Limiting Factors of Things

This is an on-going list of the limiting factors of things. Why aren't trees double the size? Why are planes the size they are? Exploring whether the limits are pre-determined, artificially placed, some sort of equilibrium convergence, or a myriad of other reasons.

TL;DR

• Once things are embedded, they may artificially place limits on things that otherwise face no physical limit.
• In other scenarios, there are physics-based issues with scaling laws.

Planes

• Lift (and wing area) scales to the square (L²).
• Weight (and volume) scales to the cube (L³).
• Weight therefore scales faster than lift, placing a ceiling on plane size.
• Jet engines also scale to the square (D²), meaning the larger you make an engine, the less efficient it becomes structurally (thrust per unit weight).
• A380’s wingspan is the largest ever (80 m).
• Other limits:
• Runway lengths
• Manufacturing limits (tooling, machinery)

Trees

Hydrostatic Pressure Drop

• Trees draw water up from roots to leaves through cohesion and tension.
• The driving force is transpiration — evaporation at the leaf creates a negative pressure at the top.
• The higher the tree, the higher the hydrostatic pressure drop (~0.01 MPa per meter).
• At some point, the tensile strength of water and xylem structure can’t sustain the suction — air bubbles (cavitation) form.
• This begins around 30 m and limits most trees to ~130 m. The world’s tallest tree, Hyperion (a coast redwood in California’s Redwood National Park), is 116 m tall.

Mechanical Integrity

• Trunks must stabilize and resist buckling.
• Weight scales to the cube (m³), but strength of cross-sectional area scales to the square (h²).
• Eventually, bending stresses and self-weight exceed the trunk’s strength.

Carbon Efficiency

• Larger trees have lower leaf area relative to volume, requiring more efficient photosynthesis.
• Taller trees struggle to intercept light; lower branches become shaded.
• Eventually, every photosynthetic surface is used for maintenance rather than growth — a metabolic ceiling.
• Tree height may plateau while lateral growth continues.

Boats

• Buoyancy increases with displaced volume (L³).
• Weight also increases with (L³), so theoretically scalable.
• The limiting factor becomes material strength — which scales with the square (L²).
• The larger the boat, the stronger (and heavier) the materials must be, reducing payload advantage.

Propulsion

• Engine power output scales with cylinder volume (L³).
• Larger engines face diminishing returns due to mechanical stress, vibration, and propeller efficiency limits.

Other limiting factors:

• Port sizes

Cities

• Cities are metabolic systems — they import energy and export waste.
• Energy systems (power grid, water pipes, sewers, waste collection) scale roughly to the square (area or length).
• Demand scales with population.

From West, Bettencourt et al., PNAS (2007), Nature (2010):

• Yinfra = total infrastructure (e.g. road length, electrical cable length, water pipe volume)
• N = population
• As a city doubles in size, total infrastructure increases by only ~85%, making it more efficient per person.
• This sublinear scaling means higher intensity of use, less redundancy, and greater fragility under stress.
• Past ~10–20 million people, cities encounter logistical friction: maintenance lag, congestion, and cascading failures.