AutoCAD Civil 3D 2011 - Corridor Editing

Civil 3D Intersection Design Tools

Five Minute Road Design using RoadEng

Advanced Road Design - Drainage and Sewer Design Overview

Traverse Correction - Bowditch Method

In Traversing the lengths of the line are measured by chain or a tape and the directions are fixed by the compass or theodolite or by forming angles with chain and a tape. The latest instruments like total station captures the co-ordinates of the points along with elevations. These instruments are also capable of recording and string the distances and angles replacing the conventional methods.

There are two types of traverse surveying i.e. Closed Traverse and Open Traverse.

1. Closed Traverse: 
   When a series of connected lines form a closed circuit, ie. When the finishing point coincides with the starting point, then it is called as a closed traverse. These closed traverse surveys has many applications like fixing the boundaries of ponds, forests etc..

2. Open traverse :
   When a sequence of connected lines extends along a general direction and does not return to the starting point, it is known as ‘open traverse’ or ‘unclosed traverse’.

Traverse Correction Procedure

Present techniques used in traversing using total station as a open traverse. The steps are as described below…

1. GPS pair points are fixed at a convenient distance, approximately about 3 to 5km. Care has to be taken that the pair of GPS points is fixed at a reliable distance (at least 60m is advised for better results) and on good monuments. These points are fixed in such a way that they are clearly inter visible and should cater for placing the total station firmly on the GPS stations,
2. Total station is to be checked for its calibration, prism constants for the prisms to be set in the instrument to avoid errors.
3. Total station is then used to conduct the traverse between the GPS points. This type of traverse ensures that the survey is started from a known pair of points and is closed on known pair of points. Care has to be taken that the last bearing is also taken for correcting the misclosures.
4. There are several methods to correct the traverse misclosures. However, in most of the cases Bowditch rule is considered to be most reliable. The other methods like transit method, Crandall method, Least Square Methods are used very rarely. The most accurate method which is known as a misclosures correction by the least square method is used when the accuracy required is very high. This method finds itself applicable in the projects like tunnel works.

1. Bowditch Rule
2. Whole Circle Bearing
3. Quandrantal Bearing

TOTAL STATION TRAVERSING ADJUSTMENT BY BOWDITCH METHOD

TOTAL STATION TRAVERSING ADJUSTMENT BY BOWDITCH METHOD

PROCEDURE FOR TRAVERSE CALCULATIONS

• Adjust angles or directions
• Determine bearings or azimuths
• Calculate and adjust latitudes and departures
• Calculate rectangular coordinates

DETERMINING BEARINGS OR AZIMUTHS

• Requires the direction of at least one line within the traverse to be known or assumed
• For many purposes, an assumed direction is sufficient
• A magnetic bearing of one of the lines may be measured and used as the reference for determining the other directions
• For boundary surveys, true directions are needed

LATITUDES AND DEPARTURES

Line	Dir	Deg	Min	Sec	Dir	Degrees	Length	Cumulative Length	Azimuthal Angles	Departure	Latitude
AB	N	26	10	0	E	N26.167E	285.1	285.1	26.167	+125.726	+255.881
BC	S	75	25	0	E	S75.417E	610.45	895.55	+104.583	+590.784	-153.700
CD	S	15	30	0	W	S15.5W	720.48	1616.03	+195.500	-192.540	-694.276
DE	N	1	42	0	W	N1.7W	203	1819.03	+358.300	-6.022	+202.911
EA	N	53	0	0	W	N53W	647.02	2466.05	+307.000	-516.733	+389.386

CLOSURE OF LATITUDES AND DEPARTURES

• The algebraic sum of all latitudes must equal zero or the difference in latitude between the initial and final control points
• The algebraic sum of all departures must equal zero or the difference in departure between the initial and final control points

ADJUSTMENT OF LATITUDES AND DEPARTURES

Line	Dir	Deg	Min	Sec	Dir	Length	Cumulative Length	Azimuthal Angles	Departure	Latitude
AB	N	26	10	0	E	285.1	285.1	26.167	+125.726	+255.881
BC	S	75	25	0	E	610.45	895.55	+104.583	+590.784	-153.700
CD	S	15	30	0	W	720.48	1616.03	+195.500	-192.540	-694.276
DE	N	1	42	0	W	203	1819.03	+358.300	-6.022	+202.911
EA	N	53	0	0	W	647.02	2466.05	+307.000	-516.733	+389.386

 

ADJUSTED LATITUDES AND DEPARTURES

Line

Dir

Deg

Min

Sec

Dir

Length

Cumulative Length

Azimuthal Angles

Departure Misclosure

Latitude Misclosue

Corrected Departure

Corrected Latitude

AB

N

26

10

0

E

285.1

285.1

26.167

+0.140

+0.023

+125.586

+255.858

BC

S

75

25

0

E

610.45

895.55

+104.583

+0.301

+0.050

+590.483

-153.750

CD

S

15

30

0

W

720.48

1616.03

+195.500

+0.355

+0.059

-192.895

-694.335

DE

N

1

42

0

W

203

1819.03

+358.300

+0.100

+0.017

-6.122

+202.894

EA

N

53

0

0

W

647.02

2466.05

+307.000

+0.319

+0.053

-517.052

+389.334

                                                                                                                                                αCorr.Dep=0      αCorr.Lat=0

The Sum of total Corrected Departure and Sum of total Corrected latitude is 0.00, proves that the traverse is balanced

RECTANGULAR COORDINATES

• Rectangular X and Y coordinates of any point give its position with respect to a reference coordinate system
• Useful for determining length and direction of lines, calculating areas, and locating points
• You need one starting point on a traverse (which may be arbitrarily defined) to calculate the coordinates of all other points
• A large initial coordinate is often chosen to avoid negative values, making calculations easier.

CALCULATING X AND Y COORDINATES

Given the X and Y coordinates of any starting point A, the X and Y coordinates of the next point B are determined by:

Line	Dir	Deg	Min	Sec	Dir	Length	Azimuthal Angles	Calculated Easting	Calculated Northing	Adjusted Easting	Corrected Northing
AB	N	26	10	0	E	285.1	26.167	+5125.726	+10255.881	+5125.586	+10255.858
BC	S	75	25	0	E	610.45	+104.583	+5716.510	+10102.180	+5716.069	+10102.107
CD	S	15	30	0	W	720.48	+195.500	+5523.970	+9407.904	+5523.174	+9407.772
DE	N	1	42	0	W	203	+358.300	+5517.948	+9610.815	+5517.052	+9610.666
EA	N	53	0	0	W	647.02	+307.000	+5001.214	+10000.201	+5000.000	+10000.000

LINEAR MISCLOSURE

The hypotenuse of a right triangle whose sides are the misclosure in latitude and the misclosure in departure.

TRAVERSE PRECISION

• The precision of a traverse is expressed as the ratio of linear misclosure divided by the traverse perimeter length.
• expressed in reciprocal form
• Example

0.89 / 2466.05 = 0.00036090
1 / 0.00036090 = 2770.8

Precision = 1/2771

Lesson Note on methods used to determine azimuth by observations of the sun.

At what time will the effects of a small error in the determination of observer's latitude be minimized when making azimuth observations on Polaris?
A. 12:00 midnight
B. when Polaris is at elongation
C. when Polaris is at culmination
D. when the LHA is 90 degrees
E. when the GHA is 90 degrees
Ans; C. At culmination the bearing is 0 at all LAT.

There are two methods by which azimuth can be determined by observation of the sun. Answer the following questions concerning these methods.


QS > Name the two methods that can be used to determine azimuth by observations of the sun.
Ana; 1. Altitude method and
           2. hour angle method.

QS>Which method is more accurate? Explain your answer.
Ans; Hour angle method—because time can be very accurately determined, and inaccuracies in measuring the vertical angle and determining refraction make the altitude method less reliable.