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On a Direct Mercator chart, a certain chart length along 45°N represents a distance of 90 NM on the surface of the Earth.The same length on a chart along latitude 30°N will represent a distance on the Earth of…

  • A
    78 NM.
  • B
    45 NM.
  • C
    73.5 NM.
  • D
    110 NM.

Distance between two parallels of latitude (along a meridian)

1 minute of latitude at any point on earth = 1 nm
1°of latitude at any point on earth = 60 nm

Distance between two meridians of longitude (along a parallel)

Meridians converge from the Equator to the Pole.
A change in longitude (degrees) will not represent the same East-West distance (nm) for different latitudes.

Departure = change in longitude (°) x 60 x cosine (latitude)

First calculate the change of longitude for the 45ºN parallel:

Change in longitude = 90 / (60 x cosine (45)) = 2,12º

Calculate the departure for the same change of longitude for the 30ºN parallel:

Departure = 2,12º x 60 x cosine (30) = 110 nm

While using both formulas we can notice that the change in longitude is constant:

D1 / (60 x cosine (latitude 1)) = D2 / (60 x cosine (latitude 2))

D1 / cosine (latitude 1) = D2 / cosine (latitude 2)

90 / cosine (45º) x cosine (30º) = 110 nm

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