TRAVERSE CALCULATIONS- PROCEDURE

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

How to Measure Angles Using a Theodolite - Part 2 Taking a measurement

How to Measure Angles Using a Theodolite

A theodolite is an instrument used commonly by builders and engineers to measure precise angles, which is necessary for large scale construction projects. A basic modern optical theodolite typically consists of a small telescope which is connected to two angle measuring mechanisms, one for measuring horizontal angles and one for measuring vertical angles. It sits atop a rotatable base with a leveling mechanism on a tripod. Once the theodolite is set up, the telescope is turned to spot the desired point and then the angle from the point that the theodolite is placed to the point spotted in its telescope can be read through the eyepiece of the scope.

Taking a measurement

Step 1

Unlock the upper horizontal clamp, and rotate the theodolite until the arrow in the rough sights is lined up with the point you wish to measure, then lock the clamp. Use the upper horizontal adjuster (not the clamp) to align the object between the two vertical lights in the sight.

Step 2

Look through the small eyepiece, and using the fine adjustment knob to get a precise horizontal line up with your object. The degrees from your reference are measured on the horizontal degree scale, the minutes and seconds on the fine adjustment scale (ex. 30 degrees 10'30").

Step 3

Unlock the vertical clamp and look through the sight while moving the theodolite up and down to find the precise spot vertically on your object that you'd like to measure. Lock the clamp and use the fine vertical adjustment knob to get a precise fix on the point you've chosen. Then look through the small eyepiece and read off the degrees, minutes and seconds from the vertical scale and the fine adjustment scale as you did for the horizontal scale. If your object is up high you'll need to do a rough horizontal adjustment first, then do the vertical measurement, then readjust for the final horizontal measurement. These two coordinates give the exact angle between your reference and your point of interest, but you can also measure the angle between two points by comparing their two measurements, or by setting the first point as the reference.

How to Measure Angles Using a Theodolite Part 1 - Setting up the theodolite

How to Measure Angles Using a Theodolite

A theodolite is an instrument used commonly by builders and engineers to measure precise angles, which is necessary for large scale construction projects. A basic modern optical theodolite typically consists of a small telescope which is connected to two angle measuring mechanisms, one for measuring horizontal angles and one for measuring vertical angles. It sits atop a rotatable base with a leveling mechanism on a tripod. Once the theodolite is set up, the telescope is turned to spot the desired point and then the angle from the point that the theodolite is placed to the point spotted in its telescope can be read through the eyepiece of the scope.

Setting up the theodolite

Step 1

Find a patch of firm level ground with a good view of what you wish to spot.

Step 2

Extend the legs of the tripod so that the theodolite will be at a comfortable level for you to use, splay them as far as they will go (most theodolite tripods will have a mechanism that will lock them when they reach their maximum separation and extension), and stick the ends of the legs into the earth as much as you can.

Step 3

Adjust the three leveling screws on the base of the theodolite so that it is level. The spherical spirit level mounted on the theodolite will give you an idea of when it is roughly level.

Step 4

Align the long spirit level with two of the three screws and readjust with those two screws to achieve a more accurate level on that axis. Then turn the theodolite 90 degrees on its base and adjust again using the third screw.

Step 5

Release the two horizontal adjuster clamps (usually large knobs on either side of the theodolite, slightly vertically offset).

Step 6

Align the upper part of the theodolite with the mark on the ring between the two sides which are connected to the horizontal clamps, then lock the upper clamp.

Step 7

Open the mirror light source on the side of the theodolite, and look through the small eyepiece. You will see three scales: horizontal, vertical, and fine adjustment. Use the fine adjustment knob on the upper part of the theodolite to align the mark with 0'00" (0 minutes and 0 seconds of arc).

Step 8

Align the long spirit level with two of the three screws and readjust with those two screws to achieve a more accurate level on that axis. Then turn the theodolite 90 degrees on its base and adjust again using the third screw.

Step 9

Release the two horizontal adjuster clamps (usually large knobs on either side of the theodolite, slightly vertically offset).

Step 10

Align the upper part of the theodolite with the mark on the ring between the two sides which are connected to the horizontal clamps, then lock the upper clamp.

Step 11

Open the mirror light source on the side of the theodolite, and look through the small eyepiece. You will see three scales: horizontal, vertical, and fine adjustment. Use the fine adjustment knob on the upper part of the theodolite to align the mark with 0'00" (0 minutes and 0 seconds of arc).

HOW TO USE A SURVEYOR'S THEODOLITE

A surveyor's theodolite is used to measure horizontal and vertical angles. These measurements are used to plot boundary lines, building foundations and utility routing. A theodolite measures distance manually by chains of standardized length or metal measuring tapes along the length of the desired angle. Land-surveying students use a theodolite as a way to learn the principles of angle measurement. Surveying on the job requires the use of more-advanced surveying instruments.

Drive a surveyor's nail into the ground at the point where you want to set up the theodolite. Angles will be measured from this point, as will distances.

Set up the tripod legs, taking care to set the height where the instrument sight will be at a comfortable eye level. Be certain to check that the hole in the center of the mounting plate is located over the nail. Press each leg into the ground by stepping on the bracket at the bottom of each leg.

Fine-tune the position of the legs so that the mounting plate on the top of the tripod is as eye-level as possible.

Remove the theodolite from the case. Most theodolites have a sturdy handle on top. This is the best place to lift the instrument. Gently place the instrument on the mounting plate and screw in the mounting knob beneath the instrument.

Adjust the theodolite to level by adjusting the tripod legs, using the bull's-eye level. Fine-tune the adjustment with the leveling knobs on the instrument.

Adjust the small sight, called the vertical plummet, at the bottom of the theodolite. This sight allows you to make certain the instrument is centered directly over the nail. Fine-tune the vertical plummet by adjusting the knobs on the bottom of the theodolite.

Look through the main scope and aim the crosshairs at the point to be measured. Twist the locking knobs to hold the theodolite in position on the exact point. View the horizontal and vertical angles in the viewing scope on the side of the instrument.

Tip

To fully understand the use of surveying instruments, take a course from a licensed surveyor. The hands-on experience is invaluable in understanding the more abstract concepts associated with mathematics and instrument operation.

Warning

Use care when transporting and operating the theodolite. These precise measuring devices are very sensitive, and they are expensive to repair if damaged.