 Hello viewers. I welcome you all for this today's session on types of canned. This is part of geometry design of railway track. I am Ashok Kumar, Assistant Professor Department of Civil Engineering, Valchand Institute Technology, Sulapur. Learning outcome of the today's session. At the end of the session, students will be able to differentiate different types of the cans and their permissible limits. In the previous session, we have derived the equation of superelevation, that is, equilibrium superelevation, taking the equilibrium speed. And today, we will see that what are the different types of the cans related to the geometry design of railway track. The first can is equilibrium can. So when the speed of a vehicle negotiating a curve is such that the resultant force of the weight, so here we have a resultant force. It is due to the centrifugal force and the weight of the vehicle which is acting downward. So now this resultant force of the weight of the vehicle and the radial acceleration is perpendicular to the plane of the rails. So what does it mean? So this resultant force is due to the weight of the vehicle and centrifugal force. This should act perpendicular to the plane of the rails. If this condition satisfies, to make this condition satisfied, we have to raise the superelevation such a way that the resultant force should be act normally perpendicular to the plane of the rails. It means the distribution of the load on the both rails are equally distributed on the both side. If this satisfies condition, then whatever the raising for to make this condition to happen, that superelevation is called as equilibrium can. And the speed which you have considered to derive this superelevation is called as equilibrium speed. Now what speed we have to consider for calculation of the equilibrium speed or equilibrium can? It is average speed or weighted average speed. How we are going to calculate the weighted average speed? Considering the all kind of the vehicles. Here N1 indicates the one speed, low speed. N2 indicates the high speed or N3 indicates the medium speed. So taking the weighted average, so that will be called as average speed. So here N1, N2, N3 are number of trains. And V1, V2, V3 are speed of the train in KMPH. So for all the majority of the Indian railways are to be provided with this equilibrium speed or average speed. So again, we have to take the suggestion from the chief engineer or track engineer, those who designed this track to decide this average speed or equilibrium speed. Now we also know that in the previous session how to derive the equation for broad gauge and meter gauge and narrow gauge. So these are the equations we have derived. Taking the various forces and resolving the forces with respect to the slope surface, these are the equations for broad gauge, meter gauge, and narrow gauge to calculate the equilibrium count. Now let us come to the another concept is count efficiency. Count efficiency occurs when train travels around a curve speed higher than the equilibrium speed. So it means all the vehicles are not travel with average speed or equilibrium speed. Some of the vehicle may go beyond the equilibrium speed because we need to save the travel time or the cost consideration. We have to allow the some of the trains to go beyond the equilibrium speed. Again, having this count efficiency. So what is the count efficiency here? It is difference of theoretical count required for high speed. Let us say the high speed is say 120 and your equilibrium speed is say 90 KMPH. So you calculate the two super elevations. One, this is theoretical. We are not going to provide this in actual ground. But the actual ground, we are going to provide the actual count. But the speed, it is going 120. So calculate the theoretical count required for 120. And for actual count, that is 90 KMPH, whatever so. So take out the difference of that. So that is called as count efficiency. So what is the limitations that difference should not exceed? So as for the broad gauge for the type of the train A and B, they have fixed the maximum count efficiency. This difference should not go beyond 75 mm for broad gauge. And that is for the group A and B. This is the A and B decided based on the high speed trains. C and D will be low speed trains like this. They have grouped this depending upon the speed. They have decided the group. So now maximum how much you can go beyond 75 mm? Up to 100 mm, we can go count efficiency with again approval of the chief engineer, those who designed the track. So with that permission, we can go up to 100 mm. It means we are allowing the vehicles to go beyond equilibrium speed, having this count efficiency of 75 mm. For meter gauge, it is 50. And narrow gauge, it is 40 mm. Another one we have a count excess. So here you can see here count excess. Again, this is for the low speed vehicles. The just previous session, the previous slide, we discussed about the high speed vehicle. And we should also restrict the vehicle to go lesser than the equilibrium speed. So that is what we call as count excess. It is occurs when train travels around a curve, speed lower than the equilibrium speed. It means whatever the equilibrium speed, some of the vehicles may go lesser than the equilibrium speed, like goods or passenger trains. They may go lesser than the equilibrium speed. So for those speed, this equilibrium speed, the whatever the count you have provided for the equilibrium speed, that itself becomes access because they are going with very low speed. And for that, we know that for low speed, the requirement of supervision is very lesser. So in that condition, if you are allowing the vehicle to go very, very lesser than the equilibrium speed, in that condition also, the vehicle may not go derail, out turn on the outer side of the curve, it may fall inner side of the curve. So it is going to overturn on the inner side of the curve. So that is why we have to restrict the vehicles to go very lesser than the equilibrium speed. Again, the count excess is axial count provided for the equilibrium speed and theoretical count required for the lower speed. So this difference, again, that should not be more than 75 mm for broad gauge. So if this difference exceeds, again, the vehicles which are coming with very low speed, they are going to overturn on the inner side of the curve. So with this picture, we can understand clearly. So this is your inner rail and this is your outer rail. Whatever the Vmax you provide it, that is for the high speed vehicle, you can provide 120 kmph. So that it is called as the ethereautical. So ethereautical is from this location, from this point to this point. Now what is the count efficiency here? This is your E actually is whatever you provide in the actual ground or actual field. So this is your, taking the average speed or equilibrium speed you have calculated the E actual. Take out the difference of ethereautical minus E actual that gives your count efficiency. So this count efficiency, this difference should not exceed 75 mm for broad gauge. So if this difference is exceeds, it means your track is not supposed to take that speed that may, your centrifugal force may come into the picture and resultant force may fall outside of the track and that condition, your vehicle is going to fall on the outer side of the curve. So we have to allow the vehicle to go up to this, allowed to go for a maximum speed considering this count efficiency. They should not go, this difference should not go, exceed 75 mm. If that exceeds, you are not able to control the centrifugal force or resultant force. What about the count excess here? You can see here count excess is the, in this case, this is the ethereautical for the low speed vehicle and again E actual. So if I take out the ethereautical for the low speed and E actual, so again this difference, this difference also should not exceed 75 mm for broad gauge. It means if you are allowing very lesser, it means this difference is goes beyond 75 mm. It means you are allowing the vehicle to go very, very less speed. So that condition, the vehicle will have, will face the centrifugal force will be very, very lesser here and that case your vehicle may fall on the inner side of the curve. So for safety consideration, we should not allow the vehicle to go beyond count efficiency and also should not go lesser this count excess. So this is what the count excess and count efficiency. So now you can pause over here and think for a moment and give the answer for this. You can locate where is the count excess and where is the equilibrium count and count efficiency looking at the resultant force. I hope you are able to locate these three terminologies. So you can see here the first one is count excess because you are provided very high super elevation. It is equilibrium super elevation provided but the vehicle is going with very low speed. In that condition, the super elevation is very, very higher for the low speed and resultant force, what is happening resultant force? It is gradually shifting inwards. It means the vehicle will over turn on this side. Okay, this is the count excess and perfect condition is equilibrium count. You can see here the resultant force is normal to the plane of the rails, perpendicular to the plane of the rails. It is perfectly acting and the load is balanced on the both the rails and count efficiency it is gradually shifting, resultant force is gradually shifting on the outer side and you will see that the outer rail will have a very wear and tear or rubbing action between the outer wheel and the rail. So this is the count efficiency but up to the 75 mm your track can able to take this the higher speed but beyond the 75 mm your track is unable to take this higher speed. So that time the vehicle will over turn on this side. So with this small animation video we can understand what is count efficiency. Let us play this video. So this is the wheel flange should not touch here. We know that if it is touches in this side it is going to be a very heavy rubbing force. It has happened. So vehicle going with equilibrium count. So this is continuously welded rails. Maximum count is allowed 150 mm but for Indian conditions we are going up to 100 mm. So this is what the count efficiency over here. You can see here this is the actual raising. This is the actual count is provided. Whatever the average speed we have taken and provided the actual count. And this is what your count efficiency. So this the additional the safety we have taken. This is for the high speed vehicles we are able to take this consideration and allow this much the the count efficiency we have provided. And this can take care the vehicles negotiating with very high speed on the course. So this is the deficiency but beyond that your track is unable to take the particular load. So in this case 120 mm is the actual count provided and 60 mm is the deficient. So it means that this is you can go up to 160 mm with having 60 mm deficiency. These are the references I have used for preparing this presentation. Thank you.