The Ascending Passageway

Section 5.4.1
Both Sir William Matthew Flinders Petrie and John & Morton Edgar complained the measurements of the ascending passageway was very difficult due to the giant granite plugs in the beginning of the passageway. (The plugs will be shown in the detail drawings). Furthermore was the floor slippery  and broken and the walls were dilapidated.
The great difficulty has resulted in different measures of the length of the passageway:

Prof. Smyth : 1544 inches.
Prof, Petrie : 1546,8 inches.

Mr. Edgar : He admitted it was too difficult, so he suggested a figure in between : 1545 inches.

From my studies of the sources I have to admit  Sir William Matthew Flinders Petrie had the most reliable measures due to his scientific approach. So,  in my work I have applied the length of the passageway from the POI (Point of Interest) to the southern end of the floor to be 1546,8 inches = 75 cubits RM = 106 remens.
In his book "The pyramids and temples of Gizeh" he wrote:

"39 ...
... From this altitude, the sloping length of the passage being 1546,8, the horizontal length will be 1389,5 and the vertical height 679,7, both being corrected for difference in the offsets of the ends."  (S5-[S39]-P29-[C2]-L26)

The measures are in inches.

Furthermore Flinders Petrie added an interesting detail:
"38 ...
... The granite plugs are kept back from slippering down by the narrowing of the lower end of the passage, to which contraction they fit."  (S5-[S38]-P28-[C3]-L20)

Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

Section 5.4.2

According to Flinders Petrie was following measured:

The height of the ascending passageway is 2,29 cubits RM in the upper end 2,05 cubits in the lower end.  (S5-[S38]-P28-[C3]-L32)

The width is 2,02 cubits RM in the upper end and between 1,82 and 1,84 cubits RM in the lower end. This is the contraction as mentioned in the above section and the reason why the granite plugs did not land on the floor of the descending passageway when released.  (S5-[S38]-P28-[C3]-L32)

Section 5.4.3
A hard task had been to measure the slope of the descending passageway with the theodolites. Of this reason there are different measures from different sources:

Edgar : 26° 18´ 10" RM
Flinders Petrie : Mentioned a mean angle of 26° 2´ 30"  (S5-[S38]-P28-[C1]-L20-21) , but in the orginal text  (S5orig-[S39]-P65-L3) another result of the measurements of the ascending passageway and the Grand Gallery together is 26° 12´ 50" RM, which seems to fit to the measurements of Prof. Smyth.
(There might be other measures in the literature.)

The measure is crucial for the orientation of the upper part of the passageways and chambers, so the measure must be correct.

To make sure which slope we proceed with we must have in mind how the ancient Egyptians measured a slope. They did not know degrees, they knew seked, which was the number of hands horizontally divided by the number of cubits vertically. The seked was a natural number maybe combined with a fraction like 1/2, 1/3, 1/4, 1/5. (Please see section 4.2.6 and 4.2.8 for further explanation.

The seked number for the 3 different measures:

Edgar : 26° 18´ 10" RM = 14,16 seked RM

Flinders Petrie : 26°  2´ 30" RM = 14,31 seked (mean angle)

Flinders Petrie:  26° 12´ 50" RM = 14,21 seked

It is convincing that 14,21 seked, which is close to 14 1/5, is the correct measure.

The conclusion is the slope of the ascending passageway is  26°  12´ 50" or 26,2139° or  close to 14 1/5 seked RM.

Section 5.4.4

Calculation of where the ascending passageway meets the floor of the descending passageway, the "Point Of Interest" POI:

Let us have a closer look on the cross section between the ascending and descending passageways, (the length of b1 is in the lowest part of the ascending passageway only 2,05 cubits RM height to prevent the plug blocks to continue further down into the descending passageway. To make sure I calculated the angles and other lengths correctly I had to ignore this special height for the moment. The plug blocks are not shown in this figure. The length h1 is hypothetical):

We know following measures:

Angle A = 26,5231°
Angle L = 26,2139°
Length b2 = 2,25 cubits
Length b1 = 2,29 cubits

The other angles and lengths can be calculated :

Section 5.4.5

Summary:

Section 5.4.6 and 5.4.7 are deleted.

Section 5.4.8

A closer look on the passageway:

From POI up to the end of the ascending passageway on floor level : 1564.6 inches = 75 cubits RM according to section 5.4.1

Section 5.4.9

Further measures according to Flinders Petrie:

The height of the plug blocks is 2,29 cubits RM in both upper and lower end.  (S5-[S38]-P28-[C2]-L29)
The width of the plug block at lower end is 1,85 cubits RM and at upper end 2,02 cubits RM.  (S5-[S38]-P28-[C3]-L20)
The length from the lower plug block at floor to POI is 3,6 cubits RM.  (S5-[S38]-P28-[C2]-L30)
These plug blocks cut out of boulder stones of red granite are not flat next to each other. The 3rd block has been 1,16 cubits RM longer originally.  (S5-[S38]-P28-[C3]-L32)

Underneath you can see the 3rd block has been cut. The photo is taken from Al-Mamouns cavity a part of the brutally made passageway into the Ascending Passageway, which unveiled the chambers and passageways in the upper part of the pyramid. Even it hurts to see this, I have to admit we in a peculiar way must be thankful to Al-Mamoun and his workers for this work. Nowadays it is prohibited to make that kind of destruction in the pyramid.

Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

Let us have a look where the plug blocks are:

And a closer look:

The 3 plug blocks are marked dark grey, (which is not the natural color) and the area marked light grey is empty nowadays, but was originally filled with a block, which fitted perfectly into the hole. It still puzzles me how the ceiling block was attached, it might have been a combination of the angles, the force of gravity to the floor and the friction to the ceiling. Cement, was used between the plug blocks and the inner walls of the ascending passageway to facilitate the movement of the blocks from the Grand Gallery to the narrowed end of the ascending passageway. The cement hardened and made it impossible to move the plug stones. It is possible the cement also was used to glue the stone in the ceiling to prevent the block falling down in the descending passageway.

The story about the missing (dropped) block in the ceiling has been explained by Flinders Petrie:
"177. The history of the destruction of the Pyramids really begins with the Arabs. They first, under Khalif Mamun, forced the great hole through the masonry, from the outside to the part commonly called Mamun-s Hole, at the beginning of the ascending passage. Had it not been for their shaking of the masonry, which let fall the stone that concealed the plug-blocks, perhaps the upper chambers would have remained yet unknown. Hearing the stone drop, they turned aside their southward progress, and burrowing some twenty feet eastwards they broke into the entrance passage, and found the fallen stone; here they saw that it had covered the beginning of another passage, and so they forced out of their hole a continuation southward and upward to get behind the granite plug; finding they only hit the side of the plug-blocks, they tracked along them in the softer limestone, until they reached the upper end, and then they rushed freely up the hitherto unused passage. Probably they found the plug at the top of the well not replaced, after the earlier destroyers; and so got down the well and forced out its lower closing, which must have been in position for the Greeks and Romans not to have been aware of the passage."   (S5-[S177]-P93-[C1]-L1)

A closer look:

Please observe some details. The red lines between the blocks are undefined spaces and the upper block (3) is nowadays partly destroyed (see above picture).

The distance from the lower corner of block 1 to POI is 74,19" RM acc. to Flinders Petrie.     (S5-[S38]-P28-[C2]-L29-30)
74,19" RM = 3,6 cubits RM = 5 remens RM.

Section 5.4.10

The space in the ceiling of the descending passageway under the lowest plug block has following dimensions all in cubits:

And a closer look:

A view with the three original plug blocks and coordinates:

Known values:
The height of the ascending passageway is 2,29 cubits RM.
The angle A is 26,2139° (See section 5.4.3)
According to section 5.4.9 the distance from the lower corner of the lowest block is 3,6 cubits RM to POI.

Calculated values:
As we know from section 5.4.4 the distance h2 between the lower intersection point (between the ascending and the descending passageway) and the POI is 2,834 cubits then the distance from the lower corner of the lowest block to the lower intersection point between the ascending and the descending passageway, which is the same as the hypotenuse in the triangle with the sides a1 and b1, is 3,6 cubits RM - 2,834 cubits = 0,766 cubits, (which is very close to 1 remen). It is of course impossible to measure today as this part of the intersection broke down when the ceiling block fell down and is missing.

Section 5.4.11

For all three plug blocks it was originally constructed like this. The distance - if any - between the lowest block - (block 1) - and block 2 is unveiled, but the original total length is estimated by Flinder Petrie:
"Thus the total length of the plug blocks would be about 203 inches, or very probably 206 inches, or 10 cubits."    (S5-[S173]-P91-[C2]-L6)
The estimation is very likely to be true as the distance  of 10 cubits appears elsewhere in the ascending passageway.

Anyway, this information give us the overview underneath:

Calculations:

coordinates:

Section 5.4.12

Let us see the complete ascending passageway again:

The upper part (without color) over the three plug blocks has a special inner structure partly composed of cover stones, partly of special stones called "Girdle" stones.

Source: Plate CX from The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

The cover stones are irregular but symmetric at the Girdle stones. For example:

And a close look:

This photo is a part of a wing of a dragonfly:

I know the plate can be hard to understand, I have therefore made a little model, so you easily can see how the girdle stones are placed. At the left side there is an entrance to the Grand Gallery.

The first and the second girdle stones:

The first, second and third girdle stones:

Please also notice the mysterious stones also called "Pointers" just after the Girdle stones starting at the West wall, shifting to the East wall and back to West wall.
The symbolic meaning of the "Pointers" is unknown, but it obvious they have a function.

The second, third and forth girdle stones:

I have measured the positions of the girdle stones from the plate CX (see above) and calculated the measures in cubits:

Internal notes:
Total length from the Grand Galley to POI : 75 cubits RM.
Diagonal h2 : 2,834 cubits.
Length of the ascending passageway : 75 cubits RM - 2,834 cubits = 72,17 cubits.
Total length of the three plug blocks : 10 cubits.
Plug block 1 to cross section at floor : 0,766 cubits.
Length from Grand Gallery to the original 3. plug block: 72,17 cubits - 10 cubits - 0,766 cubits = 61,40 cubits (originally).
Destroyed part of plug block 3 : 1,16 cubits    (S5-[S38]-P28-[C3]-L32
Length from Grand Gallery to the present (partly destroyed) 3rd plug block : 61,40 cubits + 1,16 cubits = 62,56 cubits.
Plate CX length from the Grand Galley to the 3rd plug block at floor level is 358,5 mm.
Plate CX conversion factor between mm and cubits: 62,56 cubits / 358,5 mm  = 0,1745

I have made a video of a copy of the plate CX to show the positions of the girdle stones better:

Section 5.4.13
Here is a view from East where you can see the Girdle stones marked with yellow. The red lines are imaginary, we do not know how big they are inside the masonry:

And with distances all in cubits:

Here you see another way to see the same distances:

Please observe a distance of a Girdle stone is its hypetenuse in the passageway.
The numbers 2, 4 and 6 are the first three girdle stones, which have nearly the same distance. Number 8 is the fourth Girdle stone which is a bit wider.
From the numbers 3, 5 and 7 you can see the distances between all four Girdle stones, where the distance between Girdle stones 3 and 4 is a bit smaller.

An interesting feature is following:
The distance from Grand Gallery plus the distance of Girdle stone G1 is : 18,55 cubits + 1,52 cubits = 20,07 cubits or close to 20 cubits.
The distance of Girdle stone G1 plus the distance between the Girdle stones G1 and G2 is : 1,52 cubits + 8,46 cubits = 9,98 cubits or close to 10 cubits.
The distance of Girdle stone G2 plus the distance between the Girdle stones G2 and G3 is : 1,59 cubits + 8,36 cubits = 9,95 cubits or close to 10 cubits.
Though the distance of Girdle stone G3 plus the distance between the Girdle stones G3 and G is : 1,55 cubits + 7,92 cubits = 9,47 cubits.
The distance from the Girdle stone G4 to the edge of the first plug block is 10,74 cubits.
The total distance of all three plug blocks is 10 cubits.
The distance of all three plug blocks to the lower corner of the ascending passageway is 10 cubits + 0,766 cubits = 10,766 cubits.
I just point it out as there might be an idea behind this peculiar construction.

Section 5.4.14

Coordinates for ascending passageway:

Section 5.4.15

Top view, please observe the ascending passageway seems to be just above the descending passageway. I have not found any information about a change of the azimuth compared to the descending passageway.

And a closer view:

Section 5.4.16

Personal notes concerning the ascending passageway:

Source:  Kunst & Arkitektur Egypten by Matthias Seidel and Regine Schulz, 2006 P290

My notes at the change of the angle from 26,0417° to 26,2139° in the ascending passageway and the revised calculations caused by this:

And now to the Grand Gallery ...