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Map
Projection
Q1: Define the
objective of map projections?
Map projections are attempt to portray the surface of the earth (3D) or a portion of the earth on a flat surface (2D) e.g. drawing maps on paper.
Q2: List and
define the main classes of map projections?
·
Cylindrical projections result from projecting a spherical
surface onto a cylinder (Page 72, Figure 5.B.3)
·
Conic projections result from projecting a spherical
surface onto a cone (Page 71, Figure 5.B.2)
·
Azimuthal projections result from projecting a spherical
surface onto a plane (Page 71, Figure 5.B.1)
·
Miscellaneous projections include unprojected ones such as
rectangular latitude and longitude grids and other examples of that do not fall
into the cylindrical, conic, or azimuthal categories
Q3: Discuss briefly the
distortions that resulted from
projecting 3D shape to 2D?
Some distortions of conformality, distance, direction, scale, and area always result from map projection. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties.
Q4: Define the following
terms:
·
Conformality : When the scale of a map at any point on the map is the
same in any direction, the projection is conformal. Shape is preserved.
·
Direction: A map preserves direction when azimuths (angles from a
point on a line to another point) are portrayed correctly in all directions.
·
Scale : Scale is the relationship between a distance portrayed
on a map and the same distance on the Earth.
Q5: Discuss in details the Universal Transverse Mercator (UTM) projection?
(Page 101 and Figure 6.10)
UTM projection is used to
define horizontal, positions world-wide by dividing the surface of the Earth
into 6 degree zones, each mapped by the Transverse Mercator projection with a
central meridian in the center of the zone. UTM zone numbers designate 6 degree
longitudinal strips extending from 80 degrees South latitude to 84 degrees
North latitude. UTM zone characters designate 8 degree zones extending north
and south from the equator.
Eastings are measured from the central meridian (with a 500km false
easting to insure positive coordinates). Northings are measured from the
equator (with a 10,000km false northing for positions south of the equator).
Q6: Discuss in details how to select a projection?
The first step in choosing a
projection is to determine:
·
Location
·
Size
·
Shape
These three things determine
where the area to be mapped falls in relation to the distortion pattern of any
projection. One "traditional" rule says:
·
A country in the tropics asks for
a cylindrical projection.
·
A country in the temperate zone
asks for a conical projection.
·
A polar area asks for an
azimuthal projection.
Implicit in these rules of thumb
is the fact that these global zones map into the areas in each projection where
distortion is lowest:
· Cylindricals are true at the equator and distortion increases toward the
poles.
· Conics are true along some parallel somewhere between the equator and a
pole and distortion increases away from this standard.
· Azimuthals are true only at their center point, but generally distortion
is worst at the edge of the map.
The final projection choice would
seem to be a fairly straightforward
function of minimized distortion
and special properties.
Chapter 5
Q1: Define
Scale?
Scale is the ratio of
distance on a map, to the equivalent distance on the earth's surface.
Q2: List and
define the three methods of scale representation?
1. Verbal: Scale is stated
e.g. one CM for each one KM 2.
Representative Fraction (RF): e.g.
1: 50,000
3. Scale bar: Good if enlarged/reduced (Draw Figure 6.1 on page 93)
Q3: How many
inches in one mile?
1 Mile = 1760 yards (1 Yard = 3 feet)
1 Mile = 1760 x 3 = 5280 feet
1 foot = 12 inches
1 Mile = 5280 x 12 = 63360 inches
Q4: Given a
distance of 12 Miles, express it in Km?
1 Mile = 1.6 KM
12 miles = 12 x 1.6 = 19.2 KM
Note: The units for measuring distance are
meter (m) and feet (1 m = 3.28 ft, 1 inch = 2.54 cm)
Scale
Conversion:
Q5: Express the
following Representative fraction scale into verbal ones?
1:20,000 verbal = (5cm=1km)
1:24,000 verbal = (1”=2,000ft)
1:25,000 verbal = (1cm=.5km)
1:50,000 verbal = (2cm=1km)
Q6: Express the
following verbal scales into Representative fraction scales?
1”=1mile Representative fraction =
1:63,360
1cm=1km Representative fraction = 1:100,000
1cm=5km Representative fraction =
1:500,000
1”=15.8mi Representative fraction
1:1,000,000
Q7: Angle
Conversion:
Latitudinal/Longitudinal
system is measured in terms of Degrees, Minutes and Seconds (DMS) or Degree
Decimal System (DDS)
Convert the
followings from DMS to DDS:
57o 45’
33” = 57 + 45/60 +
33/3600 = 57.759 o
44o 67’
22” = 44 + 67/60 + 22/3600 = 45.122 o
12o 34’
44” = 12 + 34/60 + 44/3600 = 12.578 o
Convert the
followings from to DDS to DMS:
13.56 = 13 + 0.56 x 60 = 13 +
33.6 = 13 33 + 0.6 x60 =
= 13o 33’ 36”
11.45 = 11 + 0.45 x60 = 11 +
27 = 11o 27’
20.87 = 20 + 0.87 x 60 = 20 +52.2 = 20 + 52 + 0.2x60=
= 20o 52’
12”
Q8: Find the great
circle distance between Washington (38 o 50’ N, 77 o
00’ W) and Moscow (55
o 45’ N , 37 o 37’ E)? (see Page 50)
Cos D = Sin a Sin b + cos a cos b cos
(difference in longitude)
Cos D = Sin 38.833 x Sin 55.75 + cos 38.833 x
cos 55.75 x cos (-77.00 – 37.62)= 0.627 x 0.827 + 0.779 x 0.563 x
(-0.417) =
= 0.518 – 0.183 = 0.335
D = cos-1 (0.335)
= 70.43 o
1 Degree of latitude = 111.2
Km (69.11 mile) ( see page 46)
Distance in miles = 70.43 x
69.11 = 4867 miles
Distance in Km = 70.43 x
111.2 = 7832 km
Q9: Find the plane
distance between point A (200, 300) and point B (600, 700) and the direction
between them?
(See page 99, Box 6.B)
D = sqrt [(x1-x2)2 + (y1-y2) 2]
D = sqrt [ (200-600) 2
+ (300-700) 2]
D = sqrt [ (-400) 2 + (-400) 2]
D= sqrt [ 160,000 + 160,000 ]
= sqrt (320,000) = 565.685 units
Direction = tan q = (y1-y2)/
(x1-x2) = (300-700)/(200-600)
tan q =
-400/-400 = 1
q = tan-1 (1)
= 45 o
The distance
between point A and B is 565.685 units and the direction is 45 degrees.
