Angle of repose

angle-of-repose

A few years ago while on vacation, I found myself in a small bookstore in Estes Park, Colorado looking for a good novel written by a “Western” author, to fit in with the locale.  The store owner recommended Wallace Stegner’s Pulitzer Prize winning story, Angle of Repose. I was unfamiliar with Stegner’s work at the time, but having now read several of his books, I would highly recommend him.  My favorite is his posthumously published collection of short stories Marking the Sparrow’s Fall. Today’s phrase comes from the title of the first Stegner book I read.

angle of repose n. the maximum slope, measured in degrees from horizontal, at which loose solid material will remain in place without sliding.

Drive by any self-respecting dam in Texas and you will typically see a large incline of rocks abutting each side of the spillway.  In order to save on space and materials, civil engineers place the rocks at the steepest angle possible without causing a rock slide.  This is known as the angle of repose; repose meaning “a state of rest.”  Add one more degree of incline and you end up with the angle of repose’s first cousin, the angle of slide, whose meaning should be self-explanatory and avoided by civil engineers at all costs.

Civil engineers love angles.  They make up a big part of their training, so it’s not surprising that there are a number of phrases that incorporate angle and relate in some way to engineering.  There’s angle of depression, used by surveyors as the angle between the point of observation and the point of the object being observed, if the object is below the observer; if it’s above the observer, the term is angle of elevation.  Other angle phrases include angle of attack, angle of deviation, angle of incidence, angle of lag, angle of lead, angle of pitch, and so on.  It’s easy for me to see why I never pursued an engineering degree.

Angle comes to us from the Greek word onkos meaning hook.  An archaic British definition of angle is a fishhook, which leads us to the word angling, a close substitute term for fishing-something else that I enjoy when in Colorado when not reading Stegner.  As any high school student can tell you, angles are a big item in geometry, the branch of mathematics that sounds like it would naturally deal with the earth, as geo- is the prefix for earth.  Geometry deals with relationships of points and angles in space-not the outer kind, but the metaphysical inner space.  So, I’ve always thought that geometry was misnamed and would be more accurately called esometry, eso- being the prefix for inner.  But I seem to be going off on a tangent.

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  1. #1 by Doug Wick on April 8, 2009 - 1:03 pm

    Love these word origins posts David. I studied Latin for 5 years and got pretty into stuff like this at one point. I’ll definitely subscribe here!

    In particular this post is interesting because these angles forces are a whole field of study in Engineering typically referred to as Rigid Body Mechanics (and I was one of the unfortunates you referred to who for some reason thought it best to struggle through that degree).

    Anyhow, a typical Rigid Body Mechanics problem involves the calculation and addition of forces on an object to find a resultant force. In the angle of repose situation, you have three forces at work – gravitational force pushing the object straight down, normal force by the surface pushing it directly away from itself, and frictional force pushing upslope at precisely the angle of the slope.

    This can get boring fast, but suffice to say that the other factors in whether the object will slide downhill (other than angle) are the mass of the object (more massive will slide more easily due to higher normal force) and the roughness of the surface (rougher surfaces will slide less easily due to increased frictional force).

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