When rain drops grow by collision and coalescence not every drop of water it hits gets absorbed by the bigger droplet. We therefore need to include an efficiency term in our equation of droplet growth.
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| Equation for the change in droplet radius over time. E represents the collection/coalescence efficiency. v_T is the terminal velocity of the drop, LWC is the liquid water content of the cloud, and ro (the funny looking p) is the density of water. We can integrate and solve this equation to determine the length of time required for a droplet to grow to some determined size. |
Below is a video by Reid Wiseman, an astronaut at the International Space Station, demonstrating the collection efficiency of a raindrop.
