shafts

Shafts in the Akhet

Upper Shafts

The upper shafts connected to the sarcophagus chamber were comprehensively surveyed by Gantenbrink (link).

The long upper section of the north shaft has an overall angle of incline of 32.60 degs, which is to within ~1/10 of a degree, sqd 11 (32.47 degs):

"After the Caviglia Tunnel, from Block No. 6 on, the shaft continues in the usual form. The angle between this point and the point of the shaft's outlet on the flank of the pyramid (we measured both points) is 32.60°."

The top 11m (36 ft) upper section is accessible and has a mean angle of incline of 31.20 degs:

"The "Mankiller" tunnel is accessible from the outside of the Pyramid, so we could manually measure the angle of shaft inclination through this section. The average angle is 31.20°, determined by 5 measurements made over a length of 11 m."

The long straight section leading to the top of the upper south shaft has an overall angle of incline of 45 degs (sqd 7):

"Block No. 5 is not accessible to conventional measuring procedures. Here, our video images show that the shaft's angle of ascent declines. From this point, all the way to the outlet on the pyramid's flank (we measured both points), the shaft maintains an angle of 45°. So, despite the extreme fluctuations in the initial section, the shaft seem to proceed with great exactitude and constancy."

Conclusions:

1. the underlying design scheme for the south shaft is most likely based on sqd 7 (45 degs), and the north shaft, sqd 11 (32.47 degs). Both seqeds are directly related to the basic geometry of a sqd 5 1/2 pyramid - sqd 7 is the diagonal of the square base of the pyramid, and sqd 11, the diagonal of the rectangle enclosing the pyramid - for Khufu's pyramid, 280 x 440 - a ratio of 7:11. The dual-shaft layout appears to have been designed with symmetry in mind, as even though the inlets of the shafts in the south and north walls of the sarcophagus chamber are not centred on the NS centre axis of the pyramid as are the lower shafts connected to the 'Queen's Chamber', the theoretical intersect of the floor lines of the shafts with the exterior face of the casing, were probably intended to have the same height above the base. Discrepancies exist between Gantenbrink's survey data and his CAD drawing, and also with Petrie's survey.

Shaft outlets on the present face of the core masonry:

"As we verified in 1992, the upper southern shaft emerges on the exterior at the 101st layer, the upper northern shaft at the 102nd layer. In this regard, Maragiolio and Rinaldi report incorrect values. (see Maragiolio and Rinaldi, "L'Architettura delle Pyramidi Menfite, Parte IV)."

Gantenbrink, S = 77.55 m (course 101; floor line extended to casing, top of course 104); N = 78.43 m (course 102, floor line extended to casing, top of course 104)

(according to Petrie, the height of the top of course 104 above the pyramid's base is 3175.35" (80.654 m) which is ~154 cubits (~0.5236 m = cubit))

Petrie, S = 77.963 m (course 102, floor line extended to casing, top of course 103); N = 78.900 m (course 101, floor line extended to casing, top of course 102)

M&R, S: course 102 (extended to casing, course 104); N: course 101 (extended to casing, 103)

Edgar bros., N: floor line extended to casing, top of course 100.

The floor level of the sarcophagus chamber, and the level of the theoretical intersect of the floor lines of the shafts with the exterior face of the casing, can be found using simple geometry related to the primary dimensions of the pyramid:

Vertical EW cross-section illustrating the design principles of the upper shaft's design:

A - B and C - D are parallel

Detail of the layout of the shafts at the sarcophagus chamber:

2. the top end of the south shaft is facing an area of the sky centred 45 deg above the horizon, and the north shaft, 31.20 degs. Using astronomy programs that take into account proper motion, precession, and set at Lat. 29.979 degs, 100 m above sea level, the sky can be precessed back in time to see if any celestial bodies, significant to the ancient Egyptians of the Old Kingdom, appeared at these altitudes due north and due south.

In the south, the distinctive 3-star asterism in the centre of the large constellation of Orion (ancient Egyptian, sAH, 'the father of the gods'), had an altitude of 45 degs at its highest point in the sky due south c.2555, and in the northern sky, the then Pole / North Star, Thuban, had an altitude of 31.2 degs at its highest point in the sky due north c.2588. (dates derived from Gantenbrink's survey and Voyager 4.5)

These astronomically derived dates are reasonably consistent with the dates given for Khufu's reign (2589 - 2566 +-50 yrs) in 'The Oxford History of Ancient Egypt', edited by Ian Shaw (Shaw 2000: 480).

The accuracy of astronomically derived dates for the shafts depends on at least three variables:

1. how accurately the AE surveyors could sight to a star or asterism due south or north.

2. how accurately the builders could build the shafts according to the architect's design

3. to what extent have the angles of incline been affected by subsidence within the pyramid's superstructure over 4500 years

How much these variables affect the date is difficult to know, but the uncertainty factor should be well within the +- 50 years for the historically derived dates.

Lower Shafts

The lower shafts cannot be accessed from the top ends, and what lies beyond the closure stones is still unknown. Gantenbrink's survey of these shafts is not as comprehensive as the upper shafts, which leaves many unanswered questions.

A 'Rope Climber' that carried a high-resolution, numeric-digital instrument designed to measure the shaft's angle of ascent was used to measure the shafts. It pulled itself up the shafts along the cable of the Upaut-2 robot, fitted with a laser guidance system.

Gantenbrink measured the length of the north shaft and its angle of incline up to the first bend of the lower inclined section. The shaft begins with a horizontal section 1.93 m long, and an inclined section about 16.57 m long. His 1994 MDIAK article states the angle of incline is 39.124 degs +- 2 degs that was determined with 14 individual measurements over a length of 15 m.

His web site published five years later has the following data: the drawing of the north shaft has the text, "angle uncertain!", and Gantenbrink states in his 'Findings' section:

"Based on 14 measurements made over a distance of 17 meters, the shaft's angle of ascent fluctuates between 33.3 degs and 40.1 degs. Block No. 4 clearly shows that a change in the angle was made at this point. To that end, the builders even cut the shaft 2 cm deep into the beginning of the floor block. The extreme angle fluctuations and the changes made to Block No. 4 would seem to indicate that, at this point, the ancient Egyptians ran into a conflict with the Great Gallery, which was being constructed at the same time, and thus were unable to adhere exactly to the originally intended shaft angle. Only further measurements in the still unexplored upper areas of the shaft will tell whether the intended angle is several degrees smaller than that of the southern shaft, or whether both shafts were to be constructed at the same angle, that is, quasi-symmetrically."

According to these figures, the slope of the lower inclined section varies from 33.3 - 40.1 degs, with a possible overall angle of 39.124 degs +-2 degs, and to complicate matters further, Gantenbrink drew the shaft with a ~43.6 deg slope. Uphaut-2, did not go beyond the first bend of the inclined section, which means most of the length of the shaft to the top was not even measured. Gantenbrink was careful to point out:

"Only further measurements in the still unexplored upper areas of the shaft will tell whether the intended angle is several degrees smaller than that of the southern shaft, or whether both shafts were to be constructed at the same angle, that is, quasi-symmetrically."

In 2003 Hawass continued the exploration of the upper section of the north shaft but AFAIK, any measurements of the length and angle of the slope, have not yet been officially published. He states in a 2005 article:

"We also sent the robot into the northern airshaft and found that after 20m the shaft bent and continued for another 8m. This bend may indicate that it was designed to miss the grand gallery and it also explains that it was carved during the construction of the pyramid. The robot continued for another 60m and then stopped in front of a door with two copper handles. It is the same distance as the door in the southern shaft with two copper handles."

Hawass's figures are unreliable as they are rounded up, 20 + 8 + 60 = 88m - for example, the first figure of 20m should be 18.5m, a rounding up of 1.5m!

Gantenbrink on the lower southern shaft:

"......the shaft inclines at an average angle of 39.6078 degs, which we determined by taking 24 measurements over a distance of 28 meters."

The inclined section of the shaft up to the closure stone is about 59.45 m (195 ft) long, but Gantenbrink only measured the first 28m (92 ft), which still leaves a further 29.49 m (97 ft). The upper northern shaft, for example, has a slight change of angle for at least the last 11 m (36 ft), so it's possible the lower shafts also have different angles of inclines for the top sections.

According to Petrie, the mean angle of incline for the lower section of the southern shaft is 38.47 degs (tantalizingly close to the 38.15 degs slope of a shaft taking the shortest route to the exterior of the pyramid), and the mean angle for the northern shaft, 37.47 degs. Petrie was a meticulous surveyor, but he was only able to measure the beginning of the lower inclined sections - he could not reach further up the shafts as Gantenbrink has done.

The layout of the lower shafts may be symmetrical, but without more survey data this cannot be confirmed, making it problematic to investigate the lower shafts for celestial alignments with any confidence.

If the two lower shafts were designed to be symmetrical and had celestial associations, then the most likely stellar candidates were the brightest star in their sky, Sirius (known in the Old Kingdom as spdt, often paired with sAH (Orion), and Kochab, one of the northern 'Imperishable Stars' (j.xmw-skjw), but without accurate survey data, its impossible to be certain.

Chris Tedder, Autumn 2008