Adjustment of a Closed

Compass Traverse
Fundamentals of Surveying

-EMLPB
Compass Traverse
• The adjustment of a closed compass traverse is similar to the adjustment of an open compass traverse except
that in a closed traverse the effects of observational errors are considered. The following are the three
important steps performed during the adjustment: (a) computing and adjusting the interior angles, (b)
selecting the best line or the line in the traverse which is unaffected by local attraction, and (c) adjusting the
observed bearings of successive lines.
Sources of Error in Compass Work
1. Bent Needle – when a magnetic compass with a bent needle is used, all observed bearings will have a
constant error.
2. Bent Pivot – a variable systematic error is introduced when a magnetic compass has bent pivot.
3. Sluggish Needle – when the magnetism of the needle is weak it tends to lag and move.
4. Plane of Sight Not Vertical – when observing the direction of a line, the line of sight may be steeply
inclined if the sight vanes are bent.
5. Electrically Charged Compass Box – the glass cover of the compass box becomes slightly charged with
electricity when it’s surface is rubbed.
6. Local Attraction – the correct pointing of the magnetic needle toward magnetic north is usually affected by
different forms of local attraction such as power transmission lines items made of iron or steel, underground
or deposits, and etc.
7. Magnetic Variations – systematic errors in compass surveys are caused by daily, annual, secular or
irregular variation in magnetic declination.
8. Errors in reading the needle – usually the source of most accidental errors in compass work is due to the
observer inability determine exactly the point on the graduated circle where the needle comes to rest.
Compass Traverse
Sample Problem 1
The following are observed bearings of a closed compassed traverse. Compute the interior angles and correct
them for observational errors. Assuming the observed bearing of line AB (“best line”) to be correct, adjust the
bearings of remaining sides.
Compass Traverse
Compass Traverse
The Engineers Transit
The invention of the first transit has been credited to Roemer, a Danish astronomer, who in 1690 used the
instrument to observed the passage of stars across the celestial meridian.
The Engineers Transit
Main Parts of the Transit
1. Upper Plate – which also called alidade, consist of the entire top of the transit. As a unit, the entire assembly
rotates about a vertical axis.
2. Lower Plate – the lower plate or horizontal circle is the scale with which horizontal angles are measured. It
is graduated on its upper face and divided around its circumference into 360°.
3. Leveling Head Assembly – consist of a bottom horizontal foot plate, four leveling screws, and the plumb bob
chain.
Measuring Angles
The most common operation performed with the engineer’s transit is the measurement of a horizontal angle.
It consists of setting up and leveling the transit over a selected point, taking a back sight on a point, and turning
the telescope through an angle to foresight another point.

Closing the Horizon

The process of measuring horizontal angles about a point is termed closing the horizon.
Measuring Angles
Measuring Vertical Angles – vertical angles are either angles of elevation or an angle of depression. These
angles are sometimes referred to as positive or negative angles.

′
(∝𝑁 +∝𝑅 )
∝=
2
Where:
∝′ = 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
∝𝑁 = 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡𝑒𝑙𝑒𝑠𝑐𝑜𝑝𝑒 𝑖𝑛 𝑑𝑖𝑟𝑒𝑐𝑡 𝑜𝑟 𝑛𝑜𝑟𝑚𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
∝𝑅 = 𝑠𝑎𝑚𝑒 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡𝑒𝑙𝑒𝑠𝑐𝑜𝑝𝑒 𝑖𝑛 𝑟𝑒𝑣𝑒𝑟𝑠𝑒𝑑 𝑜𝑟 𝑝𝑙𝑢𝑛𝑔𝑒𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
Measuring Angles
Index Correction – when a transit is used the accuracy in reading a vertical angle is affected if the line of sight
is not parallel to the axis of the telescope level tube, there is an inclination of the vertical axis, and the verticsl
circle does not read zero when telescope bubble is centered.
𝐼𝐶 = −𝐼𝐸 (index correction)
Where:
(∝𝑁 −∝𝑅 )
𝐼𝐸 = 2
(index error)
∝′ =∝𝑁 ± 𝐼𝐶 (corrected vertical angle)
Sample Problem 2
The horizontal angles about point A were measured as follows: 𝜃1 = 44°14′ , 𝜃2 = 58°59′ , 𝑎𝑛𝑑 𝜃3 =
256°50′ . Determine the horizon misclosure and adjust the measured angles by assuming that the error is the
same for each angle.
Sample Problem 3
A vertical angle was measured above the horizontal as 23°16′ with the telescope in direct position and as
23°18′in reversed position. Determine the following: index error, index correction, and the corrected vertical
angle.
Sample Problem 4
In Problem No 3, determine the same quantities assuming this time the vertical angle was measured below the
horizontal.
Measuring Angles
Sample Problem 2
The horizontal angles about point A were measured as follows: 𝜃1 = 44°14′ , 𝜃2 = 58°59′ , 𝑎𝑛𝑑 𝜃3 =
256°50′ . Determine the horizon misclosure and adjust the measured angles by assuming that the error is the
same for each angle.
Measuring Angles
Sample Problem 3
A vertical angle was measured above the horizontal as 23°16′ with the telescope in direct position and as
23°18′in reversed position. Determine the following: index error, index correction, and the corrected vertical
angle.
Measuring Angles
Sample Problem 4
In Problem No 3, determine the same quantities assuming this time the vertical angle was measured below the
horizontal.
Traversing and Traverse Computations
Interior Angle Traverse
The interior angle traverse is used principally in land surveying. The angles formed between the adjacent sides
of the illustrated closed figure are known as interior angles. These are the angles at stations A, B, C, D, E, and
F.
Deflection Angle Traverse
Is used frequently for the location of roads, railroads, pipelines, transmission lines, canals and other similar
types of survey.
Traversing and Traverse Computations
Sample Problem 5
The interior angles of a five sided closed traverse were measured as follows:
a. 118°30′ c. Not Measured e. 140°50′
b. 95°33′ d. 134°10′
If all observed angles are assumed to be correct, determine the interior angle at C. Also, determine the bearing
of each line if the bearing of line AB is 𝑁15°30′ 𝐸.
Traversing and Traverse Computations
Sample Problem 5
The interior angles of a five sided closed traverse were measured as follows:
a. 118°30′ c. Not Measured e. 140°50′
b. 95°33′ d. 134°10′
If all observed angles are assumed to be correct, determine the interior angle at C. Also, determine the bearing
of each line if the bearing of line AB is 𝑁15°30′ 𝐸.
Traversing and Traverse Computations
Sample Problem 6
Following are the observed deflection angles of a closed traverse:
𝐴 = 28°25′ 00" (𝐿) 𝐸 = 108°13′ 30“(L)
𝐵 = 68°03′ 30" (𝐿) 𝐹 = 16°50′ 00" (𝑅)
𝐶 = 120°34′ 00" (𝐿) 𝐺 = 110°00′ 30"(𝐿)
𝐷 = 58°30′ 00" (𝑅)
Traversing and Traverse Computations
Sample Problem 6
Following are the observed deflection angles of a closed traverse:
𝐴 = 28°25′ 00" (𝐿) 𝐸 = 108°13′ 30“(L)
𝐵 = 68°03′ 30" (𝐿) 𝐹 = 16°50′ 00" (𝑅)
𝐶 = 120°34′ 00" (𝐿) 𝐺 = 110°00′ 30"(𝐿)
𝐷 = 58°30′ 00" (𝑅)
Traversing and Traverse Computations
Sample Problem 6
Following are the observed deflection angles of a closed traverse:
𝐴 = 28°25′ 00" (𝐿) 𝐸 = 108°13′ 30“(L)
𝐵 = 68°03′ 30" (𝐿) 𝐹 = 16°50′ 00" (𝑅)
𝐶 = 120°34′ 00" (𝐿) 𝐺 = 110°00′ 30"(𝐿)
𝐷 = 58°30′ 00" (𝑅)
Traversing and Traverse Computations
Angle to the Right Traverse – is employed when numerous details are to be located from the traverse stations.

Azimuth Traverse – one of the quickest and most satisfactory method where at one setup of the transit or
theodolite several angles or directions can be determined.
Traversing and Traverse Computations
Sample Problem 7
A five – sided closed traverse proceeds in a clockwise direction and the angle to the right at each station were
observed as follows:
∝𝑎 = 240°30′
∝𝑏 = 238°15′
∝𝑐 = 289°53′
∝𝑑 = 220°04′
∝𝑒 = 271°13′
𝑛=5

Determine the error of

closure and adjust the
observed values on the
assumption that the
error is the same for
each angle.
Traversing and Traverse Computations
Traversing and Traverse Computations
Traversing and Traverse Computations
Sample Problem 8
Given the accompanying tabulation are observed data for a closed traverse. Determine the bearing and azimuth
from north of all traverse lines, and the angle to the right at each station.
Traversing and Traverse Computations
Traversing and Traverse Computations
Traversing and Traverse Computations
Traversing and Traverse Computations