# Average Cross Slope Calculation

My county ( Pima, Arizona ) uses a number called “average cross slope” which they define as

`ACS = (I * L)/A`

where

``````I = contour interval
L = length of contour lines in the area
A = area
``````

Given a unit square with corners (0,0) (1,1), a contour interval of 1 and two contour lines (0,0)(0,1) and (1,0)(1,1), I get `L=2,I=1,A=1` and `ACS = (I*L)/A = 1*2/1 = 2`

Using the same unit square, a contour interval of 0.5 and three interval lines (0,0)(0,1), (0.5,0)(0.5,1) and (1,0)(1,1) I get

``````ACS = (I*L)/A = (0.5*3)/1 = 1.5
``````

Since these two examples represent the same topography, I would expect the result to be the same.

Also, the county refers to average cross slope as a percentage. Intuitively, since the topography is a 45 degree angle running left to right, I would think the average slope would be 1. (slope = rise/run), or 100%

So I have three different answers for the same topography, 2, 1.5 and 1.

I’m not a GIS person, I’m a software guy and owner/builder.

Is this a common equation in GIS?

• The answer is 1. You need half of the lengths of 2 extreme contours to compute their total length. Nov 4, 2019 at 3:03
• In a real life, i.e. multiple contours the correction above will have little effect on computed slope. Nov 4, 2019 at 3:07