Beard and Chuang model

The Beard and Chuang model is a well known and leading theoretical force balance model used to derive the rotational cross-sections of raindrops in their equilibrium state by employing Chebyshev polynomials in series.

The radius-vector of the raindrop's surface ${\displaystyle r(\theta )}$ in vertical angular direction ${\displaystyle \theta }$ is equal to

${\displaystyle r(\theta )=a[1+\sum c_{n}cos(n\theta )]}$,

where shape coefficients ${\displaystyle c_{n}\cdot 10^{4}}$ are defined for the raindrops with different equivolumetric diameter as in following table

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