Monday, 20 December 2010

O.R. and some French roads

I am always intrigued when I find references to some kind of modelling which is identifiable as O.R. in obscure places. A book on the historical geography of France has provided two such observations. ("The Discovery of France" by Graham Robb)

Writing about the mid nineteenth century, "In the Landes, where carriages sank in the sand up to their axles, the engineer Chambrelent calculated that once a road reached a certain length it would be destroyed by the process that built it: 'In travelling to the point where it will be used to prolong the road, one cubic metre of stone or gravel wears out more than one cubic metre of road.'"
The modelling must have been based on some observations and statistical analysis.

Then, about roads later in the nineteenth century, "The chief engineer in the Limousin, Pierre Tresaguet, had insisted that a limit sould be placed on [road] gradients. ... The old road east of Morlaix still includes a needless climb of 15 per cent (1 in 7) because the blundering military Governor of Brittany, the Duc d'Aiguillon, preferred straight lines to the more accommodating curve of the older road that runs alongside. Thanks in part to Tresaguet, it is unusual now to find a climb in excess of 8 per cent (1 in 12). This was thought to be the steepest gradient that a fully laden mule could manage. British mountain roads seem to rise in fits and starts like step pyramids. French mountain roads go much higher, but more steadily, and can comfortably be climbed for hours by a fully laden cyclist."

So far so good; the road builders were given a constraint which had been thought about in terms of the users of the road. But there's a twist in the footnote to these comments, indicating that other people didn't make observations:

"To judge by the army handbook of 1884, it is fortunate that most road building was left to civil engineers:
Gradient on which troops can still march in good order: 25 per cent;
Gradient manageable by mounted horses and light carriages: 33 per cent;
Gradient manageable by mules: 50 per cent;
Escarpment that an infantryman can still cross by using his hands: 100 per cent (completely vertical)"

No comments: