The Mollweide projection is an equal-area projection that represents the world in an elliptical shape. This means that areas on the map are proportional to their corresponding areas on the globe. This makes it particularly useful for displaying global data, such as population density, climate zones, or land use, where the preservation of area is essential.
Mollweide’s projection is often used in world maps to balance the distortion of shapes and sizes, providing an accurate visual comparison of different regions.
Key Features
- Parallels of Latitude: The parallels are unequally spaced straight lines, but they are parallel to each other and the equator.
- Meridians of Longitude: The central meridian is a straight line, while all other meridians are equally spaced elliptical arcs that converge at the poles.
- Equal-Area Property: The projection is pseudocylindrical and equal-area, meaning it preserves the relative size of landmasses.
- Scale and Distortion: The scale is true only along the 40°44′ N and S parallels. Distortion is most severe near the outer edges and at high latitudes.
- Usage: It’s primarily used for global maps that display data distributions.
Mollweide Projection
Scale 1 : 250,000,000 | Interval 30°
Mollweide’s projection is an equal-area world map projection in which the entire Earth is represented inside an ellipse.
The equator forms the long horizontal axis, the central meridian forms the vertical axis, the parallels are straight horizontal lines, and the remaining meridians are smooth curves joining the two poles.
Step 1 – Calculate the Reduced Radius of the Earth
Take the mean radius of the Earth as approximately:
The given representative fraction is:
First convert the Earth’s radius into centimetres:
Now divide by the scale denominator:
Therefore, the reduced radius used for the construction is approximately 2.5484 cm.
Step 2 – Calculate the Dimensions of the Ellipse
In Mollweide’s projection, the world is enclosed by an ellipse whose major axis is twice the minor axis.
Major Axis
Minor Axis
Major axis = 14.42 cm
Minor axis = 7.21 cm
Step 3 – Draw the Main Axes
Draw a horizontal line AB = 14.42 cm. This line represents the equator.
Mark the midpoint of AB as O.
Through O, draw a perpendicular vertical line PN = 7.21 cm.
Since O is the midpoint:
Point P represents the North Pole and point N represents the South Pole.
Step 4 – Draw the Outer Ellipse
Draw a smooth ellipse passing through the four points A, P, B and N.
The ellipse forms the outer boundary of the complete world map.
Step 5 – Calculate the Positions of the Parallels
The parallels in Mollweide’s projection are straight horizontal lines, but they are not equally spaced.
For each latitude φ, first calculate the auxiliary angle θ from:
After obtaining θ, calculate the vertical distance from the equator:
Example: Position of 30° N
For:
Solving the auxiliary equation gives approximately:
Therefore:
Measure 1.456 cm upward from O along the central meridian to locate 30° N.
Measure the same distance downward from O to locate 30° S.
Parallel Distances from the Equator
| Latitude | Distance from Equator |
|---|---|
| 90° N | +3.604 cm |
| 60° N | +2.748 cm |
| 30° N | +1.456 cm |
| 0° | 0 cm |
| 30° S | −1.456 cm |
| 60° S | −2.748 cm |
| 90° S | −3.604 cm |
Mark these distances on the central meridian.
Through the marked points, draw horizontal lines across the ellipse, stopping each line where it meets the boundary.
Step 6 – Calculate the Positions of the Meridians
Draw meridians at intervals of 30°:
The central meridian, 0°, is represented by the straight vertical line PN.
All the remaining meridians are curved.
Their horizontal position on each parallel is calculated from:
where:
λ = longitude being plotted
λ0 = central longitude
θ = auxiliary angle corresponding to the latitude
Example: 60° E at 30° N
At 30° N:
Convert 60° to radians:
Therefore:
On the 30° N parallel, measure approximately 2.198 cm to the right of the central meridian to locate 60° E.
Measure the same distance to the left to locate 60° W.
Step 7 – Plot the Longitude Points on Each Parallel
The distance between meridians decreases progressively from the equator towards the poles.
Longitude Positions on the Equator
| Longitude | Distance from Central Meridian |
|---|---|
| 30° | 1.201 cm |
| 60° | 2.403 cm |
| 90° | 3.604 cm |
| 120° | 4.805 cm |
| 150° | 6.007 cm |
| 180° | 7.208 cm |
Longitude Positions on 30° N and 30° S
| Longitude | Distance from Central Meridian |
|---|---|
| 30° | 1.099 cm |
| 60° | 2.198 cm |
| 90° | 3.297 cm |
| 120° | 4.396 cm |
| 150° | 5.495 cm |
| 180° | 6.594 cm |
Longitude Positions on 60° N and 60° S
| Longitude | Distance from Central Meridian |
|---|---|
| 30° | 0.777 cm |
| 60° | 1.555 cm |
| 90° | 2.332 cm |
| 120° | 3.109 cm |
| 150° | 3.887 cm |
| 180° | 4.664 cm |
Plot all longitude positions symmetrically on both sides of the central meridian.
Step 8 – Join the Meridian Points with Smooth Curves
After all longitude points have been marked, join the points belonging to the same longitude.
For example, join all the points representing 60° E from the North Pole to the South Pole.
Repeat the same procedure for:
Construct corresponding curves on the western side of the central meridian.
All meridians converge at the North and South Poles. The 180° meridian coincides with the outer elliptical boundary.
Step 9 – Label and Finish the Projection
After the complete graticule has been drawn, finish the construction neatly.
- Darken the outer elliptical boundary.
- Keep the equator slightly more prominent than the other parallels.
- Keep the central meridian slightly more prominent than the other meridians.
- Label the parallels as 90° N, 60° N, 30° N, 0°, 30° S, 60° S and 90° S.
- Label the eastern and western meridians at 30° intervals.
- Write the title: Mollweide’s Equal-Area Projection.
- Mention the scale: 1 : 250,000,000.
Construction Sequence at a Glance
- Calculate the reduced radius of the Earth.
- Calculate the major and minor axes of the ellipse.
- Draw the equator and central meridian.
- Construct the outer ellipse.
- Calculate the positions of 30° N, 60° N, 30° S and 60° S.
- Draw the parallels as straight horizontal lines.
- Calculate longitude positions on each parallel.
- Plot longitude points symmetrically east and west of the central meridian.
- Join corresponding longitude points with smooth meridian curves.
- Label the projection and complete the final graticule.
