Orientational persistence length of a freely rotating chain (${\ell }_p=-b/\ln \cos \vartheta$)

With independently uniform torsion, consecutive forward tangent correlations multiply by $\cos \vartheta$. After $n$ bonds the correlation is $(\cos \vartheta {)}^n$. Matching it to $e^{-nb/{\ell }_p}$ gives the displayed decay length for positive correlation. This discrete orientational definition need not equal half the equivalent Kuhn length exactly.