Conversion from Percent to Degrees

[rolf.hoffmann]

My company mainly designs in Degrees of slope and not Percent of Slope, the way Civil 3D is designed.

It was brought to my attention that there is a flaw in our conversion to degrees in expression for labeling slopes and change in grade.

Eg. if you have a -5.0% slope going into a +5.0% slope that would be a grade change of 10.0%. 

Now lets look at the same slopes but in degrees, Please note that the conversion from Percent to Degrees is (ATAN x (Percent/100)). -2.8624 deg(-5.0%) slope going into +2.8624 deg would have a grade change of 5.7248 deg.

The problem is that the conversion of 10.0% to Degrees is equal to 5.7106.  

Can anyone shed some light on this conversion dilemma, and give some possible solutions.

Thanks Rolf Hoffmann

[wfberry]

Based on your formula what would you get in degrees for a 100% slope?

Bill

[rolf.hoffmann]

Based on the formula, a 100% slope would be labeled as 45 deg.

[wfberry]

 Please note that the conversion from Percent to Degrees is (ATAN x (Percent/100))

atan (100/100)= .785398  for a 100%  slope

I just haven't figured your formula out.

[AllenJessup]

I had thought it might be a rounding error. But I went out 12 decimal places and am still off by 0.02%. It may be that that's the limit of accuracy of those calculations.

[rolf.hoffmann · Accepted solution]

Thanks Allen for your reply.

After wfberry replied, I did some thinking that this maybe to many unit conversions.  so I rethought the process.

instead of accepting Civil 3D's grade change expression, I thought I would create my own.  

My original formula was "ATAN(gradechange), this is using the Civil 3D data from the expression editor.

Instead I wrote this, ((ATAN(GradeIn))-(ATAN(GradeOut)). what this does is solve two things. One, I stay in the same units till I use the expression in a label, and two, create my own grade change equation reflected in degrees.

So to review, the original GradeChange is in Percent, so a GC of -5.0% to +5.0% is 10.0%, which translates to 5.7106 deg.

My new Grade Change is GradeIn of -5.0% (2.8624 deg) - GradeOut of +5.05% (2.8624 deg) = 5.7248 deg. a Difference of 0.0142 deg which is only about 01 minutes difference, but this error increases with the increase of change in grade.

As a double check I did a larger Grade Change +5.0% to +100% = 95% or 43.5312 deg, compared to 2.8624 deg - +45.00 deg = 42.1376. a difference of 1.3936 deg, NOT GOOD!!

My New Grade Change shows me the true Grade Change in Deg with No errors, and I can display it in Decimal, or dms.

thanks for bumping my brain into overdrive.

[ChrisRS]

Glad you resolved this.

The underlying  issue is that slope or grade a indications of rate of elevation change with distance, not angle measurements. 

[Joe-Bouza]

Is my the display for degrees right in the composer? No conver needed