Sloping Surfaces for Dummies

Definition of slope

Give a freelancer an inch, and chances are pretty good that he or she will turn it into a paintbrush. Did that make sense? No, and neither do the internet posts submitted by some of those penny-grubbing freelancers back in the days of content farms. In case you haven't noticed (our staff at the Antisocial Network certainly have), the quality of freelance information on the internet has improved quite a bit since hungry journalism and English majors can no longer make a decent living faking knowledge and expertise. Back then, however, the money flowed freely and so did the bull: bull like that written by eHow.com's Dan Richter, a "communications" major trying to tell people "How to Calculate Horizontal Distance" (now at Sciencing.com).

Like so many of his fellow J-school grads on the site, Dan found himself operating in a vacuum: horizontal distance where? Between what points? In what units? As is usually the case with eHow contributors, Richter decided for himself what the question meant. Based on his introduction, though, we aren't really sure what that was...

"This reference is for calculating the horizontal distance between two geographic points at difference elevations and is based on the mathematical relationship between the sides of a right triangle. The mathematical horizontal distance formula is often used on maps because it does not factor in things like peaks, hills and valleys between the two points..."

After that introduction, it was pretty clear Dan was out of his depth. Why? because if you have a map, you don't need to calculate a horizontal distance; you simply measure it! Richter, however, forges ahead...

"...To successfully calculate the horizontal distance, which is also known as the run, between two points, you need to know the vertical distance, or rise, between the two elevations and the percentage of slope at the beginning of the horizontal elevation to the top of the vertical elevation."

Leaving aside for the moment, the incomprehensibility of Dan's prose (a communications major who can't communicate? how droll!), we wondered how one would get slope from a map. Dan then mangles the standard definition of slope (slope = rise / run) to "explain" how one might calculate the horizontal distance from the two knowns, slope and rise. Instead of simply solving the equation for run, however (run = rise / slope), he takes the reader through an extensive mathematical horror: "...if you have a slope percentage of 6 and a rise of 25 feet, the equation would look like 6 = (25/run) x 100..." Where did that 100 come from? We know, but shouldn't he mention it? Next, Richter says to "Multiply each side of the equation by the 'run' variable. Continuing with the example of a slope percentage of 6 and a rise of 25, the equation will look like this: run x 6 = [(25/run) x 100)] x run..."

And finally, he tells his readers to

"Divide each side of the equation by the slope percent. Continuing with the example of a slope percentage of 6 and a rise of 25, the equation should look like this: (run x 6) / 6 = 2,500 / 6. After completing the division, the equation becomes run = 416.6. The horizontal distance between the two points is then 416.6 feet."

Which, for what little it's worth after such an incredibly wordy explanation, is right: even a blind pig finds an acorn once in a while. Of course, since you're talking about a map, you already know the horizontal distance because you can just measure it...

No, what Dan's confused little mind really thinks he's talking about is the actual distance between two points on a slope. To do that, you use the Pythagorean to determine the hypotenuse of a tringle based on its two sides, the rise and the run. Now you know why we are awarding the Dumbass of the Day to someone who – more or less –- got the right answer. The reason? He answered the wrong question!

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