Hi Alex,

from my 2008 web page on the 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