Exhibit A
The curve that ruins your day
Wave energy density scales with the square of wave height: E = ⅛ρgH². It's the single fact this whole page is built on — everything below (speed, mass, force, fear) traces back to this curve.
Hover or tap a point for exact numbers. Energy density in joules per square meter of sea surface, plotted against face height in feet.
The Four Stops
From "fun size" to "call your mother"
Same ocean, same water, wildly different conversation with your insurance company. All figures use standard face-height convention (what you'd eyeball from the beach) unless noted.
The Fine Print, Honestly Delivered
How these numbers were made
Nothing here is invented. Everything is a standard coastal-engineering formula, applied plainly and labeled where it's a deliberate simplification.
Energy density — E = ⅛ρgH²
The standard linear (Airy) wave theory result for average wave energy per unit sea-surface area, where ρ = 1025 kg/m³ (seawater), g = 9.81 m/s², H = wave height (crest to trough). This is the textbook formula used across coastal engineering and oceanography.
Wave speed — c = √(g·d)
Shallow-water wave celerity at the break point, where d is water depth. Breaking depth is estimated from the breaker index (H ≈ 0.78·d, a widely used rule of thumb), so d = H / 0.78. This gives the speed of the breaking wave itself, not a paddling speed.
Water mass — a labeled simplification
There's no single "correct" mass for a breaking wave — it depends on the section you draw a box around. We model the water mass in a roughly cube-shaped chunk of whitewater about 2 meters wide, H tall, and H thick (mass = ρ × H × H × 2m). It's a ballpark for "how much water is in the part that lands on you," not a rigorous control-volume calculation.
Impact force — dynamic pressure, P = ½ρv²
The standard fluid-impact / slamming-pressure formula used in coastal and marine engineering for wave loads on structures, applied here to an estimated 0.5 m² of surfer torso. This is a ballpark of peak force, not a measured clinical injury threshold — real impacts vary hugely with technique, board, and luck.
Hold-down time — reported ranges, not a formula
Unlike the numbers above, hold-down duration isn't derivable from H² alone — it depends on wave period, how many waves are in the set, and the surfer. Ranges here reflect commonly reported figures for each size class (small-wave wipeouts of a few seconds vs. big-wave hold-downs of 20–40+ seconds, with documented two-wave hold-downs at Mavericks- and Nazaré-scale surf).
The Fear Index — energy × consequence, not vibes
Fear Index = (energy ratio vs. the 3–4 ft baseline) × (a consequence multiplier for hold-down risk, rescue difficulty, and rock/reef/crowd hazard), normalized 0–100 against the 20 ft stop. It's deliberately not linear with height — real risk compounds faster than raw energy because getting held down twice in a row is worse than twice as bad.
The Takeaway
Fear should not be linear
A 20 ft wave doesn't look "5x scarier" than a 4-footer when you eyeball it from the sand. It carries roughly 33x the energy — and because hold-downs, rescue logistics, and multi-wave sets all stack on top of that, our Fear Index puts it at 100 vs. 1. Respect the square.