Maps, Charts & Projections

D. the scale is only correct along the standard parallels

With two standard parallels a Lambert chart has its true scale along the standard parallels (smaller between them, larger outside).

A. 1 : 3,096,000

Denominators are proportional to cos lat: 3,500,000 x cos 40 / cos 30 = 3,500,000 x 0.766 / 0.866 = 3,096,000. Higher latitude, bigger chart, smaller denominator.

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C. Curve concave to the equator.

A great circle (other than a meridian or the equator) is a curve that is concave to the equator on a direct Mercator, i.e. convex towards the nearer pole.

A. straight line

On a direct Mercator chart a rhumb line is a straight line.

C. cylindrical, non-perspective & conformal

The direct Mercator is a cylindrical, mathematically derived (non-perspective) and conformal projection.

A. the angle of inclination of the meridians to each other

Meridians are parallel at the equator and meet at the poles; the angle between two of them at a given latitude is the convergency, = dlong x sin lat.

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B. curves concave to the nearer pole

On a polar stereographic chart rhumb lines are curves concave to the pole.

D. the meridian of tangency

The cylinder is wrapped round the earth touching along a chosen meridian (the meridian of tangency); scale is correct along it and expands with distance from it - the transverse version of "correct at the equator" on the direct Mercator.

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D. 1 : 3,500,000

Departure = 300 x cos 60 = 150 NM = 277.8 km = 27,780,000 cm. Scale = 8 : 27,780,000 = 1 : 3,470,000.

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D. 1.0

On a polar stereographic chart meridians meet at the pole at their true angle, so chart convergence = dlong x 1: n = 1 (= sin 90). On a Mercator n = 0; on a Lambert n = sin of the parallel of origin.

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B. is correct at the equator and expands as the secant of the latitude

The projection stretches each parallel to the length of the equator, by sec lat, and stretches the meridians by the same amount to keep it conformal. So scale at latitude L = scale at the equator x sec L - at 60 deg it is doubled.

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C. 35,000 m

7 cm x 500,000 = 3,500,000 cm = 35,000 m = 35 km (about 19 NM).

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A. Rectangular

The graticule of a direct Mercator chart is rectangular (straight, perpendicular lines; the parallels are unequally spaced).

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C. constant everywhere

On a direct Mercator chart the meridians are parallel, so chart convergency is zero (constant) everywhere.

A. with the exception of meridians and the equator, they are curves concave to the equator

Apart from meridians and the equator, a great circle on a direct Mercator chart is a curve concave to the equator (convex to the nearer pole).

A. large N/S extension

Transverse Mercator suits areas of large north-south extent.

A. scale at the standard parallels

The nominal scale of a Lambert chart is the scale at the standard parallels.

A. parallel of origin

On a Lambert conformal conic chart convergence equals earth convergence only at the parallel of origin.

A. 86Nm

70 x cos 30 / cos 45 = 85.7, about 86 NM.

C. Meridian of longitude.

Only meridians are perfectly straight on a Lambert chart; great circles are curved (nearly straight) and parallels are arcs.

B. the opposite pole

Polar stereographic: tangent plane at one pole, light at the OTHER pole - which makes it conformal. With the light at the centre it is the gnomonic (great circles straight); with it at infinity, orthographic.

A. The same as earth convergency at the parallel of origin.

Lambert chart convergence equals earth convergency at the parallel of origin and is constant over the chart.

B. is constant along a parallel of latitude

Lambert scale is constant along a parallel and varies with latitude only.

A. 23 deg

dlong 30 deg x sin 50 (0.766) = 23 deg.

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C. ellipses

Turned on its side, the Mercator shows the meridian of tangency and the equator straight; the parallels become ellipses round the poles.

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B. Direct Mercator

On a direct Mercator chart the scale expands as sec latitude, so the poles lie at infinity and cannot be shown; polar areas use the polar stereographic (or a transverse Mercator) chart.

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A. 1 : 1,852,000

Scale expands as sec lat: at 60 deg the chart is twice as big, so the denominator halves: 3,704,000 x cos 60 = 1,852,000.

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A. Places of equal elevation

Contours are lines joining places of equal elevation.

B. 60 N or S

6 cm x 9,260,000 = 555.6 km = 300 NM for 10 deg of longitude: 30 NM per degree = 60 x cos lat, so cos lat = 0.5 and lat = 60.

B. map convergence

The change of track between two points on a Lambert chart equals the map (chart) convergence.

C. 1/1296400

49 NM = 90,748 m; 7 cm = 0.07 m; scale = 90,748 / 0.07 = 1 : 1,296,400.

B. Direct Mercator

The poles lie at infinity on a direct Mercator chart.

A. 122.3NM

Distance for a given chart length varies as cos (lat): 120 x cos 10 / cos 15 = 122.3 NM.

D. 110 NM

90 x cos 30 / cos 45 = 110 NM.

A. 1:26 000 000

The 53 N parallel is 21,600 x cos 53 = 13,000 NM = 24,075 km long, drawn as 133 cm: scale 1:18.1 million at 53 N. Mercator scale varies with the secant of latitude, so at 30 S it is 1:18.1 M x cos 30 / cos 53 = about 1:26 million.

C. 088

In the southern hemisphere the rhumb line track is the GC track minus the conversion angle when heading east: 095 - 7 = 088.

B. the chart convergence between the aircraft and station meridians

The ADF gives the true bearing at the AIRCRAFT meridian (heading + relative bearing). A Lambert straight line is (nearly) a great circle, so no conversion angle is applied; but to draw it from the station the direction must be referred to the STATION meridian, which differs by the chart convergence = change of longitude x sin (parallel of origin). Then add or subtract 180 for the QTE.

A. -60 deg

Convergency = final - initial great-circle track = 290 - 350 = -60 deg (the track decreased).

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B. Decrease by 6°

Convergency = d.long x sin mean lat = 7 x sin 60 = 6 deg. Travelling west in the northern hemisphere the great-circle track decreases, here by about 6 deg.

A. Distortion increases away from the Equator.

Mercator distortion grows with distance from the equator (scale = sec lat).

C. dlong x sin mean lat

Convergency grows from zero at the equator to dlong at the pole, as the sine of latitude. Departure (distance) uses the cosine.

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D. of the same elevation above mean sea level

Contours join places of equal height; isogonals join equal variation.

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C. convergency (grid convergence)

A grid is laid over a polar chart because meridians converge so fast; grid north differs from true north by the convergence. Grid north vs magnetic north is grivation.

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C. conversion angle

A straight line on a Mercator is a rhumb line. Between the rhumb line and the great circle joining the same points lies the conversion angle = 1/2 x dlong x sin mean lat.

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D. 1 : 5,600,000

Departure = 600 x cos 45 = 424 NM = 785.8 km. 78,580,000 / 14 = 5.6 million.

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B. half the convergency

Conversion angle = 1/2 x convergency = 1/2 x dlong x sin mean lat. It is applied to a radio (great-circle) bearing to plot it as a straight line on a Mercator chart.

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C. midway between A and B

The straight line is (nearly) a great circle, whose track changes along the way. Its direction at the mid meridian equals the rhumb line track between the two points.

B. 1 : 976,000

60 x cos 48 = 40.15 NM = 74.36 km = 7,436,000 cm; / 7.62 = 976,000.

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B. Parallel and Un-equally spaced

On a direct Mercator chart the parallels are parallel straight lines whose spacing grows towards the poles.

A. 1 : 9,260,000

Departure = 600 x 0.5 = 300 NM = 555.6 km = 55,560,000 cm; / 6 = 9.26 million. (At the equator the same 10 deg would give 1 : 18.5 million.)

B. 1 : 5,000,000

600 x cos 65 = 254 NM = 470 km. 3.75 in = 9.5 cm. 47,000,000 / 9.5 = 4.9 million - about 1 : 5,000,000.

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A. 225

dlong = 90 deg. A, B and the pole form an isosceles triangle with 90 deg at the pole, so the line leaves A at 45 deg to the meridian, swinging west of the direction to the pole (180): 180 + 45 = 225.

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B. 8,000 ft

The grid MORA/MSA figure is shown in hundreds of feet: 80 = 8,000 ft, giving terrain and obstacle clearance anywhere in that square.

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A. 1 : 885,000

North or south makes no difference - only the latitude: 1,000,000 x cos 40 / cos 30 = 885,000.

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A. cylindrical

The Mercator projection is cylindrical.

B. route charts along a selected great circle

The cylinder is tilted to touch the earth along any chosen great circle, so the chart is accurate along that great-circle route - used for long-range route charts.

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B. a curve concave to the pole, nearly straight

Near the pole a great circle is very nearly a straight line, curving slightly towards the pole - concave to it. Rhumb lines curve much more, also concave to the pole.

A. 27 NM

At 60 deg the scale is doubled: 1 : 1,000,000. 5 cm = 50 km = 27 NM.

A. slightly smaller (contracted) than the nominal scale, and larger outside them

The correct answer is: slightly smaller (contracted) than the nominal scale, and larger outside them.

A. 10 cm

54 NM x 1.852 = 100 km = 10,000,000 cm; / 1,000,000 = 10 cm.