A human falling down from three times their own height (six metres or so) would be horribly injured, while bugs seem to just walk on. How does this work? Shouldn’t they be falling at a similar speed, due to gravity?
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This is yet another consequence of the infamous “square-cube law”. The volume of a shape increases faster than the surface area of a shape as it gets bigger. So, insects have proportionally much more surface area than insides compared to a much larger animal. So they experience proportionally more air resistance than a larger animal. This means they can fall from heights and not fall fast enough to hurt themselves.
This is yet another consequence of the infamous “square-cube law”. The volume of a shape increases faster than the surface area of a shape as it gets bigger. So, insects have proportionally much more surface area than insides compared to a much larger animal. So they experience proportionally more air resistance than a larger animal. This means they can fall from heights and not fall fast enough to hurt themselves.
Your assumption about falling at the same speed applies if there’s no air resistance, but there’s a lot of air resistance, and even a little bit of updraft will keep tiny bug airborne or at least greatly slow. It’s descent. On top of that, it’s not just about the speed with which an object falls. You have to consider the amount of mass involved in the collision between the ground and whatever’s hitting it. Ultimately, it comes down to the physics formula F = ma, which means force equals mass times acceleration. Assuming there was no air resistance, then the acceleration part of that formula is the same for both a person and a small insect, but the mass is greatly different. A small insect may weigh a fraction of a gram, while a human weighs 70 to 100 kg or more. Literally thousands of times more. That means there’s literally thousands of times the force acting on a suddenly decelerating human then there would be on a small insect. When you add in the effects of air resistance, the difference is even greater.
Two reasons.
First, they don’t fall at a similar speed, they fall much much slower. Their “terminal velocity” is much slower. This is because they are very very very light, and they have a lot of surface area – lots of legs and appendages that cause drag. Because they are so light and cause so much drag. Air resistance alone is enough to slow down their fall to a survivable speed. It’s pretty much impossible for an ant to die from falling.
Second, their exoskeleton. Ants all basically have their own Spartan-Super-Suit like Master Chief that keeps them solidly in place, no organs splattering around because the organs are kept nicely in place by their strong exoskeleton.
It’s like dropping a polystyrene box from hundreds of meters. doesn’t weight much to make a significant impact to cause injury/damage.
It’s because of terminal velocity, that is the point where acceleration from gravity balances out with resistance from wind. The average terminal velocity for an insect is about 2m/s, the terminal velocity for a human is about 60m/s. If both you and an insect jumped from the Empire State Building at the same time you’d reach earth a lot faster than the insect would, but if the experiment happened in a vacuum you’d be able to lock eyes with the insect and would both hit the ground at the same time and at the same speed… a blistering 86m/s or 192mph
Additionally things are just relatively stronger the smaller they are. Ants can lift 50 times their body weight, with minimal training an average child can dead hang for 2 minutes something adults struggle with, elephants can’t jump.
Two reasons.
First, they don’t fall at a similar speed, they fall much much slower. Their “terminal velocity” is much slower. This is because they are very very very light, and they have a lot of surface area – lots of legs and appendages that cause drag. Because they are so light and cause so much drag. Air resistance alone is enough to slow down their fall to a survivable speed. It’s pretty much impossible for an ant to die from falling.
Second, their exoskeleton. Ants all basically have their own Spartan-Super-Suit like Master Chief that keeps them solidly in place, no organs splattering around because the organs are kept nicely in place by their strong exoskeleton.
> Shouldn’t they be falling at a similar speed, due to gravity?
Nope! And even if they were, it wouldn’t hurt them as much.
When you fall, two forces act on you: gravity and air resistance. Gravity is ~constant for our purposes, but air resistance rises as you speed up. At some speed, called *terminal velocity*, the two balance out, where air resistance is slowing you down as much as gravity is speeding you up. For a typical human skydiving, this speed is about 100 m/s (~223 mph), which is more than fast enough to kill you on impact if you don’t have a parachute or other way to slow down.
The more area you present as you fall (that is, the more cross-sectional area you have at a right angle to your movement), the more air resistance drags on you: it’s proportional to the area, or to length^(2). But your weight, and thus the force of gravity, is proportional to your *volume*, or to length^(3). As a result, **gravity grows faster than air resistance for a larger object of the same basic shape and density**, meaning that larger objects have higher terminal velocities. Specifically, with all other factors held equal, terminal velocity rises with the square root of length.
A golf ball, for example, has a terminal velocity of around 30 m/s, much slower than a human. It isn’t as much lower as that formula would suggest because golf balls are smoother, which also affects air resistance, but it’s still much lower.
An ant, which is much smaller still, has a terminal velocity of only about 2 m/s. That’s only a bit above walking speed; even for a human that would be a more than survivable impact. You could drop an ant from space (not from orbit) and they wouldn’t die from the impact.*
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But there’s another factor here, too: the [square-cube law](https://en.wikipedia.org/wiki/Square%E2%80%93cube_law) (which we saw in another form in the previous section).
A material’s strength is defined in terms of the maximum pressure (force per area) it can take. Thus, the amount of force a beam can take is proportional to its area, that is, to its length^(2).
But the mass of an object is proportional, as above, to its length^(3). And since the force of an impact is proportional to that mass, **the strength required for a material to support itself rises the bigger the object is**.
Imagine, say, building a house out of toothpicks. It’s pretty easy to build a tiny house with them! It can be quite stable with only marshmallows for structural support. That’s because the tiny house, which is perhaps ~50x smaller in terms of lengths than a real house, needs ~50x less structural strength, and most materials are that strong. Try to build an *actual* house out of toothpicks, though, and it won’t work.
So when our ant strikes the ground at 2 m/s, they *also* benefit from the fact that – as an object ~1000x shorter than a human, give or take – their body effectively has ~1000x the structural strength that yours does. This isn’t because they’re actually stronger, it’s just a consequence of their size. If you were that small, you could lift objects many times your size, too.
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The combination of these two effects means that ants and other small creatures are pretty much totally undamaged by falls. You need to get up to the size of, say, a medium-size bird or mammal for falls to start posing a serious risk of death.
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* You might wonder why meteors manage to hit the ground so hard. The answer is that they’re going so fast that even though the atmosphere is slowing them down, it doesn’t have time to slow them down to terminal velocity, so they impact at a high speed if they survive to land at all.
Your assumption about falling at the same speed applies if there’s no air resistance, but there’s a lot of air resistance, and even a little bit of updraft will keep tiny bug airborne or at least greatly slow. It’s descent. On top of that, it’s not just about the speed with which an object falls. You have to consider the amount of mass involved in the collision between the ground and whatever’s hitting it. Ultimately, it comes down to the physics formula F = ma, which means force equals mass times acceleration. Assuming there was no air resistance, then the acceleration part of that formula is the same for both a person and a small insect, but the mass is greatly different. A small insect may weigh a fraction of a gram, while a human weighs 70 to 100 kg or more. Literally thousands of times more. That means there’s literally thousands of times the force acting on a suddenly decelerating human then there would be on a small insect. When you add in the effects of air resistance, the difference is even greater.
It’s like dropping a polystyrene box from hundreds of meters. doesn’t weight much to make a significant impact to cause injury/damage.
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