 Hello everyone, I welcome you all for this today's session on negative canned. This is part of geometry design of a railway track. I am Ashok Kumar, assistant professor, department of civil engineering, Walsh and the intro technology, Solaapur. Learning outcome of the today's session, at the end of the session, students will able to calculate the negative canned at railway crossings. So, in the earlier session, we have discussed about the what is equilibrium canned, what is canned efficiency and what is canned taxes. So, today we will see the another type of the canned that is negative, canned or negative superelevation. So, when the main line lies on a curve, so both main line and branch line over here, you can see that the when main line lies on the curve and has a turn on of counter flexure. So, what is the meaning of counter flexure? The same elevation, the both main line and branch line are crossing each other. So, leading to another branch line is crossing here, the superelevation necessary of the average speed of the trains running over the main line curve cannot be provided over here. So, what does it mean here? See the outer rail here for the main line I am talking, for the AC should be higher than BD as per the superelevation, outer rail should be higher than inner rail, that is AC should be higher than BD. Now, for the branch line if you define the superelevation, BF should be higher than AE. So, see the point A and B over here. So, for the main line inner rail is lower than outer rail that is point B is lower than point A. For the branch line point A is lower and point B is higher. So, on the same location you see that B is lower for the main line and B is higher for the branch line. So, on the same location due to the same elevation we cannot provide the meeting this criteria, providing the superelevation for the branch line and superelevation for the the main line is not possible at the same location. So, this is here how to overcome this issue where one rail is higher and one rail is lower, particularly the branch line we are getting an issue because the inner lane of the main line that is BD should be lower than AC and here the point B should be lower, but for the branch line it requires higher. So, now what we have to do here, provide the whatever the superelevation you calculate for the main line you provided and whatever the superelevation you provide for the main line you have to provide the negative superelevation for the branch line. So, here you can see that whatever the superelevation provided for the main line we are going to lower the outer rail of the branch line equal to the whatever the superelevation provided for the outer rail. So, that providing the lowering the outer rail of the branch line is called as negative superelevation. So, how to calculate this the negative superelevation for the branch line and also we have to restrict the speed on both branch line and main line because they are crossing at the same elevation. So, to avoid the accident we have to lower the speeds here we have to restrict the speeds both on branch as well as for the main line and how to calculate the negative superelevation here. So, what is the mean by negative? We are providing action superelevation for the main line that is the AC is higher, but at the same time BF we are lowering equal to an amount of what is the AC is provided that is what we have a negative superelevation. So, how to calculate this negative superelevation you can see here first you have to calculate what is the speed given on the maximum speed given on the branch line you calculate the E theoretical. So, now we know that the E actual how to calculate the E actual here? So, this is from the top of the rail to the top of this E theoretical that is what we call as canned efficiency. So, now you calculate E actual or negative superelevation for the branch line canned efficiency minus the E theoretical. So, that gives the what is the E actual or negative superelevation provided for the branch line. So, whatever E actual you providing for the branch line is equal to the your E actual of the main line or E actual of main line is equal to the E actual of negative superelevation for the branch line. So, whatever you providing actual superelevation for the branch line you have to provide the same superelevation for the outer rail or outer rail of the main rail. So, now how to calculate the speed here? If you want to calculate the maximum speed allowed on the main line you have to calculate like this you have to calculate the what is the E theoretical here. So, you know the E actual from the branch line that is equal to the E actual of main line plus you know the canned efficiency add both E actual plus canned efficiency you will get E theoretical. So, for that E theoretical you can calculate what is the maximum speed allowed on the main line. So, let us take an example to understand this in detail. Here branch line the degree of the curve is given as 5 degree and 3 degree is for the main line and if the speed on the branch line restricted to 35 kmph and asking you to calculate what is the speed on the restricted speed on the main line. So, it is a maximum speed restricted is 35 kmph. Now again using your the degree of the curve on radius relation that is r equal to 1750 by D. So, here for the branch line you have to take it is a 5 degree. So, that comes to 350 meter radius for the branch line. Now we know that for the equation for super elevation for the broad gauge. Now that is g v square upon 1.27 r. So, here g equal to 1.676 that is your broad gauge distance. Now calculate what is the E theoretical required for your branch line. So, 1.676 v square is 35 square divided by 1.27 into 350. So, that comes to 4.57 is the 4.57 centimeter is the E theoretical. Now to calculate the negative super elevation we know that the canned efficiency is taken as 7.5 centimeter. Now from the diagram you can see here the E theoretical is whatever you calculated 4.57 and canned efficiency from top of the rail to the your E theoretical is 7.5 centimeter. You can calculate the E actual that is negative super elevation that is equal to 4.57 minus 7.5 that gives you the what is minus 2.92 centimeter is your negative super elevation to be provided on the branch track. I hope you understood this the concept. So, minus 2.92 is negative you have to provide that is canned efficiency allowing maximum of 7.5 centimeter. Now I told you as whatever super elevation provided on the branch track that is equal to the same super elevation E actual on the your main line. So, super elevation to be provided on the main line track is 2.92 which is same as the super elevation of the branch line track but in the opposite direction we have to provide here. So, it means your outer rail is lowered by 2 minus 2.92 centimeter for the your branch line. So, outer rail is this is your outer rail and this is your inner rail here. So, this is where outer rail is the height is reduced by 2.92 centimeter. Now we will go for the main line. Now for the main line again you have to calculate what is the radius the required for that basis taking the degree of the curve. Now here we got 584 meter. Now you can calculate what is the E theoretical to calculate what is the speed here. So, E theoretical is equal to what is your E actual is provided whatever the E actual you provided for the branch line is equal to the E actual of main line. So, 2.92 plus the can deficiency is given as 7.5 centimeter add both this 2.92 plus 7.5 maximum we can go up to 10.42 is the E theoretical. So, now for this 10.42 what is the the maximum speed I can allow on this speed on this main track considering a can deficiency of 7.5 centimeter. So, in this case you can calculate like this put the E theoretical value and unknown is V you can calculate the what is the V here it is 67.9 km page is the restricted speed on the main line. This is the diagram the same diagram which I have explained in the previous slide. Now example 2 now we will go for we will come reverse now we will take the data of the main track and asking you to calculate the data on the branch track. So, here the we will start with the main track here what is the speed is given the speed is given on the main track is the speed is given to you that is 75 kmph calculate the what is the E actual required for this 75 kmph. Now the E actual is equal to E theoretical minus can deficiency again can deficiency is 7.6 centimeter we are taking here let us assume this 7.6 is can deficiency. So, plus 5.36 centimeter because outer rail is raising by 5.36 centimeter with respect to the inner rail. So, for the branch track I told you whatever the E actual is for the your main track is equal to the E actual of branch track. So, you have to provide the negative superlavation of minus 5.36 centimeter for the branch track now you can calculate what is E theoretical. So, E theoretical for the branch track again E actual plus can deficiency. So, that comes to 2.24 centimeter. So, now with this is for the main track I have calculated the E actual and for the E theoretical for the branch track that is 5.36 that is E actual plus 7.6. So, that comes to 2. minus 5.36 plus 7.6 comes to 2.24 for this 2.24 you can calculate what is the speed required. So, that is I have calculated it to 27 kmph. So, these are the references I have used for preparing this presentation. Thank you.