The Fourth Dynasty Great Pyramids - Geographical Orientations and Side Deviations, Part Two
Ernest Moyer demonstrates the extraordinary progression in construction control from Meydum to Giza, with the Great Pyramid casing held to ±1.5 parts/10,000 (3 centimeters over 230 meters), revealing the sophisticated engineering capabilities of the pyramid builders.
Copyright 2001, by Ernest P. Moyer
The Side Deviations
The data provide other information, clearly indicated on Figure One (from Part One). The individual side orientations of Meydum differ from one another as much as 18'. The Bent enclosure wall has a scatter of 11', while Giza 2 has 1' 52" maximum difference among the sides. The Giza 1 core is within 1' and the casing within 37" (Petrie). (For 3' 33" value by Cole see discussion below.)
This trend shows a direct relationship between polar orientation and side deviation from the mean pyramid length. The closer the structures were oriented to the pole position the less scatter they had in their side differences from the mean lengths. The engineers not only were continually improving on orientation according to some grand design — they also were continually improving on base construction to maintain individual lengths to that same grand design.
Quantifying Construction Control
The data demand that we evaluate the latter. Table II shows the calculated values of base length differences in parts/10,000 from the mean length for the respective pyramids. In this form the data help quantify the continual increase in base length control from Meydum until Menkaure, when a relapse again occurs. See Figure Two.
Although the normalized plot tends to accent improved control for larger structures, a plot of the real errors shows a similar trend. The normalized plot is useful to show the level of control.
Remarkable Precision Across Structures
Meydum was held to ±2 parts/1,000 maximum difference (30 centimeters) among its sides.
The Bent enclosure wall was held somewhat tighter.
Giza 2 was held to less than ±4 parts/10,000 (8 centimeters).
Giza 1 outer casing was held tighter than ±1.5 parts/10,000 (3 centimeters).
This is remarkable control for such large structures, hardly equaled in modern constructions. As Petrie noted for Giza 1, one could cover the error with one's thumb for a length of some 230 meters.
Table II: Base Deviations and Orientations
Calculated Base Deviations From Mean Length in Parts/10,000 and Compass Orientations in Minutes of Arc (The Mean Lengths are in meters)
MEYDUM
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 144.32 | -8.30 | +21.00 | -1.40 | -12.00 | 10.70 |
| Orientation | -24.41 | -35.40 | -23.60 | -20.60 | -18.10 |
BENT WALL
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 298.70 | -3.70 | -5.40 | -2.00 | +11.00 | 5.50 |
| Orientation | -12.45 | -4.60 | -16.70 | (?) | -16.10 |
GIZA 2
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 215.263 | -3.50 | +0.37 | +2.40 | +0.70 | 1.70 |
| Orientation | -5.44 | -5.50 | -6.20 | -5.70 | -4.40 |
GIZA 1 CORE
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 228.638 | +0.92 | -2.30 | +0.26 | +1.10 | 1.20 |
| Orientation | -5.26 | -4.60 | -5.40 | -5.40 | -5.70 |
GIZA 1 CASING (Petrie)
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 230.348 | +0.65 | -1.20 | +0.78 | -0.22 | 0.72 |
| Orientation | -3.72 | -3.30 | -4.00 | -3.70 | -3.90 |
GIZA 1 CASING (Cole)
| Measurement | Mean | N | E | S | W | Avg Deviation |
|---|---|---|---|---|---|---|
| Length | 230.351 | -4.30 | -0.43 | +4.50 | +0.26 | 2.40 |
| Orientation | -3.11 | -2.50 | -5.50 | -2.00 | -2.50 |
Analysis of the Progression
The dashed lines on Figure Two are intuitive estimates of the limits of builder control. Future measurement on the two Dashur structures should show:
- The Bent held to ±8 parts/10,000 on side lengths
- The Flat held to ±5 parts/10,000
Giza 2 again appears to fit in the sequence before Giza 1, rather than after.
Again the Step and Menkaure Pyramids could serve as terminus a quo and terminus ad quem, respectively.
Key Observation
Note that Giza 2 and the Giza 1 Core can now be distinguished for difference in control, which did not show in the compass orientations. This fact is important to our data analysis.
The progression in Table II reveals:
| Structure | Average Deviation (parts/10,000) |
|---|---|
| Meydum | 10.70 |
| Bent Wall | 5.50 |
| Giza 2 | 1.70 |
| Giza 1 Core | 1.20 |
| Giza 1 Casing (Petrie) | 0.72 |
This monotonic improvement in precision parallels the monotonic improvement in orientation shown in Part One, providing compelling evidence for conscious design control throughout the entire construction program.
Implications
The correlation between improved polar orientation and improved base length control demonstrates:
- Unified Design Intent - Both orientation and dimensional precision improved together
- Sustained Capability - The builders maintained or improved their capabilities over the entire construction period
- Intentional Demonstration - The smooth progression suggests deliberate refinement for future observers
- Extraordinary Engineering - Modern construction rarely achieves such precision at this scale
The data supports the hypothesis that the Fourth Dynasty pyramids represent a coordinated project with consistent advancement in both surveying accuracy and construction precision, rather than independent structures built by successive pharaohs with varying capabilities.
Figure 2: Progression of base length control showing monotonic improvement from Meydum through Giza 1
Ernest Moyer is author of "Our Celestial Visitors," in which he thoroughly examines the UFO and abduction phenomenon, with much new material never before published.