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

10th April 2019

## 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