Cylindrical equal area projection

Cylindrical equal area projection (also called Lambert's projection). A cylinder touches the globe at the equator, and the graticule is projected onto it with parallel rays.

The book's construction (world, R.F. 1 : 300,000,000, interval 15°):

• Radius of the reduced earth = 640,000,000 ÷ 300,000,000, about 2.1 cm.
• Length of the equator = 2πR, about 13.2 cm; divided into 24 parts of 15°, about 0.55 cm each.
• Draw a circle of radius 2.1 cm and mark the angles 15°, 30° ... 90° north and south. Draw the equator line of 13.2 cm beside it, divided into 24 parts. Draw a perpendicular at the 0° point, and carry each parallel across from the circle as a line as long as the equator.

Properties:

• Parallels and meridians are straight lines crossing at right angles.
• The polar parallel is as long as the equator.
• Scale is true only along the equator.
• Areas are correct, but shapes are distorted, more and more towards the poles: it is not orthomorphic. Area is kept equal by squeezing the parallels closer together as they are stretched sideways.

Uses: best for areas between 45° N and 45° S; good for showing the distribution of tropical crops such as rice, tea, coffee, rubber and sugarcane.

From the video: the teacher draws the cylinder being cut open into a rectangle, which is why every parallel ends up the same length as the equator.

Example (new): at R.F. 1 : 200,000,000, the reduced earth's radius is 640,000,000 ÷ 200,000,000 = 3.2 cm, so the equator line is 2 × 3.14 × 3.2, about 20.1 cm, and each 15° step about 0.84 cm.