Delta Angles for Dummies

The delta angle in pictures

The business model of the content farm formerly known as eHow.com was simple: get as many people to write as much about as many topics as possible to build an enormous library of "how-to" and "all-about" posts. From the looks of the resulting content, nowhere in that business model was there any mention of accuracy... Eager to collect ten- and fifteen-dollar stipends, unemployed journalism and English lit graduates flocked to the site, seemingly believing that their education allowed them to accurately reword any Wikipedia or DoItYourself.com post. They were wrong, and today's nominee is a case in point. Meet "communications" graduate Kathy Mair and her clueless attempt to explain, "What Is a Delta Angle?" for Sciencing.com.

For those of you who came here for an answer, the angle delta is the angle between two radii of a curve that are perpendicular to tangents to that curve. Have a look at the image above for an example. You will notice that, because the shape made by the straight lines is a rectangle, the angles at which the radii meet and the angle at which the tangents meet are the same. This is how, among other uses, highway surveyors describe a (horizontal) curve in a road. The diagonal between the two points of tangency is the chord.

Mair stumbled over a college syllabus that covered this definition, sort of, and used it to craft her version of an "answer." Sadly, she had no idea what she was talking about, so she performed a sort of mashup of the facts. Here's an example:

"A delta angle is the measurement in degrees where two straight lines, also known as tangents, intersect."

That might be useful information if Mair had had a clue as to what tangents are or that a curve is involved... but we're pretty certain she didn't. Instead of enlarging on that critical information, she embarked on a paean to civil engineering, telling her readers that,

"The intersection of roadways illustrates two tangents intersecting. Engineers focused on traffic flow use horizontal curves to create better traffic patterns between the roads. Delta angles are an important measurement used to determine the best arc to connect the roadways and prevent motorists from having to make sharp turns."

In fact, Kathy, the intersection of two roads is not "two tangents intersecting"; the intersection of two roads is just that: an intersection of two nominally straight lines. She was, however, approaching the answer: a surveyor lays out the curve she describes using three parameters: the delta angle, the chord length, and the radius of the curve. Kathy's next claim,

"When the delta angle is provided, it can be used to determine measurements including radius or chord lengths..."

...is little more than a bastardization of the reality that any two of the three parameters – delta, chord length, or curve radius – can be used to calculate the third. Had Mair even the slightest idea what she was talking about, she might have understood that. She didn't, and that's why Kathy is our Dumbass of the Day for today.

MM - GEOMETRY