I have been working on helicopter design and autorotation for a while. An Index used for this is the so-called "Autorotation Index" Evan A. Fradenborugh derives it in this work https://doi.org/10.4050/JAHS.29.73. Basically, it describes the ratio of available energy compared to needed energy for a flare.
In Equation 10 he presents the final result, but in Equation 9, he also provides a useable index that is non-dimensional. In this Equation, an influence is ϱ * g (disregarding surface-level density as it cancels out anyways). It seems obvious why a denser atmosphere increases the "energy" available, as you can create more lift in denser parts of the atmosphere.
However, I do not understand how g is also increasing this factor. If at all, a stronger gravitational pull should lower this factor as more energy is needed in the rotor to overcome gravity and land safely.
What are your thoughts on this?