Methods used to measure angle of inclination.
15 May 2002:
Glass plate, measuring 300 x 200 mm.
Faber-Castell Universal Drawing Triangle with 10mm grid, combined set-square, parallel ruler, protractor and polygon drawing aid. Transparent and non-reflective.
Plumb-line with metal 100 gram plumb bob.
Black permanent marker
Nikon F-60 camera with slide projector
Olympus C-1 zoom Digital camera
Sony Handyman Digital Video Camera
Witnessed by Egyptologist Veronique Sebro, MS Sabrine Huber (Swiss Embassy) and Michele Bauval.
The Faber-Castell Triangle was fixed with it base flush onto the top rim of the glass plate by means of super glue. Yellow tacks were placed at the four corners. Yellow tack was placed at the focal point of the protractor (midpoint of the FB Triangle base), onto which was fixed the plumb-line. Several readings were taken at various points of the Serdab structure. On the east face, measurements ranged between 17 and 18 degrees. On the west face, taken after the east face, measurements ranged between 16.5 to 16.5 degrees. Back in the UK I realised, upon examining closely the photographs, digital images and videos, that the plumb line had gradually slipped to the left of the protactor’s focal point, causing the angle measured last to appear slightly larger on the east face, and slightly smaller on the west face. Since there was also much disagreement by Egyptologists on the value of the Serdab’s angle (Edwards give 16 degrees; Lehner gives 13 degrees), I decided to return to Egypt and re-measure the angle using various methods.
29 May 2002:
Stanley 300 mm spirit level.
Staedtler Right angle square with protractor
Nikon F-60 camera
Sony Handyman DV camera
Witnessed by Dr. Sunath Maddevan, Separtment of Astronomy, PSU
The idea was to establish horizontal lines along the east and west faces of the Serdab, and use the Staedtler protractor to measure the inclinations. Reading ranged from 16 to 16.5 degrees. This method, however, was not very satisfactory as it was difficult to ensure that the oil bubble in the spirit level was giving a perfectly horizontal line. Also air temperature was over 31 degrees, causing the oil bubble to act erratically. Also placing loosely the Staedtler protractor on the Stanley spirit level was not efficient. All this made the margin of error rather large. I decided to discard this method.
30 May 2002:
I decided re-use the Faber-Castell Triangle with the glass plate and plumb line, this time making sure that the plumb line remained on the focal point of the protractor with each reading taken. This time readings were constant at very near 17 degrees, (plus/minus 20').
I also used a large 600 x 400 mm cardboard on which I had drawn angles ranging from 16 to 18.5 degrees. A plumb line was fixed at the focal point of the angles. Only the east face could be measured using this method. Readings were constant at very near 17 degrees, (plus/minus 20').
It is generally agree that a plus/minus 20' must be taken as tolerance for naked eye observation at night and also for setting out the masonry blocks. Also a small adjustment has to be made for refraction of starlight through the lower atmosphere (in this case 16-18 degrees altitude) which I estimate to be at about 10’ at temperatures of 20-35 degrees C. In my best reckoning, the ancient builders were probably aiming at a point/star in the lower northern sky having a altitude ranging from 16° 30’ to 17° 30’, and a azimuth of 2° 30’ to 3° 20’.
Photographs of the various operations will follow.
|Djoser's Serdab: Angle||361||Robert Bauval||05-Jun-02 09:13|
|Re: Djoser's Serdab: Angle||125||Jeff van Hout||05-Jun-02 13:19|
|Re: Djoser's Serdab: Angle Geometrical method||99||Robert Bauval||05-Jun-02 14:16|
|Re: Djoser's Serdab: Angle Geometrical method||93||Lee McGiffen||06-Jun-02 11:29|
|Re: Djoser's Serdab: Angle Geometrical method||89||Robert Bauval||06-Jun-02 13:44|
|Touche'||83||Lee McGiffen||06-Jun-02 14:05|