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Infinite Intelligence Intelligence GELER

Cartography Module

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PART I CARTOGRAPHY

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Cartography

I.

Conversion II.

Scales

III. Cadastral Map Number/ Sectional Map Number IV. Photogrammetry V.

Summary of Traverse Computation/ Area Computation VI. Plotting VII. Mine surveying VIII. Conversion Conversion of Units IX. Map projections/ Map sizes X.

Other terms and concepts


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Cartography

I.

Conversion II.

Scales

III. Cadastral Map Number/ Sectional Map Number IV. Photogrammetry V.

Summary of Traverse Computation/ Area Computation VI. Plotting VII. Mine surveying VIII. Conversion Conversion of Units IX. Map projections/ Map sizes X.

Other terms and concepts


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I. Conversion: Geographic to Grid Coordinates, ( , ) to (N, E) 1. Grid to Geographic Coordinates, (N, E) to ( , )

II. Scales (Map, Photo, Ground Distance) III. Cadastral Map Number/ Sectional Map Number IV. Photogrammetry 1. Terms 2. Scale determination of vertical vertical photos (flying ht., focal length, scale factor) 3. Relief displacement 4. Parallax formula 5. Flight plan 6. Angular field of view view

V. Summary of Traverse Computation/ Area Computation VI. Plotting 1. 2. 3. 4.

Map symbols Elements of of BL form Rules on map name placement/ Lettering/ Drafting Map symbols Survey symbols

VII. Mining Surveying VIII. Conversion of units IX. Map Projections/ Map sizes X. Other terms and concepts (G.E. Manual and other books) Additional:  Remote sensing  Subdivision  Solar observation  Conversion from PRS 92 to WGS 84 ( Found in GE Manual)


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CONVERSION FROM GEOGRAPHIC TO GRID COORDINATES AND FROM GRID TO GEOGRAPHIC COORDINATES Lecture notes:

I.

PTM (Philippine Transverse Mercator) Grid System = national coordinate system adopted by the Philippines to give definite location of a ground point (whether it is a lot corner, traverse point, control point, etc.) that is unique and most suitable to the locality of the Philippines.

Why so?



Most of the land surveys in the past are less reliable because it was referred to location monuments that have no geodetic positions and adjustments to basic control network.



Also these location monuments were established by means of solar observations that in turn were regarded to as being inaccurate due to variations of degree of precision.

That’s why… PTM Grid was adopted from the Universal Transverse Mercator (UTM) to: 1) give coordinates suitable to our locality 2) made our maps to be cross-referenced conveniently and efficiently efficientl y to other countries also adopting UTM such as Australia, Germany, several states in US, etc. PTM grid system adopted from the UTM Grid System for latitude 4  to 22  and longitude 117  to 125 . II.

CHARACTERISTICS OF PTM

1) 2) 3) 4)

Spheroid: Clarke’s Spheroid of 1866 Projection: Transverse Mercator in zones of 2  net width Scale factor at central meridian: 0.99995 Point of origin: intersection of equator and the central meridian of each zone N=0; E=500,000 m


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III.

IV.

ZONES Zone No.

Central Meridian

Extent of Zone

I

117

11600 to 118 30

II

119

11730 to 120 30

III

121

11930 to 122 30

IV

123

12130 to 124 30

V

125

12330 to 127 00

FORMULAS A. Geographic to Grid N = I + IIp 2 + IIIp 4 3

5

E = IVp + Vp + VIp + 500,000

Where; p = 0.0001 ( ”) = longitude of place – place – longitude longitude of CM (in seconds) B. Grid to Geographic = ’ – (-VIIIq – (-VIIIq 2 + VII)q 2 = ’ + (VIIIq 4 – VIIq – VIIq2)

In seconds; not in degrees = longitude of CM +

”

where; = IXq – IXq – Xq Xq3 – XIq – XIq5 (E – 500,000) 500,000) q = 0.000001 (E –

Remember that : I, II, III, IV, V, VI, VII, VIII, IX, X, XI are either given or determined using the table


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Infinite Intelligence GELER

Cartography Module

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SCALES

Definition:

S cale is the ratio between the distance on the map (or other medium like aerial photo, sketch, etc.) to which the distance on the ground was drawn. On a map, scale is shown numerically and graphically: 1. Numerical a. Representative fraction --------- 1:25000; 1/25000 b. Equivalent scale ----------------- 1in=200ft; 1cm=300m 1 inch on the map represents some whole number of feet on the ground 2. Graphical Scale – is a line subdivided into map distances corresponding to convenient unit of lengths on the ground. Example:

0

50

100

200

500

Remember that: In maps, graphical scale is more reliable and accurate than numeric scale especially over a period of time. This is because graphical scale adopts to the same distortion as the map due to wear and tear.

FORMULA: Dg = Sm(dm) = Sp(dp) Where; Dg = distance on the ground Sp, Sm = Scale factor Dm = Map distance Dp = Photo distance

SAMPLE PROBLEMS:

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CADASTRAL MAP NUMBER AND SECTIONAL MAP NUMBER

A. Cadastral Map Number I.

Definition: Cadastral Map – comprise area within spheriodal quadrangle  Quadrangle has 1 minute of an arc of latitude and 1 minute if an arc of longitude  PPCS; scale of 1:4000  Stable base of uniform size 54cm x 54cm

II.

Spheroidal Quadrangle

1’ = 60” 1”=31m - Northing - Length of 1’ meridian - Lat

1’ = 60” 1” = 30m - Easting - length of 1’ of parallel - Dep Note: Unless no dimensions given for length of 1’ meridian and parallel, use 1”=31m for Lat; 1”=30m for Dep.

III.

Area of each Cadastral Map Length of 1’ meridian = 60(31) = 1860m Length of 1’ parallel = 60(30) = 1800m Dimension: 1860m x 1800m Area: 334.8 has


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IV. Determination of Cadastral Map Number Rule/Convention:  the southwest corner element of the area  south parallel; west meridian  always in the form of degrees-minutes only!!! Example: 1) CM No. 12°10’ N, 123°17’ E

2) CM No. 12°10’3.15” N, 124°15’7.2” E

CM No. 12°10’ N, 124°15’ E


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3)

2

A

1

C

CM No. 10°26’3.11” N 122°18’6.7” E

D

3

B

4

From the given CM, determine the following: a) CM No. of A = (10°26’+1’)N, 122°18’E = 10°27’N, 122°18’E b) CM No. of B = (10°26’ -1’)N, 122°18’E = 10°25’N, 122°18’E c) CM No. of C = 10°26’N, (122°18’ -1’)E = 10°26’N, 122°17’E d) CM No. of D = 10°26’N, (122°18’+1’)E = 10°26’N, 122°19’E For CM No. of:

1 : 10°27’N, 122°19’E 2 : 10°27’N, 122°17’E 3 : 10°25’N, 122°17’E 4 : 10°25’N, 122°19’E


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V. Sectional Map Number From the cadastral map of A, with Cm No. 10°27’N, 122°18’E; determine the sectional map no. of: 2

1

3

3

5

6

Solution: clockwise in numbering / labeling of the sections Sec1

Sec2

A

B

NW

NE

1

2

Sec4

Sec3

C

D

SW

SE

3

4

1 = CM No. 10°27’N, 122°18’E sec.1 2 = CM No. 10°27’N, 122°18’E sec.1 -B-NE 3 = CM No. 10°27’N, 122°18’E sec.2 -C 4 = CM No. 10°27’N, 122°18’E sec.3-B-SW 5 = CM No. 10°27’N, 122°18’E sec.3 -D 6 = CM No. 10°27’N, 122°18’E sec.4 -C-SW-2


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PHOTOGRAMMETRY I. Definition: involves obtaining information about an object indirectly, by measuring photographs taken of the object. : the science and art of obtaining reliable measurements by means of photography

Categories of Photogrammetry

1. Metrical Photogrammetry – involves all quantitative works, such as determination of ground positions, distances, differences in elevation, areas and volumes 2. Interpretative Photogrammetry – involves photo-interpretation; photographs are analyzed qualitatively for identifying objects and assessing their significance. - relies on the human ability to assimilate and correlate such photographic elements as sizes, shapes, patterns, tones, textures, colors, contrast and relative location. According to type of photograph used:

1. Ground or terrestrial photogrammetry – uses photographs taken from fixed, often known points on or near the ground with the optical axis of the camera horizontal (PHOTOTHEODOLITE) 2. Aerial Photogrammetry – a high precision camera is mounted in an aircraft and photographs are taken in an organized manner as the aircraft flies over the terrain. 3. Space Photogrammetry – deals with extra-terrestrial photogrammetry and imagery where the camera may be fixed on earth, contain on board a satellite, or placed on a planet 4. Close-range Photogrammetry – involves a camera relatively close to the objects photographs According to manner of use:

1. Monophotogrammetry – uses one photo 2. Composite – uses several photographs that are joined together (should be overlapping)

Kinds of photographs

1. Vertical photographs – photographs taken where the optical axis of the camera is pointing vertically downward - nearly vertical 2. Tilted photos – tilt<= 30 No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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3. Oblique photos – photos taken such that the optical axis of camera is deviated from the vertical a. low oblique – low angle deviation from the vertical; does not include apparent horizon b. high oblique – high angle deviation from the vertical; includes apparent horizon 4. Horizontal photographs – those which are taken with the optical axis of the camera horizontal Depending on type of camera:

1. narrow angle 2. normal angle 3. wide angle 4. superwide angle

< 60 0 60 0 to 750 75 0 to 1000 >100 0

II. Scale Determination of Vertical Aerial Photographs negative plane

c'

b' d'

a’ θ

f

O c

b positive plane

f

d

a

Hm

e

Hmsl C B P A

ground plane

D

datum plane

Where; No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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O = optical axis f = focal length of camera a’, b’, c’ and d’ = images of any two ground points in the same horizontal plane of the photograph A, B, C and D = corresponding ground points of the image Hmsl = height above mean sea level H, Hmge = flying height above mean ground elev Ground plane = mean ground level whose elevation is (mge) mean ground elevation. Θ = Angular field of view Scale:

1. S = ab / AB = map distance / ground distance = f / H 2. using f and H : H = SP(f) ; where H = flying height above mean ground elevation Sp = scale factor f = focal length

S = 1/ H/f If H msl is being asked : Hmsl = Hmge + mge

SAMPLE PROBLEMS

1. GE BRD: A vertical photo was obtained using an aerial camera having a focal length of 350mm. The average scale of photo is 1:2000. If the area photographed lies at an average height of 915 ft above sea level, determine the flying height above sea level when the photo was taken. Solution: Focal length = 350 mm = 0.35 m 0.3048 m mge = 915 ft x 278.89 m 1 ft Hmge = Sp (f) = 2000 (0.35) = 700 m Hmsl = Hmge + mge = 700 + 278.89 Hms = 978.89 m


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2. GE BRD July 2000: An aerial photogrammetry is undertaken at a flying height of 12000 ft above sea level. The camera has a focal length of 8 ¼ “. Determine the scale of the photograph taken on a plane which is 2000 ft above sea level. Solution: Hmge

= Hmsl – mge = 12,000 – 2000 = 1,000 ft H Since H = S pf, Sp = F 10,000 ft Sp = 8.25 in Sp = 14545.45

X

12 in 1 ft

Therefore, the scale of the photograph is 1:14545 3. A vertical photograph was taken using an aerial camera with focal length of 215 mm and the craft lies at an altitude of 1550 m above mean sea level. If the scale is 1:5000, what would be the average ground elevation of the area photographed? Solution: Hmge

= Sp f = (0.215) (5,000) = 1075 m Hmsl = Hmge + mge Mge = 1, 550 – 1075 = 475 m

4. Points A and B on the ground measures 2350 m. If the corresponding distance on the photograph of these two points is 21 cm, using an aerial camera having 150mm focal length. Determine the altitude of the craft above mean ground elevation? Solution: Dg = Sp Dp Dg Sp = Dp 2350 m = 0.21 m = 11,190 Hmge

= Sp f = 11,190 (0.15 m) = 1678.5 m


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5. The distance between two known points on a vertical photograph is 67.5 mm. On a map of scale 1:30000, the equivalent distance is 51.5 mm. The average scale of photograph is: Solution: Dg

= Sm Dm = 30,000 90.0515) = 1545 m

Dg = Sp Dp 1545 = Sp 0.0675 Sp = 22,889 Therefore the scale is 1:22,889

III. ANGULAR FIELD OF VIEW (refer to the figure shown above for the scale determination of aerial photographs) FORMULA:

tan ½ θ = d / 2 (1/f) = d / 2f tan ( θ / 2 ) = d / 2f θ / 2 = tan –1 (d / 2f) θ = 2 tan -1 ( d / 2f )

IV. RELIEF DISPLACEMENT – occurs when the object being photographed is not at the elevation of mean datum. This depends on the position of the point on the photograph and the elevation of the ground point above or below mean datum.


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O f a

b r'

p

r H

A h P B X

Where; d = displacement of the object image on the photograph due to relief r = radial distance from the principal point due to the displaced image point ( or you can treat as radial distance of the tip of the object ) h = height of the object photographed or the elevation above mean datum H = flying height above datum

FORMULA:

d = rh / H d = rh / H


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SAMPLE PROBLEMS

1. An image of a hill is 3.5 inches from the center of the photograph. The elevation of the hill is 2000 ft. and the flight altitude is 14000 ft with respect to the same datum level. How much is the image displaced because of the elevation of the hill? Solution:

rh H (3.5 in) 2,000 ft d= 14,000 ft d = 0.5 in

d=

x

1 ft 12 in


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V. The Parallax Formula

B f

O2

O1

b1’ a2 b2 a1’

a1 b1

H

B A HA

HB datum

Where in: o1a1 // o2a1’ and o 1b1 // o2b1’

Parallax differences between one point and another are caused by different elevations of the two points. Parallax of pt. A:

P A = BC/ (H-H A)

Equation 1

Parallax of pt. B:

P B = BC/(H-H B)

Equation 2


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Parallax difference between A and B:

∆P AB = PB – P A = [BC/(H-HB)] – [BC/(H-H A)] = {BC[(H-H A)-(H-HB)]} / [(H-H A)(H-HB)] ∆P AB = [BC(HB-H A)]/ [(H-H A)(H-HB)]

∆H AB = HB - H A From equation 1:

H – H A = BC / P A Therefore;

∆P AB = [(BC)(∆H AB)] / [(BC/P A)(H-HB)] also; ∆H AB = [∆P AB(H-HB)] / P A

VI. FLIGHT PLAN – a map on which flight lines are drawn for guiding purposes

Flig ht line – nominal line passing through the middle of successive photographs FORMULAS:

1. Flying height: Hmge = Sp(f) ; Sp = scale factor f = focal length 2. De = distance between exposures De = S(1 – f.o.) Where; De = airbase (B) S = Sp(format size) f.o. = forward overlap or end lap 3. Distance between flight lines, Df Df = S(1 – s.l.) Where; S = Sp(format size) s.l. = side lap No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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4. Number of exposures per FL(flight line) = longer dimension ___________________ B or De 5. Number of FL = _______________________ shorter dimension Df 6. total number of exposures = (# of exposure per FL) (# of FL) 7. flying height above mean sea level: Hmsl = Hmge + mge


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SUMMARY OF TRAVERSE COMPUTATIONS Balance the field angles

Sta. Occ.

Sta. Obs T1

Azimuth 28-00-00

T4

313-55-00

T3

215-00-00

T2

143-20-00

T X = T4

208-01-00

T4 T3 T2 T1

Solve for the Angular Error of Closure (AEC) AECTheoretical = 30” T ; T = number of stations = 30” 4 AEC = 0001’

1)

AEC Actual = Backsight – azimuth of last line = 208001’ - 28000’ AEC = 180 001’ I.

No. of groups (for application of correction)

AEC 1’ ----- + 1 ; ---- + 1 = 2 groups 1’

1st group

T1 –T2 T 2 – T3

2nd group T3 – T4 T4 – T1

T1 – T2 T2 – T3 T3 – T4 T4 – T1

143020’ 215000’ 313055’ 028000’

1st group = 0’ correction 2nd Group = 1’ correction

Compute the bearings &/or azimuths

Line T1 – T2 T2 – T3 T3 – T4 T4 – T1

Azimuth 143020’ 215000’ 313056’ 028001’

Distance 25.64 81.35 15.65 88.12

Bearing N 36-40 W N 35-00 E S 46-04 E S 28-01 W


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IV.

Compute for the linear error of closure & the accuracy ratio of the traverse (relative error)

Line

Azimuth

Distance

T1 – T2 T2 – T3 T3 – T4 T4 – T1

143020’ 215000’ 313056’ 028001’

25.64 81.35 15.65 88.12 P = 210.76





Linear Error of Closure : LE =  Lat2 - Dep2

Dep

+ 20.57 + 66.64 - 10.86 - 77.49 lat = -1.44

- 15.31 + 46.66 +11.27 - 41.39 Dep = +1.23

 (-1.44)2 + (1.23) 2 = 1.89

Relative Error :

Perimeter 1 : ---------LE V.

Latitude

210.76 1 : -------1.89

RE = 1 : 111.51 V.

Compute the balanced latitude ( y) & balanced departures ( x)

Compass Rule: Lat = Dep =

Lat :

Distance of line (elat) perimeter Distance of line (edep) perimeter

Dep :

T1 – T2 : 25.64 (1.44) = 0.175 210.76

25.64 (1.23) = 0.150 210.76

T2 – T3 : 81.35 (1.44) = 0.556 210.76

81.35 (1.23) = 0.475 210.76

T3 – T4 : 15.65 (1.44) = 0.107 210.76

15.65 (1.23) = 0.091 210.76

T4 – T1 : 88.12 (1.44) = 0.602 210.76  = 1.44

88.12 (1.23) = 0.514 210.76  = 1.23


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How to apply cor rection?  

If the error is “negative”, correction is “positive” and will be added algebraically. If the error is “positive”, correction is “negative” and will be added algebraically.

Clat : +0.175 +0.556 +0.107 +0.602

Clat : -0.150 -0.475 -0.091 -0.514

---------------------

----------------

+1.440 -1.440 error in latitude 0

- 1.23 + 1.23 error in dep 0

Applying the correction : Original Lat T1 – T2 15.460 T2 – T3 +46.185 T3 – T4 +11.179 T4 – T1 41.904

Original Dep C Lat

CDep

Adjusted Lat Adjusted Dep

+20.57

-15.31

+0.175

+66.64

+46.66

+0.556

-0.475

+67.196

-10.86

+11.27

+0.107

-0.091

-10.753

-77.79

-41.39

+0.602

-0.150

+20.745

-0.514

-77.188

0.00 VI.

-

0.00

Compute for the coordinates :

But first, adjust bearings/azimuths & distances. Line T1 – T2 T2 – T3 T3 – T4 T4 – T1

Adjusted Lat Adjusted Dep Adjusted Bearing +20.745 -15.460 N 36-41-41.81 W +67.196 +46.185 N 34-30-5.15 E -10.753 +11.179 S 46-04-45.92 E -77.188 -41.904 S 28-29-48.31 W

Adjusted Distance 25.87 81.54 15.51 87.83

Adjusted Bearing:


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Tan Bearing = Dep/ Lat Lat: (+)N; (-)S Directions: Ex. Tan bearing = -15.460 +20.745

Dep: (+)E; (-)S

bearing = tan -1 -15.460 +20.745 bearing = N 36-41-41.81 W Adjusted Distance:  (adjusted Lat) 2 + (adjusted dep) 2 Ex. T1 – T2 :  (+20.745) 2 + (-15.460) 2 = 25.87 Coordinates: Line

Adjusted Lat

Adjusted Dep

T1 – T2

+20.745

-15.460

T2 – T3

+20.745

-15.460

T3 – T4

+20.745

-15.460

T4 – T1

+20.745

-15.460

Northings T 1 20000.00 (+20.745) T 1 20000.00 (+20.745) T 1 20000.00 (+20.745) T 1 20000.00 (+20.745)

Eastings T 1 20000.00 (assumed) (-15.460) T 1 20000.00 (-15.460) T 1 20000.00 (-15.460) T 1 20000.00 (-15.460)

VII. Compute the area by DMD method or by Coordinate method

A. Using DMD: Northing

Easting

Lat

Dep

DMD

DPA

T1

20000.00

20000.00

+20.745

-15.460

-15.460

-320.7177

T2

20020.745

19984.540

+67.196

+15.265

+15.265

+1025.7469

T3

20087.941

20030.725

-10.753

+72.629

+72.629

-780.9796

T4

20077.188

20041.904

-77.188

-41.904

+41.904

-3234.4859

(+)=1025.7469 (-)=4336.1832 2A=3310.4363 A=1655.218 sq.m. A=1655 sq.m.


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B. By coordinate method: X = Easting; Y = Northing Area = ½ X1 X2 X3 X4 X1 Y1 Y2 Y3 Y4 Y1 Area = ½ [(X1Y2+X2Y3+X3Y4+X4Y1)-(X2Y1+X3Y2+X4Y3+X1Y4)] Area = 1665.219 sq.m. = 1655 sq.m. VIII. Determination of scale to be used in plotting: Max Difference 0 - 30 30 - 60 60 - 90 90 - 120 120 - 150 150 - 180 180 - 240 240 - 300 300 - 600 600 - 900 900 - 1200 1200 - 1500 1500 - 1800 1800 - 2400 2400 - 3000

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Scale : 100 : 200 : 300 : 400 : 500 : 600 : 800 : 1000 : 2000 : 3000 : 4000 : 5000 : 6000 : 8000 : 10000

from the computer coordinates: Max (N) = 20087.941 Max (E) = 20041.904 Min (N) = 20000.000 Min (E) = 19984.540 87.941 N>E 87.941 is between 60-90; therefore the scale to be used in plotting is 1:300 IX. Coordinates of the centerline: Nc= Max N + Min N ; Ec = Max E + Min E 1 2

Nc = 20087.941+20000.00 2

Ec = 20041.904+19984.540 2

Nc= 20043.97 , Ec=20013.22 Nc= 20043

;

Ec=20013


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PLOTTING

SURVEY PLANS (Isolated and Subdivision) Guidelines: 1. The B.L. Survey Number is assigned by the Bureau of Lands Ex.

Psd-13-001602 Psd is called a survey symbol.

A survey symbol is used to designate the various kinds of surveys. Ex.

Psd – Subdivision of lots by private land surveyors Ps – Private surveys by private land surveyors Rs – Resurveys

2. A claimant may be an individual, a corporation or any recognized organization (religious, academic, etc.) 3. The site, barrio, municipality, province and island are indicated to locate the land. 4. Date of survey and approval are indicated. 5. The Geodetic Engineer signs the map. A junior G.E. may also assign but only on survey types specified on the “Manual of Land Surveys in the Philippines.” 6. Area is determined by Double Meridian Distance (DMD Method, rounded off to the nearest whole number. Use standard Lot Data Computation form to compute for the area. 7. Bearings may be grid, assumed, true or magnetic. True bearings, however, are more usual for property surveys. If bearings are magnetic, the declination is indicated. 8. Both the graphic scale and representative fraction are indicated. 9. North-South line is drawn in standard form. N

S


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10. Lot corners are small circles 2 mm in diameter drawn in black ink. Corners are numbered clockwise. Numbers are inside the lot. Boundary lines don’t pass through the small circle.

1

2 4

3

Note: The diameters of the circles are drawn so as to emphasize that the lines don’t pass through the cir cles. 11. The description of each corner as marked on the ground is written preferably at the bottom left corner of the map. If this space is crowded, it is written in any open space. Ex.

All corners marked PS are cyl. conc. mons. 15 x 40 cm. (cyl. conc. mons. = cylindrical concrete monuments, 15 cm diameter, 40 cm

high) 12. Boundary lines are full black lines heavier than those of adjoining properties. Bearing and distance of each line are in black ink and may be written in either of the following methods: a) Bearing and distance along boundary line (inside the lot)

b) Tabulated bearings and distances (when features and distances are too numerous and bearings and distances written along boundary lines, will make the map crowded).

LINES 1-2 2-3

TECHNICAL DESCRIPTION BEARINGS N14 51’E S83 26’E

DISTANCES 87.96 M. 60.81 M.


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The above table is usually placed in the upper left-hand corner of the map. If this space is crowded, the right-hand corner may be used. 13. A point of reference has known geographic coordinates: latitude and longitude . Its Northing and Easting may be true or assumed. A point of reference may be a triangulation station or Bureau of Lands Location Monument (BLLM). This point is not shown on the map simply because it is far from the area surveyed. A tie line is a line joining the point of reference and corner 1 of the lot. There are two methods to write the description of the point of reference and the bearing and distance of the tie line: a) Tabulated TIE LINE: LM 101, TALA ESTATE TO CORNER 1 N48 36’E

2989.44 M

LM 101 is the name of the point of reference. It is located in Tala estate. This table is added to the Technical Description of the lot. b) Graphical (when there is open space)


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14. Boundaries between adjoining surveyed properties are indicated by broken lines. Owner’s name and BL Survey number are also indicated.

Psu- 132776 Ronnie Natividad

15. All important features and improvements (ex. Streams, rivers, bridges, roads) are drawn true to scale, in black ink (without color) and represented by standard mapping symbols. Width of roads and rivers are indicted. Direction of the flow of water on a river is indicated by an arrow with the arrowhead in the direction of the flow. 16. Lettering must be simple, uniform and mechanical. Use of a lettering machine is imperative. 17. Lot numbers, corner numbers, notes, titles, etc. are drawn parallel to the horizontal axis of the map. Names of rivers, roads, bridges and the like follow the shape of the feature. Sometimes, names of adjoining owners follow the shape of the lot. 18. The central orthogonal axes and the coordinates of the center are drawn in red ink. Ncenter is drawn slightly above the horizontal axis near the left edge of the map. Ecenter is drawn slightly to the left of the vertical axis near the lower edge of the map. Ecenter is drawn vertically.


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Plans are drawn on the authorized BL form having the following dimensions: ¾ cm

11.5 N

TITLE 38 cm

S

50 cm You may use the BL form or a whole sheet of tracing paper. If you choose the latter, use the above dimensions. Write name, exercise number and instructor’s name outside the border of the map. THE FOLLOWING ARE APPLICABLE ONLY TO SUBDIVISION PLANS 19. If a lot is subdivided into several lots, the subdivided lots will be designated as A, B, C. etc. Ex. C.

Lot 1228 is subdivided into 3 lots, namely Lot1228-A, Lot 1228-B and Lot 1228-

20. The boundary, as in isolated surveys, has a Technical Description. In addition, each subdivided lot has its own description.

LINES

BOUNDARY BEARINGS DISTANCES

LINES

LOT 1228-A BEARINGS DISTANCES

Tie lines are observed/computed to corner 1 of the boundary and each of the subdivided lot.

LOT NOS. 1228-A 1228-B 1228-C

TIE LINE: LM 101, TALA ESTATE TO CORNER 1 BEARINGS

DISTANCES


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If the upper left or right-hand corners are not sufficient, Technical Descriptions are placed on separate authorized sheets. For this exercise, use short bond paper. 21. Numbering of lots.

2 2

1

1

4

2

2

4

3

3

4

For boundary: Numbers are drawn clockwise outside the boundary and in red ink. For subdivided lots: Numbers are drawn clockwise inside the boundary and in black ink. The assignment of corner 1 is discretionary unless the subdivided lot has a corner that is tied to a reference point. In this case, this will be corner 1 of the said subdivided lot. Corners 1,2,3,4 of Lot 1192 are outside in red ink. Tie line to corner 1 is observed. Corners 1,2,3,4 of Lot 1192-A are inside and in black ink. Tie line to corner 1 is observed. Position of corner 1 must coincide with corner 1 of boundary (Lot 1192) Corners 1,2,3,4 of Lot 1992-B are inside and in black ink. Tie line to corner 1 is computed. Position of corner 1 is discretionary. 22. Area of each subdivided lots must be indicated inside the lot. This area is not necessarily a whole number.

A= 1493.96 s . m.

A= 1056.72 s . m.

23. Corners are plotted by the Coordinate Method. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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VI.

PLOTTING BY THE COORDINATE METHOD

1. From the following data:

Referance Point

LINE

BEARING

DISTANCE

-1 1-2 2-3 -

-

-

Compute for the latitude & departure (to the nearest CM.) of each line LAT = DISTANCE x cos BEARING DEP = DISTANCE x sin BEARING In your calculator, use the polar to rectangular coordinates transformation function.

LAT is + and DEP is + when line is directed NE LAT is + and DEP is - when line is directed NW LAT is - and DEP is + when line is directed SE LAT is - and DEP is - when line is directed SW 2. For a close traverse:

 LAT = 0  DEP = 0 If  LAT ≠ 0, distribute corr ection to the longest line, the next longest line, etc. If  DEP ≠ 0, do the same (eg. A 0.01 m. correction is distributed to one line; a 0.02 m. correction is dist ributed to 2 lines equally, 0.01 m. each, etc.

3. Beginning from the Reference Point, add the adjusted LAT and DEP to compute for the coordinates (Northing and Easting) of each corner.

DEP 12

(N2, E2)

LAT12

N = N +LAT

12 Inc . No part of this doc ument may be reproduced without the written cons ent of2Infinite 1Intellig ence, E2 = E1+DEP12

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4. Determine the map scale by doing the following steps: Compute for the following: Nhighest = northing of the extreme north corner Nlowest = northing of the extreme south corner Ehighest = easting of the extreme east corner Elowest = easting of the extreme west corner Ex.

N2 N5 E4 E1

(N2, E2)

is Nhighest is Nlowest is Ehighest (N1, E1) is Elowest

(N3, E3)

(N4, E4) (N5, E5) If N’ is > E’, use N’ as the maximum difference in coordinates. If E’ is > N’, use E’ as the maximum differenc e in coordinates. Determine the appropriate map scale based on the following table. This table has been designed using the size of a standard B.L. form. SCALE 1 : 100 1 : 200 1 : 300 1 : 400 1 : 500 1 : 600 1 : 800 1 : 1,000 1 : 2,000 1 : 3,000 1 : 4,000 1 : 5,000 1 : 6,000 1 : 8,000 1 : 10,000

MAXIMUM DIFFERENCE IN COORDINATES 0 meters - 30 meters 30 meters - 60 meters 60 meters - 90 meters 90 meters - 120 meters 120 meters - 150 meters 150 meters - 180 meters 180 meters - 240 meters 240 meters - 300 meters 300 meters - 600 meters 600 meters - 900 meters 900 meters - 1,200 meters 1,200 meters - 1,500 meters 1,500 meters - 1,800 meters 1,800 meters - 24000meters 24000 meters - 3,000 meters


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5. To center the lot, compute for the following: Ncenter =

Nhighest + Nlowest 2

Ecenter =

Ehighest + Elowest 2

Ncenter and Ecenter are the coordinates of the center of the map, each rounded off to the nearest whole number. 6. For each corner, compute for: Ni = Ni - Ncenter Ei = Ei - Ecenter Where Ni = Northing of corner i Ei = Easting of corner i Ni = Distance of corner i along the vertical axis from the center Ei = Distance of corner i along the horizontal axis from the center 7. Plot the corners using a scale

If If If If

Ni is +, the point is plotted above the horizontal axis Ni is -, the point is plotted below the horizontal axis Ei is +, the point is plotted to the right of the vertical axis Ei is -, the point is plotted to the left of the vertical axis


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Ex.

Ni Position of corner i

Ei

Ni and Ei are drawn to scale.


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RULES ON MAP NAME PLACEMENT

Objective: To ensure the unambiguous identification of all the labeled map features.

1. Name should be aligned horizontally whenever possible. Recommendation: Use regular grid as guide Exception:  Align name with a straight-line feature that is not horizontal (eg. Road, pier, railroad)  Align name parallel to the lines of graticule. 2. There should be sufficient space between the name and the related symbol. Recommendation: There should be at least ½ upper case character space between the name and the symbol. 3. Name should not overlap with symbol. 4. There should be unambiguous reference between the symbol and its associated name. 5. The point symbol should be seen first and its name immediately to its right, but not on the same horizontal line. 6. Locate the name within the territory to which it refers. Exception:  If the name is placed outside a relatively linear feature, align the name along the feature’s trend.  If the feature is compact, place the name horizontally beside it (but not on the same horizontal line). 7. Name should not be placed directly on top of the line to which it relates. Recommendation: There should be sufficient space (at least ½ of the size of a lower case letter) between the bottom of the name and its associated line symbol. 8. Names and numbers must not be positioned on sharp curves, but rather where the shape of a feature is relatively smooth. 9. Words incorporating characters which reach below the normal baseline (eg. g, p, q, j) should be positioned where bends in a line symbol make their placement appropriate or below the line. 10. In areas which are congested with quantities of names and symbols, arrange names around the highly detailed area. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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11. Name should be adequately centered and should extendover the full area to which it should refer. Recommendation:  Name should stretch over approximately 2/3 of the area to which it relates.  Name should serve as a central axis for the region.  For long linear features, reduce spacing and repeat name. 12. Name referring to an area is normally placed horizontally. 13. Letters forming a name/title should be appreciated as a whole. Recommendation: Size of type may be increased. 14. Arrange curved lettering along a regular baseline. 15. Names should cross at or as near to a right angle as possible. 16. Name relating to an area and having a straight baseline should not be positioned at an oblique angle. Recommendation: Use curved lettering. 17. Name should not be unnecessarily hyphenated and displayed on separate lines. 18. Names should read from the middle of the bottom edge of the map (not to be oriented towards the other edges). Exception:  Vertical names (for roads, railroads, etc.) should be turned so that it can be read from the right side of the page. 19. Name should not fall across a line symbol. Recommendation:  Interrupt line so that the name is clearly visible. Exception:  Print linework without interruption when a line is very fine or has a lighter color. 20. Name should be placed above its associated symbol. 21. Names of harbors should be preferably toward the sea. 22. Do not spread the letters all along a river, but keep them close together. Name may be repeated. 23. Names of lakes and islands can be either outside or inside, but only in an emergency is the shoreline cut with the name. 24. Names of mountain ranges are spread along the crestline of the range and should follow the main trend very exactly. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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In cartography, symbols are everything . The very nature of a map as an abstracted representation of the Earth requires symbols to perform the abstraction. To not have symbols is to not have maps. When we first think of symbols, we tend to think of graphics representing elements that appear at points, like bridges and houses. Symbols can also be linear , representing such features as roads, railways and rivers. However, we also need to include representations of area, in the case of forested land or cleared land; this is done through the use of colour. Feature Name

Symbol

Road - hard surface, all season Road - hard surface, all season Road - loose or stabilized surface, all season Road - loose surface, dry weather Rapid transit route, road Road under construction Vehicle track or winter road Trail or portage Traffic circle Highway route number


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Railway multiple track Railway - single track

Railway sidings

Railway - rapid transit Railway - under construction Railway abandoned

Railway on road

Railway station

Airfield; Heliport

Airfield, position approximate Airfield runways; paved, unpaved Tunnel; railway, road

Bridge


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Bridge; swing, draw, lift

Footbridge

Causeway

Ford

Cut

Embankment

Barrier or gate

Lock

Dam; large, small Dam carrying road

Footbridge


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Ferry Route

Pier; Wharf; Seawall

Breakwater

Slip; Boat ramp; Drydock Canal; navigable or irrigation Canal, abandoned Shipwreak, exposed Crib or abandoned bridge pier Submarine cable Seaplane anchorage; Seaplane base

Falls


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Rapids

Direction of flow arrow

Dry river bed

Stream intermittent Sand in Water or Foreshore Flats Rocky ledge, reef Flooded area

Marsh, muskeg

Swamp Well, water or brine; Spring Rocks in water or small islands

Water Elevation


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Horizontal control point; Bench mark with elevation Precise elevation

Contours; index, intermediate

Depression contours

Cliff or escarpment Sand

Quarry

Cave

Wooded area

Orchard

Vineyard


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Sports track

Swimming pool

Stadium

Golf course

Golf driving range Campground; Picnic site Rifle range with butts Historic site or point of interest; Navigation light Elevator

Greenhouse

Wind-operated device; Mine Landmark object (with height); tower, chimney, etc. Oil or natural gas facility No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Pipeline, multiple pipelines, control valve Pipeline, underground multiple pipelines, underground

Electric facility

Power transmission line multiple lines Telephone line

Fence Crane, vertical and horizontal Dyke or levee

Firebreak Cut line School; Fire station; Police station Church; NonChristian place of worship; Shrine No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Building

Service centre

Customs post

Coast Guard station

Cemetary

Ruins

Fort


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SURVEY SYMBOLS

The following survey symbols shall be used to designate various kinds of surveys. Symbols I. Public Land Surveys New Ap As Sc Msc

DESCRIPTION

Old

- Advance Plan approved project - Advance Survey from project in progress Pc - Sales Application: Corporation Msc - Miscellaneous Sales Application by Charitable Institution and Corporation Msi Msa - Miscellaneous Sales Application by Individual Li La, L, E - Lease Application (Agricultural) by individual Lc La, L, E - Lease Application, Corporation Mli Mla - Miscellaneous Lease Application by Individual Mlc Mla - Miscellaneous Lease Application, Corporation Fli Fl, Sh - Foreshore Lease Application, Individual Flc Fl, Sh - Foreshore Lease Application, Corporation Gss - Group Settlement Surveys Ng Ig, Ff - Insular Government Land or Private Land to be acquird by the (Insular) National Gov’t Tsi - Townsite Reservation Subdivision: Individual Tsc - Townsite Reservation Subdivision:Corporation Pls - Public Land Subdivision PPls - Photo Public Land Subdivision Plsm - Public Land Subdivision Mapping PPlsm - Photo Public Land Subdivision Mapping Nr Ir, In - National (or Insular) Reservations Mr Mn - Municipal Reservations Pr Pn - Provincial Reservations -Tsa - Townsite Sales Application -Rlla - Reclaimed Land Lease Application Rs Rs - Resurvey Tb Kb - Townsite Reservation Boundary Ts Ksd - Townsite Reservation Subdivision Pld - Public Land Delimination H G - Homestead application F P - Free Patent Application Si Pi - Sales Application: Individual Rl Rec - Reclaimed Land Ac Ac - Agricultural Colony II. Private Land Surveys New Old Psu Psu - Land Surveys by private Surveyors No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Psm Psp Psn Psu-B --

Psm Psp Psn Ps, II Psi

- Private Surveys, Municipal - Private Surveys, Provincial - Private Surveys, National - Private Surveys by BL surveyors - Private Surveys, Insular

III. Subdivision and/or Consolidation A. Undecreed Property New Old Csd Csd - Subdivision Ccn Ccn - Consolidation Ccs Ccs - Consolidation and Subdivision B. Decreed Property New Old Bsd Psd Psc Bcn Pcn Bcs Pcs C.

Psd

- Subdivision by B.L. Surveyors - subdivision by Private Surveyors - Consolidation by B.L. Surveyors - Consolidation by Private Surveyors - Consolidation & Subd’n by B.L. Surveyors - Consolidation & Subd’n by Private Surveyors - Subdivision of Lots by Private Surveyors

IV. Cadastral Land Surveys New Old Cad Cad - Cadastral Surveys by B.L. surveyors Psc Psc - Cadastral Surveys by Private Enterprise Pcad - Photo Cadastral Surveys PPsc - Photo Cadastral Surveys: Private Enterprise Cadm - Cadastral Mapping Pcadm - Photo Cadastral Mapping PPscm - Photo Cad Mapping by Private Enterprise Ipb Ipb - Irrigation Project Boundary Ips Ips - Irrigation Project Subdivision

V. Mineral Land Surveys Lp Pp Cp Cl Crp Pdl Pel Ll

- Lode Patent Surveys - Placer Land Surveys - Coal Patent Surveys - Coal Lease Surveys - Coal Revocable Permit Surveys - Petroleum Drilling Lease Surveys - Petroleum Exploration Lease surveys - Lode Location Surveys


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Pl Mi

- Placer Location Surveys - Mineral Investigation Surveys

VI. Government Land Surveys New Old Flb Ab - Friar Land Boundary Fls Fls - Friar Land Subdivision Flr Flr - Friar Lands Relocation Ngl Igl, Ige - (Insular) National Gov’t Property Lease Ngs Igs - (Insular) National Gov’t Property Sale VII. General Land Surveys New Old Pb - Political Boundary - Provincial Mb - Political Boundary - Municipal Swo Swo - Special Work Orders Amd Amd - Amendment Surveys Fis - Fishpond Application Surveys Rel - Relocation Surveys Vs - Verification Surveys Sp - Special Plans Sgs - Segregation Surveys Sk - Sketch Plans Tri - Triangulation Surveys Top - Topographic Surveys Hyd - Hydrographic Surveys Ms Mp - Municipal Street Surveys Ml Mp - Monument Location Surveys Prs Prd - Provincial Road Surveys


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MINING SURVEYS

outcrop

Headframe Hoiste house

cross cut Inclined shaft

cross cut

collar

drift

vertical shaft

raise drift

sump

stope

winze

sump

Undiscovered ore

Cross section of a typical mining operation.

A dit - a horizontal of nearly horizontal passage driven from the surface for working of dewatering a mine.

Back - the top of a drift, cross cut or slope. Also called roof. B ack fill- waste rock or other material used to fill a mined out stope to prevent caving. B edded depos it - an ore deposit of tabular form that lies horizontally or slightly inclined and is commonly parallel to the stratification of the enclosing rocks.

Cage- an elevator for workers and materials in a mine shaft. Chute- a channel or trough underground, or inclined trough above ground, through which ore falls or is shot by gravity from a higher to a lower level (also spelled “shoot”)

Collar - term applied to the timbering or concrete around the mouth or top of a shaft and the mouth of the drill hole. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Cross cut - a horizontal opening driven from shaft to a vein across the course of the vein in order to reach the ore zone.

Dip- the angle at which a bed, stratum, or a vein is inclined from the horizontal. Drift - a horizontal opening in or near a mineral deposit and parallel to the course of the vein or along the dimensions of the deposit.

Entry - manway, haulage, way, or ventilation way below ground, of a permanent nature (ie., not in an ore to be removed)

Face- end wall of a drift or across cut or of bedded deposit. Foot wall- the wall or rock under a vein or under other steeply inclined mineral formations. Gangue- undesired minerals associated with ore. Gangway - A main haulage road underground Hang ing wall- the wall or rock on the upper side of steeply inclined deposits. It is also called a roof in bedded deposits.

Headframe- a construction at top of a shaft which houses hoisting equipments. Level- mines are customarily worked from shafts through horizontal passages or drifts called levels. These are commonly spaced at regular intervals in depth and are either numbered from the surface in regular order or are designated by their actual elevation below the top of a shaft.

Ore pas s - vertical or diagonal opening between levels to permit the movement of ore by gravity.

Out crop- exposed potion of the mine Pillars - natural rock, or ore supports, left in slopes to avoid or decrease the roof subsidence as mining progresses.

Raise- a vertical or inclined opening driven upward in ore from a level R ib- wall in an entry. Also simply wall. S haft - a vertical or inclined excavation in a mine extending downward from the surface or from some interior point as a principal opening through which the mine is exploited.

S ill- synonymous with floor. S tope- underground room or working area from which are is removed. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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S trike- the horizontal course, bearing or azimuth of an inclined bed, stratum or vein S ump- an excavation made at the bottom of a shaft to collect water. Tunnel- a horizontal or nearly horizontal underground passage that is open to the atmosphere at both ends.

Vein - a mineral ore. Waste- mined rock that do not contain useful mineral Winze- a vertical or inclined opening driven downward fro a point inside a mine for the purpose of connecting with a lower level or of exploiting the ground for a limited depth below a level.

COMPUTATIONS IN MINE SURVEYING

N

B

D B

θ

D

θ

C

A A Sin θ = BD/AD

B

D

A

D

dip

C

C

grade = CD/AD

dip = CD/BD No part of tan this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Shortcut:

sin θ = grade / tan (dip)


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MAP PROJECTIONS

Definition:

 

Any system of representing the parallels and meridians on a plane surface. A device for producing all or part of a round body on a flat surface.

CHARACTERISTICS CONSIDERED IN CHOOSING A MAP PROJECTION

1. AREA- many map projections are designed to be equal area, that is, one part on the map covers exactly the same area of the actual earth.  shapes, angles and scales must be distorted on most parts  other terms for equal area: E QUIVALE NT, HOMOLOGR AP HIC,

HOMALOGR AP HIC, AUTHALIC, EQUIAR EA L 2. SHAPE- normally, the shape of every small feature of the map is shown correctly  On a conformal map, there are usually one or more “singular” points at which the shape is still distorted.  Relative angles at each point are correct and the local scale in every direction around any one point is constant.  Meridians intersect parallels at 90°, just as they do on earth 3. SCALEEQUIDISTANCE- scale between one or two points and every point on the map, or along every meridian, is shown correctly.



No map projection show scales correctly throughout the map, but there usually one or more lines on the map along which the scale remains true.

4. DIRECTION AZIMUTHAL or ZENITHAL- directions or azimuths of all points on the map are shown correctly with respect to the center. 5. SPECIAL CHARACTERISTICS a. Merc ator P rojec tion - all rhumblines (lines of constant direction are shown as straight lines b. G nomonic Pr ojection- all great circle path, orthodrome or geodesic (shortest route between points on a sphere) are shown as straight lines.

c. S tereog raphi c - all small circles, as wellas great circles, are shown as circles on the map.

CLASSIFICATION OF MAP PROJECTIONS



By method of construction: CYLINDRICAL, CONIC, AZIMUTHAL, PSEUDOCYLINDRICAL, PSEUDOCONICAL


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DEVELOPABLE SURFACE- one that can be transformed into a plane without distortion. Example: cylinder, cone, plane

A. CYLINDER – If wrapped around the globe representing the earth, so that its surface touches the equator throughout its circumference, the meridians of longitude may be projected on to the cylinder as equidistant straight lines perpendicular to the equator.  Parallels of latitude marked as lines parallel to the equator  CYLINDRICAL PROJECTION B. CONE – (CONICAL PROJECTION)  Cone is tangent to the surface of the earth, touching the globe at some particular parallel of latitude. C. PLANE – a plane tangent to one of the earth’s poles is the basis for polar azi muthal projection.

   

Reference Ellipsoid: CLARKE SPHEROID OF 1866 Equatorial radius, a = 6,378,206.4m Polar radius, b = 6,356,583.8m Flattening, f = 1/294.98

CYLINDRICAL MAP PROJECTIONS

1. MERCATOR PROJECTION – well-known cylindrical map projection  Conformal  Meridians are equally spaced straight lines.  Parallels- unequally spaced straight lines, closest near the equator, cutting meridians at right angles.  Scale is true along the equator, or along two parallels equidistant from the equator.  LOXODROMES (or RHUMB LINES ) are straight lines  Poles are at infinity; great distortion of area in polar regions; suitable for east west extents.  Used for navigation


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2. TRANVERESE MERCATOR – an ordinary mercator projection turned through an angle of 90°  Conformal  Central meridian, each meridian 90° from central meridian, and equator are straight lines  Other meridians and parallels are complex curves  Scale is true along central meridian, or along two straight lines equidistant from and parallel to central meridian.  Scale becomes infinite at 90° from the central meridian  Best for north-south extent maps 3. UNIVERSAL TRANSVERSE MERCATOR  Ellipsoidal Transverse Mercator  Between latitudes 84° N and 80° S, is divided into 60 zones, each generally 6° wide in longitude 4. OBLIQUE MERCATOR PROJECTION  The same as regular mercator projection which has been altered by wrapping a cylinder around the sphere so that it touches the surface along the great circle path chosen for the central line, instead of along the earth’s equator. 5. MILLER CYLINDRICAL PROJECTION  Resembles the mercator projection but shows less exaggeration of area in higher latitudes  American version of Gall’s projection  Neither equal area nor conformal (APHYLACTIC)  Used only in spherical form  Meridians and parallels are straight lines, intersecting at right angles  Meridians are equidistant; parallels are spaced farther apart away from the equator  Poles are shown as lines.  Compromise between mercator and other cylindrical projection. 6. EQUIDISTANT CYLINDRICAL PROJECTION  Probably the simplest of all map projections to construct and one of the oldest.  Other names: Rectangular, La Carte Parallelogrammatique, Die Rechteckige Plattkater, Equirectangular 7. SIMPLE CYLINDRICAL  If the equator is made of standard parallel, true to scale and free of distortion, the meridians are spaced at the same distances as the parallels, and the graticules appear as squares.  Aphylactic  Meridians and parallels are equidistant straight lies, intersecting at right angles  Poles are shown as lines  Used in spherical form No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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CONIC MAP PROJECTIONS --- Used to show region for which the greatest extent is from east to west

1. ALBERS EQUAL-AREA  Equal area form of conic projection using two standard parallels.  Scale along the parallels is too small between the standard parallels and too large beyond them  Parallels are unequally spaced arcs of concentric circles, more closely spaced at the north and the south edges of the map.  Meridians are equally spaced radii of the same circles, cutting parallels at right angles.  There is no distortion in scale or shape along two standard parallels, normally, or along just one.  Poles are arc of great circles.  East-west expanse. 2. LAMBERT CONFORMAL CONIC  Also called CONICAL ORTHOMORPHIC  Parallels are unequally spaced arcs of concentric circles, more closely spaced near the center of the map  Meridians are equally spaced radii of the same circles, thereby cutting parallels at right angles.  Scale is true along two standard parallels , normally, or along just one.  Pole in the same hemisphere as standard parallel is a point; other pole is at infinity  Conformality fails at each point  East-west expanse  No angular distortion at any parallels, except at the poles. 3. BIPOLAR OBLIQUE CONIC CONFORMAL  Two oblique conic projections, side by side, but with poles 104° apart.  Meridians and parallels are complex curves, intersecting at right angles  Scale is true along two standard transformed parallels on each conic projection, neither of these lines following any geographical meridian or parallel  Very small deviation from conformality, where the two conic projections join.  Specially developed for a map of the Americas  Used only in spherical form 4. POLYCONIC PROJECTION  Curvature of the circular arc for each of the parallel on the map is the same as it would be following the unrolling of a cone which had wrapped around the globe tangent to the particular parallel of latitude, with the parallel traced onto the cone.  Instead of a single cone, a series of conical surfaces may be used.  For the sphere, each parallel has a radius proportional to the cotangent of latitude  Aphylactic No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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Parallels of latitude (except for equator) are arcs of circles but are not concentric Central meridian and equator are straight lines; all other meridians are complex curves Scale is true along each parallel and along the central meridian, but no parallel is “standard.” Free of distortion only along the central meridian.

AZIMUTHAL PROJECTIONS

----- Formed onto a plane which is usually tangent to the globe at either pole, the equator, or any intermediate point. Directio of azimuth, from the center of the projection to every other point on the map is shown correctly. 1. ORTHOGRAPHIC – A true perspective, in which the earth is projected from an infinite distance onto a plane. The map looks like a globe, thus stressing the roundness of the earth.  All meridians and parallels are ellipses, circles, or straight lines  Aphylactic  Center is distortion free; much distortion near the edge of hemisphere shown.  Directions from the center are true. 2. STEREOGRAPHIC – True perspective in the spherical form, with the point of perspective on the surface of the sphere at a point exactly opposite the point of tangency for the plane, or opposite the center of projection.  Conformal  Central meridian and a particular parallel (if shown) are straight lines.  All meridians on the polar aspect and the equatorial aspect are straight lines.  All other meridians are arc of circles.  Directions from the center of projection are true.  Scale increase away from the center of projection. 3. GNOMONIC – True perspective, with the earth projected from the center onto the tangent plane.  All great circles, not merely those passing through the center, are shown as straight lines on spherical form  Also called “central projection” 4. LAMBERT AZIMUTHAL EQUAL-AREA – Not a perspective projection; may be called a synthetic azimuthal in that it was derived for the specific purpose of maintaining equal area.  All meridians in the polar aspect, the central meridian in other aspects, and the equator in equatorial aspect are straight lines.  All other meridians are complex curves.  Scale decreases radially as the distance from the center, the only point without distortion. No part of this doc ument may be reproduced without the written cons ent of Infinite Intellig ence, Inc .

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