

the following. O

48.57l

46.35l

23.63ll

◊ 1.4 ERROR MESSAGES On some occasion while working on the calculators such as doing scientific calculations or executing certain programs, you might chance upon error messages as follow:

When these messages are shown, the calculator will hang for a moment. To return to normal operation, press O, or you can press !$ to locate the error and correct it. Read Appendix C in the User’s Guide to learn more about these error messages and the proper countermeasures.

Fig. 1

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◊ 1.5 OVERVIEW OF INSIGHT InSight is a library of land surveying utility programs. Each program can do one or a few specific functions. Version 1.1 has 34 functions, and there should be a few more upgrades later. We wrote a START program that accesses all the programs and put it top of the program list for convenience. However, you may write your own start program which accesses certain programs only. For this purpose, you can use the empty program files P1 and P2.

All in there are 12 core programs, 10 subprograms plus 3 interface programs. The memory size of these programs and subprograms is 15,801 bytes, which is 79% of the total memory available in FX-7400G+. In addition, 2 empty program files are put at top of program list for the user. You should ensure certain amount of free memory is available when running the program. See table in 1.5.1 below for details.

1.5.1 Program Listing and Free Memory Required

Program Brief Descriptions Size(byte) Free Memory

START Interface to access all main programs. 275 -

CURVE Interface to access CIRCULAR & SPIRAL. 134 -

COGO Interface to access TRAVRS, RADIAL, OFFSET & XSECT. 167 -

P1, P2 Empty Program Files for User 34 -

A to H Subprograms to supplement main programs. 586 -

INI Subprogram. Initialises List 1 to 5. 75 -

SP Subprogram. Supplement Circular and Spiral. 789 -

SP2 Subprogram. Supplement Circular and Spiral. 127 -

AREA Perform plane area calculation. 785 320

CIRCLE Solution of Circles using coordinates. 826 320

CIRCULAR Sets out circular/simple curve. 1074 1590

LEVEL Leveling using Height of Instrument method. 293 320

OFFSET Calculate offset, chainage and coordinates. 759 320

RADIAL Sets out with WCB, distance, and coordinates. 922 1340

TRISOLVE Solution of Triangles. 970 320

TRAVRS Close and Open Traverse, and Inverse. 2600 1340

SPIRAL Sets out transitional curves. 2151 1590

UTILITY Decimal configuration and some calculators. 500 320

VOLUME Volume calculation. 850 320

XSECT Calculate intersection and resection of point. 1918 320

Outputs from TRAVRS, RADIAL, CIRCULAR and SPIRAL are stored in lists; therefore, larger free memory is necessary for running these 4 programs than the rest.

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1.5.2 Input and Data Storage Limitations The INI program initializes the lists so user can store a maximum of 25 sets of data. For instance, in a closed traverse where there are 25 stations or less, all set out data will be stored in List 1 to List 4. However, anything beyond will cause a Dim ERROR as follow.

All entries into FX-7400G+ must satisfy the input ranges as specified in Appendix D of User’s Guide.

1.5.3 Measurement Units and Data Input InSight reads input representing length in meter (m). Output of such representation is in m as well. Angular data is entered and outputted in DMS form. For example, 53°36’24.7” is entered as 53.36247. We shall illustrate this further using the program TRIG later. When reading station position, InSight prompts first for Northing and then Easting of the station. The output of station position is in this order as well. Example: Solve the triangle in Fig. 2, given the lengths of two sides and an angle.

1. Run START, choose TRIG and then choose 2-SIDE 1A. Enter the data given and then tap l a few times to view all outputs.

O6ll

5l2ll

22.38l

26.57l

45.2716l

lllllll

Angle A = 55.432329 represents 55°43’23.29”. So, Angle B is 78°49’20.71”. The length of Side c is 19.302 m.

Fig. 2

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1.5.4 Data Error and Fail-safe Most of the utility programs have fail-safe codes written into them to prevent mathematical error and improper entry. For example, when you are at START home screen, the program only reads entry which is an integer from 1 to 8, and refreshes the screen if you enter some other values.

If you enter say 15, 20, 50 as the lengths of sides for a triangle in the TRIG program, you shall see the error message above right, because these lengths cannot possibly form a triangle. Measures are taken to ensure these fail-safe procedures do not in anyway affect the output. You will discover them as you go along using InSight.

1.5.5 Abbreviations and Symbols Used For the user interface of InSight, we adopted some common and not so common abbreviations and symbols in surveying. We also prescribed a few unusual acronyms such as TC and SC. Here is the listing of these abbreviations. We shall use them in the manual hereon.

Abbr. Meaning Abbr. Meaning

# Number of BS Back Sight

Pt Point IS Intermediate Sight

Stn Station FS Fore Sight

Ang Angle, Angular RL Reduced Level

N Northing

E Easting Stuffs Specially for CURVE

Dist Distance IP Intersection Point

Brg Bearing, WCB R Radius

A→B From A to B Lc Circular Arc Length

Chain Chainage (in m) Ls Spiral Arc Length

CTRL Control, Central Arc L Total Arc/Curve Length

REF Reference TC Straight to Circular Point

Hz Horizontal CT Circular to Straight Point

Vert Vertical Tan T Tangent Distance

dN Latitude Ext E External Distance

dE Departure TS Straight to Spiral Point

Fwd Forward SC Spiral to Circular Point

BM Bench Mark CS Circular to Spiral Point

IH Instrument Height ST Spiral to Straight Point

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PART 2 Program Libraries

◊ 2.1 START Interface Program Functions : An interface to access all main programs. To Run : Press O6l when unit is turn off.

The most important interface program in InSight is START. This program is purposely put at top of program list so it’s easy for user to start InSight. You can access all 12 main programs here. Again, to run this program, turn on the calculator and then press 6ll. The START home screen has 8 selections where each one represents a certain category of calculations. If you want to leave just hit OO and you are back to RUN mode.

START

1l 2l 3l 4l 5l 6l 7l 8l

Coordinate Geometry

Horizontal Curve

Calculation of Areas

Calculation of Volume

Solution of Triangles

Solution of Circles

COGO CURV AREA VOLU TRIG CIRC LEVEL UTI - Traverse - Offset - Radial - Resection - Intersection

- Circular - Spiral

- Heron - Coordinate - Simpson

- End Areas - Prismoidal - Grid Level

- 3 Sides - 2-Side 1A - 2-Angle 1A

- 2 Points - 3 Points

- Leveling - Dec. Fix - m2→Acre - DMS Mean - 2 Pts. Polar

Referring to the chart above, if you want to do volume calculation, you would choose VOLU with 4l, and go on from there. We shall look at each selection/programs in details later. We suggest you always run InSight from START, because certain initializations are performed in there. From hereon, we shall discuss program’s functions with the assumption that we are going to access them from START. When we begin with START, all non-angular outputs such as distance, are by default displayed in 3 decimal places, while angles are always displayed in 6 decimal places, or DD.MMSSSS. You however can use P1 and P2 to write your own start page. For support of writing program you can visit the support weblog. In any events that you are accessing these program libraries differently, please ignore explanations which refer to the START program in this manual.

START Home Screen

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◊ 2.2 Using UTILITY (UTI) Functions : DEC Fix, m

2→Arcre, 2-Pt Solve, 2-DMS Mean.

To Run : At START home screen, press 8l to enter UTI home.

2.2.1 DEC Fix (1l)

Introduction : Sets decimal places of non-angular outputs between 2 and 5. Input : 2, 3, 4, and 5 only. Output : -. Example: Set InSight to display non-angular output in 5 decimal places.

1. Select DEC Fix, choose 5, and then return to UTI home. 1l5ll

2.2.2 m2→Arcre (2l)

Introduction : Converts area quoted in m2 to its Acre equivalent.

Input : Area in m2.

Output : The same area in Acre. Example: Following previous example, convert 21,045.35 m

2 to its Acre equivalent.

1. Select m2→Arcre, enter area for the conversion. Then, return to UTI home.

2l

21045.35l

ll Note how the output data is displayed in 5 decimal places. 2.2.3 2-Pt Solve (3l)

Introduction : Calculates bearings and distance of 2 points. Input : Pt 1 (N1, E1) and Pt 2 (N2, E2). Output : Bearings of lines 1→2 and 2→1, also the shortest distance between points. Example: Given that the coordinates of Stn 1 and Stn 2 are (102 mN, -147.2 mE) and (35.7 mN, 98.61 mE) respectively, find the bearing of line 1→2 and the distance of these 2 stations as illustrated in Fig. 3.

UTI Home

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1. First select 2-Pt Solve, enter the coordinates for computation, then return to UTI home. 3l

102ln147.2l

35.7l98.61l

ll

ll

The distance between the 2 stations is 254.594 and the bearing of line 1→2 is 105°05’40.74”. 2.2.4 2-DMS Mean (4l)

Introduction : Calculates the mean of 2 angles in DMS form. Input : Two angles in DMS form. Output : Arithmetic mean of the two angles in DMS form. Example: Find the mean of the angles 67°22’47.61” and 22°37’12.39”.

1. Select 2-DMS Mean, register the 2 angles to find the mean, and then return to UTI home. 4l

67.224761l

22.371239l

ll

The mean angle calculated is exactly 45°.

Fig. 3

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◊ 2.3 Using AREA (AREA) Functions : HERON, CORDINATE, SIMPSON. To Run : At START home screen, press 3l to enter AREA home.

2.3.1 HERON (1l)

Introduction : Finds areas of a series of triangles and their total area. Input : Lengths of triangles sides. Output : Area of current triangle; total area of all triangles. We have discussed HERON earlier. Here we look at a slightly different example. Example: Find the area formed by 2 triangles in Fig. 4.

1. Choose HERON, and enter the side lengths of the bottom triangle. 1ll

48.57l

46.35l

23.63ll

2. Next opt to continue and enter side lengths of the top triangle. Then return to AREA home. l1ll

40.6l

36.94l

48.57ll

l99l

The areas of the two triangles are 540.684 m

2 and 731.847 m

2 respectively. The total area is

1272.531 m2.

Fig. 4

AREA Home

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2.3.2 CORDINATE (2l)

Introduction : Finds area of polygon using the vertices (stations). Input : Number of station and coordinates of stations, entered clockwise or anti-clock. Output : Area of the polygon. Example: Find the area of the polygon formed by these stations given here.

Station N E

1 1001.3 498.3

2 2013.7 643.9

3 1996.2 775.8

4 1301.0 790.5

5 1049.3 530.7

1. Choose CORDINATE, and register the number of stations. 2l

5l

2. Enter the coordinates of the stations to find the polygon area. Then return to AREA home. l1001.3l498.3l

l2013.7l643.9l

l1996.2l775.8l

l1301l

790.5l

l1049.3l

530.7ll

2.3.3 SIMPSON (3l)

Introduction : Finds area bounded by a line and an irregular boundary using Simpson’s Rule. Input : Number of offsets (must be odd), equidistant interval between offsets, and the

offset readings from line to boundary. Output : The area bounded by the line and the irregular boundary. Example: Find the area bounded by a line and boundary as depicted in Fig. 5.

Offset No. Distance Offset (m)

1 0 m 5.49

2 20 m 7.63

3 40 m 7.80

4 60 m 5.83

5 80 m 7.54

Fig. 5

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1. Choose SIMPSON, and then enter number of offsets and interval (d) when prompted. 3l

5l

20l

If you enter non-odd number for # Offset, the page just refreshes and returns to prompt mode. 2. Enter the offsets data for area computation. l5.49l

l7.63l

l7.8l

l5.83l

l7.54l

l

The bounded area in Fig. 5 is thus 549.8 m

2.

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◊ 2.4 Using VOLUME (VOLU) Functions : END AREAS, PRISMOIDAL, GRID LEVEL. To Run : At START home screen, press 4l to enter VOLU home.

2.4.1 END AREAS (1l)

Introduction : Computes volume using cross-section areas in End Areas method. Input : Number of areas, equidistant interval between areas, and cross-section areas. Output : Volume formed by the cross-sections. Example: The cross-section areas of an embankment are given as 70.2 m

2, 91.23 m

2 and

108.85 m2 respectively, calculate its volume. The cross-sections are all 25 m apart.

1. Select END AREAS, and enter the number of areas and the distance between these areas. 1l

3l

25l

2. Now enter the cross-section areas for volume computation. l70.2l

l91.23l

l108.85l

l

The volume of the embankment is thus 4518.875 m

3.

2.4.2 PRISMOIDAL (2l)

Introduction : Compute volume using cross-section areas in Prismoidal method. Input : Number of areas, interval between cross-section and their areas. Output : Volume formed by the cross-sections. Example: We shall revisit the example used in 2.4.1 (see above.)

1. Choose PRISMOIDAL, then enter the number of areas and interval. 2l

3l

25l

VOLU Home

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2. Next enter the area data for the volume computation. l70.2l

l91.23l

l108.85ll

The volume of the embankment calculated using PRISMOIDAL is thus 4533.083 m

3. Generally

this method is more accurate than END AREAS, and hence the differing outputs. 2.4.3 GRID LEVEL (3l)

Introduction : Computes volume by multiplying area of triangular grid to heights/depths of all 3 corner stations of each triangle.

Input : Depths/heights of corners and total of triangles each station occurs in. Output : Volume. Example: Calculate the volume of earth to be excavated over the plot in Fig. 6, with the excavation depths as given.

Station Depth (m) Occurrence

1 4.25 1

2 3.80 3

3 4.52 2

4 5.77 2

5 3.98 3

6 4.31 1

1. Go to GRID LEVEL. Enter the triangle’s base (a) and height (b) when prompted. 3l

10l15l

l

2. Enter the station’s excavation depth and grid’s occurrence. When last data is entered,

choose to end the data entry process. 4.25l1l1l

l3.8l3l1l

l4.52l2l1l

l5.77l2l1l

l3.98l3l1l

l4.31l1l

99ll

The volume of earth excavated is thus 1312 m

3.

1

10 m 15 m 2 3

4 5 6

Plot is divided into 4 triangles

Fig. 6

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◊ 2.5 Using CIRCLE (CIRC) Functions : 2 POINTS, 3 POINTS. To Run : At START home screen, press 6l to enter CIRC home.

2.5.1 2 POINTS (1l)

Introduction : Calculates centre given the radius and positions of 2 points on the circle. Input : Centre’s relative position, its radius and Pt 1 (N1, E1) and Pt 2 (N2, E2). Output : N, E of centre. Example: Referring to Fig. 7, solve the circle using coordinates of Stn 1 and Stn 2.

1. Go to 2 POINTS, and then enter centre’s relative position to the line Stn 1→Stn 2. Finally, enter both points’ position and radius.

1l

2l

270.9l

240.5l

470.3l

400.6l

173.997l

llll

The centre is thus (296.715 mN, 412.571 mE) as in Fig. 7.

Fig. 7

CIRC Home

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2.5.2 3 POINTS (2l)

Introduction : Calculates centre given the positions of 3 points on the circle. Input : N, E of all 3 points. Output : N, E of circle centre and radius. Example: Again referring to Fig. 7, solve the circle using Stn 1, Stn 2 and Stn 3.

1. Go to 3 POINTS, and then enter the stations position data. 2l

270.9l

240.5l

190l

550l

470.3l

400.6l

llll

The centre is (296.715 mN, 412.571 mE) and radius is 173.997 m, as shown in Fig. 7.

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◊ 2.6 Using TRISOLVE (TRIG) Functions : 3-SIDE, 2-SIDE 1A, 2-ANGLE 1S. To Run : At START home screen, press 5l to enter TRIG home.

2.6.1 3-SIDE (1l)

Introduction : Solves a triangle when the lengths of its sides are given. Input : Lengths of all 3 sides. Output : Lengths of all 3 sides, triangle area and the 3 internal angles. Example: Solve the triangles in Fig. 8 using the lengths of side given.

1. Choose 3-SIDE, and then enter the lengths in the order prompted. 1l

5l12l

13llll

lll

ll

The triangle is right-angled with the internal angles of A = 22°37’11.51”, B = 67°22’48.49” and C = 90°. The area is 30 m

2.

2.6.2 2-SIDE 1A (2l)

Introduction : Solves a triangle when an internal angle plus lengths of 2 sides are known. Input : Lengths of 2 sides plus 1 internal angle. Output : Lengths of all 3 sides, area and the 3 internal angles. We have discussed this function at 1.5.3 in page 5. It is designed to solve the specific triangle problem (see Fig. 9) where the known internal angle is formed by the 2 known sides.

Fig. 8

TRIG Home

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2.6.3 2-ANGLE 1S (3l)

Introduction : Solves a triangle where 2 internal angles and the length of 1 side are known. Input : Length of 1 side and 2 internal angles. Output : Lengths of all 3 sides, area and the 3 internal angles. This function helps solve a specific 2-side 1-angle triangle problem (see Fig. 10) where the 2 known internal angles are on the known side.

Example: Solve the triangle ABC given that: Side a is 25 m, angle of B is 16°15’36.74” and angle of C is 73°44’23.26”.

1. Choose 2-ANGLE 1S, and enter the data in the order prompted. 3ll

25l16.153674l

73.442326l

2. Continue tapping l to view all output data. lll

lll

ll

So the internal angles of Angle A = 90°, Side b = 7 m, c = 24 m and area is 84 m

2.

Fig. 9

Fig. 10

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◊ 2.7 Using LEVEL (LEVEL) Functions : LEVELLING. To Run : At START home screen, press 7l to start this program.

Introduction : Performs levelling run using Height of Collimation method. Input : BM, BS, IS (intermediate point sighting), and FS. Output : Instrument Height and the station’s RL. Example: Complete the following level field book using the collected field data (in bold). During this exercise, assume that the data in italic are not yet computed.

Stn. (m) BackSight I. Height ForeSight InterSight R. Level Note

BM 1.76 90.43 88.67 m

0+ 0 3.26 87.17

0+ 20 2.13 88.30

0+ 40 4.73 92.31 2.85 87.58

Turn Pt 1

0+ 60 3.21 89.10

1. After LEVEL starts, enter benchmark (BM) and backsight (BS). This would yield the Instrument Height (IH). Then, select a correct sighting for next station.

88.67l

1.76l

l7l

2. Enter the sighting data, and then choose the correct sighting for next station. Do this until a

Turn Point (Turn Pt) is encountered. 3.26ll

7l2.13l

l1l

3. Enter the Foresight (FS) and BS for the Turn Pt, and then repeat step (2) above. 2.85lll

4.73ll

99l

3.21l

ll

The field book is thus now completed.

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◊ 2.8 COGO Interface Program (COGO) Functions : Interface to access TRAVERSE, OFFSET, RADIAL, and XSECT. To Run : At START home screen, press 1l to enter COGO home.

The interface program COGO is a home screen to access 4 programs, which give us functions such as traverse, offset calculation, intersection, resection, radiation, stadia survey etc. In total there are 13 functions as illustrated at the chart below. COGO does not do any initialization.

COGO

1l 2l 3l 4l

TRAVERSE OFFSET X-SECTION RADIAL

- Closed Traverse - Connect Line - Open Traverse - Inverse

- Offset to line - Point On line

- Intersection ~ 2-Bearing, 2-Distance - Resection ~ 2 points, 3 points

- Shoot Coordinate - Bearing-distance - Stadia mapping

We shall begin by discussing the program OFFSET, followed by RADIAL, X-SECT (X-SECTION) and finally TRAVRS (TRAVERSE). Note that the programs RADIAL, TRAVERSE and XSECT store certain input and output data in lists, hence 1590 bytes worth of free memory is required when running these programs. To view these data stored in the lists, first exit from the program by either following the on screen instructions, or tap OO to halt the program. Then, press p to go to the icon menu, and then press 3 to enter LIST mode. You can scroll thorough the lists using the 4-way navigation button. Lists are initialized and their data deleted at each time you run RADIAL, TRAVERSE and XSECT. This is the same when you run the curve set out programs of CIRCULAR and SPIRAL.

COGO Home

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◊ 2.9 Using OFFSET Functions : Offset, On Line. To Run : At COGO home screen, press 2l to enter OFFSET home.

2.9.1 Offset (1l)

Introduction : Finds offset and the perpendicularity of a point relative to a reference line. Input : N, E of Station 1 and 2 of reference line, and N, E of offset point. Output : Bearing-distance of reference line, chainage and position on reference line

perpendicular to offset point, and offset to the point. Positive offset means offset is to right of reference line while negative means the offset is to the left.

Example: Referring to Fig. 10, find the offsets of points A1 and B1 from the reference line.

1. Choose Offset, and then enter positions of Stn 1 and Stn 2. 1l

500l600l

550l

510.6lll

2. Enter the coordinates of A1 and chainage and position of A are computed. Offset of A1 from reference line is also computed. l

533.6l

575.2ll

ll

OFFSET Home

Fig. 10

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3. Choose to continue and enter the coordinates of B1 for the same computation. Then, return to OFFSET home.

l1ll

508l

516.2l

lll

l99l

2.9.2 On Line (2l)

Introduction : Calculates position of known chainage on reference line and the offset points to left and to right of this position.

Input : N, E of Station 1 and 2 of reference line, the known chainage on reference line, and the offset from chainage.

Output : Bearing-distance of reference line, position of the chainage on reference line and corresponding positions of offset points to left and to right.

Example: Referring to Fig. 10 and output data from 2.9.1, find the positions of A and A1, the offset point to the right of A.

1. Choose On Line, and then enter position of Stn 1 and Stn 2. 2l

500l600l

550l

510.6ll

2. Enter the chainage and offset computed in 2.9.1 to find positions of A and A1. (Recall that chainage is 38.046 m and the offset is 17.22 m.) l

38.046ll

l

17.22lll

ll

99l

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◊ 2.10 Using RADIAL Functions : CORDINATE, BRG-DIST, STADIA. To Run : At COGO home screen, press 4l to enter RADIAL home.

2.10.1 CORDINATE (1l)

Introduction : Finds the coordinates of reference point when bearing and horizontal distance from a control point are known.

Input : N, E of the control point, bearing of control to reference point, and the horizontal distance between control and reference points.

Output : N, E of the reference point. Data →Lists : Brg→List 1, Hz Dist→List 2, E→List 3, N→List 4. Example: Compute the positions of stations A and B when given their bearings and horizontal distances relative to the control point O.

Station Line Bearing Distance (m) N (m) E (m)

O 2558.145 3115.286

A O→A 150°7’48.09” 516.618 2110.156 3372.579

B O→B 87°23’18.5” 193.282 2566.952 3308.367

1. Choose CORDINATE, and enter position of the control point O. Then enter the bearing and distance data of A. The N, E of A will be computed

1l

2558.145l

3115.286l

150.074809l

516.618ll

2. Choose to continue and enter similar data of B for the same computation. Then, return to RADIAL home. l2l

87.23185l

193.282l

ll

99l

RADIAL Home

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2.10.2 BRG-DIST (2l)

Introduction : Finds the bearing and horizontal distance of a reference point to the control point. Positions of both points are known.

Input : N, E of the control point and of the reference point. Output : Bearing of control to reference and their horizontal distance. Data →Lists : N→List 1, E→List 2, Brg→List 3, and Hz Dist→List 4. Example: Find the bearings and horizontal distances of A and B from the control point.

1. Go into BRG-DIST. Enter the coordinates of control point, and the coordinates of A. 2l

60l80l

68.8l

87.05ll

2. Choose to continue and enter coordinates of B for the same computation. Then, end the function and return to RADIAL home. l2l53.2l

93.6lll

99l

The bearings of A and B from the control are 38°41’58.15” and 116°33’54.18” respectively, and the corresponding distances are 11.276 m and 15.205 m. 2.10.3 STADIA (3l)

Introduction : Calculates horizontal and vertical distances of surveyed point relative to a control point using stadia survey.

Input : Control point’s Reduced Level (RL) and Instrument Height; horizontal angle of survey point relative to a benchmark plus its vertical angle relative to control; and also the readings of the upper, lower, and mid stadia.

Output : Horizontal and vertical distances relative to control point, and the RL of the point surveyed.

Data →Lists : Hz Ang→List 1, Vert Ang→List 2, Hz Dist→List 3, and RL→List 4.

Fig. 11

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Example: Calculate the horizontal distances and RLs of stations 1, 2 and 3 using data booked in a stadia survey. Control point’s RL is 8.537 m and Instrument Height is 1.48 m.

Stadia Readings (m) Station Hz Ang Vert Ang

Upper Lower Mid

Hz Dist

(m)

R. Level

(m)

1 18°12’ 1°25’ 0.605 1.480 1.042 87.447 11.138

2 243°35’ −0°55’ 0.804 1.702 1.253 89.777 7.328

3 118°27’ 2°34’ 1.533 2.311 1.922 77.644 11.576

1. Select STADIA, and then enter data observed for station 1. 3l

8.537l

1.48ll

18.12l

1.25l

0.605l1.48l

1.042l

lll

2. Choose to continue and enter data observed for station 2 and station 3 respectively. Then, end the function and return to RADIAL home. 2ll

243.35l

n0.55l

0.804l

1.702l

1.253l

lll

1ll

118.27l

2.34l

1.533l

2.311l1.922l

lll

99l

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◊ 2.11 Using XSECT (X-SECTION) Functions : INTERSECT (Brg-Brg, Dist-Dist), RESECT (2-Point, 3-Point). To Run : At COGO home screen, press 3l to enter XSECT home.

2.11.1 INTERSECT- Brg-Brg (1l1l)

Introduction : Computes position of an intersection point using whole circle bearings from 2 points whose positions are known.

Input : N, E of the 2 known points, bearings of lines 1→P and 2→P (see Fig. 12). Output : Internal angles at the 2 known points, and N, E of the intersection point. The known points must be entered in a clockwise manner relative to the intersection point. For example, in Fig. 12, we would first enter Stn 1 followed by Stn 2 to find P. Example: Referring to Fig. 12, by using coordinates of Stn 1 and Stn 2 and the whole circle bearings of these stations to P, determine the position of P.

1. First select INTERSECT, then Brg-Brg. Enter data as prompted on screen, and return to XSECT home when done. 1l1l

2245.612l

2016.043l

2370.264l

2120.775l

Fig. 12

XSECT Home

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97.0927l

146.3342l

lll

l99l

2.11.2 INTERSECT- Dist-Dist (1l2l)

Introduction : Computes position of an intersection point using horizontal distances from 2 points whose positions are known.

Input : N, E of the 2 known points, and horizontal distances from the points to P (see Fig. 12.)

Output : Internal angles at the 2 known points, and N, E of the intersection point. Example: Referring to Fig. 12, use horizontal distances from P to Stn 1 and Stn 2 to determine the position of the intersection point. The data must be entered in clockwise direction, relative to P.

1. First select INTERSECT, then Dist-Dist. Enter data as prompted on screen, and return to XSECT home when done. 1l2l

2245.612l

2016.043l

2370.264l

2120.775l

205.559l

180.069l

lll

l99l

2.11.3 RESECT- 2-Point (2l1l)

Introduction : Computes position of a point by observing the horizontal distances to 2 points whose positions are known.

Input : N, E of the 2 known points, and the horizontal distances from P to the 2 known points (see Fig. 12.)

Output : Position of P, internal angles at P, and bearing of the line P→1 (see Fig. 12.) Calculating point with 2 points resection is similar to finding intersection point but observation is made from the unknown point, or P (see Fig. 12.) The function 2-Point also gives the internal angle at P and the whole circle bearing of P to Stn 1 for checking purpose.

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Example: Referring to Fig. 12, calculate the resection point of P using Stn 1 and Stn 2. The stations data must be entered in clockwise direction, relative to P.

1. Select RESECT, and then 2-Point. Enter the data when prompted. The coordinates of P will be calculated, so are the internal angle of P and the whole circle bearing from P to Stn 1. 2l1l

2245.612l

2016.043l

2370.264l

2120.775l

205.559l

180.069l

llll

2.11.4 RESECT- 3-Point (2l2l)

Introduction : Computes position of a point by observing the horizontal distances to 3 points whose positions are known.

Input : N, E of the 3 known points, and the clockwise angles between first and second points, and between second and third points.

Output : The position of P and the internal angles of all 3 known points (see Fig. 13).

Example: Calculate the coordinates of P in Fig. 13 using the data given.

1. Select RESECT, then 3-Point. Enter the coordinates for all 3 stations in clockwise direction, starting from Stn 1. 2l2l

4470.53l

3420.48l

Fig. 13

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5010.84l

3380.35l

4730.45l

3880.29l

132.043022l

117.065205l

llll

l

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◊ 2.12 Using TRAVRS (TRAVERSE) Functions : CLOSED, CONNECT, OPEN, INV. To Run : At COGO home screen, press 1l to enter TRAVRS home.

These practice and adjustment techniques are employed in computations inside TRAVRS: ● Computations made in OPEN (opened traverse) and INV (inverse) are not adjusted. ● Angular error is distributed equally among all traversed stations. So if number of stations is M and the angular error is D, then:

New (Adjusted) Station Angle = Initial Station Angle + M

D

● Northing difference, dN (latitude), and Easting difference, dE (departure), are adjusted using Bowditch’s method in the calculation of coordinates.

2.12.1 CLOSED (1l)

Introduction : Calculates coordinates of successive points in a closed loop traverse using angle between successive lines and length of each line.

Input : Number of stations, N, E of the first station and bearing of line 1→2, the forward distance (length of line) and angle (left) for each station.

Output : Angle: Sum of all angles, angular error, adjustment per angle and angular error after adjustment. Linear: Sum of forward distances, dN and dE, linear accuracy, coordinates of each station, adjusted dN and dE per line, and linear error after the Bowditch’s adjustment.

Data →Lists : Fwd Dist→List 4, N→List 1, E→List 2, and Fwd Brg→List 3.

TRAVRS Home

Fig. 14

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Example: Referring to Fig. 14, calculate the coordinates of Stn 2, Stn 3 and Stn 4.

1. Choose CLOSED and then enter data for Stn 1. 1ll

4l

362.26l

220.54l

127.5255l

2. Now, enter the forward line distance and angle of each station. l115.84l

88.1254ll

99.78l

106.2111ll

140.88l

75.0335ll

99.27l

90.2239l

3. Keep tapping l to view all output data. The function will return to home once done. Below are screen dumps of angular misclosure, dN and dE misclosure, and sum of angles and distances.

The output data can be summarized as follow (forward bearings are stored in List 3).

Adjusted Station Line Fwd Bearing

dN dE N (m) E (m)

1 362.260 220.540

2 1→2 127°52’55” -71.128 91.432 291.132 311.972

3 2→3 54°14’1.25” 58.321 80.964 349.453 392.936

4 3→4 309°17’31.5” 89.218 -109.029 438.671 283.907

4→1 219°40’05” -76.412 -63.367

∑ Ang = 360°0’19” Angle Misclose = +19” Per Angle Adjustment = -4.75”

∑ Dist = 455.77 m dN Error = -0.00827 m dE Error = -0.00694 m Accuracy = 1/42230

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2.12.2 CONNECT (2l)

Introduction : Calculates coordinates of successive points in a connect-line traverse using angle between successive lines and length of each line.

Input : Number of stations, N, E of the first station and its back bearing, N, E of the last station and its forward bearing, forward distance (length of line) and angle (left) of each station.

Output : Same as 2.12.1 in page 30. Data →Lists : Fwd Dist→List 4, N→List 1, E→List 2, Fwd Brg→List 3. Example: Referring to Fig. 15 and the data provided in table, calculate the coordinates of all unknown stations of the connecting line traverse.

Station Line Angle (to left) Fwd Dist (m) Note

1 1→2 99°01’00” 225.853

2 2→3 167°45’36” 139.032

3 3→4 123°11’24” 172.571

4 4→5 189°20’36” 100.074

5 5→6 179°59’18” 102.485

6 129°27’24”

Stn 1:

2507.693 mN, 1215.632 mE

Back Brg = 57°59’30”

Stn 6:

2166.741 mN, 1757.271 mE

Fwd Brg = 46°45’24”

1. Choose CONNECT and then enter data for Stn 1 and Stn 6 (last station). 2ll6l

2507.693l

1215.632l

57.5930l

2166.741l

1757.271l

46.4524l

2. Now enter the angle and distance for each station. We shall not list any entry keystrokes here but just show a few screen dumps. The last data you should enter is the angle for Stn 6.

Fig. 15

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3. Keep tapping l to view all output data. Below are screen dumps of angular misclosure, dN and dE misclosures, and sum of angles and distances. The function will return to TRAVRS home after displaying all data.

The output data can be summarized as follow (forward bearings are stored in List 3).

Adjusted Station Line Fwd Bearing

dN dE N (m) E (m)

1 2507.693 1215.632

2 1→2 -202°59’24” -207.869 88.166 2299.824 1303.798

3 2→3 144°46’18” -113.542 80.171 2186.282 1383.969

4 3→4 87°57’48” 6.168 172.427 2192.450 1556.396

5 4→5 97°18’30” -12.71 99.241 2179.740 1655.637

6 5→6 97°17’54” -12.999 101.634 2166.741 1757.271

6→ 46°45’24”

∑ Ang = 888°45’18” Angle Misclose = -36” Per Angle Adjustment = +6”.

∑ Dist = 740.015 m dN Error = -0.14838 m dE Error = 0.14888 m Accuracy = 1/3520

2.12.3 OPEN (3l)

Introduction : Calculates coordinates of successive points of an open line traverse. Input : Number of stations, N, E of the first station and its forward bearing, forward

distance (length of line) and the angle (left) for each station. Output : N, E of successive stations. Data →Lists : Fwd Dist→List 4, N→List 1, E→List 2, Fwd Brg→List 3. Example: Find the stations’ coordinates of the open traverse described below.

Station Fwd Bearing Angle (to left) Fwd Dist (m) N (m) E (m)

1 157°0’30” 225.853 2507.693 1215.632

2 167°45’36” 139.032

3 123°11’24” 172.571

4

1. Choose OPEN and then enter data for the first station. 3ll4l

2507.693l

1215.632l

157.0030l

225.853l

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2. Enter the angles and distances data as prompted. After entry of the last data, which is the angle of Stn 4, keep tapping l to view all output data. The output data can be summarized as follow (forward bearings are stored in List 3).

Station Line Fwd Bearing N (m) E (m)

1 1→2 157°0’30” 2507.693 1215.632

2 2→3 144°46’06” 2299.781 1303.85

3 3→4 87°57’30” 2186.216 1384.055

4 2192.364 1556.516

2.12.4 INV (4l)

Introduction : INV is the inverse of traverse which calculates forward bearings and distances of successive points of a closed loop.

Input : Number of stations, and N, E of successive stations. Output : Forward bearing, line horizontal distance and (left) angle for each station. Data →Lists : Hz Dist→List 1, Fwd Brg→List 2, Ang (LEFT)→List 3. Example: Here we use the coordinates calculated in 2.12.1 as input data for INV.

Station N (m) E (m)

1 362.260 220.540

2 291.132 311.972

3 349.453 392.936

4 438.671 283.907

1. First choose INV, and enter the coordinates for each station accordingly. 4ll4l

l362.26l

220.54l

l291.132l

311.972ll349.453l

392.936ll438.671l

283.907l

2. Tap l repeatedly to view all output data. Below are screen dumps showing relevant data calculated for Station 3. You would find that these calculated values are consistent with the values shown in Fig. 14.

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◊ 2.13 CURVE Interface Program (CURV) Functions : Interface to access CIRCULAR, and SPIRAL. To Run : At START home screen, press 2l to enter CURVE home.

The interface program CURVE is a home screen to access curve setting out functions using methods of Deflection Angle, Tangent Offset and Coordinate for simple/circular curves and for transitional spiral curves. In total there are 5 functions as illustrated at the chart below.

CURVE

1l 2l

CIRCULAR SPIRAL - Tangent - Deflection Angle - Coordinates

- Deflection Angle - Coordinates

Both CIRCULAR and SPIRAL store output data in lists, so 1590 bytes of free memory is required when running them. The lists are cleared each time you run CIRCULAR and SPIRAL. We begin with Fig. 16 to explain the terms used in CIRCULAR.

CURVE Home

Fig. 16

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◊ 2.14 Using CIRCULAR Functions : Tangent, Deflection, Cordinate. To Run : At CURVE home screen, press 1l to enter CIRCULAR home.

2.14.1 Tangent (1l)

Introduction : Sets out circular curve using the tangent offset method. Input : IP chainage, IP deflection angle, radius, and chainage interval on the curve. Output : Tan T, Arc L, Ext E or versed sine, chainage of TC and CT, tangent distance

and corresponding offset at particular point on curve (see Fig. 17.) Data →Lists : Chain (of arc)→List 1, Tan Dist→List 2, Offset→List 3.

The function calculates the tangent-offset data in 2 parts. It begins at the first tangent point TC (see Fig. 17), and then when the chainage passes the curve’s midpoint, the set out calculation starts from the other tangent point, CT. Example: Use Tangent Offset method to calculate data needed to set out the circular curve whose initial data are given as follow: IP chainage = K13+827.36, IP deflection angle = 21°18’20”, radius is 350 m, and use 20 m as set out interval 1. Choose Tangent and then enter the circular curve initial data. 1l

13827.36l

21.1820l

350l

llll

CIRCULAR home

Fig. 17

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2. Enter the arc chainage interval for the setting out. Then, keep tapping l to view all output data. Here are screen dumps of data calculated for chainage K13+780 and at point CT.

The set out data can be summarized as follow.

Chainage Tangent (m) Offset (m) Others

K13+761.526 0 0 Tangent length = 65.834 m

+780 18.466 0.487 Arc Length = 130.148 m

+800 38.397 2.113 External Distance = 6.138 m

+820 58.203 4.873

+840 51.486 3.808 TC Chainage = K13+761.526

+860 31.631 1.432 CT Chainage = K13+891.674

+880 11.672 0.195

K13+891.674 0 0

2.14.2 Deflection (2l)

Introduction : Sets out circular curve using the deflection angle method. Input : IP chainage, IP deflection angle, radius, and chainage interval on the curve. Output : Tan T, Arc L, Ext E or versed sine, chainage of TC and CT. Sub-chord length,

deflection angle of set out points, and the total deflection angle (see Fig. 18). Data →Lists : Chain→List 1, SubCHORD→List 2, Deflect Ang→List 3, Total Ang→List 4. Example: Revisit the example in 2.14.1 using Deflection Angle method. The data are: IP chainage = K13+827.36, IP deflection angle = 21°18’20”, radius is 350 m, interval = 20 m.

Choose Deflection with 2l and then enter the circular curve initial data. The process is the same as the example in 2.14.1 which uses the Tangent function.

Fig. 18

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Here are screen dumps of the calculations at chainage K13+820.

The set out data can be summarized as follow. As expected the final total deflection angle is one half of the IP deflection angle.

Chainage Sub Chord (m) Deflect Angle Total Deflect Angle

K13+761.526 0 0 0

+780 18.472 1°30’43.76” 1°30’43.76”

+800 19.997 1°38’13.28” 3°08’57.04”

+820 19.997 1°38’13.28” 4°47’10.32”

+840 19.997 1°38’13.28” 6°25’23.60”

+860 19.997 1°38’13.28” 8°03’36.88”

+880 19.997 1°38’13.28” 9°41’50.16”

K13+891.674 11.673 0°57’19.84” 10°39’10”

2.14.3 Cordinate (3l)

Introduction : Sets out circular curve from remote control station. Input : N, E of IP and TC, chainage of TC, IP deflection angle, radius, N, E of the

control station and chainage of point on the curve to be set out. Output : N, E of the position on the curve at the chainage entered, and bearing and

horizontal distance from control station to the point being set out. Data →Lists : N→List 1, E→List 2, Dist→List 3, Pt Brg→List 4. Example: A circular curve of radius 350 m is to be set out from a control station C (2316.218 mN, 1862.526 mE). The IP has coordinates (2210.724 mN, 1603.922 mE) and the IP deflection angle is −25°37’18”. TC is at chainage K3+761.526 and has coordinates (2011.158 mN, 1632.274 mE). Find the bearings and horizontal distances from C to set out points A and B which are on the curve at chainage K3+795 and K3+810 respectively. 1. Choose Cordinate, and then enter the circular curve data required. 3l

2210.724l

1603.922l

n25.3718l

2011.158l

1632.274l

3761.526l350l

2316.218l

1862.526l

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2. Now enter the chainage of point A. 3795l

lll So the bearing from C to A is 220°59’26.49” and the horizontal distance is 360.61 m. 3. Choose to continue and enter the chainage of point B. Then, choose to end the function. l1l

3810llll

l99l

The bearing from C to B is 223°00’27.14” and the horizontal distance is 352.394 m. There is a fail-safe which prevents you from entering chainage which is outside of the curve’s bound. If you do, the program will remind you of the mistake with the “DATA ERROR” message. It should return to the chainage prompt when you tap l after that.

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◊ 2.15 Using SPIRAL Functions : Deflection, Cordinate. To Run : At CURVE home screen, press 2l to enter CIRCULAR home.

We begin with Fig. 19 to explain terms used in SPIRAL.

2.15.1 Deflection (1l)

Introduction : Sets out transitional spiral and circular curves using combination of deflection angle and tangent offset methods.

Input : IP chainage and deflection angle, radius, Ls, chainage interval on the curve. Output : Tan T, Arc L, Arc Lc, Ext E, chainages of TS, SC, CS, and ST (see Fig. 19.)

Arc length, deflection angle, tangent distance and offset for points on the spiral curve (see Fig. 20), and; sub-chord length, deflection angle of set out points, and the total deflection angle (see Fig. 21.)

Data →Lists : Chain→List 1, Tan Dist→List 2, Offset→List 3, Deflect Ang→List 4, and lastly, Arc→List 6.

The first part of the spiral curve of TS to SC is set out from TS with tangent offset and deflection angle methods. The circular curve of SC to CS is then set out with deflection angle method from SC. Finally, the spiral curve of CS to ST is set out from ST with same methods as the first. User is allowed to select different intervals in setting out spiral curves and the circular curve.

Fig. 19

CIRCULAR home

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Example: Two straights are joined by a transitional curve of radius 400 m. Calculate the set out data given these preliminary data: IP chainage is K3+760.45, IP deflection angle is 22°40’18”, one side spiral length (Ls) is 57.4 m. Use 20 m as set out interval. 1. Choose Deflection with 1l and then enter the transitional curve’s initial data. The computation using these data would yield more about the transitional curve. 3760.45l

22.4018l

400l57.4l

llll

lll

l

2. Enter the curve chainage interval for the set out. Then, keep tapping l to view all output data for the spiral curve of TS to SC. Here are screen dumps of data calculated for the point at chainage of K3+700. See also Fig. 20 for graphic explanation.

The set out data for the spiral curve from TS to SC can be summarized as follow.

Chainage Arc (m) Deflect Ang Tangent (m) Offset (m)

K3+651.498 0 0 0 0

+660 8.502 0°01’48.23” 8.502 0.004

+680 28.502 0°20’16.33” 28.501 0.168

+700 48.502 0°58’42.18” 48.489 0.828

K3+708.898 57.4 1°22’12.95” 57.37 1.372

Fig. 20

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3. Next you need to enter the chainage interval for setting out of the circular curve of SC to CS. For this example it is 20 m. Below are screen dumps of data calculated for position at chainage K3+760. See Fig. 21 for graphic explanation.

The set out data for the circular curve of SC to CS from SC can be summarized as follow.

Chainage Sub Chord (m) Deflect Angle Total Deflect Angle

K3+708.898 0 0 0

+720 11.102 0°47’42.44” 0°47’42.44”

+740 19.998 1°25’56.62” 2°13’39.06”

+760 19.998 1°25’56.62” 3°39’35.68”

+780 19.998 1°25’56.62” 5°05’32.30”

+800 19.998 1°25’56.62” 6°31’28.92”

K3+809.776 9.776 0°42’00.56” 7°13’29.48”

4. Finally, enter the interval again for setting out of the spiral curve of ST to CS. Its calculation is same as in setting out the first spiral curve, but from the exit tangent point of ST. The set out data for this spiral curve can be summarized as follow.

Chainage Arc (m) Deflect Ang Tangent (m) Offset (m)

K3+809.776 57.4 358°37’47” 57.37 1.372

+820 47.176 359°04’27” 47.165 0.762

+840 27.176 359°41’34” 27.175 0.146

+860 7.176 359°58’42.9” 7.176 0.003

K3+867.176 0 0 0 0

Fig. 21

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2.15.2 Cordinate (2l)

Introduction : Sets out transitional spiral and circular curves using remote control station. Input : N, E of IP, TS and control station, chainage of TS, IP deflection angle, radius,

Ls, and chainage of point on the curve to be set out. Output : N, E of the position on the curve at the chainage entered, and bearing and

horizontal distance from control station to set out point. Data →Lists : N→List 1, E→List 2, Dist→List 3, Pt Brg→List 4. Example: Revisit the example in 2.15.1 by setting out the curve from the remote control station C (2274.236 mN, 1719.534 mE). The IP has coordinates (2210.724 mN, 1603.922 mE) and TS has coordinates (2151.158 mN, 1512.547 mE). Recall that radius is 400 m, the IP deflection angle is 22°40’18”, Ls is 57.4 m, and TS chainage was calculated as 3651.498 m. Find the bearing and horizontal distance from C to set out point A which is on the curve at chainage K3+840.

1. Choose Cordinate, and then enter the spiral curve data as prompted. 2l

2210.724l

1603.922l

22.4018l

2151.158l

1512.547l

3651.498l400l

57.4l

2274.236l

1719.534l

2. Enter the chainage of point A, and then end the function after viewing all output data. 3840l

lll

l99l

So the bearing from C to A is 215°39’38.88” and the horizontal distance is 60.101 m.

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InSight User Manual

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