Digging holes for a living is an ideal place to hide from maths, not to mention reading and writing, but, unfortunately, Iron Age roundhouses only really make sense if you understand their geometry. Maths is important to help us model the nearly 2-dimensional evidence of prehistoric postholes, and encourages us to think 3-dimensionally about structures.
Roofs are made using tree trunks, which, theoretically at least, start off as cones, but when the thin pointy end is removed, the trunk becomes a ‘frustum’ of a cone (plural: frusta or frustums) -- which is one for the pub quiz.
I want to introduce you to one of the most important graphs in the study of the prehistoric built environment. I first published it, but it’s not mine; it is just an equation. 
So when we compare an average roundhouse with a large one, although only 70% larger in diameter, the latter’s roof is 3 times the size, with 3 times the weight and thrust of the former. So large roundhouses are much larger buildings than the average circular building, and more structurally challenging to construct.
- Simple angle to calculate
- Simple to construct
- Produces a balanced roof
- Minimum angle for thatch
- Uses the minimum amount of materials
- Used in Africa
The next problem is to try and appreciate what this surface graph may represent in terms of roof weight. This can be calculated theoretically, but luckily experimental archaeology can provide some ‘real’ figures.
Ignoring the porch in the calculations, the roof of our average 10m roundhouse comes in about 10 tonnes, compared with 25 tonnes for the large roundhouse. This is the ‘static’ roof load, but we can also calculate the effect of snow and ice.
As we have discussed in a previous article,  trees were grown to order to fit a particular need, and woods would be managed to produce what builders required. It’s clear that roundhouses need long straight timber from several hundred trees of specific sizes, so someone better have planned ahead – at least 60 years ahead!
To be useful for prehistoric rafters, the butt must be thick enough at the ‘thin’ end to be rigid, but not too massive and heavy at the ‘thick’ end. If we decide that the trees we need have a butt thinner than 0.3m, but at least 0.1m thick, then our theoretical tree must be harvested between 35 and 60 years old. (Figures are for illustrative purposes only; actual growth may vary -- this is an unregulated market!)
The graph demonstrates that oak trees can only produce rafters within certain limits, and while it is clearly difficult to be specific, the maximum usable rafter is probably around 14 – 15 m in length, which corresponds to those required for the largest roundhouses found.
This suggests that the largest roundhouses required the longest timbers available, and given the exponential increase in weight for conical roofs, were probably at the limits of what it was considered safe to build.
This is what our graphs have told us: Not all roundhouses are equal -- some are considerably more equal than others, and if you live in one that is the biggest available and three times as large as the average, then you are probably not an average person.
However, in the next article we will look at some real examples, and I will show something truly remarkable about prehistoric buildings and the people who designed and built them.
Sources & Further Reading:
 G. A. Carter 1998: Excavations at the Orsett ‘Cock’ enclosure, Essex, 1976. East Anglian Archaeology Report No 86.
 see: F Pryor 2004: Britain BC: Life in Britain and Ireland Before the Romans Harper Perennial [pp 235 – 238]
[3 ] D W Harding, I M Blake, and P J Reynolds 1993 An Iron Age settlement in Dorsett: Excavation and reconstruction. University of Edinburgh. Department of Archaeology Monograph series No. 1.
 http://www.butser.org.uk/iaflphd_hcc.html http://www.butser.org.uk/index_sub.html
S. C. Hawkes 1994. Longbridge Deverill Cow Down, Wiltshire, House 3: A Major Round House of the Early Iron Age. Oxford Journ. Archaeol. 13(1), 49-69.
 Karl VanDevender Ice and Snow Accumulations on Roofs, in Disaster Response Handbook
University of Arkansas, United States Department of Agriculture, and County Governments Cooperating http://www.aragriculture.org/disaster/ice_snow/ice_snow_accumulation.pdf
 James. 1989, Forester's Companion Cambridge University Press, ISBN 0631108114