Derivatives of Road Grade: Continuous or Not?

[Office_Shredder]

For reasons I cannot enumerate here it would be highly desirous if I knew the derivative of the grade of the road as a function of distance was continuous (differentiable would be even nicer) I don't suppose anybody knows what kind of regulations might exist for local or federal roads that would guarantee some kind of continuity condition on the grade of the road? The more I think about this the more I feel like it just isn't continuous. An example of such a road is a flat section, then a dip shaped like a cosine graph then a flat portion again

 

[collinsmark]

I take it you don't like speed bumps.

Pot holes are right out.

 

[lisab]

I take it you don't like speed bumps.

Pot holes are right out.

Asphalt discontinuities

 

[Ivan Seeking]

Hmmmm, this is a question for a roads scholar.

 

[LudusRex]

I understand the importance of knowing the derivative of the grade of a road as it can provide valuable information for road construction and maintenance. However, whether this derivative is continuous or not depends on various factors such as the design of the road, the materials used, and the topography of the area.

In general, it is desirable for the derivative of road grade to be continuous as it allows for a smoother transition between different sections of the road. This can improve driving conditions and reduce wear and tear on vehicles. However, in some cases, it may not be possible to achieve complete continuity due to practical constraints or safety considerations.

There may be regulations in place at the local or federal level that require certain continuity conditions on road grades, but these may vary depending on the jurisdiction and the type of road. It is important to consult with transportation authorities and engineers to determine the specific regulations and guidelines for a particular road.

In the example provided, where the road has a flat section, followed by a dip shaped like a cosine graph, and then another flat portion, the derivative of the grade would not be continuous. This is because there is a sudden change in the slope of the road at the dip, which would result in a discontinuity in the derivative. However, this may be a deliberate design choice to improve the drainage of the road or to accommodate changes in the topography.

In conclusion, while it may be desirable for the derivative of road grade to be continuous, it is not always feasible or practical. The design and construction of roads involve balancing various factors, and the continuity of the derivative of road grade is just one of them. It is important to consider the specific needs and requirements of each road and consult with experts in the field to determine the best approach.