8.Charts

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