Just some napkin calculations ...
This many visitors come to Oahu each year: 4,823,874
Hanauma Bay sees an average of 3000 visitors a day or around a 1,000,000 / year
If only 1 in 1,000 visitors lose anything of value: that's 1,000 lost items per year
Of the 1,000 items, 50% are swept off-shore or buried too deep to be recovered
That leaves 500 items of value lost on a very busy beach per year.
If detectorists have a recovery success rate of 80%, that leaves 100 valuable items left unrecovered
Figuring most items will totally sink out of reach after 3 years of being lost, each year we'd have less opportunity for recovery.
Year 1 Lost: 100 x 100% recovery = 100 lost items available
Year 2 since Lost: 100 x 50% recovery = 50 lost items in sand for two years
Year 3 since Lost: 100 x 10% recovery = 10 lost items in sand for third year
Total valuable items on the beach still left to be found on any given day: 100 + 50 + 10 = 160 items
This beach L x W is 1850 x 300ft = 555,000 ft2
This means there is one (1) lost recoverable (not buried too deep) valuable item every 3,500 sq ft. (includes water areas 60 yds off shore)
Given that an 11" search coil swept in one direction covers approx. 5 sq feet, and...
Given that at average sweep speed you cover 28 feet / minute ...
You cover about 140 sq feet per minute at average detecting speed
If you detect for 6 hours a day, you cover 8400 sq feet / hr * 6 = 50,400 sq feet per hunt ...
It would take 11 such hunts of 6hrs each with no overlap to cover the entire sand and water areas
You would collect 80% (recovery rate) x 160 total valuable times = 128 valuable items
Of course, you share the beach hunting with other detectorists, not just you ...
because they hunt randomly without knowing who else hunted, about 80% of their hunting is overlapped ...
Since random detecting is at 20% efficiency (compared to your gridded 100% efficiency) it take them 330 hours of detecting to do the same job you do in 66 hours.
If 10 different people randomly hunt each week for 2 hours - it takes almost 24 weeks (6 months) for the beach/water areas to be fully hunted.
That's 240 different hunters every 6 months covering all the beach at 80% recovery, finding 128 valuable items (leaving 32 valuables not found)
Since there are more hunters than valuables to find ... 47% of the hunters walk away with nothing (assuming each hunter only can find one item)
If 20% of the hunters find two (2) items on their 2-hour hunt at the beach ... then 83% of the other hunters walk away empty handed
This is why, despite the Hanauma Bay's huge number of visitors ... the majority of the metal detectorists never find anything valuable there.
Other beaches have half the number of tourists ... with perhaps half the lost items (80 annually) but with only 25% fewer detectorists hunting ...
That means, on
less crowded beaches you have 20% of the smart searchers finding 2 valuables, and the other 94% finding nothing valuable
I'm usually in the 94% finding nothing of value ... Oh, well.