 Hello viewers, I welcome you back on this geometric design of railway track. In this class, we will discuss about the speeds on railway track. I am Ashok Kumar, Assistant Professor, Department of Civil Engineering, Walsh and the Insur Technology, Stolapur. The learning outcome of the today's session, the students will be able to calculate the speeds with respect to the given cant or computed cant or the super elevation. So in the previous session, we have seen what are the different types of the speeds we have. One is the weighted average speed or the equilibrium speed and second one is the maximum sanction speed then the maximum permissible speed which we are allowing on the particular track. So continuation of that we will try to see how this safe speed is calculated for a given conditions. This is how we have calculated the safe speed using the railway board formula. So here considering the actual cant and cant efficiency, we have calculated what is the permissible speed or maximum permissible speed on the particular curve. This is for the transition curves we have discussed. Now for the on meter gauge we have V equal to 0.347 square root of CA plus CD into R and for the narrow gauge it is V equal to 3.65 square root of R minus 6 and this subjected to maximum of 50 kmph. And for the non-transition curves we have discussed this also in the previous session how we are going to calculate the length of the your maximum permissible speed on the basis of the your transition curves. So this applies when we have the restrictions of transition curve we provided in the site due to the site constraint or the land availability. We are restricting the length of transition curve. We always prefer to provide more length of transition curve due to the easement of the curve due to site constraint if there is any restrictions in the site we are unable to provide non-transition curves then we have to calculate the safe speed the procedure given in this slide. Now also we have seen we are calculating the four different this speed limits basis on the sanction speed, basis on the availability of actual cant and cant efficiency. The first way we are taking the what is the sanction speed given for that particular track. This is the first speed we are taking this is given by the track engineer or chief engineer of that particular track. And second one considering the actual cant the what is the equilibrium super elevation provided we are going to calculate that and again the cant efficiency CD is added to the equilibrium super elevation and adding CA and CD we are calculating what is the maximum speed allowed on the particular track and cant efficiency. And third one we have to consider the vehicles which are moving with lesser speed than the your equilibrium speed. So here again we are taking the cant excess into the consideration for the good strength they are traveling with the lesser speed say for 65 kmph for the bg and 50 kmph for the meter gauge. So first we have to calculate what is the equilibrium cant for the given good speed then we are going to see that what is the cant excess is added to this the CA and for adding this cant excess and the actual cant we are calculating the what is the maximum speed we are provided we can provided considering the goods vehicles also into the consideration or the vehicles which are moving lower speeds also consider while defining the what is the permissible speed. So now the last one the speed corresponding to the length of transition curves. So calculate the speed considering these four factors and take the least of that value will be your safe permissible speed. Now to understand this we will take one example and try to see how to calculate the safe speed for the given conditions. Now before we go for the numerical you can pause over here and think for the moment maximum permissible speed or safe speed is more than the sanction speed. So think for a moment and give me the answer whether it is a true or false I hope you are able to give me the answer. The correct answer is it is a false because maximum permissible speed is lesser than the sanction speed. We know that the first speed is defined as average speed or equilibrium speed and beyond that we have permissible speed maximum permissible speed and after the maximum permissible speed that is the last speed which is allowed for the track is sanctioned speed. Now the values given over here it is a 2 degree BG transition curve we do not have any restrictions with the transition curve. We can see that the transition curve is provided and sanctioned speed is given as 10 kmph and you are asking you to calculate the equilibrium super elevation the speed for calculating the equilibrium super elevation is also given as 80 kmph and for the good strain the speed is also given as 50 kmph. So considering this you can calculate what is the safe speed we are going to travel on this 2 degree BG curve BG track. Now first as for the steps we have to calculate the what is the equilibrium super elevation for the given equilibrium speed here. Before we go that you can take that the and the radius of the curve we can calculate taking 30.5 meter chord length that is the equation is R equal to 1750 by D where D is the degree of the curve and we have got the radius is 875 meter and now taking the G distance so the broad gauge distance the G value is given over here is 1.750 that is the distance given is centre to centre distance of 52 kg sleeper the distance given as 1750. So taking this 1750 and your speed value and R value we can able to calculate what is the equilibrium super elevation. So that is 100.8 mm is the your equilibrium super elevation or actual cant is provided. Now we have to calculate the what is the theoretical super elevation for the your the sanction speed. So sanction speed is 110 kmph so now you can calculate what is the the theoretical super elevation for this sanction speed. So taking the only changing the your V value we are able to get what is the theoretical cant for the sanction speed that comes to 190.6 mm. Now for the cant efficiency you calculate the cant efficiency we know that the ethereautical so ethereautical equals to cant efficiency e actual plus cant efficiency. So now what is cant efficiency in the sense we can see that ethereautical minus your actual cant. So this is how we are calculating so ethereautical equals to your actual cant plus your cant efficiency. Now I need the what is the cant efficiency over here I need a CD so CD can be calculated it is ethereautical minus actual cant. So now the whether it is exceeding our allowable limits of cant efficiency no it is 89.8 mm it is a lesser than 100 mm so maximum we can go up to cant efficiency of 100 mm so hence it is permissible. Now you can see here the super elevation for now we have to go for the third step that is calculating the ethereautical super elevation for your good strains again here. So for the good strain the speed is given as 50 kmph now taking the 50 kmph we are able to calculate what is the super elevation required for the good strain so that is 39.4 mm and again we have to calculate the cant excess here again the cant excess is equal to the actual cant that is your CA minus the whatever the your super elevation provided for the 50 kmph that is 39.4 so again you have to take the difference of that that comes 61.4 and we know that cant excess maximally allowed is 75 mm for the BG track so again it is lesser than 75 mm hence it is permissible. Now you can the fourth the third step we are going to calculate basis on the cant efficiency and your actual cant so we are using this railway board formula to calculate the what is the say permissible speed. So put the CA value here the actual cant is provided as 100.8 and CD as 89.8 and R is 875 so put the all the values in this equation and we are able to get the what is the maximum speed basis on the your actual cant and cant efficiency now we have to compare the all the speeds we have calculated first we have calculated basis on the given speed as 110 kmph sanctioned speed as in this case is 110 kmph and the curve as per the theoretical concentration we have calculated 110.8 that is your basis on the actual cant and cant efficiency we have calculated 110 kmph now so we have to take this least of these two here so in this case the 110 kmph is lesser than 110.1 hence we can conclude that the allow the maximum permissible speed over this curve is 110 kmph and provide the super elevation of 100.8 or let us say it is 100 mm super elevation can be provided on this particular track. So alternatively we can also calculate the solve this numerical like this you can calculate what is the your the cant for actual cant for the 110 so for the 110 it comes to 190.6 and for the C50 what is the cant it is going to come that is for the 50 kmph what is the cant it is going to come now on adding the cant the both the CA plus CE that comes to 114.4 mm now for the calculate the for equilibrium speed what is the cant required for the equilibrium speed that is C80 for that it comes to 100.8 now we have to see the lowest of these all these three in this case the lowest of three values calculated above steps is 100.8 mm therefore we can see that conclude that 100 mm we have to provide as the actual cant so comparing the C110 and C80 we can conclude that it is least values 100 mm in this case so we have to compare 114.4 190.6 and 100.8 so in this case 100.8 is lesser than all these three values so actual cant we can conclude the 100 mm and we we can calculate basis on the CA and CD so again putting all the values we are getting the value of 110 kmph as the the the speed considering the CA and CD now we can conclude the maximum speed on this curve is 110 because sanction speed itself is 110 and calculated is coming more than that we have to take least of that so that comes to 110 and we have to provide 100 mm as a super elevation actual cant in this case so these are the references I have used for preparing this presentation thank you