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AVERAGE SLOPE OF A PROFILE
Posted by mageye on November 30, 2022 at 5:58 pmDoes anyone know how cad calculates the average slope of a profile over irregular terrain.
Doing a quick search and I cant seem to find any information on how this is computed. I’m thinking its a weighted calculation.
MLSchumann replied 1 year, 9 months ago 8 Members · 26 Replies 
26 Replies

It might depend on the flavor of cad. Seems the best approach would be a least squares regression calc, but I doubt there are any using that. Civil 3D gives a mean slope for a TIN which apparently is a weighted average of the triangles over the entire surface. I know that’s different than an average slope of a profile, but I’d presume with Civil 3D it would be calculated the using the same algorithm. (Does C3D even give an average slope of a profile?)
dd 
C3D doesn’t calc an average slope in profile it calcs the slope at the edge and across each 3dface.
Surface slope tool calcs the slope of each 3dface with the single point or using 2point it calcs the difference at the selected elevations divide the length no real magic

 @mlschumann I’m going to argue that your Rocket Science diagram is showing nothing more than the slope of a line from point A to point B. Not average. Just plain old slope.

I have always used a formula involving the length of the contours and the contour interval, but for the life of me I can’t find the formula.

Here is my process using Carlson w/oem acad.
Create profile from surface file or screen entities. Create 3d line from profile. Inquiry> polyline info. The result will generate an average slope. Which is different from a simple rise over run.
My thoughts are that each vertical slope between vertices is weighted by its length to calculate the average slope of the entire profile.
I just couldn’t find any white paper on the subject.

Are we trying to find the slope (dashed line) between two points as illustrated above, which in one sense could be called the average slope …
Or are we trying to find the average magnitude (always taken as positive) over the land between the points (shorter solid lines), as a measure of roughness? The latter can be extended to an average over an area.
However, the latter has a fractal problem in that the closer together your measurement points the larger the answer as every clump or grain of soil adds more.
. 
In my experience this can be done with TopoDot in Microstation. Which is a point cloud utility. The user will need to define parameters such as minimum length and width, along with Deflections. There is also a routine within OpenRoads and InRoads. If you need consultation with this task feel free to DM me.

The question by MAGEYE is:
Does anyone [k]now how cad calculates the average slope of a profile over irregular terrain.The solution I presented is the average slope of a profile, NOT the average slope of a part of surface as provided by Dave Lindell. While Lindell’s solution may be correct for the surface contour data presented, it is not the average slope of a profile as asked in the question. A profile, by convention, is a series of line segments representing a vertical terrain or surface cross section. I have not yet seen a profile to be defined as a part of a surface.
A followup diagram presents how the solution for the average slope of a profile is determined. Of particular note is that the diagram demonstrates that the length of a slope is fundamentally the weight or influence of that slope in the solution.
And, there is good probability that a cad program determines an average surface slope using the digital terrain model (DTM) triangles instead of contours.

C3D doesn’t calc an average slope in profile it calcs the slope at the edge and across each 3dface.
Surface slope tool calcs the slope of each 3dface with the single point or using 2point it calcs the difference at the selected elevations divide the length no real magic
I’ve read that C3D calcs a weighted average slope for the TIN, presumably triangle slope/triangle area as the unit. It doesn’t, that I know of, calc an “average slope in profile” which, if it did, I would presume it uses the same algorithm (but I repeat myself). What do you mean by “at the edge and across each face”? Wouldn’t that be the data used to compute a weighted average? And where do you see this output?
I’m not trying to be contentious but I’ve made up my own spreadsheet to do this from C3D profile data for use in drainage calcs and if it’s already doing it for me somewhere I’d love to know.
If by “surface slope tool” you’re talking about the surface slope annotation that allows you to pick a single point or use a two point average, then your response is irrelevant to the OPs question.
dd 
How does cad calculate the average slope of a 3d polyline?
Below is the report of a 3d polyline that cad generates.
Low Z: 503.00 At: 4991.32,5069.74
High Z: 542.00 At: 5100.21,4976.61
Polyline length: 412.52 Slope distance: 422.70
Avg elev: 528.95 Avg slope: 14.33%, 6.98:1 OpenThe line includes 37 vertices and the two end point elevations are 503.00′ & 526.73′

How does cad calculate the average slope of a 3d polyline?
Below is the report of a 3d polyline that cad generates.
Low Z: 503.00 At: 4991.32,5069.74
High Z: 542.00 At: 5100.21,4976.61
Polyline length: 412.52 Slope distance: 422.70
Avg elev: 528.95 Avg slope: 14.33%, 6.98:1 OpenThe line includes 37 vertices and the two end point elevations are 503.00′ & 526.73′
What “cad” are you using to get this?
dd 
The OP’s question was answered by MLSchumann.
Much like the weighted mean calculation, you can set up a number of formulas, or you can simply hook the lines together and inverse the resulting bearing between the two endpoints.
The average slope of a profile has to be the slope between the endpoints, or am I not understanding what the OP wants.

Thank you all for your input.
Especially MLSchumann, your last post was exactly what I needed to for my sometimes slow feeling brain to understand things.
Most of you here are the smartest people I have contact with and why I love this site so much.
Please excuse my ignorance as I ask another question.
The formula I need to solve now is how to calculate the average slope of two lines with different lengths and different slopes.
ex: Line 1 Length = 151.79′ Slope 26.52%
Line 2 Length = 71.71′ Slope 20.03%
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