LAB Biology - file 03
Why is an Ant safe if falling from a Skyscraper? – the Square-Cube Law
Have you imagined Why a tiny Ant is safe with NO harm when falling from a skyscraper? But here, I do NOT talk about ONLY an Ant, but ALL creatures on Earth, especially those familiar to us.
So what if in your case? It's too scary to imagine… because we know the dire consequences that would happen without doubt.
This is a classic biophysics riddle. But it’s actually just cold, hard geometry…
The Terminal Velocity
In general, when an object falls, 2 main forces are at play:
● Gravity – pulling down the object.
● Air Resistance – pushing up the object.
An ant's survival depends on the balance and relationship between its mass and its surface area.
Because ants are so light and have a relatively large surface area, including legs, hairs, and their shell, ants reach terminal velocity almost instantly. Terminal velocity is the speed at which the upward drag of the air perfectly balances the downward pull of gravity.
● For a Human, terminal velocity is roughly 200 km/h (120 mph)!
● For an Ant, terminal velocity is roughly 6.4 km/h (4 mph)!
Landing at 6 km/h is just as fast as a human stepping off a curb. It does NOT matter if the ant falls from 10 stories, 20 stories, or from the edge of space. An ant will NEVER fall faster than a gentle walking pace.
Why does this difference happen? – the Square-Cube Law
The Square-Cube Law is a mathematical principle, first described by Galileo Galilei in 1638, that explains why scaling up and down a creature changes everything. The principle can perfectly explain why ants can fall from great heights with NO harm.
The Square-Cube Law dictates that as an object grows (or shrinks) in size, its volume and mass increase (or decrease) much faster than its surface area. Because ants are very small, they have a high surface-area-to-weight ratio, which protects them.
● Surface Area (growing by Square)
If you double (x 2) the size of an ant, its surface area (thus its air resistance) increases by the square ( 22 = 4 ).
● Volume/Mass (growing by Cube)
On the other hand, its volume and mass increase by the cube ( 23 = 8 ).
Accordingly, as you can imagine intuitively, as things get bigger, they get heavier much faster than they get wider. Vice versa, as things get smaller, they get lighter much faster than they get narrower.
So the volume and mass are more affected than the surface area by scaling up and down the dimensions.
Ratio = Surface Area / Volume
● Surface Area is measured in units² (Squares)
● Volume/Mass is measured in units³ (Cubes)
Because an ant is so tiny, it has a massive amount of surface area compared to its weight. This essentially works as its own parachute!
To make sense of the Square-Cube Law more intuitively, let's take a look at the diagrams below:
To understand easily, imagine a simple cube with ALL the dimensions’ units = 1.
If you double its dimensions equally, multiplying by 2:
● Length: 2X original.
● Surface Area: 22 = 4X original.
● Volume and Mass: 23 = 8X original.
Accordingly, the "Square" refers to the area, and the "Cube" refers to the volume. This unbalanced ratio is why physical properties do NOT scale linearly, and also, how Nature has ingeniously created everything well-balanced.
Let's scale up an Ant!
Let’s apply the Square-Cube Law to an ant! Suppose we have a normal ant that is 1 unit long, and we try to scale it up to be a “Gi-ant” with 10 units long!
◎ Length/Height - 10X
The Gi-ant is 10 times taller/longer.
◎ Surface area - 102 = 100
The Gi-ant has 100 times more skin and exoskeleton.
◎ Cross-section of Legs - 102 = 100
The Gi-ant’s legs are 100 times stronger. (Strength = k • Area)
◎ Volume & Mass - 103 = 1000
The Gi-ant is 1,000 times heavier!
The ant’s weight (mass) has increased by 1,000, but the strength of its legs has ONLY increased by 100. Effectively, the Gi-ant is NOW 10 times weaker relative to its own body weight.
If a normal ant can carry 50 times its weight, this Gi-ant would struggle to even stand up... The Gi-ant’s legs would be unbearable and likely buckle under the pressure of 1,000 times its own mass!
Besides, in reality, within the Earth’s atmosphere, an ant has its built-in armor. Ants are encased in chitin, which is a natural polymer. Ant’s exoskeleton is incredibly tough and flexible.
Even if an ant hits the ground slightly faster, its bones are on the outside. Their exoskeleton acts like a roll cage in a rally car. This is another factor upholding the ant's strength.
"You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.” (J. B. S. Haldane)
The Surface-Area-to-Volume Ratio
The Square-Cube Law dictates NOT only body strength, but also almost everything in biology, from breathing to keeping warm.
Oxygen Limit
The Square-Cube Law is also why we do NOT have ants the size of dogs or even humans, like in a horror movie.
Ants breathe through tiny holes in their sides called spiracles. If an ant were the size of a Golden Retriever, its volume and mass would be so massive that oxygen could NEVER diffuse deep enough into its body to keep its internal organs alive.
Heat Loss
We lose heat through our skin (surface area), but generate heat in our muscles and organs (volume).
Tiny animals, like our ant, have a huge surface area relative to their tiny volume. They lose heat very fast, so they have to keep eating constantly just to stay warm, especially in winter.
 |
| American pygmy shrew (source: Scenic Hudson) |
Tiny Shrews use a rare adaptation called Dehnel’s Phenomenon. In autumn, Shrews shrink their body mass, including organs and even their skull/brain size by 10%–20%.
By reducing their body size, Shrews can decrease their total energy requirements, requiring less food to generate body heat efficiently. It's vital when food is scarce in winter.
And Shrews maintain a very high metabolic rate and MUST keep eating 80%–100% of their body weight every day to produce enough metabolic heat to stay warm.
In winter, Shrews remain active, foraging in soil litter, rather than storing food and hibernating.
 |
| African elephant (source: African Wildlife Detective) |
On the other hand, large animals, like elephants and rhinoceros, have a tiny surface area relative to their massive volume and mass. In contrast to ants or shrews, large animals struggle to get rid of heat, especially in summer.
Elephants use their giant, thin ears as radiators to increase their surface area for cooling. By increasing blood flow to their massive ears and flapping them, elephants release heat.
In the case of Rhinoceros, they are armored by thick skin and lack sweat glands. So rhinoceroses rely on mud-wallowing and water-playing to cool down their massive bodies.
The Bigger is NOT Stronger?
As we have seen, the bigger the size, weight (mass), and volume, the faster they should grow than the surface area, which determines the strength. So if an ant grew to the size of a human, it can NEVER endure their own too heavy weight (mass), resulting in being crushed in a moment.
So, how about King Kong or Godzilla? Actually, in reality, their worst enemy is themselves…
The Tragedy of Giants
While an ant is invincible to falling from a skyscraper because an ant has too much surface area relative to its volume and weight (mass), King Kong has the opposite problem.
According to the Square-Cube Law, if you scale a normal gorilla up by 10 times:
● The gorilla’s height is 10X greater.
● The cross-sectional area of the gorilla’s bones (strength) increases by 102 ( 100X ).
● The gorilla's weight (mass) and volume increase by 103 ( 1,000X ).
Essentially, the 10X-gorilla becomes 1,000 times heavier, but its bones only become 100 times stronger. This means the gorilla got comparatively weaker by scaling up.
When the moment a movie-sized King Kong tried to take a step, his leg bones would be unbearable, likely shattered under his own weight.
Overheating Nightmare
As we have seen in the case of elephants, large animals struggle to get rid of heat. Surface area is how animals dissipate body heat, but volume is what generates body heat.
A giant creature has a massive internal furnace (volume), but comparatively, very little radiator space (surface area). So a real-life Godzilla would likely cook himself from the inside out just by standing still, unless he had a massive radiator, elephant-like ears, or a special cooling system.
 |
| Patagotitan |
Patagotitan is one of the largest land animals that ever existed, with an estimated length of 37 m (121 ft) and an estimated weight of 69 tonnes. Patagotitan reached the physical maximum limit of what biological bone can support.
To survive, these giant dinosaurs had to have legs like thick tree trunks and move their massive weight very slowly. The fast-running giant monsters in movies defy the law of gravity and material science.
An ant can NOT die from a fall of any height in Earth's atmosphere. The primary reason is the low terminal velocity caused by the high surface-area-to-mass ratio.
However, note that this ONLY works in an atmosphere. If you dropped an ant on the Moon, which has NO air, it would accelerate the ant continuously until it hit the surface, likely ending in a very tiny, very tragic accident… The Earth’s atmosphere helps us a lot, NOT only for breathing and photosynthesis.
The Square-Cube Law dictates the advantages and disadvantages of the scale in the World of biology!
Further reading (sponsored by Amazon):
● Ken Vos (2013). Biophysics For Dummies. 602 pages. For Dummies.
(sponsored by Amazon)
“Biophysics For Dummies” is a fun, easy way to get up to speed on biophysics concepts, principles, and practices! Biophysics courses are increasingly taken by students of biology, physics, chemistry, biochemistry, physiology, statistics, bioengineering, neuroscience, computer science, pharmacology, agriculture, and many more… “Biophysics For Dummies” provides a friendly, unintimidating overview of the material covered in a typical college-level biophysics course!
Table of Contents
Introduction
Part 1 Getting Started with Biophysics
Chapter 1: Welcoming You to the World of Biophysics
Chapter 2: Interrogating Biophysics: The Five Ws and One H
Chapter 3: Speaking Physics: The Basics for All Areas of Biophysics
Part 2 Calling the Mechanics to Fix Your Bio — Biomechanics
Chapter 4: Bullying Biomechanics with the Laws of Physics
Chapter 5: Sitting with Couch Potatoes — Static Equilibrium
Chapter 6: Building the Mechanics of the Human Body and Animals
Chapter 7: Making The World Go Round with Physics — Dynamics
Chapter 8: Looking at Where Moving Objects Go — Kinematics
Part 3 Making Your Blood Boil — The Physics of Fluids
Chapter 9: Understanding the Mechanics of Fluids and Cohesive Forces
Chapter 10: Going with the Fluid Flow — Fluid Dynamics
Chapter 11: Breaking through to the Other Side — Transport, Membranes, and Porous Material
Part 4 Playing the Music Too Loud — Sound and Waves
Chapter 12: Examining the Physics of Waves and Sound
Chapter 13: Grasping How Animals and Instruments Produce Sound Waves
Chapter 14: Detecting Sound Waves with the Ear
Chapter 15: Listening to Sound — Doppler Effect, Echolocation, and Imaging
Part 5 Interacting Subatomic Particles’ Influence on Biological Organisms
Chapter 16: Charging Matter: The Laws of Physics for Electricity, Magnetism, and Electromagnetism
Chapter 17: Tapping into the Physics of Radiation
Chapter 18: Fighting the Big C — But Not All Radiation Is Bad
Chapter 19: Seeing Good Biophysics in the Medical Field
Part 6 The Part of Tens
Chapter 20: Ten (or So) Tips to Help You Master Your Biophysics Course
Chapter 21: Ten Careers for People Studying Biophysics
About the Author
Cheat Sheet
