Two pairs of shafts lead off from the King’s and Queen’s chambers towards the surface of the pyramid. These shafts are quite small (about 22 X 22cm in cross-section) and were created by cutting channels along the underside of limestone blocks. These were placed on sloping bed stones and integrated with the surrounding masonry as the pyramid rose, section by section. Towards the terminations of the shafts the quality of the limestone dramatically improves. The northern shafts make various bends near the chambers to avoid the Grand Gallery. The lower ends of the shafts are connected to the chambers by short horizontal sections.
Queen’s Chamber south shaft
The upper ends of the KC shafts appear to have extended to, or near, the casing. Vyse and Perring reported the discovery of an iron plate embedded in the mortar of KC south shaft where it meets the present core masonry. They also found KC south shaft blocked with sand. On clearing this out a cool breeze entered the chamber and it was concluded that the shafts had been built to act as a ventilation system for the benefit of ‘the workers’. This idea has stuck.
The shafts are not straight but made up of straight sections. Winding lateral bends near the chambers were made to avoid the Grand Gallery so it is obvious that the builders had no interest in maintaining unbroken ‘lines of sight’ to putative stellar targets.
The Khufu shafts
The QC shafts (in blue) seem to be symmetrically placed relative to the central pyramid plane. But they do not reach the surface – they are terminated by small slabs of stone, bearing small copper rings on their upper sides. These have been compared to the doors on shrines symbolically bearing such rings connected by rope, as in the famous example from the tomb of TutAnkhAmun. They appear to signify the termination of the shafts.
Also these shafts do not quite reach the chamber walls – small membranes of stone were left in the walls of the QC by the original builders (until punched through by later excavators). Indeed the whole QC complex was effectively sealed off by the installation of the bridge at the bottom of the Grand Gallery (marked in black).
It is tempting to see this as architectural metaphor – the lower system, symmetrical but limited ; and the upper, reaching to the outside of the pyramid, presumably expressing the resolution of an important design imperative.
The KC shafts were first surveyed by Petrie. He writes –
“The air channels leading from this chamber have been already mentioned and reference has been made to Pl.xi. for the positions of their outer ends. The angles of them had not yet been accurately measured, and therefore I carefully observed them by a sliding signal and a theodolite. The angles on the floors of them at different distances from the theodolite station at the present outer ends are thus :–
|N. Channel.||S. Channel.|
|At 84 to 180|
At 180 to 300
At 300 to 372
|32º 4′ 45″|
31º 37′ 15″
30º 43′ 15″
|At 0 to 120|
At 120 to 240
At 240 to 360
At 360 to 480
At 480 to 600
At 600 to 720
At 720 to 840
|45º 25′ 6″|
45º 30′ 7″
45º 25′ 57″
45º 25′ 14″
45º 15′ 19″
44º 26′ 18″
45º 13′ 40″
” For example, on the floor of the N. channel, the angle on the part from 180 to 300 inches from the mouth averages 31º 37′ 15″; this is, of course, quite apart from whatever the dip may be from the passage mouth to those points; and it is reduced from the actually observed quantities. The above list of angles are just equivalent to observations by a clinometer, sliding to different parts of the passage. It is striking that the slope of both passages continuously increases up to the outside (except just at the mouth of the S. channel); hence these quantities, which only extend over a part of either passage, cannot give the true mean slope; probably on the whole length the means would not be greater angles than 31º and 44½º respectively.
” The N. channel has been forced open as a working passage for some way [p. 84] inwards, only leaving the floor and W. side perfect. The channel is now blocked, just below the end of the enlarged part, and on working a rod 4½ feet into the sand, it ran against limestone. The sand in the hole has blown in during gales, which sweep up sand like mist. The remains of the original channel show it to have varied from 8.9 to 9.2 (mean 9.0) in width, and to have been 8.72 and 8.74 in height.
” The S. channel is blocked by sand at 76 feet down. It is not straight in the clear length, curving more than its own width to the east; and the sides often shift a few tenths of an inch in passing from one stone to another. These details were seen by examining it with a telescope on Feb. 8, and by photographing it on Nov 2, 1881; these being the days on which the sun shines down it at noon. Its width at the top is 8.35 and 8.65, and its height 8.7 to 8.9.”
He also provides a diagram of KC shaft exits –
Petrie’s shaft exits
Petrie could only access the ends of the shafts in estimating their angles but he was confident in the positions of the exits on the pyramid faces – the south exit emerges one course of stone higher than north.
In 1964 Trimble and Badawy used Petrie’s measurements to propose that the celestial target of KC south was the belt of Orion, and in the north Thuban. That the shafts might relate to the stellar mythology seemed a more satisfying explanation of their purpose than the need to ventilate a tomb.
In 1992 Gantenbrink surveyed the shafts using a small robot and published the results on his website. He had some difficulty measuring the northern shafts because of the bends near the chambers, as well as junk left by treasure seekers trying to claw down foundational relics (a hook and a stone ball) left in QC north, presumably by the original builders. His results were rather different from Petrie’s.
Apparently using his own survey measurements Gantenbrink stated that KC shaft exits are on the same horizontal level 154 cubits above base (Petrie’s estimates are considerably lower, averaging 152.5 above base).
The mean angles of the shafts in degrees were given by Gantenbrink as follows :
KC north 32.6
KC south 45
QC north 39.1
QC south 39.6
Gantenbrink’s scheme is essentially geometric, the KC shaft angles he gives describe the shape of the pyramid –
KC north shaft (Gantenbrink) defines pyramid section
The lines of the shafts (as measured from Gantenbrink’s ‘cyberdrawings’ on his website) intersect below the chambers . For the KC shafts the intersection point is 77 above base and 22 south of centre –
Focus of KC shafts
So in Gantenbrink’s proposal the pyramid is divided into modules and the upper shafts are on the same level, like this –
Gantenbrink’s proposal for the KC shafts
How well does this scheme integrate with the geometry as we know it? The 22 cubit offset of the focus point is actually given by the root 2 construction on the height of the pyramid establishing the level of the KC –
Establishing 22 cubit offset and KC floor level
Legon, like Gantenbrink, promotes a purely geometric scheme. Using Gantenbrink’s angle for KC north, the shaft intersects the height of the pyramid 297 (99 + 198) cubits from centre. If this is taken as the ‘focus point’ for the northern shafts then, as Legon proposes, the lines of the QC shafts are established through a simple geometric construction (with slope 17/14) –
Gantenbrink and Legon’s proposals combined
In truth we don’t know much about the QC shafts. They were re-surveyed by the ‘Djedi’ team in 2010 as part of an effort to find out what lies beyond the blocking stone, by drilling through it. They found another stone, of poorer quality and lacking copper rings, blocking the shaft (NOTE 4 SHAFT HIEROGLYPHS). Their angles are given as ‘about 40 degrees’. Let’s hope the Djedi team’s detailed results are published soon.
Also using Gantenbrink’s new data, Bauval took a different approach. While Trimble and Badawy had put forward strong candidates for the targets of the KC shafts (Thuban and Orion’s belt), he proposed that the QC south shaft targeted Sirius, and QC north targeted Kochab in Ursa Minor. The striking thing here is that the two southern shaft candidates, Sirius and Orion, are the very ones we ought to expect from their roles in the stellar mythology.
Bauval believed he could extract a corrected date for Giza based on the mean angles of the shafts as given by Gantenbrink as follows –
KC north 32.6
KC south 45
QC north 39.1
QC south 39.6
The target stars at these elevations give dates as follows :
KC north Thuban 2330 BC
KC south Alnitak 2500
QC north Kochab 2350
QC south Sirius 2380
The mean of these dates is around 2400 BC. Bauval suggested that the discrepancy can be explained as building error. This is now considered too young for Khufu – the present consensus date is around 2570 BC. At this date the altitudes in degrees of these four culminating stars are –
STAR CULMINATIONS 2570 BC…………SHAFT ANGLES 2021 AD
Thuban 31.36……………………………………….KC north 32.6 (Gantenbrink)
Orion’s belt 44.98………………………………..KC south 45 (Gantenbrink)
Kochab 39.78………………………………………..QC north 40? (Djedi)
Sirius 39.02…………………………………………..QC south 40? (Djedi)
In the diagram below these altitudes (in red) are compared to shaft locations according to Gantenbrink (in blue). Because uncertainty remains over intended QC shaft angles, Legon’s strictly geometric interpretation of Gantenbrink’s figures is shown in black as a reference –
Gantenbrink’s shaft angles compared with star altitudes
The discrepancy between the altitude of Thuban at this date (31.36) and Gantenbrink’s angle for KC north (32.6) is hard to ignore and seemingly why some have abandoned the stellar hypothesis altogether. Others have looked at the survey data, such as it is, and pointed out that the angle of KC north ‘flattens out’ as it approaches the casing, implying that the builders gave geometry priority to the planning of the shafts but wished to incorporate (serendipitous?) alignments to the sky gods.
While we await the release of the survey data which would resolve these questions there remains scope for further speculation. Kochab was put forward (with Mizar in Ursa Major) as playing a part in the ‘simultaneous transit’ method of orienting pyramids. However this requires a late date for Khufu and may be a red herring.
Kochab may well be the intended target of QC north, not because of its potential role in orienting the pyramid, but because, when it reaches culmination –
Orion’s belt rises on the eastern horizon –
Or this event can be shown in whole sky view –
(It is interesting to note that the azimuth of the rising belt is about 72 degrees from north. The diagram evokes the sign for the underworld, the Duat, a five-pointed star within a circle. But this is admittedly speculation).
The selection of Kochab as a target star in the north indirectly brings attention back to Orion. But what could the mythic connections between Sirius and Kochab be to have paired them in this way?
Thuban, the target of KC north, was the pole star at the time. This shaft veers away from the meridian –
Meandering of KC north shaft
We do not know if there was some special reason for changing the azimuth of KC north in this way. It looks like an error and could mean that builders were not as concerned about precision when laying out the shafts.
It is difficult to reject Gantenbrink’s scheme because of its geometrical elegance. Even so is it true? He reports on his website that he has re-surveyed the pyramid and found that Petrie was wrong about the height of the exits. However, in the 25 years since Gantenbrink made these claims I have not found an academic source containing a formal report of his discoveries.
Nevertheless Gantenbrink was very certain of his figures. He writes regarding KC south –
“Block No. 5 is not accessible to conventional measuring procedures…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.
Regarding KC north he states that the lower part of shaft (at 32.6 degrees) changes in the upper part. He states – 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”.
At the same time we shouldn’t throw Petrie out with the bathwater – he was very specific that the levels of the KC shaft exits were not the same and, having meticulously measured the height of each course, up two corners, it beggars belief that Petrie could have bungled things in this way. Until this confusion is resolved we are prevented from making progress in understanding the meaning of the shafts.
Some of the confusion appears to arise from the survey of Giza conducted by Maragioglio and Rinaldi in the sixties. I compared the two surveys and it seemed that M + R had mis-numbered the stone courses. Puchkov has recently published an article looking at the various contradictions in the survey data and their probable causes. When hard survey data becomes available things will hopefully get resolved –
KC shaft exits. Petrie above. M + R below
The case for astronomical alignment is strong – it would seem incredible that the architect responsible for an exclusively geometric plan would not happen to notice that his two geometrically-derived southern shafts also pointed to his own gods in the southern sky, visible to all in Egypt. At the conventional date for Khufu the first two Decans, Sirius and Orion’s belt, culminated in the south at altitudes very much the same as the southern shafts. Perhaps Khufu’s architects exploited a celestial coincidence and tried to formalize it in the language of geometry – to ‘bring heaven down to earth’ as it were.
But why do we not find shafts in other pyramids? Actually we do of course in the form of pyramid descending passages which are agreed to point to the imperishable stars of the north. But where their slopes have been investigated they turn out to have been been designed geometrically and without stellar targets. Does this mean that the apparent fusion of geometry and astronomy inside Khufu was a one off?
Geometric constructs, lines and angles, the altitudes of stars, and ‘number crunching’ in general are not attractive subjects, but they were obviously important to the Egyptians. So it is to be hoped that in future investigations more attention will be paid to survey data than has hitherto been the case. Of course if Puchkov is right and radiocarbon tests provide definite proof that pyramids are 200 years older than the conventional dates then everything will need to be revised. The pyramid geometry though will remain the same.