 Hello everyone. I welcome you all for this session on overtaking side-distance on roads. I am Ashok Kumar, Student Professor, Department of Civil Engineering, Valchan, the Institute of Technology, Solapur. The learning outcome of the today's session at the end of the lecture, students will be able to appreciate or able to explain the need for overtaking side-distance on roads. Before we go into the overtaking side-distance, let us understand what is overtaking side-distance on roads. So it is just a minimum distance open to the vision of a driver of a vehicle, intending to overtake a slow vehicle ahead with the safety against the topic of opposite direction. That is the, this is known as a minimum overtaking side-distance. So you know that in a particular stream of traffic stream, all the vehicles are not going with the design speed. Some of the vehicles are going with the slow speed. So it means there must be opportunity given for a fast moving vehicle to go in the, to overtake this slow moving vehicle because every road is defined with particular design speed and associated with the level of service. So now to achieve this, so in every alignment, we have to provide the overtaking opportunity for a fast moving vehicle to overtake this slow moving vehicle considering the opposite vehicle also consideration into the consideration while overtaking. So from the picture, you can understand here the A vehicle is a fast moving vehicle and B is the slow moving vehicle and A vehicle want to overtake this slow moving vehicle B coming on the opposite lane considering the opposite vehicle there is C into the consideration. So this is the minimum distance should be available in every alignment so that the overtaking opportunity should be there for fast moving vehicles. Another way we can define this overtaking side-distance, it is the distance measured along the center of the road with an driver height that is a high level at taken as 1.2 meter and the object height is should able to see the top of object of 1.2 meter on the road surface. So driver height is taken as 1.2 meter and the driver height of 1.2 meter should see the opposite object of 1 point top of the object of 1.2 meter the distance measured between the these two vehicle are between the driver and object is called as a overtaking side-distance. So you can see here from the picture to achieve this to go into the particular the achieving this to see this opposite object we need to make this the particular vertical summit curve little bit flatter like this. So if you make the particular curve like this and the summit curve like this in this vertical curve the opposite the driver will not able to see the opposite height of 1.2 meter to have this condition of 1.2 meter we need to make the curve flatter and flatter so that there is an overtaking opportunities also possible in the vertical summit curves. So this is mainly we feel very the uncomfortable particularly when overtaking in the vertical summit curve or in the horizontal curves. So these are some of the critical locations we must ensure our self the overtaking side-distance should be there in the these two locations. The what are the the factors depends upon the OSD we can see that the different speed of the vehicles are involved here one the speed of the overtaking vehicle and the overtaken vehicle and also the opposite vehicle. So we have to arrive the this length of the overtaking side-distance considering all these three vehicles into the consideration and what about the spacing between these vehicles so we have to see the how to find out the spacing between the these two vehicle this also adds the parameter in deciding the length of the overtaking side-distance and as well as the during the overtaking operation what is the skill and reaction time of the driver. So some driver will have less reaction time some driver will have more reaction time yeah this is also depends the your overtaking operation and even the rate of acceleration of overtaking vehicle so when the opportunity is there for a driver he wants to overtake in the particular opportunity share the what is the acceleration of the overtaking vehicle also depends on the overtaking side-distance length and another one the gradient of the road particularly when a vehicle is coming in the descending gradient so if you have the when the vehicle is negotiating in the upper gradient the requirement of the stopping side-distance or overtaking side-distance will be lesser but the same vehicle if it is coming on the downward direction because of the vehicle it is coming with the higher speed and there is an grade is also involved here the momentum plus the gravity both are acting in the downward direction so because of that you need to have more overtaking side-distance or stopping side-distance in the while it is in a going in the gradient of the road. Now we will see that the what are the parameters and what are the vehicles are involved here you can see the the vehicle a1 this is the vehicle a wants to overtake the way slow moving vehicle b it is coming up with a particular speed v kmph or v meter per second so to overtake the slow moving vehicle b it has to travel for a small length or a smaller distance with the same speed of the your slow moving vehicle say the speed of the slow moving vehicle is say vb kmph or vb meter per second now even though it is coming up with the high speed of v meter per second for a smaller distance say the d1 distance this has to reduce the speed from v meter per second to vb meter per second and travel a distance of d1 that is at a speed of vb meter per second and after that once they observe that the vehicle b is going with very slow and there is an opportunity is there for to overtake now the after reaching to the distance d1 and reaching to the position of a2 the vehicle will a will accelerate and come on the opposite lane of the highway and accelerate over here and from here it accelerate the vehicle and it will overtake the the slow moving vehicle b and occupies the his original path that is reaching the position of a3 so by the time it will the opposite vehicle also the opposite vehicle that is c will also move from c1 to c2 so that is considered as a d3 now while overtaking your slow moving vehicle also take position from b1 to b2 that is denoted by b and the spacing between the slow moving vehicle and fast moving vehicle it is denoted by s here is also s and b2 to a3 is also s so total overtaking side distance is equal to a distance d1 d2 and d3 now d1 is considered as a distance traveled by the overtaking vehicle a during the reaction time t so how much is the the time taken by vehicle a1 to reach to a2 it is considered as the normal reaction time of the driver t usually we take 2.5 second is a t time to for any reaction time of the driver so during the time t the vehicle a1 will reach to a2 that is we called as a distance d1 and d2 is the distance traveled by the overtaking vehicle a during the actual overtaking operation during the time t so now from the from this position to reaching to the this position the total the overtaking time that is we denoted by capital T so this is the overtaking time t from reaching from a2 to a3 and d3 is the distance traveled by opposite vehicle from c1 to c2 that is the d3 now you think over here how to calculate the the the value of d1 and value of the d3 so can you just pause over here and try to write the equation of how to calculate the d1 and d3 I hope you able to write the equation of d1 and d2 we know that the the reaching from a1 to a2 it is the time is given as the that is a reaction time t so we know the time t and the speed of the vehicle is it is vb meter per second because we know that the the fast mean vehicle which is coming up with the vb vkmph or v meter per second is going to reduce the speed from v to vbkmph or vb meter per second because it has to travel with the same speed of the slow moving vehicle that is traveling at a vb meter per second so now we know the speed of the a1 vehicle and reaction time t I can write the equation write like this vb into small t this is how we should calculate the d1 now what about the the c1 and the distance from c1 to c2 that is d3 here I know the the overtaking time t this is the the the overtaking time t during the overtaking operation so I know the overtaking time t and this c vehicle is coming up with the speed of vkmph or v meter per second so d3 also written like this that is v into capital t so here this capital t is not the reaction time of the driver it is the overtaking time t now the question arrived here we know the d1 value in the previous slide I told how to calculate the d1 that is vb into t and and d3 is d3 is v into t so now the different vb is also given to you v is also given to you now the question arises here this is the capital t how this overtaking time t how to calculate this overtaking time t if I know this the t I can able to calculate the distance of d2 also now you can calculate this capital t using your linear motion equation that is a second equation of motion that we can use the s equal to ut plus half at square here u is nothing but the initial speed of the vehicle here at the position a2 the initial speed of the vehicle is taken as vb and t is nothing but taken as a capital t so you can write like this vb into capital t plus half at square a is the your acceleration and t again is the your capital t so like this you can calculate the your the value of capital t using the second equation of motion that is a linear motion equation you can use that and calculate the value of t so in the next presentation I will try to derive the equation of d3 and how to calculate the value of your t value so these are the references I have used for preparing the presentation thank you