  A rank is a notion in descriptive set theory that describes ranks such as the
Cantor-Bendixson rank on the set of closed subsets of a Polish space,
differentiability ranks on the set of differentiable functions in $C[0,1]$ such
as the Kechris-Woodin rank and many other ranks in descriptive set theory and
real analysis. The complexity of many natural ranks is $\Pi^1_1$ or
$\Sigma^1_2$. We propose to understand the least length of ranks on a set as a
measure of its complexity. Therefore, the aim is to understand which lengths
such ranks may have. The main result determines the suprema of lengths of
countable ranks at the first and second projective levels. Furthermore, we
characterise the existence of countable ranks on specific classes of
$\Sigma^1_2$ sets. The connections arising between $\Sigma^1_2$ sets with
countable ranks on the one hand and $\Sigma^1_2$ Borel sets on the other lead
to a conjecture that unifies several results in descriptive set theory such as
the Mansfield-Solovay theorem and a recent result of Kanovei and Lyubetsky.
