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CHARTSCHARTS
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.
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.
• 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.
• 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.
• 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.
• 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.
– 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.
• The reduced Earth is the only completely accurate small-scale representation of the Earth.
• 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
• 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
• PROJECTION: The method for systematically representing the meridians and parallels of the Earth on a plane surface.
• METHODS OF PROJECTION
• PERSPECTIVE
• MATHEMATICAL
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.
PROJECTION TYPES
PLANE PROJECTIONS
CONICAL PROJECTIONS
CYLINDRICAL PROJECTIONS
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
Projection plane
Tangent point
Light source:A. GNOMONICB. STEREOGRAPHICC. ORTHOGRAPHIC
CONICAL PROJECTIONS
• Cone placed over the Reduced Earth tangential to a predetermined parallel
• Light source in centre of globe
Further modification: Cone cutting two parallels
CYLINDRICAL PROJECTIONS
•A cylinder is placed over the reduced Earth
•Light source: centre of the globe
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.
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)
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
METHODS OF INDICATING SCALE
The 2 most commonly used in aviation are:1. 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)
2. Graduated scale line
• 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%)
• 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
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)
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?
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
MERCATOR ECUATORIAL PROJECTION
MERCATOR ECUATORIAL PROJECTION
• Cylinder tangential to globe at equator
• Light source at centre of the globe
• Complex mathematical construction
MERCATOR ECUATORIAL PROJECTION
• Meridians: • Vertical parallel lines.• Equally spaced
• Parallels: • Horizontal parallel lines • Cross meridians at right angles• distance increasing towards the poles
MERCATOR ECUATORIAL PROJECTION
• RL Straight lines• GC Curved lines convex to the nearer
pole
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
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
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
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
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
REVIEW OF MERCATOR CHART PROPERTIES
• CONFORMAL? – • SCALE CORRECT? - • CONVERGENCY? – • GC? – • RL? –
YES
ONLY AT EQUATOR
0º AND CONSTANT
CURVED
STRAIGHT LINES
REVIEW OF MERCATOR CHART PROPERTIES
• SHAPES NOT DEFORMED? –
• EQUAL AREAS? –
• ADJACENT SHEETS FIT? – • COVERAGE – • POLES REPRESENTED? –
ONLY SMALL
ONES AND AT LOW LATITUDES
NO. EXAGGERATED AT
HIGH LATITUDES
YES
UNTIL 70/75º N/S
NO_
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
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
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
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
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
LAMBERT CONFORMAL• Convergence = Ch Long x Constant of the cone• Convergence = Ch Long x Sine of P. of origin
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
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
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)
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
LAMBERT CONFORMAL
• Widely used by pilots in:
– Topographical maps for pilot navigation– Airways (radio navigation) charts– Plotting charts– Presentation of meteorological information
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
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)
REVIEW OF LAMBERT CONFORMAL CHART PROPERTIES
• CONFORMAL? – • SCALE CORRECT? - • CONVERGENCY? – • GC? – • RL? –
YES
ONLY AT STANDARD PARALLELS
YES. CONSTANT.
CONSIDERED STRAIGHT LINES
CURVED LINES
REVIEW OF LAMBERT CONFORMAL CHART PROPERTIES
• SHAPES NOT DEFORMED? –
• EQUAL AREAS? –
• ADJACENT SHEETS FIT? – • COVERAGE – • POLES REPRESENTED? –
ALMOST NOT
NO. EXAGGERATED AT H.L(SCALE TOO EXPANDED)
YES. IF SCALE
AND STANDARD PARALLELS THE SAME
LATITUDES EXCEPT ABOVE 80º
NO
POLAR STEREOGRAPHIC
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.
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)
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.
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.
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
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
SPOT HEIGHTS• To point out critical elevations• Indicate height AMSL
•Highest elevation of chart
CONTOUR LINES
• Lines connecting places of equal elevation, normally AMSL.
• Indicate Gradient and Height.
HATCHURES
• Short lines radiating from high ground.
• Sometimes used instead of regular contour lines
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.
SHADING OF SLOPING TERRAIN
• Graduated shading to the SE side of elevated terrain and on NW side of depressions
• Three-dimensional effect
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
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