  Collagen fibrils are versatile self-assembled structures that provide
mechanical integrity within mammalian tissues. The radius of collagen fibrils
vary widely depending on experimental conditions \textit{in vitro} or
anatomical location \textit{in vivo}. Here we explore the variety of
thermodynamically stable fibril configurations that are available. We use a
liquid crystal model of radial collagen fibril structure with a double-twist
director field. Using a numerical relaxation method we show that two
dimensionless parameters, the ratio of saddle-splay to twist elastic constants
$ k_{24}/K_{22}$ and the ratio of surface tension to chiral strength
$\hat{\gamma} \equiv \gamma/(K_{22}q)$, largely specify both the scaled fibril
radius and the associated surface twist of equilibrium fibrils. We find that
collagen fibrils are the stable phase with respect to the cholesteric phase
only when the reduced surface tension is small, $\hat{\gamma} \lesssim 0.2$.
Within this stable regime, collagen fibrils can access a wide range of radii
and associated surface twists. Remarkably, we find a maximal equilibrium
surface twist of $0.33$ rad ($19^{\text{o}}$). Our results are compatible with
corneal collagen fibrils, and we show how the large surface twist is needed to
explain the narrow distribution of corneal fibril radii. Conversely, we show
how small surface twist is required for the thermodynamic stability of tendon
fibrils in the face of considerable polydispersity of radius.
