How do small insects not get hurt by raindrops?

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It's easy to intuitively think of raindrops hitting small organisms as being equivalent to cinder blocks falling from the sky and hitting us, but that's not how it plays out.

Raindrops are not moving very fast, nor are they heavy. For a raindrop to be considered a raindrop it has to be between roughly .5mm - 6mm (about the size of a fly at the largest).  A big raindrop has a terminal velocity of about 10 m/s (20 mph), with smaller drops down closer to 0.9 m/s (2 mph).  That's basically to say that there isn't much energy in any given raindrop to do a lot of damage with.

Another part is that smaller creatures are quite strong and tough as a result of the Square-cube Law. This is why an ant or a spider is proportionally so strong and an element of this is why a mouse generally won't fall fast enough to get seriously injured whereas a horse or an elephant will splash from a long fall. Also why a raindrop falling on a shrew or a butterfly isn't the equivalent of a cinder-block falling on a human.

Raindrops can certainly hinder small organisms, but that tends to be more an issue of surface tension, heat loss, splashing and water flow, and things like that rather than the actual impact of the water droplet.

For many flying organisms fog (and, to a certain degree, drizzle) is actually  much more difficult thing to deal with as the tiny water droplets are suspended in the air and they accumulate on the surface of the flying organism, adding a lot of weight. This is why you usually don't get mosquitoes buzzing about when it's foggy.

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