16 MayNerd Alert: What Does “Percent Grade” Really Mean?by Carey Spreen, Certified NerdAt some point in your life you may have wondered what those“6% Grade” or “8% Grade” signs you see on steeply inclinedroads really mean, and how they correlate to the angle of the slopein degrees – I know I have! If you haven’t ever wondered that, youmay just want to stop reading this right now. Math ahead!Thanks to those of you who are still reading, thank you – Ihope you’ll find it interesting.About a year ago I signed up for one of the 90-minute sessionsat the Porsche Experience Center in Atlanta, where you can drive amodel of your choice (and sometimes two models of your choice)to get a feel for how they perform on various courses. The sessionI took was the Cayenne Off-Road Experience, because I own a2008 base Cayenne and am interested in exploring the unpavedportions of Texas and elsewhere. I also would like to get otherCayenne owners interested in the same thing, perhaps putting onoff-road (or at least unpaved) tours to interesting destinations.Anyway, the Cayenne Off-Road session consists of about anhour on the paved courses (1-mile road course, slick track, kickplate, and wet skidpad) and the last half hour on a custom-madeoff-road section, which featured a 50-degree concrete staircaseto climb, as well as a 70-degree hard-packed dirt slope to climband then descend down the other side. The Cayenne (the one Igot to drive was a 2019 Turbo with the 541-hp turbo 4.8-literV8 – all I could say was “wow”) handled the staircase climb withno problem, but when we got to the 70-degree slope, I hesitated,because it looked like a vertical wall from where I sat, plus itdidn’t have off-road tires, or even all-season tires – it had lowprofileperformance summer tires on 21-inch wheels. However,my coach told me to take it slowly and drive straight up to thetop, so I trusted him and did just that. The Cayenne handled itlike a drive to the grocery store.However, at the top, there was an equally steep slope backdown, which was there to show howthe Cayenne’s descent control featureworked. You put it in descent mode,then tell it at what speed you want todescend (in 1-mph increments), giveit a little gas, and it takes care of therest. My coach had set it for 3 mph,10% Grade - 5.7 degreesand once we started down the hill, theCayenne maintained that speed allthe way down to where it leveled out.I didn’t touch the brake or accelerator20% Grade - 11.3 degreespedals; all I had to do was steer. Aninteresting feature for sure.Anyway, this got me wonderinghow this 70-degree slope wouldappear as a “XX% Grade” sign onmountain roads. As I’m sure youknow, the percent grade is calculatedas the vertical rise (or drop) of theslope divided by the horizontalVisual Representation of % Grade vs. Angle100% Grade - 45 degrees 275% Grade - 70 degreesdistance covered, expressed as a percentage. For example, if aslope is such that my altitude increases (or decreases) by 1 footfor every 20 feet of horizontal distance that I travel, that comesto 1/20 = 0.05, which is 5%. If I rise (or drop) 1 foot for every 10feet of horizontal travel, that’s a 10% grade. If you take that toan extreme, ascending (or descending) 1 foot for every 1 foot ofhorizontal travel, that’s a 100% grade.However, you have probably realized that 1 foot up and 1 footforward results in only a 45 degree angle, and that’s the clue as tohow percent grade and degree of slope are related: trigonometry!If you took any trigonometry classes, you may recall the termssine, cosine, and tangent. If your memory is really good, you mighteven remember the memory aid SOHCAHTOA, which keeps trackof which sides of a right triangle apply to calculating the sine, cosine,and tangent of an angle. The TOA part means “tangent = opposite/ adjacent,” which directly applies to our sloping mountain road.For a roadway, the opposite side is the vertical distance, and theadjacent side is the horizontal distance. So since the tangent of theangle is the percent of the slope, the inverse tangent (or arctan) ofthe percent of the slope is the angle of the slope.Using our handy-dandy scientific calculator, which is anaccessory on every Windows PC, entering 45 degrees and clickingthe “tan” button yields a result of 1, which is 100%. By the sametoken, entering a 1, then clicking “Inv” and then “tan” (i.e.inverse tangent or arctan) produces a 45. Just remember that tocalculate smaller percent grades, be sure to divide the percentnumber by 100 to express it as a decimal amount.Going back to our previous examples, that 5% grade is a pitiful2.86-degree angle. Similarly, a 10% grade is a 5.71-degree angle.Doesn’t sound like much, and any Porsche can climb those slopeswithout even breathing hard, but an 80,000-lb semi really struggleswith even just that 2.86-degree slope, as anyone who has beenstuck behind a loaded 18-wheeler onmountain road can attest.Which brings us back to thoseslopes at the Porsche ExperienceCenter. That 55-degree staircaseturns out to be a 143% grade, andthe 70-degree slope would be signedas a 275% grade if you were ever toencounter one on the highway.So in theory, what percent gradeis a 90-degree angle? Well, ourscientific calculator tells us that an89-degree slope is a 5,729% grade,and an 89.9-degree slope is a57,729% grade, so what does thatmean for our vertical wall? Thecalculator says that it’s undefined,in other words, infinity. Sorry, butnot even a Cayenne Turbo canhandle that one . . .
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