An ant may be able to survive me flicking it – but proportionally-speaking, I would not be able to survive such a thing. Is it happenstance that this is the case? Is there a “perfect” size for this universe?
In: Physics
The square-cube law gives scale to the universe. If you were scaled down 100 times you’d weigh 1000000 times less but you’d be 10000 times weaker. So, relatively, you’d be 100 times stronger and could survive being flicked.
It’s not just strength and weight; many other things about how your body works are affected in the same way. Some are related to surface area and scale by a square law; others are related to volume and scale with a cube law. That’s why different sized animals have different shapes and work in different ways. Insects don’t even need lungs to breathe as large animals do. And if we really could scale you down 100 times like Ant Man, you’d die instantly.
The key issue is that an object’s volume increases in proportion to L^3 for every increase in length L. Doubling the length of a cube’s edge will mean 8 times the volume: 2^3 = 8.
For the cube, that means *a lot* of mass that’s farther away from the surfaces that provide a support structure. Lots of unsupported gooey innards. It also means that structural demands on the support structure are greater, due to the total mass being so huge.
Elephants have found an ideal size for their environments and lifestyle. They can easily make a 100 mile trek for new water in dry seasons, while their ant neighbors just die. They don’t often have to survive great falls, either. It works for them…!
F = M * A
Therefore the less mass an object (or creature has), the less force they experience.
Let’s say you have a 0.5lb object and you accelerate it at 20m/s^2 (in comparison, a falling object accelerates at 9.8m/s^2, otherwise known as gravity, until it reaches its terminal velocity). That object would experience 4.536 N (Newtons) of force during acceleration. If you accelerate a human who weighs 160lbs at that same speed, they experience 1451.5 N of force, significantly higher than the small object.
We also are built quite a bit differently than insects, the way our circulatory system is design the more force applied to us the more likely it will cause significant damage as a result of our blood essentially sloshing around inside us, bursting blood vessels on one side and depriving the other side of oxygen-rich blood. Insects don’t have the same system and as a result don’t have this problem.
The short answer is: the ant is much ‘tougher’ than you because it is much smaller than you are.
But there are two reasons why the ant is tougher. There are a couple of factors at play:
**1). First is the Square Cube Law, or the Law of Scaling, or Law of Proportions**
Let’s say we shrunk you down to the size of an ant using a ray gun like Wayne Szalinski’s in the movie *Honey, I Shrunk the Kids*. Once you got your bearings, you would quickly realize that you are MUCH stronger (and tougher) relative to your size than you were when you were ‘big’. *In truth, you’d actually die immediately, but that’s another story.* The reason you’re so ‘tough’ now is because your surface to volume ratio is much *higher*. In other words there’s *more of you*, relative to your weight and volume.
To illustrate this point further, imagine (small-shrunken) you and (big not-shrunken) me standing on opposite ends of a diving board and we both do belly flops into a pool. You wouldn’t feel much when your belly hits the water because your belly only has to support your body weight, which is about a milligram or so. I, on the other hand, would feel the pain. My belly would have to support almost 200 pounds.
**2). The second (and less important) factor at play here is what we call “terminal velocity”.**
This effect is also related to mass and surface area. But, it is more about how an object’s speed (and acceleration) is is affected by gravity and the surrounding air. Remember, when we shrink you, there’s *more of you relative to your weight* (proportionally less volume). This means that as your shrunken self falls, the air is interacting more with your body relative to your weight than mine.
To illustrate, we’ll use the same example of the diving board above. Only this time, you are diving into a drained swimming pool (no water). When you jump, you won’t fall very fast, because relative to your weight, there’s more surface area to slow you down, and the air stops you from speeding up too fast. You stay at that speed and can’t go any faster. When you hit the concrete pool bottom, it won’t hurt too much because you weren’t going fast enough. In fact, you’d be ok if you jumped off the top of the CN Tower into the drained pool because your top speed or “terminal velocity” wouldn’t be “fast enough” to hurt you when you hit the concrete. The air resistance to mass is higher for small animals like ants, which is why they can’t be seriously injured from being dropped from any height.
TDLR:
Proportionally, an ant has more surface area and less weight, and more importantly, less volume which makes it tougher.
My favorite YouTube channel does a great video on this, actually. It turns out every scale of life has its own challenges and risks. Enjoy!
Is it the size or the exoskeleton? Would a human the size of an ant survive being flicked? Would a normal size human survive a proportionate event wearing a suit of armor?
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