Find The Stopping Sight Distance To Avoid Head on Collision - Mathematical Problem and Solution - Civil Engineering

Wednesday, 10 April 2019

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) = SSD1SSD2 = (153.6+82.19) =235.79m
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