 I welcome you all for the today's session on Design of Vertical Summit Curves on Roads. Myself, Pashok Kumar, Aston Professor, Department of Civil Engineering, Vulture and Insur Technologies, Sallapur. Learning outcomes of today's class. At the end of the session, students will be able to calculate the length of vertical summit course. We know that when vehicle travelling along one grid, on this section vehicle travelling on one grid is to move on to another grid. So, opposite to that, this grid is another grid. A change of direction of motion in the vertical plane is involved. So, these vertical curves are required to ease of the change in the gradient. So, we need to connect this plus G1 and G2 by a smooth vertical curve. So, this curve will have ease of the change in the gradient. So, the main criteria behind the designing of vertical curve is the side distance. The vehicle coming on this side should be able to see the object on the opposite side. So, here you can see that the vehicle coming on this section should be able to see the opposite vehicle. So, that he can stop the vehicle or slow down his vehicle speed or taking a diversion. So, this will reduce the happening of accidents on the vertical curves. Summit curve forms when ascending gradient meeting another ascending gradient. So, here the deviation angle is n equal to n1 minus n2. We know that deviation angle is algebraic difference of ascending gradient and descending gradient. So, here plus n1 minus of minus plus n2, so that becomes n1 minus n2. Here ascending gradient meeting a level ground. So, in this case n equal to n1, ascending gradient meeting a descending gradient. So, in this case n equal to n1 plus n2 and descending gradient meeting descending gradient. So, there is another formation of vertical summit curve. So, here in this case n equal to n2 minus n1. Now, let us pause this video and try to give the answer for this question. Is there any necessary of transition curves in the vertical summit curve? We know that the transition curve we already designed in the horizontal curve. Now, let us pause the video and give me the answer for this question. Whether is there any requirement of transition curve in vertical summit curve? I hope you are able to give the answer for this question. The correct answer is looking at this diagram you can understand. The vehicle is going in the upward direction and the gradients in the vertical curve. Now, when it is going in the upward direction, the centrifugal force is acting on the upward direction and gravity is in the opposite direction. So, due to this the part of the self-weight of the vehicle is released or relief is given to the self-weight. So, this further the stresses or whatever the pressure on the tire is also released. And also the further the suspension system of the vehicle the stresses also reduced on the suspension system of the vehicle. So, this will have an advantage where the centrifugal force is in upward and gravity is in downward. There is no all the pressure will be nullified over here. So, this will be added advantages. So, in this case there is no requirement of any transition curve because the centrifugal force is already contracted by this arrangement with the gravity. And another one is having a smaller deviation angles in the vertical curve. We do not require we do not feel any discomfort to the passengers. One is the centrifugal force is not there because of that we are not going with the transition curve. Another is having a very smaller deviation angle. So, here the deviation angle is very small. So, in this case the discomfort to the passengers is also lesser. And another one we are designing the vertical curves considering the side distance criteria and length of the curve is larger in this case. So, in that case there is a shocks or vibrations any jerks that will be not there in the summit curve. So, because of all these reasons so transition curve is not required in the summit curve. Here the main criteria behind designing the vertical curve as I told you to provide a side distance. So, we know that the side distance is classified as stopping, intermediate and overtaking side distance. To minimum you try to provide a stopping side distance. The reason the what is the stopping side distance it is the height of the driver is considered as 1.2 meter and object height is 0.15 meter. If the driver can able to see at height of 1.2 meter and object of height of 0.15 meter on the curve the distance available in front of him is we call as a stopping side distance. So, in this case minimum you can provide a stopping side distance. If the land is available we can still go with a flatter gradient flatter gradient. So, in that case the length of the curve will be larger. So, we can go for thinking on providing the intermediate side distance. So, safety will be higher in the intermediate side distance. If still land is available we can go for overtaking side distance. So, overtaking side distance in this case the driver height is taken as 1.2 meter and object height is also taken as 1.2 meter. So, overtaking side distance means very flat curve. So, in this whatever you are looking this the steep gradient still we have a very flat curve. The length of the curve is larger in that section and the driver have enough distance available in front of him to take a proper action on the summit curves. Let us find out what is the ideal shape of the summit curve. Circular summit curve here this gives the constant side distance because we are designing vertical curves considering the side distance criteria. It gives a very constant side distance. Another one is the shape we are following with the parabolic curve. For a smaller angles both the summit curves and parabolic curve simple parabolic curves follow the same path. But we are insisting to go with a parabolic curve. The reason behind this selecting ideal shape of the summit curve is a parabolic. It is easy arithmetic calculations and coordinate calculations are easy and layout in the field is also easy. So, all together for smaller angles theoretically this circular summit curve is okay. But for considering these advantages all these advantages we are selecting a simple parabolic curve as ideal shape for the summit curves. Let us go for finding out the length of summit curve. As I told you we have to consider the stopping side distance criteria. Here length of curve is more than stopping side distance. In this case you can observe this diagram. Here the height is 1.2 meter and the object height over here is considered as 0.15 meter. So this distance is called as a stopping side distance. In this case the length of the curve is more than stopping side distance. And the n is the division angle. The equation for a simple parabolic curve for when length of the curve is more than stopping side distance. So that gives put the h value as 1.2 meter and the small h as 0.15 meter. So that gives you l equal to ns square upon 4.4. Second case when the length of the curve is less than stopping side distance. So that case the equation is again put the h value as 1.2 and the small h as 0.15. The equation reduces to 2s minus 4.4 upon n. Again considering the overtaking side distance here we are expecting the length of the curve to be more. To have the overtaking operation in the summit curve. So that case the equation is given by ns square upon 8h. So in this case we know that the h is 1.2 meter. So put the h value as 1.2 meter the equation reduces to ns square upon 9.6. When the length of the curve is lesser than overtaking side distance. So it is given by 2s minus 8h upon n and again h is 1.2 meter. The equation is 2s minus 9.6 upon n. Now we need to design for whenever we have the state section. So here one of the state section another state section we are connecting these two. Two alignments are connecting. Here if I leave that same as it is without providing any length of curve. It becomes a kinks on this section. So this kink will have a shocks or any discomfort to the passengers discomfort to the vehicle movement. So now we have we require to have minimum length on these sections. So according to the codal provisions depending upon the speed of the vehicle the minimum length is given as 60 meter. So here it is a maximum grade change is a 0.5 percent. So the grade change is you have to take the algebraic difference of plus a1 and minus a2. So if I take these gradients the algebraic sum is 0.5. So taking that value you can observe as a deviation angle is going reduces the length of the curve is increasing. Another table given by the codal provision here we can while we designing the horizontal curves. You can keep this table as readymade table for what side distance you are designing. If you are going with the stopping side distance and 100 kph you can directly calculate the what is the length of the curve that is 73.6 multiplied by the a. So how to calculate the a is nothing but your deviation angle only. So if I take the algebraic difference of this one this so that becomes a put the a value multiplied by the 73.6. So that gives you a length of the curve for stopping side distance. So suppose if you are going for overtaking side distance so I told you the length of the curve will be still higher compared to the stopping side distance. So higher safety is in the overtaking side distance. So this case one example is given if I take 0.6 percent and length of the curve is 73.6 into a that gives you 191.36. So whenever you are designing the vertical alignment keep this table readymade table with you so that you can cross check whether you are designing as per the codal provisions or you are keeping the minimum length as per the codal provisions. These are the references I have used for representing this presentation. Thank you.