Grand Gallery

Section 5.5.1 

The 10th of January 1988 when I and my wife came out from the ascending passageway and could straighten ourselves up, we saw the amazing Grand Gallery. 

A breathtaking view I will never forget. 

For this experience I owe King Khufu, his genius architects, his administrative and logistic staff  and also all his specialized workers many thanks for this fantastic result. The Grand Gallery looked like the path to heaven - (maybe this was exactly the intention).



Here is a picture taken by Edgar in 1910 from the floor, the lowest part, of the Grand Gallery, looking South. Behind the helper you can see the passageway into the "Queens chamber".
You can hardly see the end of the Grand Gallery, it is ascending into the darkness like the sky in the night.

552 Grand Gallery gulv III DSC09475jpg

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


Section 5.5.3

Flinders Petrie had these valuable comments to the angle and position of the Grand Gallery floor:
"For the angle of the passage, and its straightness, it will be well to consider it all in one with the gallery floor, as they were gauged together all in one length."
(S5orig-[S39]-P64-L27-29)

"This , when corrected for lower signal being .3 too high, gives 26° 12´ 50" for mean angle of both passage and gallery together."
(S5orig-[S39]-P65-L2-4)

"Hence the floor of the gallery intersects the S. wall at 1689.0 +/- .5 above the pavement; at 61.7 +/- .8 S. of the Pyramid centre;  "
(S5orig-[S45]-P72-L18-19)

Please observe the lengths informed by Flinders Petrie are always in British inches.
1689 inches = 81,91 cubits.
61,7 inches  = 3 cubits

From this we can calculate the coordinate where the floor of the Grand Gallery intersects the Southern wall, which of course is an imaginary point due to the top stone above the ramp.
For a better understanding please see my drawing below, the coordinate we are looking for is in the end of the dotted line:
 553 Grand Gallery floor overview closerPNG

The coordinate is: (4400/2-30, 2800-819 ) = (2170,1981)
Now we have the direction and the point where the imaginary floor line meets the South of the Grand Gallery.

Section 5.5.4

Let us start where we came into the Grand Gallery from the ascending passageway.  The old picture below is showing the end of the ascending passageway where it continues a bit into the Grand Gallery. On the right side you can see the lowest part of the eastern ramp-bench.


554 Plate CXLVIXPNG

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

It seems there had been a mechanical abrasion in the middle part of the floor of the end of the ascending passageway. Please observe the picture was taken before 1910, which is before the massive entry of tourists as we see nowadays. There is a similar abrasion in the top stone in the high end of the Grand Gallery. Please see section 5.5.9

I assume the abrasions were caused during the building of the pyramid.



Section 5.5.5

If we turn around, then the left (eastern) side and the right (western) side at the floor of the Grand Gallery differs from each other. The workers removed a couple of stones on the western side of the ramp-bench near the northern wall to make a passage downwards to the descending passageway. The mouth of this passageway is shown here by some drawings and a photo by Mr. Edgar. 
555 Plate CXLVIIPNG
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910


Underneath is a drawing which shows the well from another angle.

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

The old photo underneath shows the same.  There is still a part of the original stone in the western corner of the Grand Gallery.
555 Plate CXLVIPNG
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910


Section 5.5.6

Let us have a closer look on the well showing the western wall and ramp-bench in the Grand Gallery to the left and the end of the ascending passageway to the right:

556 REV1 Entrance and ascending passage and Grand Gallery detail start - west view med blank closerPNG

(I have made a full line to show the supposed original intention of the corner where the upper part of the ramp-bench hit the Northern wall. Above picture in the previous section 5.5.5,  you can see the corner is broken.)

Flinders Petrie measured the position of the well from the Northern wall:
"As, however, the position of its mouth has been supposed to have a meaning, it should be stated that the opening is from 21,8 to 49,0 horizontally from N. wall of gallery on floor."
 (S5orig-[S46]-P74-L26-28)

My comments:
21,8" = 1,06 cubits RM
49,0" = 2,38 cubits RM

Flinders Petrie measured also the offset on the eastern ramp to the floor from the North wall to the the position of the well from the North wall to the ramp end in the South:
"20,9"
 (S5orig-[S45]-P71-L24)

My comments:
20,9" = 1,0 cubit RM
Please observe that the offsets on the western and eastern ramp-benches varies from 20,7" (1,00 cubit) to 21,5" (1,04 cubits) and from 20,3" (0,98 cubits) to 21,6" (1,05 cubits), respectively. 

On this point of the western ramp-bench the vertical height is :
1 / cos 26,2139° = 1,1 cubits

The mouth of the well in North South direction is then 2,38 cubits RM  - 1,06 cubits RM = 1,32 cubits.


With measures in cubits:

556 REV1  Entrance and ascending passage and Grand Gallery detail start - west view med ml closerPNG

And coordinates:

556 REV1 Entrance and ascending passage and Grand Gallery detail start - west view med coordinates closerpng

Section 5.5.7

Calculations for the coordinates:

557 calcPNG

Special remarks:
Flinders Petrie has a measure from ground zero to the floor level 52" = 2,52 cubits from the door opening which is 858,4" = 41,6295 cubits, which corresponds to 416pixels.
In the calculation no. 5 I refer to this. My ground zero has the value 2800 minus 416 = 2384
The point of the mentioned measure is (2990 - 25, 2384) = 2965,2384
557 tablePNG
Source:  (S5orig-[S40]-P66-L4)


*In calculation no. 6 I have added 10 pixels = 1 cubit to find the coordinate. Please see the Plate XIII underneath made by Edgar. I have marked the height yellow.
This value of the height in the well is assumed, I cannot verify it in any sources. I have tried to compare drawings and photos, but in vain - so far.

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



Section 5.5.8

Internal notes for me only:
The drawings in section 5.5.6 are "close view" versions with another solution. Therefore the calculations and coordinates differs from the overview drawing.
The solution is 446 pixels per 2.6 cubits, which is 171.5 pixels per cubit.

1. 1043-182, 739-86 = 861,653
2. 861-226, 653-103 = 635,550
3. 635, 550-189 = 635,361
4. 635, 366+189+154 = 635,704
5. 635, 704+172 = 635,876
6. 635+226, 876 = 861,876

1,1 cubits = 189 pixels is the vertical height between ramp floor and ramp-bench.
0,9 cubits = 154 pixels is the vertical height between the floor to the "Queens chamber" and the ramp floor extended line.
0,6 cubits = 103 pixels is the vertical height between the ceiling of the passageway to the "Queens chamber" and the ramp floor.
1,0 cubits = 172 pixels is the vertical height between the floor of the well and the floor of the passageway to the "Queens chamber" .
0,33 cubits = 51 pixels is the vertical height of the step at the end of the ascending passageway.
1,3 cubits = 223 pixels is the vertical height between the floor of the well and the end of the ascending passageway .
1,32 cubits = 226 pixels is the horizontal length in the bottom of the well.
0,5 cubits = 86 pixels is the vertical height between the floor of the G.G. and the end point of the floor of the ascending passageway in G.G.
1,06 cubits = 182 pixels is the horizontal length from the well to the Northern wall in G.G.
1,5 cubits = 257 pixels is the vertical height between the ramp floor extended line and the end point of the ceiling of the ascending passageway.
1,1 cubits = 189 pixels is the vertical height between the floor of the ascending passageway and the ramp floor extended line at the Northern wall in G.G.
2,6 cubits = 739-293 = 446 pixels is the vertical height in the ascending passageway.
1043,293 is end point ceiling of ascending passageway
1043,550 is end point ramp-bench into the North wall of G.G.
1043,739 is end point floor of ascending passageway
 


Section 5.5.9

Let us take a detailed look into the Southern part of the Grand Gallery. As mentioned in section 5.5.3 we have the direction and the point where the imaginary floor line meets the South of the Grand Gallery which is (2170,1981).

First an overall view:

559 Grand Gallery overall without measues and coordinatesPNG

The complete length of the Grand Gallery:

559 Grand Gallery overview whole length without measues and coordinatesPNG

And closer to the top stone:

559 Grand Gallery top stone without measues and coordinatesPNG

Flinders Petrie:
"At the upper end of the gallery, we have already stated the S. wall to be 61,7 +/- ,8 S. of the Pyramid centre; and hence the face of the great step at the head of the gallery (which descends behind both floor and ramps) is (61,7 - 61,3) = ,4 +/- ,8 S. of the Pyramid centre."
Source: (S5orig-[S46]-P74-L33-36)

My comments:
The mentioned measures above are as usual i inches.
61,7" = 2,99 cubits RM
61,3" = 2,97 cubits
0,4"    = 0,02 cubits
My drawings is limited to an accuracy of 1 decimal in cubits, so the width is rounded up to 3 cubits RM. 
The 0,02 cubits should not be shown in my drawing as the measure is below the 1 pixel, but in this case I have chosen to show it on the drawing even 1 pixel is equal to 0,1 cubits, which is 5 times bigger than the real value. This decision does not have an impact on the position of the South wall.

Flinders Petrie:
"And the sloping floor seems to be also out of level by an equal amount in the opposite direction; since on the half width of the step (i.e. between the ramps) the height of the step face is 34,92 or 35,0 on E., and 35,80 or 35,85 on W."
Source: (S5orig-[S46]-P75-L9-11)

My comments: 
On East side:
34,92" = 1,69 cubits RM
35,0"   = 1,70 cubits RM
On West side:
35,80" = 1,74 cubits RM
35,85" = 1,74 cubits RM
It is clear the top stone or "step" is not perfectly horizontally. In my drawings it does not really matter as the accuracy is limited to +/- 0,1 cubits. The result is therefore the same on both sides : 1,7 cubits RM (which is 17 pixels).

We know from section 5.5.6 that the vertical height of the ramp-bench is 1,1 cubits. 
The vertical height from the ramp-bench to the edge of the top stone is therefore 1,7 cubits - 1,1 cubits = 0,6 cubits.

Flinders Petrie:
"Then the top of the step will (by above measures) be here 34,88 above actual floor end, and the step dips about ,64 to the S.wall at this part; so the top of the step at the S. wall is 34,88 + ,64 -30,08 = 4,16 (say+/-,2) above the virtual floor end at the line of taping."
Source: (S5orig-[S46]-P75-L18-21)

My comments:
34,88" = 1,69 cubits RM
0,64"    = 0,03 cubits RM
30,08" = 1,46 cubits RM
4,16"    = 0,2 cubits

With measures all in cubits:

559 REV1 Grand Gallery top stone with measures and without coordinatespng

It is impressive how close the Northern edge of the top stone is on the Apex - the middle of the pyramid. The distance is 0,02 cubits RM is equal to 1 cm !
I assume it was the intention to place the edge of the top stone in the middle of the pyramid. The idea might have been to mark a point between the ascending structure and the entrance of the passageway to the antechamber and the "Kings" chamber, which hereafter is horizontal.  

With coordinates:

559 REV 1 Grand Gallery top stone without measures and with coordinatespng

From section 5.5.3 we calculated the coordinate where the floor of the Grand Gallery intersects the Southern wall is (2170,1981).
The top stone intersects with the southern wall at (2170,1981-2) = (2170,1979).
The North-South length of the top stone is 3 cubits. the northern edge is therefore (2170 + 30,1979) = (2200,1979) which is shown in the drawing as ("2201",1979) to mark the small difference from Apex.
The height from the edge of the top stone to the ramp-bench is 0,6 cubits, the ramp intersects to the top stone at ("2201",1979 + 6) = ("2201",1985).
The vertical height of the ramp is 1,1 cubits, the floor of the ramp  intersects to the top stone at ("2201",1985 + 11) = ("2201",1996).

A much closer look on the intersection between the imaginary line and the upper face of the top stone is here:
559 Top Stone new drawing offset detail Ijpg

As you can see the imaginary line , which is prolonged from the floor of the ramp, hit the floor of the Antechamber only 0,4 cubits (=21 cm) from the edge of the Southern wall in the Grand Gallery.

Charles Rigano mentioned "The single block forming the Step does not stop at the Gallery wall but extends an additional 66" into the Ante Chamber".
Source: (S11-P53-L15-16)
My notes:
66" = 3,2 cubits

Flinders Petrie mentioned in a table:

559 Lngde af top stone i h t FlindersJPG
Source: (S5orig-P75-table)

My notes: 
61,32" = 3 cubits RM (Face of the Northern edge of the step to the Southern wall of Grand Gallery)
64,90" = 3,14 cubits RM (Length from the Southern wall to the joint where the granite begins)
As Flinders Petrie measured along the floor and the top stone is a lime stone then the length of the top stone in the North - South direction is 3 cubits + 3,14 cubits = 6,14 cubits RM in total.

I think it is an interesting structure as the Southern wall secure the top stone and prevents the stone from moving - especially downwards into the depths of the Grand Gallery. The top stone could withstand a huge downwards force during the construction of the pyramid. 

Are there any indications of forces which had been applied to the top stone? 

Edgar took a photo of the top stone, which gives you a better idea how it looks like. It was taken against the South - West corner of the Grand Gallery:

559 Topstone i Grand Gallery plate CVXIPNG
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

Nowadays the top stone has been "repaired", maybe to avoid any accidents when tourists move around on the stone.
It is more or less the same kind of a mechanical abrasion in the middle part of the top stone as we saw in the floor of the Grand Gallery, see in section 5.5.4 . In 1910 it could still be seen. If you examine the picture carefully you can see a trace in the middle of the eroded part of the top stone. It looks like a rope has been running there. If this is so, then the top stone somehow has been a part of the building process of the pyramid.

Lowest in the picture you can see the ascending floor of the Grand Gallery and on both sides there are ramp-benches leading up the top stone. On the Western side a piece of the ramp-bench has been broken off. 

In the background you can see the entrance to the small passageway to the antechamber and hereafter the "Kings" chamber.


Section 5.5.10

Let us have a closer look on the old picture.

5510 Topstone i Grand Gallery plate CVXI closerPNG
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

1. It is not possible to judge whether the missing part of the top stone is due to an abrasion or made for a purpose. If you ignore the angle from which the photo is taken, then it seems the top stone has a smooth surface  in the rounded part from the vertical center of both the ramp-benches . There is a possibility the shape has been made by the workers for a purpose.
2. If you examine the line under "2", then it starts from the very top of the top stone and ends at the bottom of the rounded part. 
3. Where the line "2" ends you see a clear round abrasion, which could have been made by a running rope.  Under the rounded abrasion is a vertical abrasion, which could have been caused by a rough rope or by water to cool down the rope caused by the friction against the stone.
4. Just above the "4" point there is a line that could have been caused by a stone which the workers dragged up and hit the top stone hard because of an accident.

If any of my readers have another explanation, please let me know.

I have tried to make a drawing by hand from the North side:

5510 Top Stone new drawingjpg

It is hard to figure out how far the abrasion hit the top stone in the North - South direction, but a photo taken nowadays give us a good indication:

5510 Top stone after repairjpg
Source:  https://commons.wikimedia.org/wiki/File:Herses-grande-pyramide.jpg

The line which forms a half circle behind the banister is the border between the original top stone and the repaired part. The repaired part seems to begin on the middle of the top stone.
 
The top stone seen from above:

5510 Top stone top viewpng

With measures:

5510 Top stone top view med mlpng

The width of the holes are 0,327 cubits RM or close to 1/3 cubits.

The East-West coordinates are:

5510 REV 1 Top stone top view med coordinatespng

Eastern hole:
2031,2200-30 = 2031 (E-W) ,2170 (N-S)
2031,2170+10 = 2031 (E-W) ,2180 (N-S)   
2031+3,2180 = 2034 (E-W) ,2180 (N-S)  
2034,2180-10 = 2034 (E-W) ,2170 (N-S)  

Western hole:
2071,2200-30 = 2071 (E-W) ,2170 (N-S)   
2071,2170+10 = 2071 (E-W) ,2180 (N-S)  
2071-3,2180 = 2068 (E-W) ,2180 (N-S)   
2068,2180-10 = 2068 (E-W) ,2170 (N-S)  

I have tried to make a 3D drawing of the top stone seen from North to South. I apologize for the low quality of my work - I am not used to make these drawings  :
You can read the measures and the coordinates are mentioned below in a table. 

5510 Top Stone 3d rev2jpg
 
5510 Top Stone 3d coordinatesjpg
The coordinate 1979  in cursive indicates the top stone is 0,05 cubits higher in the Western side than the Eastern side, but the measure is below the accuracy in my general drawings. 


Section 5.5.11

Let us focus on the top surfaces of the ramp-benches. On the picture in section 5.5.2 you can see rectangular holes cut down in the ramp-benches close to the walls. You can also see niches behind the holes cut into the walls.

Unfortunately Flinders Petrie did not register the number of holes, but he had following remarks:
"One remarkable point is that the holes are alternately long and short, on both sides of the gallery; the mean of the long holes is 23´32, with an average variation of ´73, and the mean of the short holes is 20´51, with average variation of ´40. Thus the horizontal length of a long hole is equal to the sloping length of a short hole, both being one cubit. This relation is true within less than half their average variations."
Source: (S5orig-[S46]-P72-L27-32)

My remarks:
As the sloping lengths for each hole and the spaces between them are not mentioned I must disregard from the average variations. Furthermore, it seems the variations are relatively small which confirms my decision.
Long hole: 23´32 inches = 1,13 cubits RM;   ´73 inches = 0,04 cubits 
Short hole: 20´51 inches = 1,0 cubit RM;      ´40 inches = 0,02 cubits

Another important measure Flinders Petrie mentioned:
"Ramp End ... 1815´5 Distance on Slope"
Source: (S5orig-[S45]-P71-L39)

My remarks:
1815,5" = 88,0456 cubits RM, which in my drawings I round down to 88 cubits.

Charles Rigano wrote following remarks:
"At the top of each platform 25 niches are cut into each wall (total 50) most of which have an angled trapezoidal feature chiseled across its face. There are 27 rectangular holes cut downwards into each side platform (total 54). The rectangular holes are next to the walls and generally centered on the niches cut into the side walls; the two rectangular holes against the north (lower) face of the Gallery do not have companion side niches.
All of the 50 side niches and trapezoidal features are completely filled with blocks and mortar of the type used elsewhere in the pyramid with the exception of the 7th and 11th side niches from the bottom on the west side, the first of which is empty and the second has a hole cut into the mortar. Because the depth of only two side niches is known, we cannot determine if opposing side niches were of different depths to facilitate insertion of a beam as is the case with the holes at the entrance to the Upper Horizontal Passage".
Source: (S11-P51-L16-26)

On the same page he wrote in a table :
"Depth (Into Platform)    7,0" - 11.5"  
Width (From Gallery Wall)  5,5" - 6,5"
Source: (S11-P51-L10 in the table)

On page 50 Charles Rigano mentioned following measures in the table:
"Width - Bottom Including Side Platforms  6´  10" (4 cubits)
Width - Between Side Platforms  3´  5"  (2 cubits)
Side Platforms   20,5" Wide  20,5" High (1 cubit square)"
Source: (S11-P50-L7 in the table)

My remarks:
7" = 0,34 cubits RM and 11,5" = 0,56 cubits RM. (depths)
5,5" = 0,27 cubits RM and 6,5" = 0,32 cubits RM. (widths)

Luca Miatello inform following in source 15:
"The holes are 14 cm wide, 18 cm deep, and their mean length alternates regularly between 52,1 cm (one cubit) and 59,2 cm (Petrie, 1883:72)."

My remarks about the holes in the ramp-benches:
14 cm = 0,27 cubits RM = 0,53 foots. (wide)
18 cm = 0,34 cubits RM = 0,49 remens. (depth)
52,1 cm = 1 cubit RM = 7 hands. (short length)
59,2 cm = 1,13 cubits RM = 8 hands. (long length)

There are 27 holes on each ramp-bench.
If you see the picture in section 5.5.9 it is obvious there is no hole adjacent to the top stone.
In section 5.5.5 you can see the picture showing where the ascending passageway end in the Grand Gallery. In the corner you can see the first hole. Taking in consideration that the hole is shorter than the horizontal length of the end of the floor of the ascending passageway, which is 1,06 cubits, I conclude the first hole is the short one of 1,0 cubit RM.



Section 5.5.12

The spaces between the holes are not measured, so I have to assume the sloping lengths of the spaces are the same.
As the ramps start with a short hole of a sloping length of 1 cubit RM and alternates with the long holes of the sloping length of 1,13 cubits RM and there are 27 holes in each ramp-bench and the series of holes and spaces end with a space and the total sloping length of each ramp-bench is 88,0456 cubits RM, we can calculate the sloping length of each space.
In fact we can see it as 13 sequences consisting of a short hole + a space + a long hole + space and in the end there is one short hole and a space before the top stone.
 
5512 calcPNG

The pixels are as usual for internal use only and are processed to calculate the coordinates and the drawings (10 pixels = 1 cubit).
The horizontal axis is calculated as the sloping length x COS 26,2139°.
The vertical axis is calculated as the sloping length x SIN 26,2139°.   



Section 5.5.13

The bottom of the holes have the same slope as the ramp-benches and the inner sides of the holes are perpendicular to the bottoms, see the drawings underneath.

It took some weeks before I realized the sides of the holes were not vertical, but perpendicular to the surface of the bench-ramp. This little misunderstanding cost me a lot of efforts to correct the calculations underneath. The incident also showed me with a cruel clarity how the small grey cells may mislead me. Afterwards I understood the holes may have been made before the stones were mounted in the Grand Gallery. 

There are two different sloping lengths L of the holes on these ramps: 1 cubits RM and 1,13 cubits RM.
Please see my drawing below with a horizontal line:


5513 Real hole in GG rev1JPG

Please see the drawing below of Mark Lehner showing an example of a hole (3) (here called notch) in the ramp (1), the niche (4) and the trapezoidal cutting (5) in the wall (2)  parallel to the ramp: 
5513 tegning af hul i rampe MarkPNG
Source S15,  "Niches, Slots, Grooves and Stains: Internal Framework in the Khufu Pyramid?" of Mark Lehner published in https://www.academia.edu/36645718/Niches_Slots_Grooves_and_Stains_Internal_Frameworks_in_the_Khufu_Pyramid 

Please see my detail drawing of the holes  of the Grand Gallery. It shows the holes in the eastern ramp-bench, the western ramp-bench is similar except the escape passageway near the northern entrance. Please see the coordinates underneath in section 5.5.14
s = Short hole
l = Long hole

Eastern ramp-bench:
5513 drawing of holes Eastern side ramp benchJPG


Western ramp-bench:
5513 rev 2 Western side Grand Gallery overview whole length without measues and coordinates with holes HIGH solutionpng

The corner at the Northern wall has been broken, please see the pictures in section 5.5.5, it is not possible to draw this section correctly. However in section 5.5.6. I have made a detail drawing to show the supposed original intention of the corner.

Section 5.5.14

As mentioned in section 5.5.11 the holes in the ramp-benches have these dimensions :
14 cm = 0,27 cubits RM = 0,53 foots. (wide)
18 cm = 0,34 cubits RM = 0,49 remens. (depth)
52,1 cm = 1 cubit RM = 7 hands. (short length)
59,2 cm = 1,13 cubits RM = 8 hands. (long length)

And according to section 5.5.12 the spaces between the holes are 2.198 cubits each.

As the holes alternate as short and long, all the holes have following lengths and coordinates on both ramp-benches (the western ramp-bench does not have the first hole "1s" at the Northern wall due to the escape passageway or well.):

According to section 5.5.6 the ramp-benches start at 2990,2375 and end at 2200,1985 according to section 5.5.9
(Please observe due to rounding the end point in the table is calculated to 2200,1986 which divert from the real coordinate.)

5514 Oversigt over coordinater West and East REV 3JPG

Calculations:
Sloping lengths at 26.2139° , cubits : The sloping lengths of the short and long holes are measured, the sloping length of the Spaces of 2.198 cubits is calculated in section 5.5.12
The total of cubits is a simple addition ends with 88.038 cubits.
The pixels used for the drawing in section 5.5.13 is calculated as cubits x 10

Lengths, cubits, X axis for the short hole: 1.0 cubit RM x cos 26.2139° = 0.8972 cubits (= 0.9 cubits rounded).
Lengths, cubits, Y axis for the short hole: 1.0 cubit RM x sin 26.2139° = 0.4417 cubits (= 0.4 cubits rounded).
Lengths, pixels, X axis for the short hole: 0.9 cubits x 10 = 9 pixels.
Lengths, pixels, Y axis for the short hole: 0.4 cubits x 10 = 4 pixels.

Lengths, cubits, X axis for the Space: 2.198 x cos 26.2139° = 1.9719 cubits (= 2.0 cubits rounded).
Lengths, cubits, Y axis for the Space : 2.198 x sin 26.2139° = 0.9709 cubits (= 1.0 cubits rounded).
Lengths, pixels, X axis for the Space : 2.0 cubits x 10 = 20 pixels.
Lengths, pixels, Y axis for the Space : 1.0 cubits x 10 = 10 pixels.

Lengths, cubits, X axis for the long hole: 1.13 cubit RM x cos 26.2139° = 1.013 cubits (= 1.0 cubits rounded).
Lengths, cubits, Y axis for the long hole: 1.13 cubit RM x sin 26.2139° = 0.4991 cubits (= 0.5 cubits rounded).
Lengths, pixels, X axis for the short hole: 1.0 cubits x 10 = 10 pixels.
Lengths, pixels, Y axis for the short hole: 0.5 cubits x 10 = 5 pixels.

Coordinate 2990,2375 is the start point at the Northern wall where the ramp-benches hit.
The upper Northern point of the first hole (on Eastern ramp-bench) is therefore 2990,2375.
All upper coordinates of the holes and Spaces are calculated this way:
For example is the Northern upper coordinate of the first hole "1 short": 2990, 2375 
The Southern upper coordinate of the first hole "1 short": (2990-9, 2375+4) = 2981,2371  , (the 9 and 4  are mentioned above).
The  Northern upper coordinate of the first Space starts at 2981,2371 and Southern upper coordinate is (2981-20, 2371+10) = 2961,2361
The next holes and Spaces are calculated in the same way.

The depths of the holes are measured to be 0.34 cubits RM.
The lower coordinates of the holes and Spaces are calculated from the upper set of coordinates.
Depth, X-axis: 0.34 cubits RM x sin 26.2139° = 0.1502 cubits (=0.2 cubits rounded).
Pixels, X-axes: 10 x 0,2 = 2 pixels.
Depth, X-axis: 0.34 cubits RM x cos 26.2139° = 0.3050 cubits (=0.3 cubits rounded).
Pixels, X-axes: 10 x 0,3 = 3 pixels.
For example is the Northern lower coordinate of the first hole "1 short": (2990-2, 2375+3) = 2988,2378  , (the 2 and 3 are mentioned above).
The Southern lower coordinate of the first hole "1 short": (2981-2, 2371+3) = 2979,2374 , (the 2 and 3 are mentioned above).
The other holes are calculated the same way.


Section 5.5.14

Top view of the ramp-benches.

Flinders Petrie noted:
"By plumb-line measure at the S. end, the roof on the E. side is inside the floor edge (or overhangs) 20.50, and on the W. side 20.40. On the S. end (eliminating the lean) the projections is 20.9, and on N. 20.4; mean of all, 20.55, for the sum of the seven projections of the laps, or one cubit, the laps being then one palm each in breadth. Thus the laps overhang the ramps along the gallery sides, and the space between the ramps (2 cubits), is equal to the space between the walls at the top."
Source: (S5orig-[S46]-P74-L15-21)

My notes:
Maybe it was easier just to measure the breadth of the ramp-benches. Anyway the note of Flinders Petrie gives us more information.
20.50" = 0,9942 cubits or 1 cubit NM.
20.40" = 0,9893  cubits or 1 cubit NM.
20.9"   = 1,0136  cubits or 1 cubit NM.
20.55" = 0,9966  cubits or 1 cubit NM.

With other words the breadth of the two ramp-benches is 1 cubit NM each and the space between the ramp-benches is 2 cubits RM, which is the same space between the walls in the ascending passageway. Please see the picture in section 5.5.4. The Western wall of the ascending passageway is aligned to the side of the ramp-bench. As the spaces between the walls are the same (2 cubits RM), then the Eastern wall is also aligned to the other ramp-bench.

According to the top view in section 5.4.15 the end coordinates in the East - West direction are 2041,2990 and 2061,2990 respectively.
As the breadth of the ramp-benches is 1 cubit NM each, then the Northern corners of the Eastern ramp-bench hits the Northern wall at the coordinates (2041-10,2990) = 2031,2990 and 2061,2990 respectively.
The Northern corners of the Western ramp-bench hits the Northern wall at the coordinates 2061,2990 and (2061+10,2990) = 2071,2990 respectively.

A similar calculation can be made where the ramp-benches hit the top stone at South.
The Eastern ramp-bench hits the top stone at 2031,2200 (at East) and 2041,2200 (at West).
The Western ramp-bench hits the top stone at 2061,2200 (at East) and 2071,2200 (at West).

Drawing for internal use only. (The Well or Pit is shown with coordinates):  

5514 Top view november 2019JPG


Section 5.5.15

The coordinates for the holes and spaces in the Eastern ramp-bench:

5515 Eastern ramp bench coordinatesJPG



Section 5.5.16

The coordinates for the holes and spaces in the Western ramp-bench:

5516 Western ramp bench coordinatesJPG


Section 5.5.17

In section 5.5.13 you saw this excellent drawing of Mark Lehner:

5513 tegning af hul i rampe MarkPNG
Source S15, "Niches, Slots, Grooves and Stains: Internal Framework in the Khufu Pyramid?" of Mark Lehner published in https://www.academia.edu/36645718/Niches_Slots_Grooves_and_Stains_Internal_Frameworks_in_the_Khufu_Pyramid 

Compare the drawing to this photo:

niche ved hul i rampe IVJPG
Source: S17.  http://grahamhancock.com/phorum/read.php?1,269522,269576
(Hole 4s)

and to another photo:

niche ved hul i rampe VJPG
http://thepyramids.org/p-016-great-pyramid-khufu-cheops-233-039-cavity-grand-gallery.html

For those who has not visited the pyramid I can assure you both photos and the drawing are correct. Let me explain:
Mark Lehner call the rectangular holes for "slots" and above the "slots" are "niches" cut into the wall. Across the niches are chiseled a trapezoidal structure called "trapezoidal cutting".  In my opinion it is not a trapezoidal structure, but a parallelogram as both the opposite sides are parallel. 

Anyway, in "Niches, Slots, Grooves and Stains: Internal Framework in the Khufu Pyramid?" by Mark Lehner published in https://www.academia.edu/36645718/Niches_Slots_Grooves_and_Stains_Internal_Frameworks_in_the_Khufu_Pyramid  : 
"4. The niches, numbering 25 were cut, 18 to 20 cm deep and 67 cm high, into the side walls above all but the upper southermost and lower nothermost of the notches. The top and bottom edges are horizontal. the bottom north corners are even with the sloping top of the ramp benches while the south corner is 10 - 13 cm lower, consequently part way inside the accompanying notch. The outer top and north edge of at least some of the niches are bevelled.
5. The niches were closed with limestone patch (Flicken) or plugs. The beveled edges were filled with mortar. The bottoms of the patch stones slope even with the slope of the upper surface of the bench-ramp. Below this, the niches were filled with limestone fragments and mortar. L. BORCHARDT reported that, where the patches had broken or the mortar fill had fallen away, the well-trimmed inside surfaces of the niches were fresh, clean and white as though they were little used before being closed by the patches.
6. Trapezoidal cuttings, (Streifen, striures, incisions) about 2 to 3 cm deep, were chiseled across the patched niches and onto the adjacent wall surface. The cuttings are 10 cm above the tops of the ramp benches and roughly parallel to the slope of the ramp-benches. The lengths of the cuttings vary from 55 to 70 cm. The cuttings are missing from the northernmost patched niches at the low end of the Grand Gallery."
Source: (S15-P102-L17-32)
   
According to Charles Rigano there are 25 holes out of 27 in each ramp-bench which have these niche and trapezoidal features.  Charles Rigano wrote following in the book "Pyramids of the Giza Plateau":
"All of the 50 side niches and trapezoidal features are completely filled with blocks and mortar of the type used elsewhere in the pyramid with the exception of the 7th and 11th side niches from the bottom on the west side, the first of which is empty and the second has a hole cut into the mortar."
Source: (S11-P51-L21-23)

In the figure on the same page mention Charles Rigano some figures in a table:
"Side Niches (In Walls") :
Height: 26"
Width: 11"
Depth: 8"
Source: (S11-P51-table)
 
My comments: The first picture is hole marked 4s ( or the 7th hole ) showing the empty hole and the 11th hole is the hole marked "6s".

Section 5.5.18

With other words, the only niche we can describe is the one connected to hole marked 4s, which is a short one. All the other niches might be of the same sizes, but we cannot be sure. The consequence of this is, that I avoid to calculate the coordinates for all other niches.

As you can see on the picture, it has not been easy to measure the dimensions of the niche at the short hole 4s and different sources have different answers:

The hole 4s has following dimensions:
Length: 1 cubit RM
Width: 0,27 cubits RM
Depth: 0,34 cubits RM

The angle is: 26,2139°

The niche has following dimensions from sources in a certain order, where Mark Lehner is the most reliable :
Depth:
Mark Lehner: 18-20cm , Source: ( S15-P102-L17), equal to 0,34-0,38 cubits
Miatello: 20cm ,  Source: ( S16-P3-1C-L7) , equal to 0,38 cubits
Rigano: 8" ,  Source: (S11-P51-table) , equal to 0,388 cubits
The depth of the niche at 4s is 0,38 cubits.
  
Height:
Mark Lehner: 67cm , Source: ( S15-P102-L17) , equal to 1,28 cubits  
Miatello (source S16): 60cm (average) ,  Source: ( S16-P3-1C-L26) , equal to 1,146 cubits  
Rigano: 26" , Source: (S11-P51-table) , equal to 1,261 cubits
The height of the niche at 4s is 1,28 cubits.

Width:
Mark Lehner: ?
Miatello: 32 cm , Source: ( S16-P3-1C-L26) , equal to 0,61 cubits  
Rigano: 11" , Source: (S11-P51-table) , equal to 0,533 cubits
See below.

Southern bottom corner in the hole:
Mark Lehner: 10-13cm , Source: ( S15-P102-L20) , equal to 0,19-0,25 cubits
See below.

It is not the big secret the dimensions "Width" and "Southern bottom corner in the hole" puzzles me. Let me prove what is right and wrong.
Underneath is a drawing of the upper part of hole 4s which is aligned with the surface of the ramp-bench seen from the western side. 

5518 Projection af hul 4sjpg

The upper part of the hole 4s is illustrated by a 26,2139° sloping imaginary line with a sloping length of 1 cubit.
The dotted lines in the upper part of the drawing symbolizes the niche.
The northern lower corner of the niche hit the imaginary sloping line of the hole.
The southern lower corner of the niche descend 0,19 cubits to 0,25 cubits into the hole marked "c".
The sloping length of the hole where the niche cut the imaginary line is marked a´
The remaining parts of the sloping line are marked b´ so b´ + a´ + b´ = 1 cubit.

According to Miatello the width of the niche is 0,61 cubits  
Rigano has informed the width of the niche is 0,533 cubits
Let us make some calculations to judge who is right, we can make two calculations based on both c = 0,19 cubits and c = 0,25 cubits:
5518 calcJPG
It is obvious that Miatello is not right, it is not possible the width is 0,61 cubits.
Let us turn around and make the calculation of the length c based on the number of Rigano:
5518 calc IJPG
which is close to 0,25 cubits mentioned by Mark Lehner.

Rigano has informed the right figure of 0,533 cubits, if  the lower southern corner descent 0,25 cubits into the hole 4s.

Does it make sense ? Let us calculate the sloping lengths a´and b´ :
 5518 calc IIJPG

Result:
a´= 0,6 cubits
b´= 0,2 cubits

The so called  trapezoidal cuttings has these measures:
(The sides are parallel to the ramp-bench).

Depth:
Mark Lehner: 2-3cm, Source: ( S15-P102-L28), equal to 0,04-0,06 cubits
Miatello: 2-3cm , Source: ( S16-P3-1C-L23) , equal to 0,04-0,06 cubits
The depth of the trapezoidal cuttings at 4s is 0,04-0,06 cubits.
 
Height:
Mark Lehner: ?
Miatello (source S16): 20cm, Source: ( S16-P3-1C-L24) , equal to 0,38 cubits  
The height of the trapezoidal cuttings at 4s is 0,38 cubits.

Length:
Mark Lehner: 55-70cm,  Source: ( S15-P102-L17), equal to 1,05-1,34 cubits
Miatello: 55-70cm, Source: ( S16-P3-1C-L24) , equal to 1,05-1,34 cubits
The length of the trapezoidal cuttings at 4s is 1,05 cubits

Lower side above ramp-bench:
Mark Lehner: 10-13cm , Source: ( S15-P102-L29) , equal to 0,19-0,25 cubits


Section 5.5.19

The measures are approximate values, so in this case I have chosen not to add RM. As the figures are not precise it could be helpful to receive a second opinion from the readers.
All these figures helped me to issue a drawing, the measures are in cubits:


5519 Billede af tegning af niche rev 4jpg

The drawings show the same niche at the hole 4s but seen from two different angles.

As mentioned the measures are not precise. From that perspective I dare to point out that some of measures might have been intended to be the same.
The depth of the hole of 0,34 cubits could have been intended to the same measure as the height of the trapezoidal structure of 0,38 cubits and the depth of the niche of 0,38 cubits as well. Normally I would not play with figures, but in this case I cannot resist. If the intended measure was the average between 0,34 cubits and 0,38 cubits = 0,36 cubits then this value is equal to 0,5 remens or 10 fingers. Is it a coincidence? Maybe - maybe not.

Another interesting measure is the offset of the bottom of the trapezoidal structure above the ramp-bench of 0,19 cubits, which is very similar to the sloping distance of 0,2 cubits, which is the same as 1/5 cubits.

Furthermore the height of the niche is 1,28 cubits which is exactly the same as 9 hands.

We can conclude the measures of smaller structures were defined as a simple fraction of cubits or in natural numbers of remens, hands (palms) or fingers.

Section 5.5.20

Let us see a top view at the floors:

5520 Top view GG on DescendJPG

The black lines are the ascending and descending passageways. The green lines represent the Grand Gallery. 

A closer look on the Southern part at Apex (center of the pyramid):

5520 Top view GG on Descend closer viewJPGJPG

The passageways are East of the North-South center line.
The entrance from the Grand Gallery into the antechamber (southern part of the topstone) at the North-South coordinate 2170 is more or less in the same position as the entrance of the subterranean chamber at 2180, but of course placed higher up in the pyramid. The difference is 10 pixels or 1 cubit = 0,524 metres. 

Section 5.5.21

Let us focus on the walls and the roof in the Grand Gallery. For this purpose, we need an additional figure in the set of coordinates as the walls and the roof. Until now the coordinates consisted of two coordinates, either (N-S, Up-Down) or (E-W, N-S). Until now it has been sufficient, and we saved some space in the drawings.

In this section we need to define an expanded set of coordinates as (N-S, Up-Down, E-W) or (X, Y, Z) as in a "normal" coordinate system.    

The four corners where the walls hit the "floor" are:
The northern wall at the eastern corner hits the ramp-bench at: 2990, 2375, 2031
The northern wall at the western corner hits the ramp-bench at: 2990, 2375, 2071
The northern wall at the eastern corner hits the imaginary floor line at: 2990, 2386, 2031
The northern wall at the western corner hits the imaginary floor line at: 2990, 2386, 2071
The southern wall at the eastern corner hits the top stone at: 2170, 1979, 2031
The southern wall at the western corner hits the top stone at: 2170, 1979, 2071

Section 5.5.22

Edgar published a picture of the North side of the Grand Gallery, where you easily can see the corbelled walls on all sides.

5522 Grand Gallery Northjpg
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910

A recently taken picture of the walls:

5522 Grand Gallery pict of todayJPG
Source:  http://www.touregypt.net/featurestories/greatpyramid3.htm
Please ignore the staircase and the angle irons inserted in the walls to prevent fractions falling down.  I have chosen this "new" picture to give you a better idea how the walls look like. Even the roof was not made smooth, but the stones are angled. Flinders Petrie had a good explanation:

"The roof of the gallery and its walls are not well known, owing to the difficulty of reaching them. By means of ladders, that I made jointing together, I was able to thoroughly examine both ends and parts of the sides of the gallery. The roof stones are set each at a steeper slope than the passage, in order that the lower edge of each stone should hitch like a paul into a ratchetcut in the top of the walls; hence no stone can press on the one below it, so as to cause a cumulative pressure all down the roof ; and each stone is separately upheld by the side walls across which it lies."
(S5orig-[S46]-P72-L33-40)


Section 5.5.23

All the walls consist of a basis and 7 laps and in the 3rd lap there is a groove on the eastern and western walls, let us see which measures we have:

Flinders Petrie:
"The remarkable groove in the lower part of the third lap, along the whole length of the sides, was measured thus, perpendicularly :
(S5orig-[S46]-P73-L40-41)
5523 tableJPG
(S5orig-[S46]-P73-L42-45)

My comments:
N.W. 11,7" = 0,567 cubits RM close to 4 hands RM (palms)
N. E. 11,8" = 0,572 cubits RM = 4 hands RM (palms)
S. W. 11,2" = 0,543 cubits RM 
S. E. 11,0" =  0,533 cubits RM
Mean 11,4" = 0,553 cubits RM
N.W. 5,4" = 0,262 cubits RM
N.E. 5,7" = 0,276 cubits RM
S.W. 5,1" = 0,247 cubits RM close to 1/2 foot or 7 fingers
S.E. 5,1" =  0,247 cubits RM close to 1/2 foot or 7 fingers
Mean 5,3" = 0,257 cubits RM
Mean difference  -6,1" = 0,296 cubits RM or close to 2 hands (palms)

Flinders Petrie:
"At the S.W. it is cut to a depth of -8 inch, at the S.E. to -6 (?) ; the upper edge of it is often ill-defined and sloping."
(S5orig-[S46]-P73-L46-47)

My comments:
S.W 0,8" = 0,039 cubits RM close to 1 finger.
S.E 0,6" (?) = 0,029 cubits RM (?)


Section 5.5.24

The dimensions in the Grand Gallery is a challenge as my sources miss a lot of genuine measurements. Even my favorite source Flinders Petrie had difficulties to measure for example the vertical height of the Grand Gallery. I have different measures from different sources, and they might be correct all of them depending on where they measured. To understand the problem, I have copied the old drawing of Edgar. I have inserted 4 red lines to visualize the problem. The heights of each lap are missing, also the height of the basis of the walls under the laps.  

5524 Hvor er der mlt 2JPG
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910  (Red lines and blue numbers are added by me).

(You can also see the groove in the third lap mentioned in the previous section).

Line I: Even it has been extremely dangerous to measure this height, it should be possible.
Line II: I cannot imagine this measure has ever been made. But, this height is the "true" vertical height.
Line III: It could be possible to measure there, but it is not the "real" height".
Line IV: This measuring line is very possible and the most convenient, but is it the "true" vertical height?  


Section 5.5.25

Another tricky point is that the roof is not smooth, but the stones are angled as explained in section 5.5.22

If you see the yellow marked area of the roof of the drawing med by Edgar, then you might understand the measuring problem of the "true" vertical height:

5525 Roof Grand Gallery Side 64 EdgarJPG 
Source: The Great Pyramid Passages And Chambers" Volume 1 by John and Morton Edgar, 1910  (page 64)

Let us examine the different sources: