How to Calculate and Draw Mercator's Projection | Sanjib Mandal | SanGeotics

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Mercator’s Projection
Hello friends, Welcome to my RUclips channel. Today I am going to discuss about on a new topic that is Calculation, Construction and different properties of Mercator’s Projection or Cylindrical Orthomorphic Projection. This is the 3rd lesion of Map projection series. In the 1st lesion we had been discuss about Polar Zenithal Stereographic Projection and 2nd lesion we had been discuss about Cylindrical Equal Area Peojection. Which link is Provided into Description.
Now we Calculate and Construction of Mercator’s Projection. Problem: Here, Draw a Mercator’s projection or Cylindrical Orthomorphic Projection for World Map on R.F = 1:295000000 at 20 ͦinterval.
Calculation:
Step - 1: Radius of Generating globe reduced to given scale (R) = Radius of Earth / Denominator of R.F, Earth radius is constant, it is 640 000 000 whole divided by Denominator of R.F is 295000000, is equal to 2.17.
Step - 2: Meridian have to be drawn at 20 ͦ interval 180 ͦW, 160 ͦW, 140 ͦW, 120 ͦW, 100 ͦW, 80 ͦW, 60 ͦW, 40 ͦW,20 ͦW, 0 degree, 20 ͦE, 40 ͦE, 60 ͦE, 80 ͦE, 100 ͦE, 120 ͦE, 140 ͦE, 160 ͦE, 180
Step - 3: Parallels have to be drawn at 20 ͦ interval, 80 ͦN, 60 ͦN, 40 ͦN, 20 ͦN, 0 ͦ, 20 ͦS, 40 ͦS, 60 ͦS, 80 ͦS
Step - 4: Division along the equator and Parallels at an interval 20 ͦ spacing the Meridian, is equal to 2πR/360 ͦ x Interval, = π x R means 2.17 whole divided by 180 into interval means 20 ͦ , is equal to 0.76 cm.
Step - 5: Height of any parallel above the equator at 20 ͦ interval is equal to 2.3026 into R Into log tan (90 ͦ+ π / 2), these is the constant formula.
Now we construct the table:-
The table head as ᵩ, R, (90 ͦ+ᵩ/ 2), and 2.3026 x R x log tan (90 ͦ+ᵩ/ 2). Under the ᵩ caption we write the Parallels as 20 ͦN & S, 40 ͦ N & S, 60 ͦ N & S, 80 ͦN & S. Next, R means radius, radius is 2.17 cm. Next, 2.3026 into R is 2.17 into log tan (90 ͦ+ ᵩ / 2) is 55 is equal to 0.77 cm. Similarly we calculate the remaining heights of the parallels from the Equator as 1.65, 2.86 and 5.29 cm.
With the help of this table we draw a Mercator’s projection.
1st, Draw a pair of straight lines intersecting each other at right angles. These lines will represents the equator and the central Meridian respectively.
Next for spacing the parallels at varying distance from the equator as per calculation shown in the table of step - 5. Draw a Horizontal lines through this points to represent the Parallels.
Then, divide the Equator at equal space by the equation (2πR/360 ͦ x Interval) for spacing the Meridians. After that erase the extra extended lines and level the latitudes as 0 ͦ, 20 ͦN, 40 ͦN, 60 ͦN, 80 ͦN, 20 ͦS, 40 ͦS, 60 ͦS, and 80 ͦS and also level the longitude as 0 degree, 20 ͦE, 40 ͦE, 60 ͦE, 80 ͦE, 100 ͦE, 120 ͦE, 140 ͦE, 160 ͦE, 180 ͦ, 20 ͦW, 40 ͦW, 60 ͦW, 80 ͦW, 100 ͦW, 120 ͦW, 140 ͦW, 160 ͦW, 180 ͦ.
Finally, mark the boundary. Put the scale at the bottom, we can draw Linear scale or simply put the R.F value as 1:295 000 000. And also give a suitable title as MERCATOR’S PROJECTION.
Also can also draw the World Map on this projection, like this,
Now we discuss the different properties of Mercator’s Projection.
1, All parallels are straight lines and equal in length to that of the equator.
2. All meridians are also straight lines, drawn parallel to each other.
3. All parallels and meridians intersect each other at right angles.
4, All meridians are spaced at equal distance on the equator
6. Any straight line drawn in any direction on a Mercator's Chart passes all parallels and navigation, where it is easy for sailing along a series of constant bearing.
9. However the area property in this projection is greatly distorted. The areas lying the higher latitudes are shown larger than the true scale. Greenland being truly 1/10th of the Size of South America is projected even larger than South America in Mercator's Projection.
10. The poles cannot be shown on this projection.