Exponential cloud collector growth
= Exponential cloud collector growth
{title2=$R=R_0e^{\alpha_Rt}$}
If a spherical collector falls with $u_R=k_RR$ through constant liquid-water content $L$ and efficiency $E$, neglecting condensation and small-droplet fall speed, then $\dot R=\alpha_RR$ with $\alpha_R=k_RLE/(4\rho_l)$. A uniform updraft gives $h(t)=Ut-(k_RR_0/\alpha_R)(e^{\alpha_Rt}-1)$. The formula is valid only while the assumed cloud conditions hold.