TRAVERSE CALCULATIONS

TRAVERSE CALCULATIONS

PROCEDURE FOR TRAVERSE CALCULATIONS

Adjust angles or directions

Determine bearings or azimuths

Calculate and adjust latitudes and departures

Calculate rectangular coordinates

BALANCING ANGLES OF CLOSED TRAVERSES

An example of a calculation involving interior angles is available.

ADJUSTING ANGLES

Adjustments applied to angles are independent of the size of the angle

Methods of adjustment:

Make larger corrections where mistakes were most likely
Apply an average correction to each angle
Or a combination

Never make an adjustment that is smaller than the measured accuracy

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

The latitude of a line is its projection on the north-south meridian and is equal to the length of the line times the cosine of its bearing

The departure of a line is its projection on the east-west meridian and is equal to the length of the line times the sine of its bearing

The latitude is the y component of the line and the departure is the x component of the line

LATITUDES AND DEPARTURES

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

CALCULATION OF LATITUDES AND DEPARTURES

Using bearings

Station
Bearing
Length
Latitude
Departure
A
N 26° 10'E
285.10
+255.88
+125.72
B
S 75° 25'E
610.45
-153.70
+590.78
C
S 15° 30'W
720.48
-694.28
-192.54
D
N 1° 42'W
203.00
+202.91
-6.02
E
N 53° 06'W
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

CALCULATION OF LATITUDES AND DEPARTURES

Using azimuths

Station
Azimuth
Length
Latitude
Departure
A
26° 10'
285.10
+255.88
+125.72
B
104° 35'
610.45
-153.70
+590.78
C
195° 30'
720.48
-694.28
-192.54
D
358° 18'
203.00
+202.91
-6.02
E
306° 54'
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Compass (Bowditch) Rule 

ADJUSTMENT OF LATITUDES AND DEPARTURES

Station
Azimuth
Length
Latitude
Departure
A
+0.08
-0.06
26° 10'
285.10
+255.88
+125.72
B
+0.18
-0.13
104° 35'
610.45
-153.70
+590.78
C
+0.21
-0.15
195° 30'
720.48
-694.28
-192.54
D
+0.06
-0.05
358° 18'
203.00
+202.91
-6.02
E
+0.18
-0.14
306° 54'
647.02
+388.48
-517.41
A
TOTALS
2466.05
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Balanced
Balanced
Station
Latitude
Departure
Latitude
Departure
A
+0.08
-0.06
+255.88
+125.72
+255.96
+125.66
B
+0.18
-0.13
-153.70
+590.78
-153.52
+590.65
C
+0.21
-0.15
-694.28
-192.54
-694.07
-192.69
D
+0.06
-0.05
+202.91
-6.02
+202.97
-6.07
E
+0.18
-0.14
+388.48
-517.41
+388.66
-517.55
A
TOTALS
-0.71
+0.53
0.00
0.00

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:

COORDINATES

Balanced
Balanced
Station
Latitude
Departure
Y-coord
X-coord
A
10000.00
10000.00
+255.96
+125.66
B
10255.96
10125.66
-153.52
+590.65
C
10102.44
10716.31
-694.07
-192.69
D
9408.37
10523.62
+202.97
-6.07
E
9611.34
10517.55
+388.66
-517.55
A
10000.00
10000.00
TOTALS
0.00
0.00

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

definition latitude and longitude

Latitude

Lines of latitude measure north-south position between the poles. The equator is defined as 0 degrees, the North Pole is 90 degrees north, and the South Pole is 90 degrees south. Lines of latitude are all parallel to each other, thus they are often referred to as parallels.

The memory rhyme I use to help remember that lines of latitude denote north-south distance is:

"Tropical latitudes improve my attitude"

One degree of latitude is

60 nautical miles, 69 statute miles or 111 km.

One minute of latitude is

1 nautical mile, 1.15 statute miles, or 1.85 km.

Longitude

Lines of longitude, or meridians, run between the North and South Poles. They measure east-west position. The prime meridian is assigned the value of 0 degrees, and runs through Greenwich, England. Meridians to the west of the prime meridian are measured in degrees west and likewise those to the east of the prime meridian are measured to by their number of degrees east.

The memory rhyme I use to help remember that lines of longitude denote east-west distance is:

"Lines of LONGitude are all just as

LONG as one another."

With this saying in my mind, I picture all of the longitudinal meridians meeting at the poles, each meridian the same length as the next.

Symbols for degrees, minutes and seconds:

°	Degrees
'	Minutes
"	Seconds

The three common formats:

DDD° MM' SS.S"	Degrees, Minutes and Seconds
DDD° MM.MMM'	Degrees and Decimal Minutes
DDD.DDDDD°	Decimal Degrees

Degrees, Minutes and Seconds

DDD° MM' SS.S"

32° 18' 23.1" N 122° 36' 52.5" W

This is the most common format used to mark maps. It's also the most cumbersome to work with. It's a lot like telling time…

There are sixty seconds in a minute (60" = 1') and

There are sixty minutes in a degree (60' = 1°).

Keeping in mind a few easy conversions between seconds and decimal minutes will help when working with maps that use degrees, minutes and seconds.

15 seconds is one quarter of a minute or 0.25 minutes

30 seconds is one half of a minute or 0.5 minutes

45 seconds is three quarters of a minute or 0.75 minutes

Degrees and Decimal Minutes

DDD° MM.MMM'

32° 18.385' N 122° 36.875' W

This is the format most commonly used when working with electronic navigation equipment.

Decimal Degrees

DDD.DDDDD°

32.30642° N 122.61458° W

or +32.30642, -122.61458

This is the format you'll find most computer based mapping systems displaying. The coordinates are stored internally in a floating point data type, and no additional work is required to print them as a floating point number.

Often the N-S and E-W designators are omitted. Positive values of latitude are north of the equator, negative values to the south. Watch the sign on the longitude, most programs use negative values for west longitude, but a few are opposite. This saves a lazy western hemisphere programmer from having to type in a minus sign before most of their longitude values.

Which format should you use?

First off, if you are working with other people who have agreed upon a format to use, then you should probably use that format.

Next, you will want to look at the maps, lists of coordinates, and any software you may be using. If you can find a consistent format among them, your work will be easier.

You can set your GPS to display any one of these three formats. Locations can be entered into the GPS with the selected format, and then by switching the display format setting, viewed in a different format.

I frequently choose to use the Degrees and Decimal Minutes format, even though the USGS maps I'm using are marked in Degrees, Minutes and Seconds. The markings on the map are all at either 0, 15, 30, or 45 seconds. By remembering the "quarter minute conversions" of 0.00, 0.25, 0.50, and 0.75, I can quickly do the conversions in my head.

A Quick Guide to Using UTM Coordinates

Standing at the center of the marker shown on the map below, a GPS unit set to display position in UTM/UPS format, would report a location of:

Let's look at where the various parts of the UTM position come from on the map.

The map has grid lines spaced every kilometer or 1000 meters. The grid is labeled with UTM coordinate values. The vertical grid lines determine East-West position and the horizontal grid lines determine North-South position.

Look along the bottom edge of the map at the labels for the vertical grid lines.

The label,

, reads "seven hundred and six thousand meters East." The label,

, is an abbreviation for,

The two grid lines are 1000 meters apart. The horizontal grid lines are labeled in a similar manner.

The 10S is the Grid Zone Designation you are in. The Grid Zone is necessary to make the coordinates unique over the entire globe.

The top set of numbers, 706832, represent a measurement of East-West position, within the Grid Zone, in meters. It's called an Easting. Using a map with a 1000m grid, the first digits are come from the label for the grid line to the west of the position. The last 3 digits are the distance in meters measured from the western grid line.

The bottom set of numbers, 4344683, represent a measurement of North-South position, within the Grid Zone, in meters. It's called a Northing. Using a map with a 1000m grid, the first digits are come from the label for the grid line to the south of the position. The last 3 digits are the distance in meters measured from the southern grid line.

Using various tools to plot and measure UTM positions on a map

Using a grid style tool to plot/measure a UTM position with 100m precision

The precision of the Easting and Northing measurements

A UTM coordinate's Easting and Northing are both distance measurements made in meters. But this leaves us with a dilemma when we have not measured with one meter precision. What to do with the unknown digits. Let's look at the Easting of a point that is 146m east of the western grid line. T hat would, in our example above, give it an Easting of 706146m E. But on a large scale map, no tool will be able to measure to the nearest meter. At best you'll get 10 meters, and if you're eyeballing it you'll be good to get 100m accuracy. But we still have to write all the digits down to the meter. The convention is to fill in the unknown/unmeasured digits with zeros, and to avoid any rounding up. So our easting becomes 706140m E or 706100m E. The trouble is we don't know if the location we are measuring was located with great accuracy at 706100m E, or if we just did a 100m rough measurement and the location could have an easting between 706100m E and 706199m E. One possible solution is to write the Easting an Northing in kilometers, using as many digits after the decimal point as we have measurement accuracy. For more on this idea check out our page on kUTM Coordinates.

For improved clarity, write the measurement units with the Easting and Northing

In the world of map coordinates, there are a lot of different coordinate formats. If you just run a bunch of digits together with no spacing or units, you run the risk of having someone else misunderstand what coordinate format you are using. In the case of UTM, I suggest writing "m E" for "meters East" after the Easting, and "m N" for "meters North" after the Northing. When communicating a coordinate by voice, say the words "meters East" after the Easting and "meters North" after the Northing.

There are several documented cases where a string of digits was passed, usually by voice, to someone else who misinterpreted the coordinate format. In one case this led to the rescue helicopter being sent 30 miles away from the actual incident.

More details about UTM Grid Zones

The world's 60 UTM zones

The UTM coordinate system divides the earth into 60 zones each 6 degrees of longitude wide. These zones define the reference point for UTM grid coordinates within the zone. UTM zones extend from a latitude of 80° S to 84° N. In the polar regions the Universal Polar Stereographic (UPS) grid system is used. Note that there are a few exceptions to zone width in Northern Europe to keep small countries in a single zone.

UTM zones are numbered 1 through 60, starting at the international date line, longitude 180°, and proceeding east. Zone 1 extends from 180° W to 174° W and is centered on 177° W.

Each zone is divided into horizontal bands spanning 8 degrees of latitude. These bands are lettered, south to north, beginning at 80° S with the letter C and ending with the letter X at 84° N. The letters I and O are skipped to avoid confusion with the numbers one and zero. The band lettered X spans 12° of latitude.

Eastings and Northings within a zone

A single grid zone measures about 20,000km tall and only about 700km wide. So the above diagram has been compressed in the vertical axis by about 15X. The eastern and western zone boundaries are truly much straighter.

A square grid is superimposed on each zone. It's aligned so that vertical grid lines are parallel to the center of the zone, called the central meridian.

UTM grid coordinates are expressed as a distance in meters to the east, referred to as the "easting", and a distance in meters to the north, referred to as the "northing".

Eastings

UTM easting coordinates are referenced to the center line of the zone known as the central meridian. The central meridian is assigned an easting value of 500,000 meters East. Since this 500,000m value is arbitrarily assigned, eastings are sometimes referred to as "false eastings"

An easting of zero will never occur, since a 6° wide zone is never more than 674,000 meters wide.

Minimum and maximum easting values are:

160,000 mE and 834,000 mE at the equator

465,000 mE and 515,000 mE at 84° N

(Exceptions to this will be found in the unusual zones in northern Europe.)

Northings

UTM northing coordinates are measured relative to the equator. For locations north of the equator the equator is assigned the northing value of 0 meters North. To avoid negative numbers, locations south of the equator are made with the equator assigned a value of 10,000,000 meters North.

Some UTM northing values are valid both north and south of the equator. In order to avoid confusion the full coordinate needs to specify if the location is north or south of the equator. Usually this is done by including the letter for the latitude band.

If this is your first exposure to the UTM coordinate system you may find the layout of zones to be confusing. In most land navigation situations the area of interest is much smaller than a zone. The notion of a zone falls away and we are left with a simple rectangular coordinate system to use with our large scale maps.

Topographic Survey Requirements

Sanitary Sewer Overflow (SSO) Control

and Wastewater Facilities Program

Topographic Survey

Requirements

City of Baton Rouge/Parish of East Baton Rouge

Department of Public Works

Submitted by

Prepared by: Tim Jett

Reviewed by: Jennifer Baldwin

Approved by: James Hawley

Revision 1

August 2009

MKE/092380086 III REV. 1 / AUGUST 2009

Contents

Section Page

1. Introduction........................................................................................................................1-1

2. General ................................................................................................................................2-1

3. Control Points .....................................................................................................................3-1

4. Survey Limits and Cross Sections...................................................................................4-1

5. Utility Locations .................................................................................................................5-1

6. Deliverables........................................................................................................................6-1

MKE/092380086 1-1 REV. 1 / AUGUST 2009

1. Introduction

This document provides requirements for surveying performed for projects associated with

the City of Baton Rouge/Parish of East Baton Rouge (C-P) Sanitary Sewer Overflow (SSO)

Control and Wastewater Facilities Program. The term Engineer is defined as an engineering

design firm under contract with the C-P and producing engineering design work on the

Program. These requirements are provided to encourage consistency in the design approach

used by various Engineers.

While the purpose of these requirements is to assure uniformity, it is not intended to stifle

Engineer’s creativity, design innovation, and ingenuity. Engineers shall review these

requirements and adopt them for design of the facilities for which they are responsible.

Engineers are ultimately responsible for their design, and this responsibility is in no way

diluted or absolved by these requirements.

It may be necessary for the Engineer to deviate from these requirements. In such cases, the

Engineer shall immediately bring this matter to the attention of the Program Manager (PM)

by completing and submitting the form included in the Program Requirements for Engineers.

The PM reserves the right to allow or disallow the deviation from the requirements. If the

deviation will impact design contract terms, then a Supplemental Agreement will be

negotiated between the Engineer, the PM, and the C-P.

MKE/092380086 2-1 REV. 1 / AUGUST 2009

2. General

The surveyor shall follow the current standards of practice as outlined in the Laws and

Rules of the Louisiana Professional Engineering and Land Survey Board in conducting

surveys. As such, all work shall adhere to modern surveying theory, practice, and

procedures. Surveys shall be performed in English units and all data collected shall be

reduced to state plane coordinates.

If right-of-way or servitude maps are required for the project, they shall be prepared in

accordance with the Program Right-of-Way Map/Real Estate Standards.

MKE/092380086 3-1 REV. 1 / AUGUST 2009

3. Control Points

Horizontal and vertical control points for design, topographic, boundary, and construction

surveys shall meet the accuracy of surveys for a Class A (Urban) Survey as outlined in the

Rules of the Louisiana Professional Engineering and Land Survey Board. Horizontal control

shall be NAD 83 (92) and vertical control shall be NAVD 88. Surveyor shall only use EBR 88

monuments.

As part of the C-P SSO Program, the C-P Department of Public Works (DPW), in

conjunction with the U. S. Army Corps of Engineers, New Orleans District, has established

20 vertical control benchmarks to be utilized for surveying performed as part of the

Program. Information related to these benchmarks including their locations is available on

the Program Web site at www.brprojects.com/sewer/pages/contractor_guidelines.htm.

MKE/092380086 4-1 REV. 1 / AUGUST 2009

4. Survey Limits and Cross Sections

The Engineer shall perform survey work to determine all surface features and at or below

ground elevations at the project site and/or located within the right-of-way along the entire

alignment and other areas as may be necessary to develop plan and profiles and site plans

for the recommended project. The Engineer may choose to utilize Global Positioning System

(GPS) data for mapping of x-y coordinates. The scope of the surveying work shall include,

but not be limited to:

• Determining boundary conditions (site property boundary, temporary and permanent

servitude widths determined, and rights-of-way-widths).

• Confirming existing facilities controls and elevations with current survey and

Establishing additional survey control points where required.

• Identifying mapping options and develop preliminary and/or final design mapping.

• Performing field survey in State Plane Coordinate control. All existing surface features

within the project limits shall be shown. Surface features include, but are not limited to,

edge of pavement, pavement type, curb, gutter, sidewalks, retaining walls, driveways,

parking lots, utility poles, utility towers, overhead electric lines, pavement markings

(including type of pavement marking), traffic lights, traffic signs, all other signs, tree

type and trunk diameter, drainage channels (including invert and water surface

elevations at sewer line crossing), water bodies (ditches, streams, creeks, rivers, ponds,

etc.) including invert and water surface elevations at sewer line crossing, railroads,

structures, bridges, columns, telephone boxes, fences, gates, and all other surface

features. The size and type of all surface features shall be shown.

• Performing phased or final design level mapping.

• Defining legal issues and constraints (ownership’s, zoning, servitudes, etc.).

• Obtaining parcel maps and ownership information within the project limits. Property

corner surveys shall be conducted within the project limits. All existing lot numbers and

plat information shall be shown.

• Field surveying pavement match points (curbs, gutter, sidewalk, pavements, etc.).

• Researching and showing records of existing adjacent public utility systems.

• Plotting all existing utilities (see Louisiana R.S. 38:2223).

• Field surveying and showing on drawings all underground features and utilities within

the project limits. These include, but are not limited to, sanitary and storm sewers,

water, gas, electric, telephone, cable, fiber optic, traffic loops, services (water, sewer, gas,

and all other services), manholes (including top and invert elevation), utility vaults

(including top and invert elevation), valve boxes (water valves, sewer valves, gas valves,

and all other valves, including top and invert elevations), storm inlets (including top and

TOPOGRAPHIC SURVEY REQUIREMENTS

REV. 1 / AUGUST 2009 MKE/092380086

invert elevation), junction boxes (including top and invert elevation), utility

appurtenances, cleanouts, water meters, lift stations (wet wells, dry wells, and aboveground

piping and valves, including top and invert elevations for wet wells and dry

wells and surface drains and centerline elevations for above-ground piping and valves),

septic systems, storage tanks, and all other underground features. The type, size,

alignment, depth, and top and invert elevations of the underground features shall be

noted. Slopes and flow lines shall be noted for existing sewer lines. Materials of

construction of underground utilities shall be provided where available.

• Survey existing building floor elevations at all identified pump station sites. Provide one

XYZ coordinate on flat open ground in the immediate vicinity of each of the identified

existing and proposed pump stations.

If applicable, special areas or elements to be mapped (using GPS data) include:

• Hazardous materials

• Archaeologically important areas

• Wetlands/endangered species

• Flood plains

• Geotechnical exploration drill holes and test pits

MKE/092380086 5-1 REV. 1 / AUGUST 2009

5. Utility Locations

The Engineer shall collect as-built utility drawings and utility inventory from the Program

Manager. The surveyor shall collect all visible utilities and utility markers and show them

on the survey plans. The surveyor shall also call LA One Call and collect location of the

underground utilities as indicated by LA One Call. Surveyor shall submit call or reference

number received from LA One Call to the Program Manager as verification of the request

for utility locations. If additional utility location activities are included in the Project scope,

such as potholing, the surveyor will also include the locations of all utilities located by these

additional activities on the survey plans and profiles, as applicable.

MKE/092380086 6-1 REV. 1 / AUGUST 2009

6. Deliverables

The survey shall include the following deliverables, to be submitted with other design

deliverables, as appropriate.

• Copy of all survey notes and field roll

• Plan and profiles broken into 24 x 36-inch sheets with station and offset to all utility

poles, fire hydrants, building corners, headwalls, and drainage structures

• Vertical profiles showing the existing centerline ground surface above the proposed pipe

or structure, drainage pipes, pipeline crossings, utilities, ditch centerlines, and other

critical information

• AutoCAD drawings, in accordance with the Program CAD Requirements, showing all

collected data in three dimensional coordinates along with the required pen setting files

• Drawing files in pdf format at full size (24 x 36)