A RECENT STATEMENT statement to the BBC from a Canal & River Trust engineer regarding the Whitchurch Breach caught my attention, writes Ralph Freeman:
'How they built things in the olden days was quite empirical, if they stood up, they stood up.
Whereas today we're very much into science and numbers..
The clear inference is that pioneer canal engineers were mathematically challenged and/or worked purely by guesswork.
This is simply not true. Engineers like John Smeaton and Thomas Telford relied heavily on mathematics, and their structures are still standing 200 years later. When faced with exceptionally complex calculations, Telford even consulted leading mathematicians at the Royal Society—proving that know-how, not guesswork, built the network.
By the turn of the 19th century, the core mathematical foundations of civil engineering were already well established. Here is a look at the tools and science available to them during the canal era.
Applied Science and Structural Theory
Forces and Balance:
Engineers used Newton’s laws of motion to calculate forces and ensure structures stayed in static balance, preventing walls or bridges from tipping over.
Arch Design:
The geometry of stone arches was mathematically analysed to trace how weight passed through the masonry, ensuring the arch would not collapse or slide out of alignment.
Beam and Column Calculations:
Mathematical formulas were used to work out how much timber, iron, or stone beams would bend under weight, and to predict when tall supports might buckle.
Material Limits:
Early engineers used stress and strain calculations to determine the maximum loads timber, stone, and cast iron could safely hold.
Surveying and Site Work
Triangulation and Leveling:
High-precision trigonometry was used with spirit levels and sighting instruments to map catchment areas and chart long-distance canal routes across varied terrain.
Earthworks Geometry:
Precise geometric rules allowed engineers to calculate the volume of earth needed to be dug out (cut) and moved to build embankments (fill), ensuring balance across the site.
On-Site Calculation Tools
Logarithm and Trig Tables:
Long before digital calculators, printed tables allowed engineers to turn complex multiplication, division, and angle calculations into simple addition and subtraction.
Slide Rules:
Slide rules were standard field tools by the mid-1700s. Specialised versions existed specifically for measuring timber and calculating masonry volumes on site.
Sectors:
A jointed scale (resembling a folding rule) allowed draughtsmen to solve proportional calculations, scale drawings and work out angles directly on the drafting board.
Summary
It is a sobering thought that engineering students in the 1960's (including me) were still using log tables, trig tables, and slide rules—the exact same core calculation tools used by the canal builders almost two centuries earlier.
What people often overlook is that having a computer can enable an engineer to reach the wrong conclusion much faster!
What really matters is the underlying understanding of the subject, not the speed/ease of computation.
Ralph Freeman BSc(Hons)