The critical angle is the angle between the near-ground vertical wind shear vector and the storm-relative inflow at the surface, evaluated by Esterheld and Giuliano through the lowest 500 meters. When the value is near 90 degrees, essentially all the horizontal spin in the inflow layer is aligned with the storm's motion and therefore streamwise.
The geometry
Horizontal vorticity in the inflow layer is perpendicular to the shear vector that produced it. The storm-relative wind is the direction the inflow is actually moving into the updraft. When those two are perpendicular to each other, the horizontal vortex tube is aligned parallel to the inflow, which is the definition of streamwise vorticity.
So a critical angle near 90 degrees is not itself the goal. It is the geometric shortcut that says the two vectors have arranged themselves so that the vorticity generated by the local shear is already pointing where the storm is going.
What Esterheld and Giuliano found
The 2008 study in the Electronic Journal of Severe Storms Meteorology examined proximity soundings for tornadic and nontornadic supercells. Significant tornadoes clustered tightly around 90 degrees, roughly plus or minus 10 degrees. Weak tornadoes clustered around 90 degrees but with a broader spread, closer to plus or minus 30 degrees.
Nontornadic supercells sat noticeably further from 90 degrees, with the bulk of cases centered near 110 degrees and a similar 30 degree spread. The separation is not clean, but the distributions are meaningfully different from one another.
How forecasters use it
The critical angle serves as a fast diagnostic on a hodograph. Rather than integrating the full SRH stack, a forecaster can eyeball the low-level segment and the storm motion dot, and if the two vectors are close to perpendicular, note that the near-ground shear layer is set up to feed the updraft streamwise spin.
It is most useful as a compare-and-contrast check between soundings on the same day. A shift toward 90 degrees as the boundary layer evolves, or a departure from 90 degrees as a cell interacts with an outflow boundary, both matter more than the exact number in isolation.
Where it misleads
The critical angle only describes the geometry of one shallow layer. A profile that hits 90 degrees at the surface but flattens above can still produce weaker mesocyclones than a curved profile with a less clean surface angle. Later work reviewing the parameter across larger sounding samples has found less dramatic separations than the original 2008 dataset showed, so it should be treated as a supporting hodograph feature rather than a switch.
As with everything storm-relative, the number depends on the assumed storm motion. Anchored cells, splitters, and boundary interactions can move the storm off the expected right-mover motion, and the critical angle it actually experiences may differ from what a mesoanalysis calculates.