 Hello everyone. I welcome you for this today's session. I am Ashok Kumar, Assistant Professor, Department of Civil Engineering, WALCHEN Institute of Technology, in this class, we are going to discuss about the transition curves on roads. Learning outcomes. At the end of the session, students will be able to describe the objective of transition curves and select the ideal type of transition curves on roads. Let us understand the function of a transition curves in horizontal alignment. Our transition curve is having a curve of having a varying radius. Why varying radius? You can see here, at the state path, the radius is infinity. And the centrifugal force P equal to 0 because the P, that is the centrifugal force, m e square upon r c, if I put the r value as infinity, automatically the P value is 0, the centrifugal force is 0. And from here onwards, the radius starts decreasing. And we are getting some value at this point r equal to r 1 and r equal to r 2 and r equal to r c, that is a start of the circular curve. We are getting a full designs radius. If I put the value of r equal to r 1, here denominator is lesser. Obviously, the centrifugal force is increasing. So, you can see here, the centrifugal force is increasing up to this point and here onwards it is constant. Now, the centrifugal force is increasing from this point. It means, if you do not have any transition curve in between, if I join the circular curve directly to the state path, having the centrifugal force, it applies a sudden jerk on the vehicle or lateral sway on the vehicle. So, what will happen? A sudden jerk and lateral sway, it causes the discomfort to the passengers sitting inside as well as the steering of the vehicle, the smooth steering of the vehicle will not be able to possibly to turn the steering safely. That is the main, the hazardous will happen without having any transition curve. If I design the transition curve over here between circular and state path, now we can introduce the centrifugal force gradually from this point to this point and this point and here onwards it is constant. So, start of the circular curve, we will be having a transition. Again at the end of the circular curve, we will be having another transition. Now, first application of the transition curve to introduce this centrifugal acceleration gradually from straight path to circular path. So, that they are not be having any discomfort as well as the smooth steering of the vehicle is also possible. Second application of the transition curve is for super elevation. Here the normal super elevation is camber that is 2.5 percent. Now, I want to take this 2.5 percent at the circular path, it is 6 percent or 7 percent depending upon the speed and the radius the super elevation is designed. Here it is 7 percent. So, now 2.5 to 7 percent, I cannot directly increase suddenly from 2.5 to 7 percent. So, this transition length if I use it, I can increase gradually having a suitable rate of super elevation, increase gradually super elevation from 2.5 to 3, 4, 5, 5.5, 6, 6.5 and 7 percent up to the circular path. Again from circular path it is 7 percent. Again from 7 percent to 2.5 percent, another end of the transition curve. So, transition curve will helps you to gradually introduce the super elevation from normal camber to designed super elevation. This is the second application of a transition curve. Third application again widening. At the curve we are depending upon the radius and speed we are increasing the width of the pavement at the curves. Now, the widening width is here suppose it is a 0.9 meter. So, from 0 to 0.9 meter again I will be using the transition curve to gradually introduce the extra widening on the pavement. So, this will helps you to introduce gradually the widening on the pavement. Third application is aesthetically it looks very pleasant appearance having a transition curve on the roads. So, these are the overall objective of a transition curves. Now, to fit this transition curve we need to here we can see here that we are shifted the original circular curve for a some distance. So, this is required to set out this accommodate this transition curves on the circular curve we need to shift this distance. So, how to calculate the shift it is given by Ls square upon 24r. So, this r is the radius of the curve and Ls is the length of the transition curve. Let us summarize the overall objective of a transition curve this is used the to introduce the gradually the centrifugal force so that they are not be having any sudden jerk on the vehicle. And turn the steering of the vehicle gradually for its own comfort and safety and gradually introduce the design super elevation and widening at curves as well as it looks very pleasant appearance or aesthetically it looks very good having a transition curves. Requirements of a transition curves radius of the curvature should decrease gradually from infinity to the minimum. So, because at the state point it is infinity and it should goes on decrease at the start of the transition at the start of the circular curve. So, infinity to the designed value rate of change of centrifugal acceleration should be uniform gradually introduced. So, this will take care about the discomfort or undesirable locate oscillations if you are introducing the centrifugal acceleration gradually and uniformly. So, there will not be problem with any discomfort or oscillations or lateral sway. Radius of the curvature should be inversely proportional to the length of the curve from the starting point. So, all these conditions will be fulfilled by spiral. So, spiral is the ideal transition curve where it will take care all these the points to set out in the field. We got different types of the transition curves. We got spiral, laminiscate and cubic parabola. Among all I told you the spiral fulfills the all the conditions. So, why it is fulfilling? For a up to 4 degree we can see here all this spiral laminiscate and cubic parabola the path followed by all this curves are same. But after the 4 degree are more than 9 degree are larger angles we are trying to what will happen the radius is not uniform the rate of change of the radius is not uniform. When the radius is not uniform automatically your the centrifugal acceleration is also not uniform. Other than increasing when the radius starts increasing automatically the centrifugal acceleration starts decreasing. So, that causes the hazardous are accident at that particular location. So, laminiscate and cubic parabola is holds good for smaller angles. But when you go larger angles the spiral fulfills the ideal condition. Spiral or clothite here as I told you the radius of the curve is inversely proportional to the length of the curve. And this will take care about the centrifugal acceleration when the radius is inversely proportional to the length of the curve the rate of change of centrifugal acceleration is uniform throughout the length of the curve. We can introduce the centrifugal acceleration uniformly. And this will take care having designed spiral length we can control the centrifugal acceleration at particular points. So, that is another advantage of having a spiral. And for easily setting out in the field we can set out and we can easily calculation part spiral is easy setting out is easily as well as the execution and construction of the spiral is easy in the construction. And it is given by L r equal to L s into R c the L s is length of the transition R c is the radius. So, that is L s into R c equal to constant c. Bernoulli's lemniscate here as I told you for smaller angles this Bernoulli's lemniscate holds good here is also the radius is inversely proportional to the length of the curve. But the problem is for larger angles higher than 4 degree the rate of change of radius or rate of change of centrifugal acceleration is not constant. So, when there is this is not constant will not able to control the centrifugal acceleration the rate of change of centrifugal acceleration. So, when the radius is not constant when your centrifugal acceleration is also not constant. For smaller angles this holds good cubic parabola again here is also the radius the curve is inversely proportional to this x and here is also this is also a type of the transition curve. But for the radius and the rate of change of radius and rate of change of centrifugal acceleration is not constant when the reflection angle is goes beyond the 9 degree. So, this is not ideally suitable for construction of the highways because this is not the points the ideal transition will not able to when angle is goes beyond 30 degree or higher than higher than 9 degree. So, this will not able to having the transition properties. Now, let us pause the video and try to select the correct answer where the rate of change of radius is constant in which type of the curve whether it is spiral, cubic parabola or Bernoulli's MNISC or all the above. I hope you are able to select the correct answer the correct answer is spiral in the spiral your rate of change of radius and centrifugal acceleration is uniformly introduced. So, spiral is the correct answer. These are the references I have used for presenting this presentation. Thank you.