There was a news article recently about a member of Britain’s royal family walking “dangerously close” to the edge of a cliff (see for example here). The concern people had was almost that there is a limiting distance from the edge – move beyond it and everybody falls off the cliff. You could argue that this “cliff edge” approach is what the drafters of highway design guidelines sometimes use in highway design. For example, suppose a guideline gives a figure of 420 metres for minimum horizontal radius at a speed of 100 km/hr. The implication is then that if the road is designed using a value of 419.99 metres, all the vehicles would fly off the edge of the road.

The new German design guidelines for minimum horizontal radius might provide one example from many standards which have something of this approach. The following table below gives some recommended values for minimum horizontal radius from Germany (ref. 1615), together with values from Switzerland for comparison.

As the figures are presented – one specific value for a combination of ( minimum radius / road type / superelevation / speed) – it looks as if:

- Drivers travelling at 80 km/hr on a motorway will fly off the road if the radius is < 280 m
- Drivers travelling at 80 km/hr on a rural road will be safe down to a radius of < 230 m

*German guidelines for minimum horizontal radius*

It is interesting to see how the German guidelines develop values for minimum horizontal radius. They take the conventional formula:

Rmin = V2 / 127 (e+f)

And then apply some special ideas to it:

- They appear to apply a modification factor to measured values of side friction (f). This modification factor depends on the road class. For motorways the factor is 0,877
- They apply a second modification factor to give maximum permissable values for side friction. This is because total friction has to be shared between tangential and side friction.This second factor varies with road type. For motorway main carriageways and a superelevation of 6%, the factor is 40%.

So it looks like the formula for minimum horizontal radius should read:

*For a particular class of road K*

RK (min) = V2 / 127 [e+ (fK * nK /100) ]

*Comment*

Some of the above might sound a bit unfair to the German standards and in fact I think they are about the best I have come across so far. I haven’t yet seen mention of uncertainty or factor of safety in the main reference (ref. 1615) although I suspect that it is hidden in the modification factors somehow, and probably elsewhere as well. Thefollowing figure from (ref. 1617) must be based on the new standards (but I am not sure which one). It shows three zones of usability (good, usable and “to be avoided”) where the grey “usable” zone looks like a zone of uncertainty – certainly not a single, “cliff-edge” value.

It would be interesting to see a similar chart for other highway geometric parameters. For example, a chart for minimum horizontal radius might look like the following:

The figure actually shows two curves, one for the Swiss benchmark values (CHV) for minimum horizontal radius from the table above, and one for values of CHV+10%.

The next chart plots the German and Swiss values for minimum horizontal radius from the table. It suggests that they are very similar:

The German values are mostlywithin 10% or even 5% of the Swiss values (ok, I know some of the figures are based on different values for superelevation). I am not sure that 5% doesn’t represent such a minimum difference that perhaps there is no advantage in having different values for different road types (Germany).

The Swiss figures for minimum horizontal radius are 17 years older than the German figures, and are probably based on a different theory / application of the conventional formula. Yet they are quite similar to the German values, so that one might even risk the idea that there is no advantage in having different values for different countries.

*References*

732 – Switzerland, “VSS 640-080 Projektierung, Grundlagen (basics of road design)” VSS, 1991

1615 – Germany, “Richtlinien für die Anlage von Autobahnen”, fgsv; 2008

1617 – Germany, Wolf et al, “Strassenplanung”, Werner Verlag; 2013