Kavrayskiy VII projection

The Kavrayskiy VII projection is a map projection invented by Soviet cartographer Vladimir V. Kavrayskiy in 1939 for use as a general-purpose pseudocylindrical projection. Like the Robinson projection, it is a compromise intended to produce good-quality maps with low distortion overall. It scores well in that respect compared to other popular projections, such as the Winkel tripel, despite straight, evenly spaced parallels and a simple formulation. Regardless, it has not been widely used outside the former Soviet Union.

The projection is defined as

$${\displaystyle {\begin{aligned}x&={\frac {3\lambda }{2}}{\sqrt {{\frac {1}{3}}-\left({\frac {\varphi }{\pi }}\right)^{2}}}\\y&=\varphi \end{aligned}}}$$

where ${\displaystyle \lambda }$ is the longitude, and ${\displaystyle \varphi }$ is the latitude in radians.

The inverse would then be $${\displaystyle {\begin{aligned}\varphi &=y\\\lambda &={\frac {2x}{3{\sqrt {{\frac {1}{3}}-\left({\frac {y}{\pi }}\right)^{2}}}}}\end{aligned}}}$$