05 July 2012

Normally abnormal

Normal and abnormal are among those words that don't mean a lot without knowing the context; 'rapid', I avoid entirely having hung around with both nuclear physicists and astrophysicists, for whom rapid can mean a femtosecond, or 100 million years. It's normal to be hotter or colder than normal.  It would be highly abnormal to always be right at normal.  While perfectly good English, let's do some work to make this real for understanding weather and climate.

One sense of 'normal' we have is the average value.  The average temperature for July 2nd in my area is, say, 86 F (30 C).  This is a useful figure, at least in the sense that we then expect temperatures to be closer to that than, say, 50 C, or 10 C.  But it would be highly abnormal -- something seldom seen -- for the temperature to be exactly 86 F for five consecutive July 2nds.

To take a comment of mine from Tuesday, we had about 1 hour of winds averaging 50 mph (22 m/s) in the recent storm.  Such winds are highly abnormal, in that the average is 5-10 mph.  But there are 8766 hours in a year.  It is normal, I believe (haven't pulled down the full data set), for at least 1 hour in the year to average 50 mph here. One sense of normal is the arithmetic average.  Another is 'what are the winds you see less than 1% of the time'?  That would be the 99th percentile winds -- you get that or faster 87.66 hours per year.  99.9th percentile is 8.766 hours, which I think is about right for 50 mph in this area.  99.99th percentile is something you expect to see about 50 minutes each year (maybe this is where we were).  In other words, it is normal to be that abnormal.

One importance of this is that if you are designing a building, or power grid, windmill, or anything else exposed to the winds, and would like it to last at least one year, you need to design for over 3 days of those rare, 99th percentile winds.  And still almost an hour of the exceedingly rare 99.99th percentile winds.  It's normal, predictable, expectable, and expected, to get those winds.  If you want it to last a decade, you need to design for (at least) an hour of the extremely uncommon 99.999th percentile winds.  If you want it to last 100 years, which a number of things -- Statue of Liberty (thank you France) and Brooklyn Bridge, for instance -- have endured, you need to be prepared for 99.9999th percentile winds.  That's a lot of 9s!

The fact that humans have built structures that have lasted that long shows that we are capable of doing so.  We even have some that are around seven 9s -- have lasted 1000 years.  Then again, all of these long-lived structures have also had maintenance routinely through their lives.  Design for endurance without maintenance is a different and more challenging matter.

But even as we are capable of designing structures to last for decades or centuries, we often don't.  Or, even if designed for decades -- with routine maintenance -- we don't always do that maintenance.  In both cases, there's the reality of money.  It costs to do maintenance, and it costs to build for greater expected endurance.  If we know what to expect, we can make the best decisions of how to balance the costs of maintenance and building for endurance versus the weather.  No big deal if my backyard shed is flattened by a once in a decade wind.  But it's a very big deal if my house is.


David B. Benson said...

The Roman baths at Cluny (now part of Paris) had three barrel arches as roofs of the three different tmeperature baths. Built in about 400 CE, one of the three barrel arches still stands, not having received any maintenance until relatively recently.

Robert Grumbine said...

Ah, good. As I said, not impossible to design/build for endurance, just harder. Now that you mention the Romans, the Pont du Gard aqueduct comes to mind, and that's from around 50 CE. If anything, these very old structures had anti-maintenance. It was not uncommon for materials to be taken by locals for other uses.

I wonder what the age record is for a structure that is still standing? I discount things like the Pyramids. They basically have nowhere to fall down _to_. Pile up sand and you get a cone. Stonehenge is 4000-5000 years old, and I think some of the stones were still standing and stacked, rather than more modern reassembly.