Tuesday, 7 October 2014

Barrier functions

If you have searched for "Barrier functions" and are interested in one way of optimising a nonlinear function subject to constraints, look away now.  This blog entry is not about that topic, but I could not resist the joke.

Exeter is built on the River Exe - hence its name.  The river is prone to flooding, and just over fifty years ago, there were some disastrous floods which damaged a great deal of property.  As a consequence, flood relief channels were dug parallel to the river, to divert some water - in effect to make the river wider when the river flow peaked.  The Exe is a fairly short river (about 60 miles) and its flow reacts to rainfall quickly, so that a storm in its headwaters leads to flooding at Exeter within 12 to 24 hours.   After more floods in the last few winters, there are plans to deepen the flood relief channels, and work on one site is under way.

That is quite close to our house, and Tina and I have a convenient walk, from our home, down to the river across one bridge, along the footpath that is bordered by the flood channel, across a second bridge and back home.  If we don't stop, it takes 45 minutes, but we often do stop, to look at birds or to talk to friends we meet.  (We call it the "Sunday morning walk" because we used it to give us exercise when we were both working, and we could do it before going to church on Sunday.  When we went trekking in Nepal, we prepared for that journey by repeating the circuit as often as we could.)

The construction site is a large one, and the contractors have had to fence the area to keep out dogs and stray children.  But it must not be impenetrable in case any of these do manage to cross it.  There are no dangerous materials on the site, as they and the equipment are kept in a secure compound a short way away.  The fence acts as a deterrent, and is about 3500 feet long.  So, how would you design a fence at minimal cost for such a site? 

Off the shelf solutions:
  •  Rentable fencing panels;  idea rejected due to cost, aesthetic appeal (nil) and being more than is needed.
  •  Posts and plastic mesh fence; idea rejected due to being insufficient deterrent and lack of aesthetic appeal.
  •  Barbed wire fence; rejected because the footpath is well used by walkers and cyclists and the fence woul be too close to them.
  •  Post and rail fence; insufficient barrier and very expensive

So, the site workers have erected a fence with posts and wire mesh, topped with three strands of strong wire.  The wire mesh reaches from the ground to a height of about 800-900mm, and the parallel strands of wire are about 50mm, 150mm and 250mm above the top of the mesh.  The barrier is almost impenetrable for dogs and children, but an adult could cross - with a little difficulty - if it were necessary to retrieve a dog, a child, etc

I suspect the components are disposable in spite of the waste of material.  The wire mesh is probably a standard size, but someone has had to decide on the design, which is where Operational Research could be of value.  The design has these decision variables:
  • (a) mesh size (from manufacturer's range)
  • (b) mesh shape
  • (c) width of the mesh
  • (d) number of wire strands
  • (e) position of each wire strand
  • (f) separation of posts on straight runs

All of these were probably decided by rules of thumb (aka heuristics) but the sight of the site and its fence made our most recent walk more interesting as we thought about the decisions.