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Vertical curves minimum alg. diff.

Vertical curves minimum alg. diff.

Vertical curves minimum alg. diff.


I have heard that a minimum algebraic difference in vertical grades of 0.50 requires no vertical curve to be designed. Is this true? Does anybody know where can I find a reference about this?


RE: Vertical curves minimum alg. diff.


I believe that this depends upon where your are working.  Here in Loveland, CO. they define a maximum algebraic difference befor a curve is needed, not a minimum.  As stated in the "Larimer County Urban Area Street Standards" adopted January 2, 2001 in Chapter 7.4.1.B.

2. Grade Breaks:
"No single point grade break shall exceed 0.40 percent."

3. Requirements for Using Vertical Curves:
"Vertical curves are required for grade changes that exceed 1.0 percent.  Both centerlines and the curb and gutter flowlines shall be designed with vertical curves to meet the requirements of Standard Drawings 7-17 and 7-18.  A series of grade breaks may be used in lieu of a specified vertical curve as long as the series of breaks meet the vertical curve criteria in the Standards for the design speed.  K-values for design shall conform to Table 7-3 or Table 7-4.

"In sag curves on flow line, the minimum grade requirement shall override the slope within the vertical curve."

What happens between 0.4% and 1.0%?  I don't really know but that's how it's written.  Now, aren't you glad you don't work in Larimer County?


RE: Vertical curves minimum alg. diff.


Thanks for your response, Brian. I am currently working at El Paso, Texas, but I haven't found an AASHTO reference where it actually says that. I would like to count on that because many projects we do rely on it.

I wouldn't hurt if this reference is available no matter what our logic says that that the curve derived from this small difference is going to be a very flat one.



RE: Vertical curves minimum alg. diff.

Depends on where you are, for example we use 1% at Ramp intersections, paved aproaches are on the order of 5%.  I think you need to explain your situation.  I can't really think of a situation where you could not use a vertical curve if you wanted to.

RE: Vertical curves minimum alg. diff.

Hi, wolfhnd:

I mostly do street horizontal and vertical alignment design. However, I heard from a teacher that a algebraic difference of more than 0.5% is required to design a vertical curve. Does this apply to highway design? Do you know of a reference about this issue?

Thank you,


RE: Vertical curves minimum alg. diff.

The crown in most highways is a break over of 4% that should give you a good feel for what we are talking about.  I can check our manuals but I don't think that you need to worry about a 0.5% change in grade.  I have been designing highways for years and have never had the call to use a change of grade Of less than maybe 1%.  At speeds under 45 mph you can get away with alot more.

RE: Vertical curves minimum alg. diff.

Good question.  I am in the lowcountry and typically have .5% grades.  In ITE's Guidelines for Urban Major Street Design (Chapter 6 Grades, pages 23-26) discusses minimum slope or max K (rate of vertical curvature) for crest is 143 and the same for sag locations.  And in all cases the minimum length vertical curve is approximately taken as three times the design speed (in MPH).

Our state (South Carolina) DOT has a design manual that gives min and desirable k values for Stopping SD, Passing SD, and Decision SD. And for drainage purposes a max k = 167 for curbed pavments.

I would love some field experienced person to back this up due to my growing skepticism of handed down practices that don't have the testing behind them.  I do have a problem with trust.

RE: Vertical curves minimum alg. diff.

0.5% grade change is not noticable unless there are distinct straight lines that highlight the change, eg kerbs and footpaths over long lengths. I regularly work with road grades of 0.33% and don't have any problems with 0.50% grade changes.

For example if you have an incoming grade of 1% and an outgoing grade of 1.5%  and apply a vertical curve of say 20m length, then the resultant shift in elevation at the mid point is only 0.008m above the grade IP. Which is 0.10m above the start point and 0.15m to the end point. In a practical sense a grader operator will not get the accuracy required to construct this given that most tolerances are +-0.010m.

Even if your VC was to be a reasonable length of say 100m then the respective increase in shift of elevation is still relatively small compared to the overall look and would not be noticable. So from a practical point of view it is simply not worth designing a VC for a grade change of 0.50%.


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