  The setting is a square-tiled surface X. We study the quantity KVol, defined
as the supremum over all pairs of closed curves, of their algebraic
intersection divided by the product of their length, times the volume of X (so
as to make it scaling-invariant). We give a hyperbolic-geometric construction
to compute KVol in a family of Teichm\H{u}ller disks of square-tiled surfaces.
