Does anyone know the % and degree (steepness) of a hill 1.6 miles long and ascending 700ft?
Algebra was never my thing. Then again, school was never my thing.
Thanks,
Oblong
I don't know the math: Hills % and degree
I stand corrected
Michael,
Thanks for the timely response and thanks for showing the math. Even I can follow that. Now, the next time I ask the same question about another hill, you'll know why school wasn't my thing - too lazy.
Thanks again,
Oblong
"But close and a very good approximation. % Gradient is rise/run, the vertical rise over horizontal run -- the ""legs"" of a triangle. Your method incorrectly employed the triangle's hypotenuse. Knowing a climb's length and vertical rise, the horizontal run can be calculated as follows:
(length^2 - vertical rise^2)^1/2
In words, the square root of the length squared minus the vertical rise squared.
Hence:
(8448^2 - 700^2)1/2 = 8419 feet horizontal run
Slope = 700/8419*100 = 8.315%, whereas the ""incorrect"" formula calculated to 3 decimal places is 8.286%. On steeper grades, the error would be a bit more pronounced.
The angle in degrees is simply the inverse tangent of 0.08315 = 4.75 degrees. Not sure where you came up with idea that angle is % gradient * 90."
you can get the same answer another way:
1.6 * 5280 = 8448 ft is the distance you travelled up the hill.
sine of angle x = 700 / 8448 = 0.08286
angle x = 4.75 degrees is the angle of the incline
tangent of 4.75 degrees = 0.083145 = 700 / y
y = 8419 feet is the horizontal distance you travelled
700 rise / 8419 run = 0.0831 or 8.31% grade or steepness.
I used the formula initially because you don't need a trig table or trig calculator -- not that we all don't have one. An old habit I guess.
Percent of grade is the relationship between the vertical rise and the horizontal distance traveled. If you travel 100 feet and rise 10 feet, that is a 10% grade.
If you rise 25 feet in 100 feet, that is a 25% grade.
If you rise more than you travel horizontally, you can have a grade over 100% but you cannot travel that on a bike or motor vehicle, it would be steeper than a stair.
Most people find hills more than 5% to be difficult and modern roads are usually designed with grades not exceeding 5%.
John Z is completely correct in his calculations here but most people do not seen to understand what grade really is and why a 100% grade is only 45 degrees.
Its a little nuance of Civil Engineering...
Exactly, a good way to put it.
It is a term used by people who engineer roads and deal with relatively small slopes which can be safely driven on in all types of weather.