Re: Overtaking with speed
Posted: Wed Jul 18, 2007 2:36 pm
Horse wrote:Please!
I can't find it, but I can reproduce it.
* * * *
The example was an overtake on a car travelling at 50mph. Everyone has 1g braking and 1s reaction times. The overtaking car can accelerate at 0.2g (that's 0-60 in about 14s) at 50mph. Cars are 3m long.
The danger zone is defined so that a car is in the danger zone when it cannot stop behind the target car when it exerts maximum braking, until the time when it is clear of the nose of the target car.
In each example we calculate time in danger.
Momentum overtake
Approach at 70mph and clean pass.
i) How far behind does danger start?
50mph car stops in (v^2=2as)
70mph car stops in (vT + v^2/2a)
So danger starts 56m behind target.
Relative to first car, danger zone extends 62m and is travelled at 20mph so
TED = 6.9s
More generally - http://tinyurl.com/2q57wz
Triangle overtake
Safe offside following position is at 50mph thinking distance = 22.3m
So distance to clear is 28.3m, covered relative to target at a starting speed of 0 and with acceleration of 0.2g. (s=1/2 at^2)
TED = 5.4s
More generally - http://tinyurl.com/yulumz
Edited to correct braking value in Momentum example and html formatting.