www.cheops-pyramide.ch Copyright 2006 Franz Löhner and Teresa Zuberbühler
Chambers and passages inside the pyramid of Khufu
The King's chamber lies on 43.03m  and is lined with granite. On top of the chamber are five so called relieving chambers (see below). A granite sarcophagus lies in the chamber, but it is not known if there ever was a corpse put to rest there; a mummy or grave goods haven't been found inside the pyramid.
Plan of the King's chamber:
Dimensions of the King's chamber:
The ancient Egyptians didn't know the theory explaining the Pythagorean
theorem (a² + b² = c²) but they knew from experience, that
they could form right angles by using a so called primitive Pythagorean
triple (for example 3²+4²=5²). As the King's chamber shows,
they used this knowledge expertly when building.
According to some Egyptologists  the inside of the sarcophagus was hollowed out using a bow drill and copper bits. To chisel the precise corners inside the sarcophagus and to make reliefs they suggest that chisels and scrapers made from stone were used, not metal tools. The sarcophagus is made from hard granite, so how could it have been hollowed out using only copper tools?
Franz Löhner calculated, that if you use drills made from copper
you would have needed 16 to 18 years to fashion the sarcophagus. Copper
wears off immediately and because it is very soft and granite very hard,
the tools would have to be reforged all the time. Without iron
tools it is not possible to drill granite or to chisel the precise corners
or a relief!
The largest granite beams were used for the so called relieving chambers.
The beams are about 2m thick and 8m long, between them lie limestone beams
and the whole structure is covered with a gabled roof also made from limestone.
Here the largest granite beams were used, they weight from 40 to 50 tons
and had to be brought to a height of 43 to 65 meters (= tip of the gable).
The lifting of these beams is challenging but not a insurmountable problem,
if you use Franz Löhner's heavy duty track system.
We only know about the stress-relieving chambers because in 1837 Howard Vyse had small tunnels dug and blasted, but we don't know about what lies on top of the gable. If you compare the configuration of the King's chamber with the way the entrance to the pyramid was built you notice, that two layers of stone blocks were used there to form a double gabled roof. For this reason some archeologists conjecture, that there might be another layer of limestone slabs lying on top forming a double gabled roof.
Why build these chambers?
The purpose of the relieving chambers probably was to absorb the enormous pressure on the King's chamber and to redirect it into the surrounding stones. Because granite has a higher compressive strength than limestone (160 - 240 N/mm² instead of 80 - 180 N/mm²) the builders mainly used this type of rock. Compressive strength is the capacity of a material to withstand axially directed pushing forces.
Damage observed in the stress-relieving chambers
1. The roof is slightly caved in, because the two gables don't lean flush on each other anymore
2. The limestone supports are straining from the enormous pressure (arrows)
3. The original plaster bond between the upper western granite beams and the western wall has moved by 15cm
4. Because 98 meters of stone press on the hard granite chamber, the softer limestone around it shifted and lowered by 15cm. The southern wall was injured and the chamber warped. The first and fifth stone course subsided and from the eastern corner a long fissure is running through several stones .
5. The roof beams are contorted by 4 cm and the second, third and forth beam have burst at several places.
6. The so called air shaft is bent, perhaps because of the lateral pressure.
The King's chamber was built high up on 43.03 meters - other pyramids had chambers underground or positioned only a few meters above ground. For Khufu's pyramid the master builders had to deal with totally new problems.
Because several granite beams have burst or otherwise been damaged and the softer limestone around the chamber has been lowered by 15cm, some people think, that the stress-relieving chambers should be called "stress-creating" chambers . But the fact, that the King's chamber hasn't yet collapsed shows, that the pyramid builders had found a solution that worked for thousands of years!
The entrance used today to enter the pyramid is a breach underneath the original entrance to the pyramid. Nowadays you go directly to the Grand Gallery bypassing three large stones blocking the corridor.
The Grand Gallery is very impressive, it is 46.71m long, the roof is
8.74m high and the walls are made from granite. The roof forms a 26°-angle
 and consists of seven corbels. With Franz Löhner's
heavy duty track system you can transport the granite blocks you need
here up to the appropriate height with no problems.
It is interesting, that the so called corbelled vault was "invented" at the same time as the larger pyramids were built. The first corbelled vault was built in the pyramid of Meidum, then Sneferu's pyramids and Khufu's pyramid followed :
Why was this new building element employed? A corbelled vault is used,
if the distance from one wall to the other is too large, so a piece of
stone put flat can't overcome it. Interestingly this new building element
abruptly appears and is executed right away on a very high level. Then,
two generations later it is already not employed anymore (Khafre's pyramid
only has gabled roofs, Menkaure's pyramid vaults).
Three granite stones were once suspended in the antechamber to the King's chamber. These so called portcullises were probably lowered after the funeral ceremonies and blocked the access to the tomb. Their purpose was to impede tomb raiders from entering. There were also 25 to 26 large blocks lowered into the Grand Gallery , blocking it completely. This system didn't help much - the robbers probably climbed over the lowered portcullises and chiseled off enough of the granite over the entrance to the burial chamber to be able to enter. Portcullises are also known from the Bent pyramid and from Khafre's pyramid.
manner how those heavy portcullis slabs were suspended uses the
same principle as Löhner's rope roll. Ropes were slung over
a round longitudinal support (= roll) and then tied to a cross beam. The
rope glided over the beams and the huge weights were moved, but there
was no wheel or axle involved. The slabs were probably held in position
by wooden supports . The same principle was
used to lower other portcullises and stone plugs into corridors and shafts
- putlog holes for the wooden beams were found in several tombs.
The round cross beams were resting on specially shaped stones, which
had a semicircular cut on top. Franz Löhner thinks, that the tracks
he suggests for the sledges were also anchored to the pyramid flank on
similar looking Tura stones.
Moving image, how the portcullises were lowered (click on Anck symbol www.chufu.de) / Illustration portcullis / Photo side joints for the ropes / semicircular cuts for the beams / anchoring the tracks according to Franz Löhner
These shafts start from the King's chamber and the Queen's chamber upwards and to the north and south. The air shafts, which start in the King's chamber are better known. They are made from limestone, except where they cross the granite walls of the chamber. The exit of the northern shaft was enlarged by tomb robbers to a depth of 11m , and part of the shaft destroyed. The southern exit of the shaft to the surface of the pyramid was restored. It is not known, if the shafts were covered by the outer casing stones or not, because the stones are not there anymore. Both shafts are not straight, but slightly bent .
There are also 2 shafts originating from the Queen's chamber, but they were covered up originally. These "Air shafts" were discovered in 1872 by Wayman Dixon who put a piece of wire through one of the joints and realized, that the wall sounded hollow at two places. He then broke open the wall and discovered the shafts which have a diameter of 20 by 20cm.
In 1993 the engineer Rudolf Gantenbrink  sent a robot into the air shafts. After 66m he discovered a stone blocking the access to the rest of the shaft. In 2002 another robot (Pyramid Rover 2) was sent in again, this time with the cooperation of National Geographic and the blocking stone was drilled through. Behind it was a small empty space and a second blocking stone. If there is a third blocking stone or if anything else can be found in the shaft is not known.
Those shafts only exist in the pyramid of Khufu but are not known from other pyramids. This is probably the reason why speculations about the purpose of these shafts are banded about. The explanations go from "should have helped the Ba of the pharaoh to be able to enter and exit"  to some undefined logistic function or that they point to the Orion or to the Polar star.
If you discuss the function of these shafts you shouldn't forget, that at least two of the shafts were completely covered. So one thing is clear - they can't have been there to get fresh air into the tombs, for that they would have to be open on both sides.
upuaut project Gantenbrinks robot explores the air shafts in the Khufu's
pyramid - excellent three
dimensional drawings of the shafts with scale.
The three Queen's pyramid lie 56.2m (=107 cubits) from the eastern edge of Khufu's pyramid (photo). Like Khufu's pyramid all satellite pyramids have an angle of inclination of nearly 52° . The ground where those pyramids were built is sloping slightly to the south, this is probably the reason, why their corners are not exactly right-angled. The side lengths measured are from 45.2 to 49m (87 to 90 cubits). Some Egyptologists calculate 88 cubits which would be a fifth of the side length of Khufu's pyramid. They think that, notwithstanding the sloping ground the builders wanted, that the tips of the pyramid would be optically on the same height (G1a = 56 cubits=29.3m, G1b = 58 cubits=30.25m) . Because the outer casing stones of those pyramids were removed we also don't know, if they were step pyramids (as you would assume seeing the pyramids now) or if they had a smooth outer surface.
The exact date, when those satellite pyramids were built is not known. Some Egyptologists think, all three were built together, others reckon, that the most northern pyramid, G1a was built first, because it lies on the best building ground. Then the pyramid G1b would follow, it lies 10-12m from the first one and last G1c would have been built, because it lies on the most unfavorable building ground of the three and is built quite close to G1b (4-6m). Goyon thinks, that the satellite pyramids were only built, when most of the main pyramid was already finished .
Archeologists are not yet sure, for whom the pyramids were built. They were named after queens (Hetepheres G1a, Meritites G1b, Henutsen G1c) but these attributions are quite hypothetical because no inscriptions were found.
Khufu's pyramid complex with the four satellite pyramids (the attribution as the queens burial places is not certain  - G1a Hetepheres, G1b Meritetes, G1c Henutsen and the recently discovered G1d)
South of Khufu's pyramid lies the small pyramid G1d, which
measures 23 x 23m, with an angle of inclination of 52° .
It is interesting, that 23.05m are exactly 44 cubits, which again are
a tenth of the side length of Khufu's pyramid (440 cubits). This satellite
pyramid was only found in 1993 by Z. Hawrass and is interpreted as a cult
pyramid (like the small pyramid G2a near Khafre's pyramid). During the
excavations a pyramidion was also found.
 D. Arnold Lexikon
der Ägyptischen Baukunst
www.cheops-pyramide.ch Copyright 2006 Franz Löhner and Teresa Zuberbühler