Wikipedia (here) quoting Thomas Kuhn says that a paradigm is “a set of practices that define a scientific discipline at any particular period of time” and that (here) “competing paradigms are frequently competing accounts of reality which cannot be coherently reconciled”. In the field of highway geometric design, Norway is one of a number of countries which has its own paradigm on highway geometric design. Among the topics which its documents describe is a concept of road dimension classes – (Dimensjoneringsklasser) and how uncertainty is dealt with in determining minimum horizontal radius. Here for example, the values of side friction are a function of speed limits and “safety factors”, where the safety factor is a function of traffic volume, speed limit and road class.
Here I should add that the following notes are “as I understand the source Norwegian documents”, since these documents are in Norwegian (not one of my main languages).
Norway defines four road types
- Major national road
- Other main roads
- Secondary roads
- Access roads (minor roads)
These are sub-divided into 17 dimension classes based on traffic flow and speed limit (see fig. 1).
A re-sort of the details in the above table leads to (fig.2). This omits the access road classes since they are not related to ADT, although they would be expected to have low ADT as well as low speed limits. Some interesting points from table 2 are
- There are no design classes for a speed limit of 70 km/hr
- Two ADT / speed combinations have more than one dimension class
(Ref. 1601) refers to the conventional formula for calculating minimum horizontal radius
Where fk – is the side friction factor to be used in design
However the Norway standards do not apply this formula directly. Rather, they add a series of adjustments or safety factors, so that the value for V, the speed limit (or design speed) used is actually
V adjusted := V + ΔVt + ΔVpt
Where from (ref. 1601 page 18)
- ΔVt is a speed addition to allow a factor of safety (possible values are 0, 5, 10 and 15 km/hr, with different values applied to different dimension classes)
- ΔVpt appears to be a “speed profile supplement” which is meant to allow for a perceived tendency of drivers to increase speed on better roads. Its value rises from 0 (for minimum horizontal radius) to 10 km/hr in inverse proportion to the horizontal radius.
The value for side friction is also adjusted by a factor of safety such that
f k design = fk * factor of safety (F2)
This factor of safety can have a value of either (0, 1.10, 1.25, 1.50 or 1.75) – see (ref. 1601 page 54). It varies with the dimension classes. So arguably the conventional formula for minimum horizontal radius becomes, for a particular dimension class of road type, ADT and speed:
Rmin = (V + ΔVt )2 / [127 (e max + (fk* F2 )) ]
Values for side friction and minimum horizontal radius
(Ref. 1198 table C.2) gives values for minimum horizontal radius and dimension class:
Taking the max and min values for each speed value gives the following chart (the line in red represents benchmark values from the Swiss standard, (ref. 732):
Values for side friction (before applying any factor of safety) are similar to the benchmark Swiss values (see fig. 4):
The point I want to make is that there are different ways of allowing for uncertainty in highway geometrics, and Norway offers another approach. This approach is interesting (it does seem a bit complicated, but this may be due to working with a partial translation of extensive texts). I am sure a wider audience would benefit from an English-language translation of the two reference documents.
It does appear that Norwegian practice applies a series of adjustments and concepts to the highway geometric design so that the overall practice forms an integrated design concept – but one which engineers trying to establish their own approach cannot easily use to pick the bits they like (so as to “mix and match” bits of Norwegian practice with bits from say German or Australian practice).
1198 – Norway, “Hb-017 Veg og gateutforming (Road and street design), Statens vegvesen; 2013
1601 – Norway, “Hb_265 – Premisser for geometrisk utforming av veger (premises for geometric design of roads), Statens vegvesen; 2013
732 – Switzerland, VSS “VSS 640-080 Projektierung, Grundlagen (basics of road design)”, 1991