Automobile Braking on Very Steep Downgrades

Author(s): Navin

Slidedeck Presentation:

1C - Navin


Frequently collision reconstructionist ask: How should the influence of very steep down grade be incorporated into speed estimates from emergency inline braking skid marks? A very steep grade is defined, by the author as 10 to 30 percent. They may be found in mountainous areas or at the embankments of major rivers and ravines across Canada. The research's main aim is to give direction to collision reconstructionist as to the best method to incorporate steep downgrade effects into vehicle performance or to calculate braking speed from skid marks. In-line braking test skids were carried out on grades from 1 to 28 percent found within the urban area of Metro Vancouver. The pavements were asphalt, both dry and wet. The same vehicle and driver were used throughout with locked wheel and ABS braking at 60km/h except at 40km/h on the 28 percent grade. The measurements were made with; a radar gun, a shot marker, two different optical readers and an accelerator.

The usual grade related equation for the speed at the start of skid is v2= 2d(µ-G/100)g; d is the stop distance, µ is the coefficient of friction, G/100 is the down grade (or gradient) and g is gravity constant. This equation works acceptably well for gentle grades usually assumed to considerably less than 10percent.

Vehicle deceleration on very steep down grade did not always behave as well as suggested by the traditional theory. There is some mechanism during emergency braking that reduces the deceleration to values much lower than expected.

On dry pavements at downgrades of 10 percent or more the speed estimation error was greater than ten percent. A logit-like model reduced the error. The logit-like model for the “vehicles drag factor” is; {2µ-G/100-µ/[e-(50µ-G)/10]}. This is an entirely empirical model designed to fit the data for both dry locked wheel braking and wet ABS braking.

The traditional method of incorporating the down grade worked for ABS braking on dry pavement. Either equation gave acceptable results for wet downgrade pavements.

Locked wheel braking on steep wet downgrades did not produce consistent results. The research was on residential roads and keeping the roads adequately soaked during the tests was at times problematic.

The answer to the original question has uncovers a lack of good experiments and any reasonable mechanical explanations as to the mechanism of steep downgrade emergency barking. Explanation of pneumatic tire pavement interaction is difficult enough for level pavements. Downhill braking seems to raise the difficulty to another level. The results will be of interest to those responsible to accurately reconstruct collisions. Others who must estimate the safety impact of highway design elements and those responsible for policies concerning road design may also find the analysis useful.