Horizontal radius – more doubts about the conventional formula

Johan Granlund recently sent me two papers he has published which discuss horizontal radius (see references below).

In “Safer Curves on Multiple Lane Roads” (Ref. 1996) he points out that vehicles do not always follow the alignment of a curved road, but often change lanes at the same time, and here “when shifting lane quickly, the vehicle experience a transient “curve radius” much sharper than indicated by the road curve radius”. In the same paper he notes that the Swedish design code only allows certain discrete values of cross slope (a factor in calculating horizontal radius), and that

A design chart that calls for unnecessary cross slope adjustments of the existing cross slope …. just to meet one of a few allowed discrete values, with no relevance what so ever to Newton´s laws of physics, has of course extremely poor benefit/cost ratio when restoring old paved roads.


It is of no value to demand a few fixed cross slope values; target cross slopes should be expressed as a range instead

In “Lowered crash risk with banked curves designed for heavy trucks” , (Ref.1997) Mr. Granlund and his co-authors (Irene Haakanes and Razia Ibrahim) conclude that (amongst other points) :

  • For roads where same speed limits apply for both passenger cars and HGV´s, (….) the need       for road superelevation is       given by HGV’s rather than by cars. Hence road design codes should use models of HGV´s rather than of passenger cars.
  • The demand for superelevation increases with height of centre of gravity of the vehicle and with the lateral displacement of the centre of gravity(weight transfer).
  • A conclusion was that the traditional point-mass “car model” can underestimate the superelevation needed for safe HGV operations.

The authos also say that

  • Virtually all road design codes illustrate the calculation of superelevation demand with a model of cornering forces acting on a passenger car, not on an HGV.

So that

  • several road design codes worldwide may be stating suboptimal values for superelevation / crossfall in horizontal curves, roundabouts and ramps


The two papers referred to question the validity of the theory behind most design codes’ method for calculating horizontal radius. They can be added to a growing number of sources (some referred to in my paper, Ref. 3). Maybe engineers should now be asking whether some road accidents are not caused by the driver, but by bad incorrect road design theory.


1996 – Sweden, Granlund, “Safer Curves on Multiple Lane Roads,” Transport Research Arena Europe 2010

1997 – Sweden/Norway, Granlund, Haskanes and Ibrahim, “Lowered crash risk with banked curves designed for heavy trucks”; HVTT13, San Luis, Argentina, 2014


About roadnotes

Robert Bartlett is an international consultant with over 30 years of professional experience as a highway and traffic engineer with leading companies and organisations in several countries, including Germany, China (Hong Kong), Qatar and the UK. Specialised in urban studies, transport and the use of GIS, research has included new ideas on subjects such as the study of social justice using GIS, the dimensions of vehicles, and comparative geometrics (highways and transport).
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