north carolina property mappers association advanced mapping … · 2015-08-04 · position. the...

NCPMA ADVANCED MAPPING

5-1

NORTH CAROLINA PROPERTY MAPPERS ASSOCIATION

ADVANCED MAPPING

SECTION 5B

ANGULAR MEASURES


5-2

5B.1 Angles

Determining the location of points and orientations of property lines frequently depends on

measurements of angles and direction. In mapping, directions are given by bearings and

sometimes by azimuths.

Angles measured in mapping are classified as horizontal. Horizontal angles are the basic

measurements needed for determining bearings and azimuths. They are most often directly

measured in the field by a total station, theodolite or transit. Many years ago early surveyors

used a hand held compass to measure angles.

A purely arbitrary unit defines the value of an angle. The sexagesimal system used in the

United States and many other countries is based on degrees, minutes, and seconds. In Europe

the grad or gon is a standard unit based upon the metric system.

The degree is defined as 1/360 of a circle. One degree (1) equals 60 minutes, and 1 minute

equals 60 seconds. Divisions of seconds are given in tenths, hundredths, and thousandths.

The kinds of horizontal angles most commonly measured in surveying are (1) interior angles,

(2) angles to the right, and deflection angles.

Interior angles, shown in Figure 5B-1, are measured on the inside of a closed polygon. The

angle at each apex within a polygon is measured. A check can be made on their values

because the sum of all angles in any polygon must equal (n-2) 180, where n is the number of

angles.

Figure 5B-1

Interior angles

N


5-3

Exterior angles, located outside a closed polygon, are explements of interior angles. See

Figure 5B-2. The advantage to be gained by measuring them is their use as another check,

since the sum of the interior and exterior angles at any station must total 360.

Figure 5B-2

228°

210°

279°

310°

233°

E

A

D

C

B


5-4

Angles to the right are measured clockwise from the rear to the forward station. See Figure

5B-3.

Figure 5B-3

Angles to the left, turned counter clockwise from the rear station.


5-5

Deflection angles are measured from an extension of the back line, to the forward station.

They are used principally on the long linear alignments of route surveys. Deflection angles

may be measured to the right (clockwise) or to the left (counterclockwise). Clockwise angles

are considered plus, and counterclockwise ones minus. Deflection angles are always smaller

than 180, and the direction of turning is identified by appending on R or L to the numerical

value. See Figure 5B-4.

Figure 5B-4

Deflection angles.


5-6

The three basic requirements to determine an angle are (1) reference or starting line, (2)

direction of turning, and (3) angular distance, see Figure 5B-5.

Figure 5B-5

Basic requirements in determining an angle.

5B.2 Direction of a Line

The direction of a line is the horizontal angle between it and an arbitrarily chosen reference

line called a meridian. The most common meridian used is an astronomic (often referred to

as geodetic or true) meridian. At any point, it is the north-south reference line that passes

through the earth's geographic poles.

A magnetic meridian is defined by a freely suspended magnetic needle that is influenced by

the earth's magnetic field only. As stated earlier, hand held compasses were used extensively

for early boundary surveys in the United States. The resulting property descriptions, many of

which the mapper encounters today, were given in terms of magnetic directions.

A compass consists of a magnetized steel needle mounted on as pivot at the center of a

graduated circle. Unless disturbed by a local attraction, such as metallic objects and direct

current electricity, the needle aligns itself with the earth's magnetic field and points toward

magnetic north (in the Northern Hemisphere). In 1990, the north magnetic pole was located

at approximately 77 north latitude, 102 west longitude. It is constantly moving.


5-7

The earth's magnetic forces align the needle and pull or dip one end of it below the horizontal

position. The angle of dip varies from 0 near the equator to 90 at the magnetic poles. In

the Northern Hemisphere, the south end of the needle is weighted with a very small coil of

wire to balance the dip effect and keep it horizontal. The position of the coil can be adjusted

to conform to the latitude in which the compass is used.

As a compass is turned, the needle continues to point toward magnetic north and gives a

reading that is dependant on the graduated circle position.

5B-3 Azimuths

Azimuths are horizontal angles measured clockwise from any reference meridian. In plane

and boundary surveys azimuths are measured from north.

Azimuths range from 0 to 360 in value, and they do not require letters to identify the

quadrant. Thus, the azimuth of OA, as shown in Figure 3-14, is 65; OB, 145; OC, 205,

OD 300° they may be true, magnetic, or grid depending on the reference meridian used.

Figure 5B-6

Azimuths.


5-8

5B.4 Bearings

Bearings represent one system for designating directions of lines. The bearing angle of a line

is defined as the acute horizontal angle between a reference meridian and the line. The angle

is measured from either the north or south toward the east or west, to give a reading smaller

than 90. The proper quadrant is shown by the letter N or S preceding the angle, and E or W

following it. Thus, a properly expressed bearing includes quadrant letters and an angular

value. An example is N 80 E:

In Figure 5-13 all bearings in quadrant N0E are measured clockwise from the meridian.

Thus, the bearing of line OA is N 70 E. All bearings in quadrant SOE are counterclockwise

from the meridian, so OB is S 35 E. Similarly, the bearing of OC is S 55 W and that of

OD, N 30 W.

Figure 5B-7


5-9

True bearings are measured from true meridian, magnetic bearings from the local magnetic

meridian, and grid bearings from the appropriate grid meridian. Magnetic bearings can be

obtained in the field, by the surveyor, by observing the magnetic needle of a compass, and

used along with measured angles to get computed bearings.

Comparison of Bearings and Azimuths

Bearings Azimuths

1. Vary from 0 to 90 Vary from 0 to 360

2. Require two letters and a numerical value Require only a numerical value

3. May be true, magnetic or grid, forward or back same as bearings

4. Are measured clockwise and counterclockwise Are measured clockwise only

5. Are measured from North and South Are measured from North only

Example direction for lines in the four quadrants (azimuths are from North):

N 54 E 54

S 68 E 112 (180 - 68)

S 51 W 231 (180 + 51)

N 15 W 345 (360 - 15)

5B.3 Magnetic Declination

Magnetic declination is the horizontal angle from the true geographic meridian to the

magnetic meridian. An east declination exists if the magnetic meridian is east of true north; a

west declination occurs if it is west of true north.

Because the magnetic pole positions are constantly changing, magnetic declinations at all

locations also undergo continual changes.

A chart showing magnetic declinations for a specific epoch of time is called an isogonic map.

Lines on such maps connect points that have the same declination are called isogonic lines.

The line made up of points that have zero declination is termed the agonic line. On it the

magnetic needle defines true north as well as magnetic north.

Figure 5B-6 is an isogonic map covering the contiguous 48 states of the United States for the

year 1990. The agonic line (heavy solid line) cuts diagonally across the country through

Wisconsin, Illinois, Kentucky, Tennessee, Alabama, and northwest Florida. It is gradually

moving westward. Points to the west of the agonic line have east declinations; points to the

east have west declinations. The annual change is shown on the left and right side of the

figure. They aid in estimating the declination a few years before and after a chart is made.


5-10

For example, Cleveland, Ohio, had a magnetic declination of about 7 W in 1990, and an

average annual change of approximately of 5.5' westerly. Thus, Cleveland's estimated

declination in 1995 is 7 W 5 x 5.5' = 7 28' W.

Figure 5B-8

Isogonic chart showing distribution of magnetic declination (solid lines) and annual

change (dashed lines) in the United States in 1990. (Courtesy U.S. Geological Survey.)

In retracing old property lines run by compass or based on the magnetic meridian, it is

necessary to allow for the difference in magnetic declination at the time of the original survey

and at the present date.

Surveys based on a state or other plane coordinate system employ a grid meridian for

reference. Grid north is the direction of true north for a selected central meridian, and held

parallel to it over the entire area covered by a plane coordinate system.


5-11

Review Exercises

Section 5B

Exercise 5B-1

A property line X-Y is drawn at a bearing of N 30° W. it is followed by another line Y-Z

drawn at a bearing of N 72 ° 30’ W. What is the deflection angle to the left?

Exercise 5B-2

A property line A-B is drawn at a bearing of N 25° 30’ E. It is followed by another line B-C

drawn at a bearing of S 42° 30’ E. What is the deflection angle to the right?


5-12

Exercise 5B-3

Assume the magnetic bearing of line AB in 1878 was N26° 15’E. The declination at the time

and place was 7° 15’ W. In 1999 the declination was 4° 30’ E. What is the magnetic bearing

in 1999?

Exercise 5B-4

The magnetic bearing of line XY in 1925 was N 46° 28’E when the declination was 3°

30’ W. The declination now is 1° 45’ E. What magnetic bearing should a surveyor be using

to retrace XY.


5-13

Exercise 5B-5

The magnetic bearing of a property line X-Y in 1917 is S 78° 30’ E. The magnetic

declination for that time and location was 6° 45’ W. What is the True bearing of property

line X-Y?

Exercise 5B-6

The magnetic bearing of a property line A-B in 1865 is N 10° 15’ E. The declination is 5°

15’ East for that year and location. What is the true bearing of line A-B?


5-14

Exercise 5B-7

A property line is established in 1925 with a magnetic bearing of N 46° 28’ E. The magnetic

declination at that time is 3° 30’ W. What is the true bearing of the property line? What is

the magnetic bearing today if the declination is 2° 15’E?

Exercise 5B-8

Convert the following azimuths to a bearing:

Azimuth 302° 30’ equals a bearing of:

Azimuth 140° 15’ equals a bearing of:


5-15

Exercise 5B-9

Plot the following description:

Begin at point A; thence with an azimuth of 52, 230' to point B; thence with a deflection

angle to the right of 28, 395' to point C; thence S20W, 500' to point D; thence on an

azimuth of 280, 280' to point E; thence with a deflection angle to the left of 35, 150' to

point F; thence N2E 275' to the point of beginning.

Note: Plot at 1”=100’

A


5-16

Exercise 5B-10

Plot the following description at 1”=200’:

A tract located in the Town of Marlow, Ninth Civil District of Franklin County, Tennessee,

to-wit:

Beginning on the north bank of Lick Creek, the S.E., corner of this tract, a former elm on the

North bank of the creek a short distance above the Indian Camp; running thence N 11° 30’E

19.7 poles to a stake; thence N 4° 30’ W 12 rods to a stake in ravine; thence up said ravine N

20° W 10.25 poles, N 34° 18 poles; N 65° W 14.5 poles to a down beech and the south

boundary of a 830 acre grant; thence North 87° West 13.75 chains along a marked line of

stones to a stake in the center of the gully; thence down the gully; mostly S 3° E., to a stake;

thence S 84° 30’ E 860 feet to a dogwood tree; thence S 63° 30’ E 7 chains to the elm on

Lick Creek and the point of beginning, containing by estimation 24 acres, more or less.


5-17

Solutions

Solution 5B-1

Solution 5B-2


5-18

Solution 5B-3

Assume the magnetic bearing of line AB in 1878 was N26° 15’E. The declination at the time

and place was 7° 15’ W. In 1999 the declination was 4° 30’ E. What is the magnetic bearing

in 1999?


5-19

Solution 5B-4

The magnetic bearing of line XY in 1925 was N 46° 28’E when the declination was 3°

30’ W. The declination now is 1° 45’ E. What magnetic bearing should a surveyor be using

to retrace XY.


5-20

Solution 5B-5

The magnetic bearing of a property line X-Y in 1917 is S 78° 30’ E. The magnetic

declination for that time and location was 6° 45’ W. What is the True bearing of property

line X-Y?


5-21

Solution 5B-6

The magnetic bearing of a property line A-B in 1865 is N 10° 15’ E. The declination is 5°

15’ East for that year and location. What is the true bearing of line A-B?


5-22

Solution 5B-7

A property line is established in 1925 with a magnetic bearing of N 46° 28’ E. The magnetic

declination at that time is 3° 30’ W. What is the true bearing of the property line? What is

the magnetic bearing today if the declination is 2° 15’E?


5-23

Solution 5B-8


5-24

Solution 5B-9

Plot the following description:

Begin at point A; thence with an azimuth of 52, 230' to point B; thence with a deflection angle to the right of

28, 395' to point C; thence S20W, 500' to point D; thence on an azimuth of 280, 280' to point E; thence with

a deflection angle to the left of 35, 150' to point F; thence N2E 275' to the point of beginning.

Note: Plot at 1”=100’


5-25

Solution 5B-10

Plot the following description at 1”=200’: A tract located in the Town of Marlow, Ninth Civil District of Franklin County, Tennessee, to-wit: Beginning on the north bank of Lick Creek, the S.E., corner of this tract, a former elm on the North bank of the creek a short distance above the Indian Camp; running thence N 11° 30’E 19.7 poles to a stake; thence N 4° 30’ W 12 rods to a stake in ravine; thence up said ravine N 20° W 10.25 poles, N 34° 18 poles; N 65° W 14.5 poles to a down beech and the south boundary of a 830 acre grant; thence North 87° West 13.75 chains along a marked line of stones to a stake in the center of the gully; thence down the gully; mostly S 3° E., to a stake; thence S 84° 30’ E 860 feet to a dogwood tree; thence S 63° 30’ E 7 chains to the elm on Lick Creek and the point of beginning, containing by estimation 24 acres, more or less.

north carolina property mappers association advanced mapping … · 2015-08-04 · position. the...

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