ToES Diary January 2019

Breaking up the items of bronze from the temple would not be easy.  If we assume that it would be necessary to tip over the two bronze columns, this prompts a computation of their weight.

They were 18 cubits high with a capital of 5 cubits at the top (Jeremiah 52:21).  The lower section was 12 cubits in circumference and 4 fingers thick.

The volume of metal in this cross section can be found from:
Outer circumference = 12 cubits = 6 metres = π * D
Thus the outer diameter D = 6 / π = 1.9 m, so the outer radius R = 0.95 m

Thickness of the column was 4 fingers or about 0.1 m, so the inner radius r is about 0.85 m.

Area of a doughnut section A = π * (R² – r²)
A = π * (0.95² – 0.85²)
A = π * (0.902 – 0.723)
A = π * 0.18
A = 0.565 m²

If we assume that the capital was a similar mass for each metre of height, we have a total height of 18 + 5 cubits = 23 cubits or 11.5 m.

Volume V = 11.5 * A
V = 11.5 * 0.565
V = 6.5 m³

The density of bronze is approximately 8,700 kg/(m³).

Thus the total mass of bronze in each column is about 8,700 * 6.5 = 56,600 kg or almost 57 tonnes.  However, if the capitals were more substantial items, given the networks and pomegranates that decorated them, they may well end up weighing significantly more than a comparable length of the column.  The total weight for column and capital may end up being closer to 60 tonnes.

Natural ropes have a much lower breaking strain than the synthetic ropes we use now.

A 2″ manila rope (made using the fibres from the abaca plant found in the Philippines which is stronger than any other natural rope materials known) has a breaking strain of 10,500 kg (see http://phoenixrope.com/rope-products/natural-rope/manila-rope/).  Thus, six 2″ ropes would be sufficient to tip over such a column.  Each rope would require about 200 men each exerting 50 kg of force to generate 10,000 kg in a rope.  That means 1,200 men for the six ropes.  Long ropes would be required since the ropes would be reaching up to the top of the column, and standing 200 people along a rope for pulling would take about 50 m of rope at least.  Assuming that in the 50 m, the rope could rise from 1 m to 1.5 m, similar triangles suggests that the rope would have to be about 1,050 m long to rise the 10.5 m from 1.0 m to 11.5 m at the same gradient.  Based on information from the Phoenix Rope and Cordage website referred to above, such a rope would weigh 1,500 kg.

This is not a practical length for such a rope.  In fact, the manufacturers now sell this rope in only 183 m (600′) and 366 m (1,200′) lengths.  To use such short lengths, the rope would need to pass underneath some form of bar that could resist the upthrust generated by having 200 men pulling as hard as they could on a shorter rope that sloped much more steeply between the top of the column and this suggested horizontal bar.  For example, if a 183 m rope were used (which would still weigh 264 kg!) the rope would have to slope 10.5 m upwards in 133 m.

If we call the angle of the rope θ (theta), then sin(θ) = 10.5 / 133, which gives an angle of 4.53 degrees.  If the rope carries a load of 10,000 kg, the vertical component of this would be almost 800 kg and it would be hard to get the rope to slip smoothly over the bar.

Overall, it seems that a much better method would be to excavate/shatter the foundation on one side of each column to undermine the column until it falls.

It would still be a big job as it would be necessary to excavate for one metre under the column to get to the centre of the column which was almost 2 metres in diameter.  To actually tip the column over, it needs to tilt enough that its centre of gravity is beyond the support point;  ie, if the centre of gravity is half way up the 2 m diameter column (at a height of 5.75 m), it must be 1m out from vertical at that point.  Using similar triangles, this requires a hole that is 175 mm deep or about 7″ and reaching under to the centre of the column.

Complete removal of foundation stones may be easier, while using fewer, shorter ropes to give a little extra force as necessary.