Hi Dorothea,
Interesting thread. I’ve had some experience in using GIS to identify high risk curves in New Zealand. Our approach is based on the idea is that a tight curve is not necessarily a dangerous curve – it all depends on the context. For example, drivers are much more likely to lose control and have a serious crash on a tight curve at the end of a long straight, compared to a tight curve along a winding section where driving speeds are already very low. Relying on crash data can give you an idea of problem areas, but it's not very helpful for low volume roads where crashes tend to be more sporadic and "random".
In our GIS models, we first identify curves from a road centreline. Then we model vehicle speeds along the road centreline (acceleration on straights, deceleration on curves) to determine the approach speed to each curve. The difference between the approach speed and the appropriate speed for the curve then determines whether it is “dangerous”. Our models are relatively complex in that we also factor in the overall terrain (eg vehicle speeds are generally lower on mountainous roads) and driver behaviour (eg drivers tend to brake within 70 metres of a curve and don’t accelerate on straights less than 200 metres).
Our methodology uses Model Builder and some Python scripts - no special software. We do quite a bit of editing to get the centreline into a suitable format for extracting curves and running our models.
If you are interested in our methodology, I wrote it up an article for the New Zealand Surveying+Spatial magazine last year (see page 19 onwards here: https://issuu.com/nzis/docs/s_s_march_2016).
Hope this is helpful? I'm happy to elaborate further if you have any questions.
Dale