Dimensions for these examples, except where noted, were taken from the RCAHMS Canmore website which provides access to the National Monuments Record of Scotland.
For brochs, which are circular or sub-circular.
Internal surface area = area of circle = π r², where r = radius
Surface area of roof = area of curved surface of a cone
= ½ (circumference of base) X (slant height)
= ½(2π r X l)
= π r√(r²+h²) [l = √ (r²+h²), for 45°pitch roof, h = r]
= πr√(2r²)
= πr √2 r
≈Approx. 4.44r²
Maximum rafter length
= √(2r²), where r is radius or half the breadth
Loch an Duin, Barvas, Lewis
Externally 18.8 NE-SW by 16.8 transversely. So 17.8 average.
Wall thickness is 3.8 at the W, 3 at the E. So 3.4 average
Therefore internal space has diameter 15.4m, radius 7.8m
Internal surface area = 191 square metres
Roof surface area = 270
Max rafter length = 11m
Dun Borve, Lewis
Internal diameter 31´6" = 9.6m
Evidence for scarcement, possible second floor.
Internal surface area = 72.4 (144.8)
Roof surface area = 102.3
Max rafter length = 6.8m
Loch an Duna, Bragar, Lewis
Internal diameter is 13m
Internal area = 132.7
Roof surface area = 187.6
Max rafter length = 9.2m
Dun Stuigh, Great Bernera
External diameter of 13.7m average, walls 3m thick. Internal 10.7
Internal area = 89.9
Roof surface area = 127.1
Max rafter length = 7.6
Rudh'An Teampuill, Toe Head, Harris
45° = 13.7m internal
Internal area = 147.4
Roof area = 208
Rafter = 9.7m
Dun Borve, Harris
14.1m overall, 3.1m wall = 11 metre internal
Internal area = 95
Roof area = 134.3
Rafter = 7.8
Clett an Dun, Taransay
Average diameter of 17.65m, with 3.5m walls = 14.15m internal
Internal area = 157.3
Roof area = 222.3
Rafter = 10.9
Seana Chaisteal, Pabbay (RCAHMS 1928)
53ft diameter, 10ft wall = 13.1m internal diameter
Internal area = 136.8
Roof area = 193.4
Rafter = 9.3m
Dun Na Mairbhe, North Uist
13.8m internal
Internal area = 149.6
Roof area = 211.4
Rafter = 9.8m
Dun Na Buail' Uachdraich, Eochar, South Uist
External 50ft, walls 12ft.
Internal area = 167.4
Roof area = 236.6
Rafter = 10.3
Dun Bhuide, Eochar, South Uist
54ft external, 12.5ft wall
Internal area = 124.7
Roof area = 176.2
Rafter = 8.9m
Dun Mor, Loch an Duin Mhoir, West Gerinish, South Uist
10.2m internal, scarcement
Internal area = 81.7 or 163.4
Roof area = 115.5
Rafter = 7.2
Loch Druim An Iasgair, South Uist
36ft internal, oval?
Internal area = 94.6
Roof area = 134.3
Rafter = 7.8
Dun Buidhe, Loch Dun Mhurcaidh, Benbecula
c.18m diameter external, 3-6m wall
Internal area = 143.1
Roof area = 202.2
Rafter = 9.6m
Dun A'Chaolais, Vatersay
Internal 29'6" (RCAHMS 1928), 8m (OS 1965). Average 8.5m, scarcement.
Internal area = 56.8 or 113.6
Roof area = 80.2
Rafter = 6m
Dun Cuier, Barra
Internal diameter 29ft = 8.8
Internal area = 60.8
Roof surface area = 86
Rafter = 6.2
Dun Mor, South Uist (Parker Pearson and Sharples 1999, 4)
Internal diameter = 5.5m
Internal area = 24 (with one floor)
Roof surface area = 34
Rafter max = 3.9
Dun Mor Vaul, Tiree (Parker Pearson and Sharples 1999, 4)
Internal diameter = 8m
Internal area = 50.3
Roof area = 71
Rafter = 5.7
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