Oak Island

Zena Helpern Documentation

La Formule Hydraulic System

I examined the parchment document titled La Formule.

There is an obvious line dividing it into two parts.

The leaders you see - the : : . triangles and dots - are French 1680s word separators.

Above the line - La Formule - is the formula, the inputs.

It reads as French engineer shorthand for a hydraulic calculation:

shaft depth approximately 30-36 m,

drain length approximately 120-150 m to the coastal swamp,

tidal head 1.5-2.0 m from Mahone Bay tides, and slope to finger drains approximately 1:20.

Below the line - La Valeur - is the value, the output.

It is the calculated result:

water volume 12,000-15,000 m³ per cycle, flow rate 0.8-1.2 m³/s on high tide, and flushing capacity for a ship careening basin.

12,000-15,000 m³ per cycle means per tide, about 12 hours 25 minutes. 12,000 m³ is 12 million liters, 3.17 million US gallons, 424,000 cubic feet - about five to six Olympic swimming pools of water moving in one tide to flush silt.

I measured the ground to test the formula.

My dropped pin at the north intake is at 44°30'54.61"N 64°17'16.61"W, elevation 5 ft, on the beach at Smith's Cove.

My Google scale across that section of the island is 300 m.

Under this reading the formula gives 150 m for each shaft. Two shafts total 300 m.

That makes the formula total and the ground distance the same: 300 m, or 923 French feet.

The conversion is: 1 pied du roi = 1.06575 English feet = 0.32484 m. 150 m = 461.8 pieds du roi. 300 m = 923.5 pieds du roi = 154 toises.

That is 77 toises per leg.

The north drain from Smith's Cove intake to the middle shaft is 150 m, and the south drain from the swamp shipyard output to the middle shaft is 150 m.

The total is 300 m, which matches the 300 m Google scale.

The middle shaft is where the 90-ft stone was found.

Top of that shaft is 30 ft above sea level.

The stone at 90 ft depth is 60 ft below sea level.

The stone says "FORTY FEET BELOW TWO MILLION POUNDS ARE BURIED."

In French units that would have been 40 pieds and 2,000,000 livres.

One livre poids de marc is 1.079 English pounds.

I calculated thrust at that depth.

Forty feet below the stone is 130 ft deep, which is 100 ft below sea, or 30.48 m head.

Hydrostatic pressure p = rho g h = 1025 9.81 30.48 = 306,500 Pa = 44.4 psi. Force F = p x Area.

On an 18 ft x 18 ft vault cap, 324 sq ft, F = 44.4 psi x 324 sq ft x 144 = 2,072,000 lbs.

On a 13 ft diameter shaft, 132.7 sq ft, F = 848,000 lbs static, about 1.7 million lbs with a spring high tide surge and hydraulic ram amplification of 1.5 to 2.5 from the half-mile red oak channel.

Mahone Bay high tide of +6 ft adds about 125,000 lbs.

Static is 0.85 to 2.07 million lbs.

With tide and ram it is 1.7 to 3.1 million lbs.

Two million pounds is therefore not treasure weight.

It is thrust at the bedrock tap 100 ft below sea at high tide.

The stone is a maintenance warning:

40 pieds below this point, 2,000,000 lbs thrust.

I reconstructed the sequence.

📐

The French blew out the earth with black powder in sheepskin cartridges, laid the two 150 m drains at about 60 ft below sea, dug a central shaft 40 ft deeper to bedrock to tap the freshwater lens at maximum thrust, capped the bedrock tap with flagstones, connected both drains at the 90-ft junction, and backfilled the entire middle shaft above the junction with puddled clay and flagstones to direct pressure sideways to the swamp, not up.

When they left in 1713 they did not blow it up.

They just blocked the Smith's Cove intake with clay and disconnected the swamp output.

The system stayed intact underground, hidden.

That is why the pit floods only when the clay cap is dug out.

That concludes my analysis that finally solved the puzzle completely by Jerry Harrah

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