tailieunhanh - Vehicle Crash Dynamics P2

Slipping on an Incline due to Down Push From the solutions for Ps and Pd above, the relationship between them can be obtained and is shown as follows: Given a coefficient of friction, :, and an inclination angle, 2, it can be concluded that (1) Pd | Fig. Slipping on an Incline due to Down Push 0 -Pd Fy - mg sin0 0 SFz 0 N mg cos0 where Fy p N p mg cos0 Pd Jg p cos0 - sin0 For Pd 0 then p tan0 From the solutions for Ps and Pd above the relationship between them can be obtained and is shown as follows Since pcos0 - sin0 pcos0 sin0 pcos0 - sin0 pcos0 sin0 1 one gets Pd . Ps d Given a coefficient of friction p and an inclination angle 0 it can be concluded that 1 Pd Ps for 0 0 0r where 0r angle of repose tan-1 p 2 Pd Ps for 0 0 and 0 0r The relationship Pd Ps can also be verified by the curves shown for the side and down pushes shown in Fig. . Special Cases 1 for no inclination 0 0 the normalized push P W where W mg is equal to the coefficient of friction p . P W .9 for both side push and down push when p shown in the plot 2 for no normalized push P W 0 then the inclination angle 0 is equal to the angle of repose tan p . for p 0 tan p 42 deg. shown in the plot . Fig. Normalized Push to Slide on an Incline 2002 by CRC Press LLC Calculation of Safe Distance for Following Vehicle Use the kinematic relationships and derive the formula below for the safe distance as a function of initial velocities and decelerations of both leading and following vehicles 10 11 . Fig. Safe Distance 1 2 2b2 2 1 2 ----V1 2b 1 where Tr Following driver s reaction time bv b2 Deceleration rates ls Safe distance The first term in the equation for ls based on the kinematic relationship 3 in Eq. is the total braking distance required for the following vehicle 2 to stop the second term for the leading vehicle 1. The difference of the first two terms is then the minimum safe distance needed for no collision. The third term is the extra distance needed due to the reaction time of the driver in the following vehicle to apply his brakes. Special Cases If v1 0 the minimum safe distance needed is the braking distance to stop for the following vehicle the first term . If v1 v2 and b1 b2 the .