Highway engineering

# Find The Stopping Sight Distance To Avoid Head on Collision – Mathematical Problem and Solution

# Find The Stopping Sight Distance To Avoid Head on Collision

Here, a mathematical problem is taken to determine the value of minimum stopping sight distance to avoid head-on collision of two cars, when the value of the braking efficiency is given.

## Mathematical Problem

Find minimum stopping sight distance to avoid head-on collision of two cars approaching at 90 Km/h and 60Km/h. Use reaction time 2.5 sec, coefficient of longitudinal friction is 0.7 and brake efficiency of 50 percent in either case.

## Mathematic Solution

Given,

- V1 = 90 Km/h
- V2 = 60 Km/h
- t = 2.5 sec
- f = 0.7
- Braking efficiency (η) =50% =0.5( note: brake efficiency reduces the coefficient of friction by 50%)

now,

Stopping Sight Distance of first car (SSD1)

= (0.278V.t + V²/254fη)

= 0.278⨯90⨯2.5 + 90²/254⨯0.7⨯0.5

= 153.6m

Stopping Sight Distance of second car(SSD2)

= (0.278V.t + V²/254fη)

= 0.278⨯60⨯2.5 + 60²/254⨯0.7⨯0.5

= 82.19m

so, stopping sight distance to avoid head-on collision of the two approaching cars (SSD) = SSD1 + SSD2 = (153.6+82.19) =235.79m

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