The Mercator Chart Flashcards
On a mercator chart, a rhumb line appears as a -
straight line
On a mercator chart, convergency at the poles =
zero. There is no convergency on a mercator chart
Meridians on a mercator chart is -
parallel straight lines
The scale of a mercator chart is only correct at the -
equator
On a mercator chart, great circles are -
curved towards the poles
The mercator latitude limits are -
75 N and 75 S
Scale calculation:
Latitude = 60 N
scale at the equator = 1:1 000 000
1 000 000 x cos 60 = 500 000
The scale increases towards the poles
Scale calculation:
The scale at 30 S is 1: 1 000 000
What is the scale at the equator?
The scale decreases towards the equator:
1 000 000 / cos 30 = 1 154 701
In order to convert a great circle bearing(radio bearing) to rhumb line bearings, what must be applied to the great circle bearing?
Conversion angle
Radio bearings on a mercator is a -
great circle track which is curved(towards the poles)
Before applying the relative bearing, magnetic heading or compass heading must first be converted to -
True.
When the scale increases, the value?
reduces
When the scale decreases, the value?
Increases
On a mercator, the scale increases towards the?
Which means the value?
poles
Decreases
On a mercator, the scale decreases towards the?
Which means the value?
Equator
Increases
when a problem includes longitude difference, what formula should be considered?
Departure formula
How to calculate:
Determine the distance in cm between meridians 1 degree apart on a chart the scale of which is 1:2 000 000 at 40 N
60( the distance) x 185 300cm x cos 40 / 2 000 000
How to calculate:
On a Mercator chart the distance between meridians 173 W and 177 E is 33cm. The latitude at which the scale is 1: 3 000 000 is?
- First find the difference in longitude:
Remember that whenever you add longitude, and it results in a value, you must subtract 360.
177 + 173 = 350
350 - 360 = 10
- Find the corresponding distance of 10 degrees and the scale:
10 x 60 = 600nm
Which means 33cm = 600nm.
600 x 185 300cm = 111 180 000cm
now 33cm = 111 180 000cm
111 180 000cm / 33 = 3 369 090cm
the scale is 1:3 369 090
- Use the ABBA formula:
Denom A x cos B = Denom B x cos A
= 3 369 090 x cos B = 3 000 000 x cos A
Thus, 3 000 000 / 3 369 090 = cos 0.89
Inverse of cos 0.89 = 27 degrees.
Which trig function should be utilised with mercator scale problems -
cos of latitude
All charts used for navigation must be -
orthomorphic/conformal (plotted bearings are correct)
How to solve.:
An aircraft in the southern hemisphere obtains an RMI bearing from a VOR station of 058°. Station variation is 22° E, variation at the aircraft is 19° E. The deviation is 2° W and the conversion angle between the aircraft and the VOR is 4°. On a mercator chart the bearing to plot from the station is:
First of all, only the conversion angle and the VOR variation apply. The bearing obtained need to be converted to true, since all maps are true and not magnetic.
The aircraft heading is irrelevant, since we do not need the aircraft’s heading in order to plot QTE from the station. Thus, compass deviation is also irrelevant.
The received bearing = 058° + 22 = 080. Therefor relative to the beacon the aircraft is roughly to the west(080 + 180). Draw a diagram with straight meridians.
On the mercator chart, a rhumb line will be straight, which is also the required track in this question.
The great circle track will be a curved line bias to the poles, draw it.
Now we can apply the conversion angle.
first take
will the change of long of two points on the same parallel differ with latitude on the mercator?
No, since the meridians parallel. No convergency with latitude.
How to solve:
An aircraft flying due east along the 20°N parallel covers a distance of 14cm in 27 minutes on a Mercator chart, The scale of the chart is 1: 1 000 000 at 35°N. the aircraft’s ground speed is:
the corresponding earth distance of 14cm at 20°N, 35°N and at the equator, without multiplying or dividing by the cos(lat), differ significantly (scale not constant). The reason we use the scale formula is to find the actual scale at a given latitude, I.E the cosine of lat rectifies the scale error, and thus provides the actual corresponding earth distance.
First find the equator scale:
Remember that scale decreases towards the equator(value increases) and increases towards the poles (value decreases).
scale at the equator = 1 000 000 / cos 35° = 1 220 774
scale at 20°N = 1 220 774 x cos 20° = 1 147 152.
scale at 20°N = 1: 1 147 152
14cm = 16 060 140
14cm = 86.67nm
- 67 / 27min = 3.2nm per minute
- 2 x 60 = 192nm per hour.
= 192knots.
For mercator radio bearings, always apply convergency & variation where -
the bearing is measured
