Empirical relation between projected proper length and two-lobe proper volume for RGs from Ineson et al. (2017), Oei et al. (2022, 2023b). The power law–like trend motivates Eq. (24). The green fit is based on giants only, whilst the grey fit is based on all RGs. V_GRG is the mean two-lobe proper volume of the shortest possible giants (i.e. giants for which l_p = l_p, GRG), while γ is the exponent of the power law. For self-similar RG growth, γ = 3.