Abstract

Terminal velocity—the maximum speed an object reaches when falling through a fluid such as air—is a key determinant of whether a fall is survivable. This paper compares the terminal velocities of various animals and inanimate objects, analyses how size, shape, posture, and surface texture affect drag, and explores what body designs minimize terminal velocity. Special attention is given to small mammals (cats, squirrels, mice), birds, seed structures, and engineered examples (parachutes, wingsuits, airfoils, and “parachute” toys). We then generalize design principles that minimize terminal velocity and discuss implications for biomechanics, biomimetic engineering, and safety design.

1. Introduction

When objects fall, they accelerate under gravity until drag forces balance weight. At that point, acceleration drops to zero and the object falls at a constant speed: the terminal velocity. For a falling organism, terminal velocity often determines whether impact is fatal, injurious, or harmless.

Different animals and objects have dramatically different terminal velocities:

A spread-eagle human might hit ~50–60 m/s. A streamlined human skydiver can reach ~70–90 m/s or higher. A small rodent or an ant can fall from large heights and walk away. A milkweed seed or dandelion pappus falls so slowly that it can drift with light breezes.

These differences are not arbitrary; they reflect a consistent physical relationship between mass, area, shape, and drag coefficient. They also reflect engineered strategies to slow descent: spreading limbs, having large surface area relative to mass, using porous appendages, or creating controlled turbulence.

This paper will:

Review the basic physics of terminal velocity. Compare the approximate terminal velocities of selected animals and objects. Analyze which body designs minimize terminal velocity and why. Draw general design principles applicable to both biology and engineering.

2. The Physics of Terminal Velocity

2.1 Basic equation

For an object falling through air, terminal velocity v_t occurs when upward drag equals downward weight:

mg = \frac{1}{2} \rho C_d A v_t^2

Where:

m = mass of object g = acceleration due to gravity (~9.81 m/s²) \rho = density of air (~1.2 kg/m³ near sea level) C_d = drag coefficient (dimensionless; depends on shape and orientation) A = reference area normal to flow (m²)

Solving for terminal velocity:

v_t = \sqrt{\frac{2mg}{\rho C_d A}}

From this, we see that terminal velocity is proportional to the square root of (mass / (C_d × area)). To minimize v_t:

Decrease mass m Increase area A Increase drag coefficient C_d (Or decrease air density \rho, but that’s not design—just environment.)

2.2 Scaling and body size

If we imagine geometrically similar animals scaled up or down:

Mass m roughly scales with length³ Surface area A roughly scales with length²

So mass/area scales with length. Larger versions of the same shape are heavier per unit area and thus have higher terminal velocity. That’s why small animals can fall safely from heights that would kill larger animals.

3. Comparative Terminal Velocities: Animals and Objects

Values below are approximate and meant to illustrate orders of magnitude, not precise measurements. They assume “typical” postures (e.g., a cat spreading limbs vs. a human in various positions).

3.1 Human examples

1. Human skydiver, stable belly-to-earth position

Mass: ~75 kg Effective area A: ~0.7–0.8 m² (spread) Drag coefficient C_d: ~1.0–1.3 (rough estimate for spread human)

Plugging into the equation gives a typical terminal velocity ~50–60 m/s (~180–215 km/h), which matches widely cited skydiving values.

2. Human skydiver in head-down, streamlined position

Same mass, smaller area (~0.2–0.3 m²), lower C_d

Terminal velocity can rise to ~70–90 m/s or more (~250–320 km/h).

Key takeaway: By changing body configuration (posture), the same organism can nearly halve or double terminal velocity.

3.2 Cats and other small mammals

Cat (domestic, 4–5 kg)

Cats are famed for their survival from high-rise falls (“high-rise syndrome” studies). A relaxed, spread posture—legs splayed, fur fluffed—increases area and drag, reducing terminal velocity.

Mass: ~4–5 kg Estimated area + posture: lower mass/area ratio than a human Typical estimated v_t: around 20–30 m/s (72–108 km/h)

This is far below a human’s. Combined with flexible skeletons, joint structures, and impact distribution via limbs and soft tissue, cats can survive falls that would be fatal to humans.

Squirrels (0.3–0.6 kg)

Tree squirrels, especially, often fall or jump from heights.

Mass: ~0.5 kg Large fluffy tail, extended limbs; high area relative to mass Likely v_t: ~10–15 m/s range (rough order of magnitude)

Flying squirrels take this even further with patagia (skin membranes), approaching gliding/parachute performance.

Mice (~20–30 g)

Mice are an extreme case in the “small mammal” group.

Mass: ~0.02–0.03 kg Very low mass, modest area Their mass/area ratio is tiny

Estimated v_t can be low enough that the impact from typical building heights is non-fatal. Classic physics arguments note that a mouse could, in principle, be dropped from a tall building and survive, whereas an elephant would be crushed.

3.3 Very small animals: ants and insects

Ants

Ants are so small and light that drag forces quickly balance their minuscule weight.

Mass: ~1–10 mg Cross-sectional area: disproportionately large relative to mass

Result: terminal velocities of only a few m/s or less. Impact forces are tiny; surface tension effects, bounce, or simple body rigidity easily dissipate them. This is why ants falling from high places typically survive.

Dragonflies, beetles, etc.

Many insects don’t fall passively—they flap, orient, or “parachute” using wings. Even when wings are folded, their body size ensures relatively low terminal velocities compared to larger vertebrates, though still higher than ants.

3.4 Birds

Birds actively control descent using wings and tail. Passive terminal velocity depends on whether wings are spread or folded.

Wings spread (glide or stall): birds generate lift and drag. They can almost hover or descend very slowly at high angles of attack. Wings folded (diving raptors): shape becomes streamlined, area decreases, drag coefficient drops dramatically.

For example:

Peregrine falcon in a hunting stoop: can exceed 80 m/s (or more). This is effectively a controlled dive, intentionally maximizing terminal velocity. Typical small bird landing: flares and stalls, achieving very low descent speeds on impact—only a few m/s.

Birds are an example where control surfaces + posture allow both minimization and maximization of terminal velocity on demand.

3.5 Seeds and plant structures

Plants have evolved an incredible variety of “fall-slowing” designs to disperse seeds:

Dandelion pappus seeds Lightweight seed attached to a radial tuft of filaments. Creates a porous, draggy “parachute” that exploits vortex rings and turbulent drag. Terminal velocities can be centimeters per second—so low that seeds can be carried horizontally by very gentle breezes. Maple samaras (winged seeds) One or two wing-like extensions cause autorotation. Rotational motion increases drag and decreases descent speed, while also producing horizontal drift. Cottonwood / poplar fluff Fibrous, fluffy extensions with massive surface area and tiny mass. Very low terminal velocity; fiber tufts behave almost like tiny parachutes.

In these cases, maximized effective area and induced unsteady flow (vortices, flutter) result in extremely low terminal velocities.

3.6 Inanimate objects: spheres, plates, parachutes, and toys

Spheres

Drag coefficient ~0.4–0.5 at high Reynolds numbers (depending on roughness). For a steel ball of given radius, v_t is relatively high because of high density and modest area.

For example, a steel ball of radius 1 cm (~33 g) falls much faster than a foam ball of the same size, simply because m is bigger while A and C_d remain similar.

Flat plates

Plate face-on to flow: C_d ~1.1–1.3 For a lightweight plate, this makes terminal velocity low. Turn it edge-on: area plummets and v_t rises.

Parachutes

Parachutes are deliberately designed to minimize terminal velocity. A typical skydiving parachute might:

Increase effective area from ~0.7 m² (body alone) to 10–25 m² or more. Maintain a relatively high drag coefficient, often >1.0.

This lowers terminal velocity drastically to ~5–7 m/s (think 18–25 km/h), a speed a human can survive comfortably while landing with proper technique.

Parachute toys (army men, plastic parachutes)

Very low mass Disproportionately large, thin canopy Terminal velocity can be slow enough that descent looks almost floaty.

4. Body Designs that Minimize Terminal Velocity

From the equation v_t = \sqrt{\frac{2mg}{\rho C_d A}}, the design levers are:

Lower mass m Higher area A Higher drag coefficient C_d

4.1 High area-to-mass ratio

Principle: For a given shape and drag coefficient, higher A/m → lower v_t.

Examples:

Small mammals vs large mammals: A mouse is “all surface, little mass.” An elephant is “lots of mass per unit surface.” Seed structures: big surfaces (pappi, wings, hairs) for negligible mass. Feathers, fur, fluff: increase effective area and also trap air, increasing drag.

In design terms, thin, wide, lightweight structures with large projected area and low density will fall slowly.

4.2 Increasing drag coefficient C_d

Drag coefficient measures how “resistant” a shape is to flow. Rough, bluff, or porous shapes often have higher C_d than streamlined shapes.

High C_d shapes:

Flat plates normal to flow Bluff bodies (cubes, broad disks) Deployable canopies (parachutes) Puffy, irregular, highly textured surfaces

In biology:

Fluffy fur (as in squirrels and some arboreal mammals) Feathered wings, tails (birds) Porous seed pappi (dandelion, milkweed)

In engineering:

Parachutes and drag chutes Airbags or inflatable decelerators for planetary entry vehicles Wingsuits (rougher surface, extended limbs, fabric panels).

4.3 Posture and body configuration

A key variable is not just anatomy but attitude—how the body is oriented:

Humans: Spread eagle → large area, moderate C_d → low v_t (50–60 m/s). Head-down streamline → small area, reduced C_d → higher v_t (70–90 m/s). Cats and squirrels: Limbs spread, tail extended: increases area, raises drag. If they were to fall in a curled ball, terminal velocity would be higher and injury risk greater. Flying squirrels / sugar gliders: Use patagium like a living wingsuit, increasing both area and controllability of descent. Birds: Wing and tail configuration can shift descended speed from a high-speed stoop to a low-speed flare.

Thus, symmetric extension of limbs and appendages in the direction perpendicular to fall is a universal low-tech way to reduce v_t.

4.4 Exploiting unsteady aerodynamics: flutter, rotation, vortices

Some designs reduce terminal velocity not only by large area but also by inducing unsteady flow phenomena:

Autorotating seeds (samaras) generate vortices along their leading edges, enhancing lift and drag. Fluttering leaves and paper: unsteady, oscillating motion can increase mean drag relative to a rigid plate. Dandelion pappi exploit a stable toroidal vortex ring that forms above their filaments; this unusual flow structure gives high drag for very low mass.

For engineered systems, rotating or deforming surfaces can likewise increase drag without significantly increasing mass.

5. Comparative Design Typology for Low Terminal Velocity

We can classify low-terminal-velocity designs into several archetypes:

5.1 The “Parachute” type

Key features:

Large, relatively rigid or semi-rigid canopy High drag coefficient Low canopy mass

Examples:

Human parachutes Jellyfish bell (in water; analogous principle) Some seed pappi and diffuse fibers that approximate thin canopies.

5.2 The “Wingsuit / Patagium” type

Key features:

Membranes between limbs expand area Controlled shape via active musculature or structural supports Provides both drag and lift, allowing glide as well as descent control

Examples:

Flying squirrels, colugos, sugar gliders Wingsuit skydivers Some frogs and lizards with webbed limbs or skin flaps.

5.3 The “Fluffy / Bristled” type

Key features:

Numerous thin filaments (fur, feathers, hairs, pappi) Porous but draggy structure Lightweight, high area

Examples:

Dandelion seeds, milkweed seeds Thick winter fur in some arboreal mammals (as a side effect, can slow falls slightly) Fuzzy caterpillars (though falling is not their main design purpose).

5.4 The “Rotating Flier” type

Key features:

Asymmetric wings or offsets that induce rotation Angular momentum stabilizes orientation Lift and drag generated by rotating surfaces

Examples:

Maple samaras Some engineered autorotating toys (e.g., schoolyard helicopter seeds made from paper) Autogyro-style decelerators.

5.5 The “Tiny and Tough” type

Key features:

Very small body mass Moderate area Terminal velocity low simply because object is tiny Impact energy = ½ m v² is small even at modest speeds

Examples:

Mice, shrews (relative safety from falls) Ants and other small insects Dust particles, spores.

6. Design Rules for Minimizing Terminal Velocity

Summarizing, to minimize terminal velocity:

Maximize effective area A Spread limbs, add membranes or canopies, use extended appendages. Design bodies or devices with large projected area relative to mass. Maximize drag coefficient C_d Avoid streamlined shapes; instead use bluff, irregular, or porous shapes that create turbulence. Use rough surfaces, protrusions, or filaments to disrupt flow. Minimize mass m for a given function Lightweight materials; low density. In biology, small animals are inherently safe from falls compared to larger ones. Exploit active posture and control Allow organisms or devices to adopt a high-drag orientation autonomously (reflexive limb spreading, automatic deployment). Design stable attitudes that naturally present maximum area to the fall direction. Harness unsteady aerodynamics when possible Encourage flutter, tumbling, or rotation if stability is not critical and drag enhancement is. Alternatively, use rotating wings or shrouds to simultaneously add lift and drag.

7. Applications and Implications

7.1 Biomechanics and animal survival

Understanding how body design affects terminal velocity explains:

Why small animals survive falls that would kill larger ones. How creatures in arboreal or aerial environments were designed with gliding membranes, long tails, or fluff. Why behaviors like limb spreading during falls are strongly selected for and commonly observed.

It also provides insight into injury patterns in domestic animals (e.g., cats) and potential interventions (e.g., modifying building features to reduce dangerous fall distances).

7.2 Bio-inspired engineering

Engineers can draw from these principles to design:

Improved parachutes and decelerators inspired by seed pappi and samaras. Compact emergency descent devices that deploy like seed structures. Lightweight drones that can “fail safe” by deploying draggy surfaces upon power loss. Protective systems for fragile payloads that mimic fluffy or bristled structures.

7.3 Safety and fall-protection systems

For humans:

Wingsuits and suits with deployable drag panels for extreme sports. Clothing or gear designed to automatically increase area in a fall (e.g., airbag clothing plus drag flaps). Design of rescue equipment or child safety devices that limit terminal velocity without complex mechanisms.

8. Conclusion

Terminal velocity is governed by simple physics, but the variety of strategies that animals and objects use to minimize it is astonishing. From the mouse’s inherent smallness to the cat’s limb-spreading reflex, from the fluffy dandelion seed to the engineered parachute, the theme is consistent:

Big area, low mass, high drag coefficient, and smart posture yield low terminal velocity.

By comparing animals and inanimate objects, we see a continuum of solutions shaped by both evolution and engineering. Understanding these solutions not only explains striking natural phenomena—like why ants survive long falls—but also guides the design of safer, more efficient fall-slowing technologies for humans and our devices.