This document provides information about basic concepts related to charts used for aviation purposes. It discusses key terms like maps, charts, projections and distortions that occur when representing the spherical Earth on a flat surface. It also describes different types of projections including plane, conical, cylindrical and their characteristics. Specific projections like Mercator and Lambert Conformal are explained in more detail.

1. CHARTS

2. BASIC CONCEPTS
• MAP OR CHART: Representation of the
spherical Earth or a part of it at smaller scale
on a flat surface.
• Difference: Maps have more geographical
characteristics represented than charts.

3. Once known the spherical form of the Earth,
mapmakers faced the basic problem of
projections: How to represent the Earth
surface on a plane surface.
Aeronautical charts are used for flight
planning purposes and for in flight navigation.

4. • The conversion from a sphere to a plane
cannot be made without distortion and a map
or chart will consequently not present a true
picture of the spherical surface.
• Distortion leads to the misrepresentation of
direction, distance, shape, and relative size of
the features of the earth’s surface.

5. • A small zone of the terrestrial surface is
approximately like a plane surface, so on its
representation there are no many distortions.
• When a big area is represented, distortions are
many more and completely unavoidable due to
the pronounced curvature of the Earth.

6. • In mapmaking distortion can NOT be
eliminated at all, but it can be more or less
controlled. It is possible to minimise those
errors that are most detrimental to an aviator.
• Charts are made with different characteristics
depending on the purpose of the chart and its
practical use.

7. • IDEAL CHARACTERISTICS A PROJECTION
SHOULD COMPLY WITH
– Constant scale
– Areas correctly represented in their correct relative
proportions to those on the Earth.
– Both GC and RL represented as straight lines,
overcoming the problem of convergence.
– Positions easy to plot
– Adjacent sheets fitting together with the graticule
of lat. and long. aligned from one sheet to the next.
– Bearings on chart identical to the corresponding
bearings on the surface of the Earth.

8. – Shapes correctly represented.
– Parallels and Meridians intersecting at right angles
as on the surface of the Earth.
– Worldwide coverage.
• As it is impossible for a map to have all the
characteristics of the Earth’s spherical surface,
the mapmaker must select THE MOST
DESIRABLE CHARACTERISTICS and preserve
these on the map, depending on the purpose
of that map.

9. • The reduced Earth is the only completely accurate
small-scale representation of the Earth.

10. • For navigation it is important that:
– Bearings and distances are correctly represented
– Both easily measured
– Course flown is a straight line
– Plotting of bearings is simple
TO OBTAIN THESE PROPERTIES, OTHER PROPERTIES
MUST BE SACRIFICED

11. • Earth’s surface: too irregular to be represented
simply. Approximations have to be made by
using less complicated shapes
• VERTICAL DATUM (zero surface)
– MSL (from which elevation is measured)
• 3 TERMS when measuring elevation:
- topographical surface
- ellipsoid (oblate spheroid): regular geometric
representation
- geoid : equipotential surface of the Earth’s gravity
field

13. • PROJECTION: The method for systematically
representing the meridians and parallels of
the Earth on a plane surface.
• METHODS OF PROJECTION
• PERSPECTIVE
• MATHEMATICAL

14. METHODS OF PROJECTIONS
• PERSPECTIVE PROJECTIONS: Mapmakers
work from the “Reduced Earth” which is a model
earth (globe) reduced in size to the required
scale.
• A light source, at
some given point within the
globe, projects the shadows
of the graticule of the globe
onto a piece of paper.

15. PROJECTION TYPES
PLANE PROJECTIONS
CONICAL PROJECTIONS
CYLINDRICAL PROJECTIONS

16. PLANE/azimuthal PROJECTIONS
• Points on Earth directly projected to a flat
plane tangent to the Reduced Earth.
• Light source:
• Centre of globe: Gnomonic projections
• At the opposing point of the tangent point:
Stereographic projections
• At the infinite: Orthographic projections

17. Projection plane
Tangent point
Light source:
B. GNOMONIC
C. STEREOGRAPHIC
D. ORTHOGRAPHIC

18. CONICAL PROJECTIONS
• Cone placed over the Reduced Earth
tangential to a predetermined parallel
• Light source in centre of globe

19. Further modification: Cone cutting two parallels

20. CYLINDRICAL PROJECTIONS
•A cylinder is placed over the
reduced Earth
•Light source: centre of the
globe

21. METHODS OF PROJECTIONS
• MATHEMATICAL: Derived from a
mathematical model that is designed to
provide certain properties or characteristics
that cannot be obtained geometrically in
perspective projections.
• Mathematical projections are most widely
used.

22. CONFORMALITY
• The most important in air navigation.
• A chart is said to be ortomorphic or conformal when:
1.Scale is the same in all
directions from any given point
of the chart. (In short
distances from that point)
2.meridians and parallels
on the chart cut across
each other at right angles,
just as they do on the
Earth.
(Directions correctly presented and distances measured correctly)

23. SCALE
• Relationship between distance measured on the
chart and the corresponding real distance on the
surface of the Earth.
• SCALE = CHART DISTANCE / EARTH DISTANCE
BOTH CD AND ED IN THE SAME UNITS

24. METHODS OF INDICATING SCALE
The 2 most commonly used in aviation are:
• Representative fraction: Expresses the ratio
of a unit of length on the chart to its
corresponding number of similar units on
the earth.
e.g. 1 / 1000000 or 1 : 1000000
(means 1 inch/cm/… of CL represents
1million inches/cm… of ED)
5. Graduated scale line

25. • For most projections the scale will vary within
the coverage so that the scale is given for a
particular point or particular latitude.
• You will find some aeronautical charts
referred to as being “constant scale”, which
means that, by restricting the coverage, the
scale errors are minimum (limited to
percentages as 1%)

26. • In “constant-scale charts” (charts with little errors)
distances may be measured with graduated scale
lines usually displayed in the bottom margin of the
chart. (Often including measurements in NM, SM,
Km)
• There’s a THIRD method of indicating scale:
GRADUATED SCALE ON SOME MERIDIANS.
• Often used for measuring distances
• It is of course the latitude scale in which 1’ lat along
meridian =1 NM on Earth
• Thus it is the most accurate scale to use on any map or
chart, as it will be correct at any latitude

27. COMPARING SCALES
• 1: 500000 LARGER SCALE than 1: 1000000
• 1: 500000 covers a small area in detail
• 1: 1mill not as much detail can be shown
• Larger scale maps (as 1: 250000) are normally
used to covering smaller areas than small scale
maps (as 1: 1000000)

28. SCALE EXERCISES
• How many NM are represented per inch in a
chart scale of 1:2500000 ?
• We have a chart with scale 4inches = 1 statute
mile. Express that scale in a representative
fraction.
• If 100 nm are represented by a line of 7.9
inches of longitude in a chart, ‘Which is the
longitude of a line representing 50km?

29. SCALE EXERCISES
• If scale is 1:250000, ‘Which is the distance in the
chart between 32º11’N 06º47’E and 30º33’N
06º47’E?
• In a chart that has a scale of 1:250000. ‘Which
distance in inches will separate points A (20º33’N
150º08’W) and B (21º37’N 150º08’W)?
• It takes 15min 12sec for an aircraft to cover a
distance of 6.6 cm between A and B in a chart with a
scale of 1:2000000. Calculate Ground speed

30. MERCATOR ECUATORIAL PROJECTION

31. MERCATOR ECUATORIAL PROJECTION
• Cylinder tangential to globe at
equator
• Light source at centre of the
globe
• Complex mathematical
construction

32. MERCATOR ECUATORIAL PROJECTION
• Meridians:
• Vertical parallel lines.
• Equally spaced
• Parallels:
• Horizontal parallel lines
• Cross meridians at right angles
• distance increasing towards the poles

33. MERCATOR ECUATORIAL PROJECTION
• RL Straight lines
• GC Curved lines convex to the nearer
pole

34. MERCATOR ECUATORIAL PROJECTION
• Scale only accurate (correct) at the Equator
• Scale expansion towards the poles: function of
the secant of the latitude
• Scale given for a particular latitude
• No linear scale index at the bottom of this chart
(no fixed scale)
Scale at Lat.A= Scale at Equator x secant of Lat.A

35. MERCATOR ECUATORIAL PROJECTION
• CONFORMAL CHART
• Scale is the same in all directions measured
from any point on the chart.
• All angles are depicted correctly
• Chart convergence constant = 0
• Not an equal area projection
• Adjacent sheets will fit N-S and E-W

36. MERCATOR ECUATORIAL PROJECTION
• Track can be measured at any meridian
• GC routes must be drawn first in a chart
where GC are straight lines.
• Long distances (+300NM) lines must be
sectioned out to be measured

38. PLOTTING BEARINGS
• GC bearings and radials: curved
• They must be converted to RL before plotted
on the chart by:
• C.a formula
c.a = ½ chlong x sinMlat
• Conversion scale on chart

40. PLOTTING
• FOR NDB:
– Convert MB to TB using a/c variation
– Apply conversion angle
– Take reciprocal to get R/L from beacon
• FOR VOR:
– Take reciprocal of RMI to get radial
– Apply conversion angle
– Convert into TB using the station variation

41. REVIEW OF MERCATOR CHART
PROPERTIES
• CONFORMAL? – YES
• SCALE CORRECT? - ONLY AT EQUATOR
• CONVERGENCY? – 0º AND CONSTANT
• GC? – CURVED
• RL? – STRAIGHT LINES

42. REVIEW OF MERCATOR CHART
PROPERTIES
• SHAPES NOT DEFORMED? – ONLY SMALL
ONES AND AT LOW LATITUDES
• EQUAL AREAS? – NO. EXAGGERATED AT
HIGH LATITUDES
• ADJACENT SHEETS FIT? – YES
• COVERAGE – UNTIL 70/75º N/S
• POLES REPRESENTED? – NO_

43. CONICAL PROJECTION
• Cone placed over the reduced Earth
• Tangential along one parallel of latitude
(parallel of origin or standard parallel)
• Light source at the centre of the globe
• Scale expands away from the tangential
parallel
• Unwrapped cone: forms a segment
representing the 360º of real Earth

44. CONICAL / LAMBERT
• Constant of the cone (c.c) – Ratio between the
developed cone arc (size of the segment) to
the actual arc on the Earth covered by the
chart (360º)
• C.c = sine latitude of the parallel of origin
• C.c is always a number between 0-1
• Also known as “n” or “convergence factor”,
used to calculate convergence of meridians

46. LAMBERT CONFORMAL
• Entirely mathematical projection
• Cone placed over R.E intersecting the sphere
along 2 parallels of latitude: the standard
parallels
• Parallel of origin: about halfway between the
standard parallels

47. LAMBERT CONFORMAL
• Scale correct at standard parallels
• Scale minimum at Parallel of origin
• Scale contracts between standard parallels
• Scale expands outside the standard parallels
• Scale considered “constant” constructing the chart
with the 1/6 rule

48. LAMBERT CONFORMAL
• Meridians: straight lines converging towards
nearest pole (pole of projection)
• Parallels: arc of concentric circles equally
distanced centred on the nearest pole.
• Meridians and Parallels intersect at right
angles

49. LAMBERT CONFORMAL
• Convergence = Ch Long x Constant of the cone
• Convergence = Ch Long x Sine of P. of origin

50. LAMBERT CONFORMAL
• Conformal chart
• Convergency (convergence angle) = Actual
angle on a chart formed by intersection of two
meridians
• Convergence :
– Constant due to meridians being straight. (“chart
convergence”)
– Not correct as on the Earth convergence increases
with latitude as sine latitude

51. LAMBERT CONFORMAL
• Chart convergence:
• Larger than Earth
convergence at lower
latitudes than parallel of
origin
• Less than Earth convergence
at latitudes higher than
Parallel of origin

52. LAMBERT CONFORMAL
• GC: approximately a straight line (actually
curve concave towards the parallel of origin)
• RL: curved lines concave to the nearest pole
(directions equal to parallels of latitude
directions)

53. LAMBERT CONFORMAL
• Can be regarded as having the property of
correct shapes of area
• Different Lambert conformal charts will fit N/S
and E/W if scale and standard parallels are the
same

54. LAMBERT CONFORMAL
• Widely used by pilots in:
– Topographical maps for pilot navigation
– Airways (radio navigation) charts
– Plotting charts
– Presentation of meteorological information

55. LAMBERT CONFORMAL
• Measuring courses: use the mid-meridian
between the two positions.
– Accurate value for mean GC courses of departure
and destination.
– It is in effect a RL course value.
– For distances < 200 NM or near the Equator:
deviation insignificant
• The same in South Pole

56. LAMBERT CONFORMAL
• Measuring distances : use the latitude scale
(found on some of the meridians) for more
precision. If not: use the “constant scale” for
the whole chart
• Plotting bearings: (easier as GC straight)
– Only TB (exceptions)
– VOR bearings and others given and measured by the
station : plotted from station’s meridian
– ADF bearings: measured and plotted from aircraft’s
meridian. (must be corrected for convergence)

57. REVIEW OF LAMBERT CONFORMAL
CHART PROPERTIES
• CONFORMAL? – YES
• SCALE CORRECT? - ONLY AT STANDARD
PARALLELS
• CONVERGENCY? – YES. CONSTANT.
• GC? – CONSIDERED STRAIGHT LINES
• RL? – CURVED LINES

58. REVIEW OF LAMBERT CONFORMAL
CHART PROPERTIES
• SHAPES NOT DEFORMED? – ALMOST NOT
• EQUAL AREAS? – NO. EXAGGERATED AT H.L
(SCALE TOO EXPANDED)
• ADJACENT SHEETS FIT? – YES. IF SCALE
AND STANDARD PARALLELS THE SAME
• COVERAGE – LATITUDES EXCEPT ABOVE 80º
• POLES REPRESENTED? – NO

59. POLAR STEREOGRAPHIC

60. POLAR STEREOGRAPHIC
• Perspective projection.
• For use in polar areas.
• Meridians: straight lines radiating from the
centre.
• Parallels: series of concentric circles
increasingly spaced from the centre.
• Meridians and Parallels intersect at right
angles.

61. POLAR STEREOGRAPHIC
• Scale correct at the pole. Increases slightly from
the Pole. (less than 1% above 78.5ºlat)
• Shapes/areas distorted away from pole
• CONFORMAL CHART
• If Equator represented (full hemisphere):
scale Equator = 2 x Scale Pole.
• Formula to calculate scale on these charts:
Scale Lat A = Scale Pole : cos2 (45 – ½ Lat A)

62. POLAR STEREOGRAPHIC
• GC : curves concave to
the Pole. The closer to the
centre of projection, the
more it will approximate
to a straight line.
• RL: curved = spirals
toward the Pole.

63. POLAR STEREOGRAPHIC
• Convergence only correct around the Poles.
• Chart convergence sufficiently accurate for
practical use.
• Convergence = Ch Long
• Coverage: from 65-70º N/S to the nearest
Pole.

64. POLAR STEREOGRAPHIC
• Measuring courses: near the Poles using the
mid-meridian.
• Measuring distances: using the latitude scale
up along a meridian.
• Bearings plotted as in Lambert conformal
projections

65. METHODS OF SHOWING RELIEF
• Terrain elevation above MSL may be indicated in
different ways:
1. SPOT HEIGHTS
2. CONTOUR LINES
3. HATCHURES
4. COLOURING OR TINTING
5. SHADING OF SLOPING TERRAIN

66. SPOT HEIGHTS
• To point out critical elevations
• Indicate height AMSL
•Highest elevation of chart

67. CONTOUR LINES
• Lines connecting
places of equal
elevation, normally
AMSL.
• Indicate Gradient and
Height.

68. HATCHURES
• Short lines
radiating from
high ground.
• Sometimes used
instead of regular
contour lines

69. COLOURING OR TINTING
• To further emphasise
relief indicated by
contour-lines.
• Colour legend on each
chart.
• To designate areas within
certain elevation ranges.
• Darker colours mean
higher terrain.

71. SHADING OF SLOPING TERRAIN
• Graduated shading
to the SE side of
elevated terrain and
on NW side of
depressions
• Three-dimensional
effect

72. CONVENTIONAL SIGNS
• Cultural features or man-made structures
• Landmarks hazardous to low flying aircraft
• Natural features
• Information
related to
aerodromes
• ICAO ANNEX 4:AERONAUTICAL CHARTS STANDARD
SYMBOLS