Stone Circles and Measuring
Wheels.
(Article by Michael Spender, 2012)
INTRODUCTION
This article has two parts. In the first we show
that it is possible that Neolithic stone circles were laid out
using a measuring wheel to set the diameter and we point out
that this will lead quite naturally to integer value perimeters.
When the evidence is examined in greater detail we discover that
a universal wheel may have existed one with a radius producing a
circumference equal to the Megalithic Yard. In the second part
we look at the Avebury Circle in some detail and explore the
possibility that the 98 stone outer construct is partly
elliptical and partly circular and in so doing we find that
there is evidence that the layout does follow the Megalithic
Yard theory.
PART ONE: MEASURING WHEELS
BASIC THEORY
Neolithic humans have revealed extreme ingenuity
in the building of their stone monuments. Some of these
constructs are perfect circles while others are elliptical. It
seems fairly unanimous that circular constructs were used to
mark important solar events to assist in agricultural
efficiency. This would be especially important where seasonality
affects crop growth but not so important in regions where hours
of sun shine and darkness are evenly balanced. Thus in southern
climes we find elliptical constructs such as Nabta Playa in
Egypt and the Mzoura Circle in Morocco but in Northern Europe,
circular constructs predate ellipses. This does suggest that
ellipses had different, probably additional functions when
compared to circles It has been argued (1)
that there was a change from circular to elliptical layouts
because it was apparently easier to obtain integer value
perimeters using ellipses than with circles. We believe that
quite the opposite is true.
Consider using a measuring wheel to determine the
radius of a stone circle. If the wheel has radius r then its
circumference will be:
c = 2r.pi
And the marked out radius of the stone circle
will be:
R = nc =
2nr.pi
Where n is the number of wheel rotations used to
mark out the radius of the stone circle. The circumference of
the stone circle will be :
C = 2pi(2nr.pi)
Now we believe that by trial and error Neolithic
man would discover that by using the same measuring wheel to
assess this circumference, C would be divided into a whole
number of segments each of length:
L = C/c =(2.pi.2nr.pi)/(2r.pi)
= 2n.pi
And since to an excellent approximation pi
= 22/7, they would be able to predict quite precisely how many
segments there will be as long as they restricted values of n to
multiples of seven (and plausibly some fractions). Thus
n = 7/4, 7/2, 7, 14, 21, 28...........etc
Moreover they could decide how many stones they
wanted to erect and how many segments would be allocated to
each. Note that the segment length is independent of r so in
principle any size measuring wheel could be used.
A great many theories exist about stone circles,
the positions, number and significance of the stones in the
constructs here we simply want to test the idea of using a
measuring wheel to lay them out. The idea is testable for, if a
wheel was used, the diameters of the constructs will be
multiples of pi
by virtue of the fact that each diameter is
4nr.pi
In table1 the data for several stone circles was
collected which shows that the diameters of the circles are
multiples of pi. We have rounded some numbers up or down
to the nearest whole number and feel justified in doing so
because of likely errors in the measurements of the diameters
used. The stones are often huge leading to errors of order +/ 1
m and they may not still be in their original locations as a
result of earthquakes. As an example consider the Mzoura Circle,
it is listed at 57.7m in diameter and with that dimension we
found that the diameter was 18.3pi, but take account of a
+/ 1 m error range and we find the diameter to lie between 18pi
and 18.6pi.
TABLE 1 PARAMETERS RELEVANT TO MULTIPLES OF pi.
Name of Circle. 
Diameter (m). 
Xpi Rounded. 
Number of Wheel Rotations on diameter. 
Number of Wheel Rotations on Radius. 
Stone Spacing (MW) 






Nabta Playa (Egypt) 
3.69 
1 
4.4 
14 
0.5 
Mzoura (Morocco) 
57.7 
18 
69 
217 
1 
Aubrey Holes (UK) 
86.6 
28 
104 
326 
6 
Sarsens (UK) 
30 
10 
36 
113 
4 
Avebury North (UK) 
97.4 
31 
117 
366 
14 
Avebury South (UK) 
103.6 
33 
124 
389 
13 
Avebury 3 
103 
33 
123 
387 
12 (ref 2) 
Avebury Outer (UK) 
331.6 
106 
397 
1246 
13 
Brodgar (UK) 
104 
33 
124 
391 
7 
Stanton Drew Great (UK) 
113 
36 
135 
425 
1 
Stanton Drew NE (UK) 
34 
11 
41 
128 
11 
Stanton Drew SE (UK) 
40 
13 
48 
150 
19 
Almendres (Port) 
11.4 
4 
13.6 
43 
2 
Almendres (Port) 
18.8 
6 
23 
71 
3 
Column 3 in
table 1 shows that, the diameters, after rounding, are multiples
of pi, suggesting
the use of measuring wheels in the constructions. We will look
in more detail at Avebury in part 2 of this note.
The multiplier, the number of times pi
divides into the diameter is X = 4nr
We investigated to determine whether there is a
universal value of r, for the measuring wheel (MW). This work is
shown in table 2 where it will be seen that there is some
evidence for a universal wheel of radius 0.133 m, and a
circumference of 0.836 m. This value has been used to calculate
the wheel rotations in columns 4 and five in table 1. The stone
spacings are then found by dividing the usually estimated number
of stones into the perimeter wheel rotations.
If the same size measuring wheel was used for all
the circle constructs, a universal wheel would show up because a
common value of r will emerge when the expression:
r =X/4n where n takes values 7/4, 7/2, 7,14, 21
...........etc.
is evaluated for all the circles and various
values of n. We find the results shown in table 2.
TABLE 2 COMMON WHEEL RADIUS ?
Name of Circle 
Values of (r) for Various Values of (n) 
n =

X/4 
7 
14 
21 
28 
35 
42 








Almendres 
0.9 
0.128 
0.064 
0.042 



Nabta Playa 
0.925 
0.132 
0.066 
0.044 



Almendres 
1.5 
0.214 
0.107 
0.071 



Stanton Drew N 
2.7 
0.387 
0.192 
0.l28 
0.096 


Sarsens 
2.75 
0.392 
0.196 
0.130 
0.098 


Stanton Drew S 
3.175 

0.226 
0.151 
0.113 
0.091 









n = 

35 
42 
49 
56 
63 
70 








Mzoura 
4.7 
0.134 
0.111 
0.095 



Aubrey Holes 
6.9 


1.140 
0.123 
0.109 
0.098 
Avebury N 
7.75 


0.158 
0.138 
0.123 
0.110 
Avebury S 
8.25 


0.168 
0.147 
0.131 
0.117 
Avebury 3 
8.19 


0.167 
0.146 
0.130 
0.117 
Brodgar 
8.25 


0.168 
0.147 
0.131 
0.117 








n = 

70 
77 
84 
91 










Stanton Drew Outer 
9.07 
0.130 
0.118 
0.107 
0.098 










n = 

175 
182 
189 
196 
203 









Avebury Outer 
26.375 

0.145 
0.139 
0.134 
0.129 

The process is akin to looking for a lowest
common factor. The divisor can only take certain values so the
numbers listed for r are discrete values not interpolations.
Further analysis reveals that there are:
Five numbers in a range 0.14 to 0.149 m whose
average is 0.145 m
Ten numbers in a range 0.13 to 0.139 m whose
average is 0.133 m
Five numbers in a range 0.12 to 0.129 m whose
average is 0.125 m
Seven numbers in a range 0.11 to 0.119 m whose
average is 0.113 m
If there is a universal wheel its radius is
probably between 0.13 and 0.139 m with a likely value of 0.133
m.
The circles are far apart geographically so it is
unlikely that the choice of the radius is coincidental but
rather the result of an oral tradition passed along from
generation to generation. It is quite exciting to note that a
wheel with a radius of 0.133 m would produce a perimeter of
0.836 m (2.74feet), which is only 0.7% greater than the accepted
value of the Megalithic Yard. What exactly Neolithic humans
based this radius on remains mysterious but we like to think it
had some celestial origin in keeping with the constructions
being surveyed.
PART TWO: THE AVEBURY CIRCLE
It seems reasonable that Neolithic communities,
like all species in new environments, first looked for solutions
to specific pressing problems threatening their survival. Then
having identified the issues, they sought solutions in the
simplest possible way. The origin of the Neolithic humans seems
to be in areas near the equator where growing food is not really
a seasonal problem since there, the days are evenly divided
between light and dark the entire year and only water
availability is an issue. Neolithic monuments in these regions
are elliptical probably because the people had time to explore
more interesting phenomena than events like sun rise. When
Neolithic man began to move west and north into Europe,
seasonality created problems associated with agriculture, for
example, when to sow and how long until harvest time? Stone
circles with a good view of the horizon, present a simple,
effective way to determine from sun risings and settings,
whether the days are lengthening out or not and when the winter
is approaching. This is an event recorder and it is not
surprising that this kind of structure was used extensively in
Europe. Once an agricultural calendar was in place however, its
builders would have the time to look at more challenging
(interesting) problems. For example eclipses, irregularities in
moon cycles and the rising and setting of star constellations.
The design of an observatory to study these
latter types of phenomena would reflect the paths taken by the
heavenly bodies through the sky and be shaped, to match the
celestial equator, somewhat elliptical to make studies of
spatial relationships easier.
The construction of an elliptical locus is
achieved using two stakes and a sufficiently long string. It is
not too far removed from the process of creating a circular
locus. There are many examples of elliptical stone constructs.
The earliest of these appears to be Nabta Playa in Egypt built
around 4,000 BC. There is an important construct in Morocco
called the Mzora ring, also an ellipse. Both track several solar
features. The Cromlech dos Almendres is the oldest in Europe and
shows clearly how these structures developed. The first
construct there is a set of concentric circles then apparently
1000 years later a pair of concentric ellipses was added to the
site. The circles predate the ellipses. It seems clear that the
idea of using elliptical stone structures to track the relative
movements of sun and moon and to study eclipses spread eastwards
and northwards.
The Avebury Circle is newer than the Cromlech and
is well documented. The earliest parts of Avebury are three
perfect stone circles. Much later, the circles were surrounded
by a ditch and bank henge, the largest in Europe. At the same
time 98 large stones were set up inside the henge. The pattern
of construction follows that of the Cromlech, first the circles
then the complex shape of the Avebury construct. It seemed
worthwhile to see whether the locus of the Avebury stones could
be found. The detailed map shown in the article “AveburyA
Present from the Past” (3)
was used as follows:
An axis was drawn from stone 24 to stone 73.
because literature suggested that it was an important solar line
of sight and we then found that an orthogonal axis, drawn
through the mid point of 2473 passed through the Ringstone so
this was aesthetically pleasing and anyway, after considerable
trial and error we discovered that this was the only pair of
orthogonal axes that intersected at their mid points. On the
scaled map the 2473 axis measured 11cm which translated to
343.75m. The published diameter of the Avebury Circle is 331.6m
but its shape is quite irregular and the diameter can be as
large as 343.9m and as small as 321.9m. The axis as drawn
divided the stones into two groups, 48 south of the line
comprising the stones numbered 74 to 98 plus stones1 through 23,
and 50 stones north of the axis comprising the stones numbered
24 to 73. The point of intersection of the axes fell close to
stone 213 on the “North Circle”. Using the point of intersection
as centre, a circle of radius 5.5cm (171.9m) was drawn. It
passed through all the stones from 74 to 98 in the SE sector but
otherwise the fit was erratic, sometimes within and sometimes
outside the standing stones. We concluded that although the
Avebury construction is not a circle, the stones in the SE
segment do lie on a circular locus.
An ellipse seemed more likely to represent the
locus of the stones in the NE and NW sections of the henge. The
axis perpendicular to the 2473 axis was produced to the
northern perimeter of the stones. It terminated midway between
stones 48 and 49. This is slightly east of the north entrance
way. When produced to the southern perimeter this line passed
through the Ringstone and terminated just east of the south
entrance, between stones 98 and 97. Thus the semi minor axis (b)
and semi major axis (a) of the prospective ellipse could be
found and hence its foci calculated. The semi major axis was
5.5cm (171.9m) and the semi minor axis measured 5.1cm
translating to159.4m.
The distances of the foci from the centre of such
an ellipse are found from the formula:
f = +/ √(
a² b
²)
The foci were at +/ 2.05cm translating to
+/64.0m.
Only original standing stones were used to test
the criteria for their positions on the locus of an ellipse
using the formula
S(n)f(1) + S(n)f(2)= 2 a
Where S(n) is a particular stone f(1) and f(2)
are the foci, Sf is the distance from the particular stone to
one of the foci of the ellipse, and a is the semi major axis.
Stones 30, 40, 44, 68, 73 in the north section and stones 6,
10,14, 16 in the south section were tested. Numerical results
are shown in table3.
TABLE 3 MEASUREMENTS (Taken from map
(Ref: 3)
Stone Number 
Sf (1) p 
Sf (2) q 
p + q 




68 
3.8 
7.5 
11.3 
73 
3.8 
7.5 
11.3 
30 
7.3 
3.9 
11.2 
40 
6.6 
4.8 
11.4 
44 
6.0 
4.8 
11.3 
16 
6.9 
3.4 
11.3 
14 
6.6 
3.7 
11.3 
10 
6.8 
4.5 
11.3 
6 
6.4 
5.0 
11.4 






Sum: 
101.6 


Average: 
11.3 




77 
3.3 
7.3 
10.6 
78 
3.4 
7.2 
10.6 
98 
5.6 
5.5 
11.1 
The measurements indicated a value for (a) of
176.9m about 5m, 3% greater than expected. We tested stones 77,
78, and 98 in the southwest sector. The results are also shown
in Table 3 but they do not support the idea of an elliptical
locus.
As the location of the original axis was somewhat
arbitrary, the average of the length of the chosen semi axis and
the semi axis indicated by the measurements and calculation
above was used in further calculations, namely 174.4m. We now
consider the geometry and stone placements using the idea of a
measuring wheel with circumference 0.836 m. We note first that
the major axis will be 348.8 m or111 pi and the minor
axis at about 318.8 m will be 101 pi. Again we see the
idea of multiples of pi entering into the dimensions. We
can convert the dimensions of the axes into MW and find the
major axis is 417 MW and the minor axis 381 MW. The
circumference of an ellipse is not a simple calculation but to a
first approximation may be written:
C= pi (a+b)
Where a is the semi major axis and b the semi
minor axis.
The Avebury construction is, as we have seen,
roughly one quarter circle and three quarters ellipse, so the
actual elliptical circumference is:
3C/4 = 3pi (a+b)/4
Evaluated for the Avebury ellipse this becomes
787.5 m or 942 MW. There are 73 stones on the elliptical section
so the stones are placed on centres 13 MW apart.
The circumference of the quarter circle is 270.1
m which translates to 325 MW and since there are 25 stones on
the circular locus they are placed on centres 13 Wheels apart,
the same as those on the ellipse. So we find that the Avebury
stones do conform to Thom's theory, provided their loci are
correctly identified.
DISCUSSION:
It appears the two older Avebury circles were
used in two ways; to set up the required agricultural calendar
for the region and, to record full moon risings and settings. In
total the circles have 57 stones. This seems similar to the
Cromlech dos Almendres. There, the older circles are concentric
and one set is clearly marked with perfect circles. The number
of stones in the Avebury circles, 57 is similar to the number of
Aubrey Holes so we think they measure the same events. The same
number of stones features in the Cromlech elliptical construct,
basically two, one month moon cycles.
Consideration of the assessment of spatial
relationships leads us to suggest the following. The obelisk
stone could be used to sight the movement of the moon by an
observer standing at the elliptical stones. The observer moved
clockwise around the ellipse as the moon moved east to west.
Simultaneously, a second observer standing at the elliptical
stones would follow the shadow of the obelisk cast by the sun,
noting to which stone the shadow pointed. Elongation would be
measured by the number of ellipse stones separating the sun and
moon at some agreed moment.
Sightings on rising star constellations could be
made from the north entrance of the henge at sun set. Avebury
bears an uncanny resemblance to the Nabta Circle in Egypt even
to the placement of three stones in the south circle perhaps
representing “Orion's Belt” and since his feet and Sirius are
missing, this would be the sky at the beginning of spring.
Declination measurement seems problematical
without the introduction of another tool, a stave perhaps,
something that could be marked according to directions given by
an observer stationed in the ditch. One person holds the stave
upright and slides his hand upwards until the moon is obscured
from the observer in the ditch. The position of the mark would
then give a relative measure of declination. A daily repetition
over several years would eventually provide the information the
users needed to predict moon swings, stand stills and so on.
Another and particularly attractive idea, is the use of the
Celtic Cross the “Wheeled Cross” to measure declination.
According to Crichton Miller this type of instrument is
extremely ancient predating the building of the pyramids for
example, yet quite capable of measuring angles of declination
with great precision.
The Neolithic people left no written records, so
how all these their data would be remembered and passed down
through generations is a mystery even greater than the stones
themselves. But if some credence is given to the ideas discussed
above then one more mystery is how a Megalithic Wheel came into
existence. We are inclined to think that the idea is originally
MiddleEastern, that it would bear some relationship to the
moon, the planets, the stars and the sun, just because of what
was to be built, temples to these celestial objects. We suggest
for consideration, the apparent separation of the Moon and Venus
at the first new moon after the vernal equinox.
CONCLUSIONS:
1. There is strong evidence that true Neolithic
circles were set out using measuring wheels and that the
diameters of true circles were deliberately chosen to be
multiples of seven wheel rotations so that the resulting circle
had a perimeter equal to an integral number of rotations of the
same wheel.
2. That Thom's Megalithic Yard distance probably
results from the use of a measuring wheel with a perimeter of
0.83 m. Such a wheel would have a radius of 0.132 m. Our
calculations showed up a measuring wheel with radius 0.133 m or
circumference 0.836 m, about 0.7% larger than the Megalithic
Yard.
3. That 3/4 of the the Avebury Henge was
deliberately constructed on an elliptical locus with semi major
axis of 174.4 +/ 5m, a semi minor axis of 159.4 +/ 5m, and
eccentricity e= 0.37.
4. That the SE quadrant was constructed on a
circular locus with a radius of 171.9+/ 5m.
5. The major axis of the ellipse is orientated
south west to north east and the minor axis south east to north
west and passing through the Ringstone.
6. Avebury was conceived as a multipurpose
facility which why its layout is complex.
7. Avebury was built with a view to studying
relationships like elongation and declination Using the
elliptically located stones in the NE, NW, and SW sectors and
events like the rising of constellations using the stones
located on the circular segment in the SE sector.
(Contact the Author:
michaelrspender@gmail.com)
(More
about Avebury)
(More
about Stone Circles)
(More
abut the Megalithic Yard)
