Assessing the angle
of slope of existing pyramids
The
majority of all Egyptian pyramids are now in such a state of
ruin that it is very difficult to assess the original height
of the pyramid even if the base measurements can be accurately
determined. In the few preserved pyramids there are a number
of methods that can be used. The first involves measuring the
slope of the remaining casing stones. It has been found that
slight local variations occur. Averaging these give an approximate
guide to the height of the pyramid. An example is the pyramid
of Pepi II which I.E.S. Edwards estimated as being 171 feet and
a base of 258 feet3. This gives an angle of slope of 52.97ø
determined from a few casing stones.
Flinders Petrie in his measurement of the
Great Pyramid listed the angles of slope from the remaining casing
stones as:
Casing stones in situ on N. face
= 51°46'45"
Casing stones 5 overturned =
51° 52'
Casing stone fragments (18 no)
= 51°53'4"



Casing stones of the
Northern Stone pyramid of Seneferu

To supplement these calculations Petrie
carried out a number of additional checks involving accurately
surveying the corner stone inclines and the height to the final
existing level. This method has been adopted by other surveyors
where applicable. None of the capstones, or pyramidions remain
so completely accurate assessment is not possible. Nevertheless
a very close approximation can be given particularly with the
better preserved pyramids. Using all of these methods Petrie
arrived at a figure of 51°52' +/ 2' for the angle of slope
of the Great Pyramid. Other pyramids on the Giza plateau had
slightly greater variations depending upon their state of preservation.
For example the pyramid of Menkaure is given as 51° +/ 10'.
Based on these methods the angles of slope
of the best preserved pyramids from the IIIrd to VIth dynasties
can be listed as follows:
Maidum:
N. Stone Pyramid:
Bent pyramid(1):
Bent pyramid(2):
Khufu:
Khafre:
Menkaure (a):
Menkaure (b):
Userkaf:
Sahure:
Neferikare:
Nyuserre:
Teti:
Pepi II: 
51.88°
43.6°
54.52°
43.35°
51.87°
53.13°
51.19°
51.85°
53°
50.19°
53°
51.85°
53°
53° 

 The Pyramids of
Khafre and Khufu

(Note: Recent evidence suggests that the
pyramid of Menkaure was not set on a square base; one side being
335 feet whilst the other 343 feet. This will produce two different
angles of slope one of 51.85° and the other of 51.19°.)
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