Some months ago, in another thread about another topic, Scott Creighton tabled a brilliant idea as to how the "gable" blocks at the summit of the Kings Chamber tower may have been positioned.
This got me looking more closely at the "gable" block arrangements within G1 Kings Chamber, Queens Chamber and the exposed blocks above the original entrance.
Firstly I have no idea where the term "gable Block" originated as they in fact appear to be compressive, triangular trusses.
Anyway a quick look at The Mar G drawings seemed to indicate that some exploratory tunneling had been carried out in the recent past, Perring? resulting in that it has been pretty well established as to the length and depth or penetration of the blocks forming the roof of the Queens Chamber.
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It seemed apparent to me that here we are in fact looking at a cantilever, in fact two, angled and mutually supporting cantilevers.
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A quick calculation showed that these roof blocks are in fact supporting a vertical load of in the region of 9500 tons.
A considerable load for any single arch, In fact I know of nothing in stone, even approaching that figure.
Apart from the fact that the design engineers were able to have conceived of a cantilever, an even more remarkable fact is that they were able to accurately calculate the vertical moments on an angled cantilever in order to maintain equilibrium on both sides of the fulcrum, even taking into account the effect on the block caused by the angular block rotation away from the horizontal.
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In the Drawing above the forces A and B (Pink) are downward, vertical and equal.
The Fulcrum (green F, green line) is displaced outward by the block rotation.
Thus dividing the block upper length in to two equal halves (black A and B), which of course is necessary in order to maintain balance.
If the dimension (Black A) were longer, it would, through mechanical advantage have the effect of raising the (Black B) section.
The inverse would be true if the dimension (Black B) were longer with respect to (Black A)
Therefore the ancient engineers were capable of mathematically predicting and accommodating the gargantuan 9500 ton load bearing down on this feature. Remarkable.
The Kings Chamber seems to follow the same pattern, although supporting a lesser load.
As far as I am aware no tunnels have been excavated in order to determine the lengths of the KC roof blocks.
It would be possible to apply the same formula to the KC blocks.
The blocks immediately above the original entrance are clearly plain compressive trusses, no cantilever. they are supporting considerably less load.
This "belt and braces" approach in the QC seems to have stood the test of time, and possibly similar in the KC.
Next question is why did they feel the need to displace the KC blocks vertically upward by orders of magnitude from an obviously necessary horizontal ceiling?
This got me looking more closely at the "gable" block arrangements within G1 Kings Chamber, Queens Chamber and the exposed blocks above the original entrance.
Firstly I have no idea where the term "gable Block" originated as they in fact appear to be compressive, triangular trusses.
Anyway a quick look at The Mar G drawings seemed to indicate that some exploratory tunneling had been carried out in the recent past, Perring? resulting in that it has been pretty well established as to the length and depth or penetration of the blocks forming the roof of the Queens Chamber.
It seemed apparent to me that here we are in fact looking at a cantilever, in fact two, angled and mutually supporting cantilevers.
A quick calculation showed that these roof blocks are in fact supporting a vertical load of in the region of 9500 tons.
A considerable load for any single arch, In fact I know of nothing in stone, even approaching that figure.
Apart from the fact that the design engineers were able to have conceived of a cantilever, an even more remarkable fact is that they were able to accurately calculate the vertical moments on an angled cantilever in order to maintain equilibrium on both sides of the fulcrum, even taking into account the effect on the block caused by the angular block rotation away from the horizontal.
In the Drawing above the forces A and B (Pink) are downward, vertical and equal.
The Fulcrum (green F, green line) is displaced outward by the block rotation.
Thus dividing the block upper length in to two equal halves (black A and B), which of course is necessary in order to maintain balance.
If the dimension (Black A) were longer, it would, through mechanical advantage have the effect of raising the (Black B) section.
The inverse would be true if the dimension (Black B) were longer with respect to (Black A)
Therefore the ancient engineers were capable of mathematically predicting and accommodating the gargantuan 9500 ton load bearing down on this feature. Remarkable.
The Kings Chamber seems to follow the same pattern, although supporting a lesser load.
As far as I am aware no tunnels have been excavated in order to determine the lengths of the KC roof blocks.
It would be possible to apply the same formula to the KC blocks.
The blocks immediately above the original entrance are clearly plain compressive trusses, no cantilever. they are supporting considerably less load.
This "belt and braces" approach in the QC seems to have stood the test of time, and possibly similar in the KC.
Next question is why did they feel the need to displace the KC blocks vertically upward by orders of magnitude from an obviously necessary horizontal ceiling?