## Basic formula for stopping sight distance

What it is
Stopping sight distance (SSD) is the distance taken by a vehicle travelling along a road sees an object on the road before him, and comes to a stop just before he reaches it.

The theory
The distance is based on the idea that a driver making such a stop is involved in three steps:

• he sees that something has to be done (because of e.g. an obstacle on the road)
• he decides what to do (decides to brake to a stop)
• he does it (brakes to a stop)

So that:

SSD = PD+RD+BD

where
SSD = stopping sight distance
PD= distance travelled whilst the driver perceives an obstacle on the road
RD= distance travelled whilst the driver decides how to react (in this case, by braking) and starts to react
BD= distance travelled whilst the vehicle brakes to a stop.

There are different ways of calculating SSD

1. assume a constant deceleration rate

SSD = 0,278 V (Tp + Tr) + 0,039 V2 / a

2. assume that the braking distance component is related to friction and road gradient)

SSD = 0,278 V (Tp + Tr) + V2 / [254 * (f ± Gr)

Where:

• V = initial speed, in km/hr
• Tp = perception time (secs)
• Tr = reaction time (secs)
• f = longitudinal friction
• a = deceleration in m/sec2

The two formulae can be found various documents, e.g. formula 1 in (ref. 831) and formula 2 in (ref. 857).

Where the theory doesn’t work

1. At night. If the object is not illuminated and there is no street lighting then you can only see as far as your headlights. If the object is another vehicle and its rear lights are on, you will see beyond your headlights but may take longer to perceive what’s going on and to react to it.

2. If the vehicle is not a car. Typical heavy vehicle stopping distances for heavy vehicles can be up to 2.75 times those of a car (Lay,ref. 1635), whilst stopping distances for bicyclists is of course much less. Most guidelines quote SSD for cars.This problem can be reduced if heavy vehicles are subject to “vehicle type” speed limits (see e.g. ref. 857 page 27).

3. On curves. Here some of the available friction is taken up by radial friction which helps prevent the vehicle spinning off the road.

4. In three-dimensional space. Where a combination of longitudinal gradient, superelevation and vehicle length is not allowed for in the basic formulae.

Where the application of the theory varies

• Different values for the input parameters such as perception-reaction times, deceleration, friction
• Different values for perception-reaction time (Lay Ref. 1635 page 428 refers t0 2.5 secs in rural areas and 1.5 secs for urban areas)
• Assumption of different values for friction with different vehicle speeds
• Different types of vehicle
• Different definitions of speed V

Typical values

Table 1: Some values for the input parameters

Table 2: Some values for SSD (against speed in km/hr)

Health warning

The values for SSD quoted in guidelines are usually for cars driving on wet roads with an asphalt or concrete surface, in daylight and good visibility, with a comfortable level of braking deceleration, and with various secondary provisos (car brakes and tyres in good condition, 90th %ile driver (ref. 1639 “a deceleration rate of 3.4 m/sec2 is considered to be comfortable for 90% of drivers”)and not impaired by e.g. alcohol,and so on.)

References

167 – UK, Hobbs, “Traffic planning and engineering” Pergammon Press; 1974 (page 288)

713 – USA, AASHTO “A policy on geometric design of highways and streets”; 1994

831 – USA, AASHTO – “A policy on the geometric design of highways and streets”; 2011

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

1635 – Australia, M.G. Lay, Handbook of road technology vol.2 – traffic and transport”, Gordon and Breach; 1990 (see Section 19.2)

1639 – USA, Illinois DOT “Bureau of local roads and streets, chapter 28 – sight distance”; 2006

Footnote

This is part of on-going research, use at your own risk