 to all of you. I am Mr. Seshkan B. Gosavi, Assistant Professor, Department of Civil Engineering, Valchan Institute of Technology, Sulapur, presenting an online educational resource on setting out compound curves. The learning outcomes of this online educational resource are the students will be able to explain the need of compound curve. The students will be able to calculate the elements of compound curve. The students will be able to explain the field procedure for setting the compound curves. Earlier we have seen variety of elements of simple circular curves. It consisted of an alignment starting with change zero at the extreme bottom left location which reaches to a point of intersection p i at this location. And there is another alignment which is moving towards this side. The intersection point is having a chain H and there is a deflection angle delta at that particular point of intersection. We have already discussed that we are provided with radius of curve based on which we calculated the tangent length. We calculated the length of the long chord. We were able to calculate the length of the curve as well. Here a sketch of a compound curve is presented for our reference. See the difference. In a simple circular curve there was a straight curve starting from point of curvature T1 and ending out at this point which was in that case point of tangency. However because of some practical difficulties it may be the water's course, it may be the structure which is sensitive because of which if T2 point cannot be taken at this location. We have a liberty of shifting that particular point at some other location. But that can be done with the help of some other simple circular curve of some other radius. Meeting the previous curve which has begun from T1 and therefore from T1 to T2 the first curve of radius R1 and the deflection angle delta 1 comes. However from T2 onwards another curve having a radius R2 is introduced with a deflection angle delta 2 which finally reaches at the point T3 as has been shown over here. So remember here there are two different curves having two different radias meeting together at the common point T2 and therefore we are having several components in the design. Conventionally we were having a single tangent length from B to T1. However in this case we are having small T1 and small T dash 1 combined together making the tangent length B to T1. Similarly on the forward direction we have got T dash 2 and T2 combining together to give us forward tangent length B to T3. The deflection angle delta is still here however for the first curve the central angle is delta 1 therefore deflection angle is also delta 1 and for the second curve central angle is delta 2 and therefore deflection angle is delta 2. Now because two different curves of two different radias moving in the same direction are combined together this is called as the compound curve. We have got a special element over here in the form of the alignment D which is nothing but the common tangent which is tangential to both the curve at a common tangent point T2 as has been indicated here. See the elements that I have discussed in the earlier sketch where we are having a total deflection angle delta which is same as that of simple circular curve. The first and second deflection angle are delta 1 and delta 2. The radius of first and second curve are assumed to be r1 and r2 respectively. Channage of intersection point B is assumed to be i. It can be any real number. The first tangent length T1 is equal to r1 and delta 1 by 2. Remember here r1 is radius of first curve delta 1 is first deflection angle. Second tangent length T2 is equal to r2 tan delta 2 by 2 length of the curve r delta pi by 180 conventionally we were talking about but in this case it is r1 delta 1 pi by 180 for the first curve length and second curve length r2 delta 2 pi by 180 combined together giving us a combined length of the curve l. Channage of point of curvature T1 is channage of intersection point minus small t1 plus small t dash 1 and channage of common tangent point T2 is equal to channage of t1 plus r1 delta 1 pi by 180 that is the length of the circular curve with a radius r1. Channage of point of tangency is channage of t2 plus r2 delta 2 pi by 180. Here the mystery must be regarding these two components t dash 1 and t dash 2. See if we will remember the sketch we have mentioned over there that the common tangent length t will be small t1 plus small t2 because at that point both the curves are meeting together and symmetrically both the tangent lengths are there therefore mere addition of these two tangent length of first curve and second curve gives us the total tangent length or combined tangent length for both the curves. Capital delta is equal to delta 1 plus delta 2 this can easily be proven because if we will visit the earlier sketch over here this is shown as delta this is delta 1 and delta 2. As we know this being delta this particular value will be 180 minus delta and 180 minus delta plus delta 1 plus delta 2 is equal to 180. So obviously the respective deflection angle delta will be equal to delta 1 plus delta 2. You can see where this is delta and the central angle is delta 1 for first curve delta 2 for the second curve combined together delta 1 plus delta 2 and conventionally we know that the central angle is equal to total deflection angle. So delta is equal to delta 1 plus delta 2 can easily be proven in this manner. By the sign rule if you will go back to the triangle over there B D and E this triangle the length of side B D is T dash 1 length of the other side B E is T dash 2 and D length is the total tangent distance T that is T 1 plus T 2. Now T 1 R 1 tan delta 1 by 2 and T 2 R 2 tan delta 2 by 2 being known to us we can compare or use the sign rule. The respective angle over here is 180 minus delta the opposite side is T. So T divided by sine of 180 minus delta will be equal to T dash 1 divided by sine of its opposite angle delta 2 will be equal to T dash 2 divided by sine of its opposite angle delta 1. So this particular formula can be used in the derivation of T dash 1 and T dash 2. So sine 180 minus delta divided by T is equal to sine delta 1 by T dash 1 is equal to sine delta 2 by T dash 2 which by rearranging we can easily conclude that T dash 1 is equal to T into sine of delta 1 by sine delta and T dash 2 is equal to T into sine delta 2 by sine delta. Here you are requested to pause the video and answer some recap questions. See the need of the compound curve I have already elaborated that when a simple circular curve is inserted and if the end point is becoming inconvenient because of some geographical difficulties in that case we will have to change the radius of the curve and insert some other circular curve of some other radius to shift the tangent point at the opposite end or second tangent point. At which of the points the third light will be required to be set in compound curve this needs the knowledge that we have already had regarding the simple circular curves. See it is assumed that the change of intersection point I is given to you based on which by deducting T dash 1 and further by deducting T 1 we will get change of T 1 over here. Great. We need the next point on the curve to be a station whose change is directly divisible by unit chord length. So full station. For that you need to insert one sub chord and thereafter number of unit chords will be last chord will be once again a sub chord. Based on the knowledge of these chord lengths we can easily calculate the tangential angle and the deflection angles. And by setting the deflection angles from station T 1 the first curve T 1 to T 2 can easily be set. So initially for measuring this angle delta you need to set a third light here. Secondly by setting the third light at T 1 you need to set the first simple circular curve and for setting this last part of the circular curve you need to shift the third light at T. At T what do we do is we keep the third light at T we align the telescope with 018 on the horizontal circle that capital T 1 will be visible and then we revert the telescope to get the other direction. And then by releasing upper clamp we will adjust the second deflection angle over here and rest of the curve will be set. So in all B, T 1 and T 2 are three points at which third light will be set. Use the references of surveying SK Dugal volume 2 by Tata McGrawill publication and civil engineering terms for your reference. Thank you very much.