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On a Direct Mercator chart projection at latitude 30°S, a distance of 80 NM is represented by 3 cm. Using the same chart, 3 cm at latitude 45°N represents...
  • A
    65 NM
  • B

    80 NM as well

  • C
    57 NM
  • D
    98 NM

The Direct Mercator is a cylindrical projection and its parallel of origin is the Equatror.

Generally, the scale for a Direct Mercator chart is given by the formula:

  • Scale at any latitude = Scale at the Equator x 1/cos Latitude.

The scale expands as the secant of the latitude. So, as scale varies with latitude, it is normal for a Mercator scale to be given at only one latitude, which is called "scale latitude" and for scale at other latitudes to be calculated using the formula above.

When working with questions comparing distances and scales on a Mercator projection at different latitudes, we use the equation:

  • "ABBA": Earth DistanceA(or Scale Lat A) x cos Lat B = Earth DistanceB(or Scale Lat B) x cos Lat A.

For this question, using the "ABBA" equation, we get:

Earth distance at 30o x cos 45o = Earth distance at 45o x cos 30o ⇒
Earth distance at 45o = (Earth distance at 30o x cos 45o) / cos 30o
Earth distance at 45o = (80 NM x cos 45o) / cos 30o = 65 NM.

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