 Hello viewers, I welcome you all for this today's session on geometry design of railway track. In this class, we will try to discuss about the speed on track, various types of the speeds on track. Myself, Pashok Kumar, Aston Professor, Department of Civil Engineering, Walchand Institute Technologies, Swalapur. Learning outcome of the today's session, at the end of the session, students will able to differentiate different types of speeds used in railway track and also calculate the speed with respect to the given cant or computed cant or superelevation. So in the previous session, we have discussed about the various types of the cans, that is equilibrium cant, cant deficiency, cant excess and negative superelevation. So in this class, we will discuss about the different types of the speeds used in the railway track. So we know that speed is the rate at which we are covering any distance and every train is allowed to move three speeds actually. One is average speed, maximum speed, maximum speed may be on straight track or on curves. So here, we are going to see that what kind of the speed we are going to provide in the railway track and how we are going to running these speeds in different types of the tracks. So first, we will see about the average speed or equilibrium speed. Then we will come to about the maximum speed or say permissible speed. The various speeds depends on the length of the section and number of stoppages. We know that in the average speeds, we are going to consider what is the length of the each section. If the number of stations are there and in between, we have number of sections. So how many stations it is covering and how many length it is covering. So depending upon that, we will decide the average speed. And we know that it is distance divided by the total time will give the average speed. So let us see how we are going to calculate the average speed. In the previous sessions also, we have got to know the average speed or weighted average speed is calculated n1v1 plus n2v2. It is taking more or less the weighted average of all the vehicles which are number of vehicles are travelling with different speeds. Coming to the next speed is after average speed is maximum speed. So we have to, not always we have to go with the average speed. Sometime we need to go with higher speed, maximum speed where we considering number of stoppages are lesser. So because it is no use that if you are having more number of stations and you are saying we are going with higher speed, maximum speed here. So as the number of stoppages are lesser, then only we are going to accelerate the vehicle and get that particular maximum speed. By the time you are going to accelerated and then you will receive one more stations. That means that you are going to reduce the speed and again you are going to get a time for acceleration and de-acceleration. So there we are not going to call that is a maximum speed. So here wherever we have number of the stoppages are lesser, that is possible to go with the maximum speed. So again we have to reduce the travel time. For that we are going with the maximum speed and when you are going provided the particular track with higher speed, ensure that the safety measures are taken care or not. Otherwise there might be possibility of the accident also. Some of the high speed corridors which I have taken over here is Amdabad-Numbay or Pune corridor, Amdabad-Numbay Pune corridor where we are traveling up to 350 kmph. So some of the Gatiman Express 160 kmph, then Rajdhani, Shatabdi, all these trains, they are nearly reaching up to 150 kmph. So in this case we should think about the safety, whether the proper safety measures, our track is able to take this speed or not, whether we have proper super elevation or not. So these things are taken care when we are deciding this the higher speeds. After the maximum speed, we have another speed is maximum sanctioned speed. So we know that the maximum sanctioned speed is defined by the track engineer. Again we have to take permission of the chief engineer, the particular person designed the track engineer. He knows what the maximum I can allow beyond this the maximum permissible speed. This is only used during the emergency condition with again with a prior permission of authorities. Without that we are not supposed to go with this maximum sanctioned speed. Now the issue comes here, if you are going in a state track, we are not having any issue. But when you are vehicle is traveling on curves, there we have to definitely define the what is the safe speed or maximum permissible speed on the curves. On the curves, we have may be constrained with the radius or degree of the curve or may be constrained with the your transition curve. So if you have any side constraint, we have to define the safe speed on curves. Otherwise it will be end up with the derailment of the track on that or there is an wear and tear of the track due to the higher speed on that particular curve. So now for any track, they should move with the speed which is lesser than the safe speed or maximum they are attained this up to the safe speed, we can attain it. But preferably to go lesser than this safe speed. So after this only we have a maximum permissible speed. As I told you the sanctioned speed comes after this safe speed. It means we have the another speed after the safe speed is maximum sanctioned speed of the track. But again that to be used only during emergency condition with prior permission from the track engineer. Otherwise you are not supposed to go with reaching up to sanctioned speed. So on the straight track in this case is limited by the maximum speed defined bar for every train. So every train is defined what is a speed has to travel on that particular track. Now take a pause over here and think for a moment and answer this question. Section scaring less goods traffic higher value of can't access should be allowed and for section scaring predominantly free traffic value of can't access allowed should be kept low. What is the answer for that? I hope you are able to select the true or false. The correct answer is a true. What are the factors we are considering in the safe speed over here? We are considering that what is the safe speed for the curves? Depending upon the type of the gauge we have broad gauge, meter gauge and narrow gauge considering the various width we may select what is the safe speed. And radius of the curve we know that the radius is directly related into the safe speed as the more the radius is we can negotiate that particular curve very easily, lesser radius we have to restrict the speed. Super elevation again the super elevation we know that it is the square of the directly proportional to the square of the velocity and inversely proportional to the radius. Again considering the speed what kind of the radius and what kind of the speed we have to decide the what is the super elevation and safe speed. So transition curve length some due to the always better to go with a transition length. Transition curve provides the introduce a centrifugal acceleration gradually if you have any restrictions in the length of transition curve then there you have to require to reduce the safe speed or permissible speed. And we have to always try to put this resultant force center of the track considering the resultant of the centrifugal force and weight of the vehicle. Now we have Martin's formula to calculate the safe speed for broad gauge and meter gauge you can see here for transition curve is V equal to 4.4 square root of r minus 70 and V is in kmph r is in radius meter. For non-transition curves we have 4 fifth of the speed calculated using equation 1. For non-transition we take the 4 fifth of this value that will be your safe speed. For narrow gauge we have V equal to 3.65 square root of r minus 6 and again it is subjected up to 50 kmph. Again for non-transition curves we have V equal to 2.92 square root of r minus 6 and again subject to 40 kmph. But Indian railways are not using no longer using these equations. So what are those equations they have modified let us see in this. So these are the equations considering the they have defined the safe permissible speed considering the can't access, can't deficiency and actual can't provided. So here on broad gauge we are using this railway board formula that is simplifying 0.27 square root of CA plus CD multiplied by r. Again here is CA is the actual can't or equilibrium can't and CD is your can't efficiency and r is in radius and meter. And on meter gauge you have 0.347 square root of CA plus CD into r and narrow gauge we have 3.65 square root of r minus 6 again subject to maximum of 50 kmph. For this is for the previous slide which we have discussed it is for the transition curves whenever you have a no restrictions of transition curves there is no site constraint of transition curve in that condition this the formula holds good to calculate the safe speed. So when we have non-transition curves so we have non-transition curve with can't this is how we are providing the virtual transition that is 14.6 meter on broad gauge and 13.7 meter on meter gauge and 10.3 meter on narrow gauges. For non-transition curve with can't we are providing the super your safe speed to calculate your safe speed considering the can't gradient not to exceed 1 in 360 on broad gauge and 1 in 720 on meter gauge and narrow gauge. So non-transition curve with no can't we have permissible can't efficiency to be gained or lost or use rate of change of can't efficiency as 35 mm per second for broad gauge and 55 mm per second for meter gauge. So curve with inadequate transition we are providing the actual can't or can't efficiency with considering to its limiting value or considering rate of change of can't efficiency within their limits. So now how do you calculate the maximum permissible speed on curves we are taking the least of this comparing the calculating the four speeds by this method and taking the least of the speed limits mentioned over here. So first we have to take care the maximum sanction speed of the train that is authorized by the commission of railway safety first we this is the first speed we have to take it and second speed is considering the can't efficiency and considering the actual can't we are calculating the what is the safe speed. So this is the second the safe speed we are calculating considering the can't your actual can't and can't efficiency and third one it is based on the low speed vehicle that is considering the good strain they are traveling with the lesser speed. So for that also we are calculating the speed and fourth criteria considering the transition curves corresponding to the length of the transition curves. So consider the speed for all this four method and take the least of the value as the safe speed and also we have to consider the maximum can't efficiency is 100 mm and can't access is 75 mm on broad gauge and 65 mm on meter gauge while calculating the your safe speed. So these are the references I have used for preparing this presentation thank you.