Cableizer

Length corrugated sheath (pitch)

The length L or width of the corrugation, called pitch, acc. CIGRE TB 880 Guidance Point 30

In order to solve for $L_{pitch}$ with a given $F_{cor,sh}$ and $H_{sh}$ we have to solve a transcendental equation to get $\beta$. It has no closed-form solution in terms of elementary functions and can only be solved numerically (e.g. Newton-Raphson or fixed-point iteration). Once we have $\beta$ we can solve a quadratic equation. Based on the physical geometry constraint from TB 880 ($H_{sh} ≤ 0.5 \cdot L_{pitch}$), the + root generally satisfies this for realistic corrugation profiles.

Symbol
$L_{pitch}$
Unit
mm
Formulas
$\beta = \frac{L_{pitch} \cdot H_{sh}}{0.25\,L_{pitch}^{2} + H_{sh}^{2}} \;\longrightarrow\; F_{cor\_sh} = \frac{\arcsin(\beta)}{\beta} \;\longrightarrow\; \sin(F_{cor\_sh}\,\beta) = \beta \;\longrightarrow\; 0.25\,\beta\,L_{pitch}^{2} - L_{pitch}\,H_{sh} + \beta\,H_{sh}^{2} = 0$
Used in
$F_{cor,sh}$
Effective length per unit pitch length corrugated sheath
$L_{cor,sh}$
Length corrugated sheath [mm]