  This paper reports on the efficacy of the G\"ortler number in scaling the
laminar-turbulent boundary-layer transition on rotating cones facing axial
inflow. Depending on the half-cone angle $\psi$ and axial flow strength, the
competing centrifugal and crossflow instabilities dominate the transition.
Traditionally, the flow is evaluated by using two parameters: the local
meridional Reynolds number $Re_l$ comparing the inertial versus viscous effects
and the local rotational speed ratio $S$ accounting for the boundary-layer
skew. We focus on the centrifugal effects, and evaluate the flow fields and
reported transition points using G\"ortler number based on the azimuthal
momentum thickness of the similarity solution and local cone radius. The
results show that G\"ortler number alone dominates the late stages of
transition (maximum amplification and turbulence onset phases) for a wide range
of investigated $S$ and half-cone angle ($15^{\circ} \leq \psi \leq
50^{\circ}$), although the early stage (critical phase) seems to be not
determined by the G\"ortler number alone on the broader cones
($\psi=30^{\circ}$ and $50^{\circ}$) where the primary crossflow instability
dominates the flow. Overall, this indicates that the centrifugal effects play
an important role in the boundary-layer transition on rotating cones in axial
inflow.
