Who is Scott?

The name figures in a formula to determine line capacity in the Indian Railways. There's no clarity about how it got attached to the formula

Every area or discipline has its own jargon and the Indian Railways (IR) is no different. One of the most opaque of terms is “line capacity”. On the face of it, this shouldn’t be.  The simplest definition of capacity is something like the following: “The maximum number of trains that can be moved in either direction over a specified section of track over a period of 24 hours.” This is easy to understand, but understanding can be deceptive. There are interrelated elements, like the number of trains, average speed, stability and heterogeneity. As the number of trains increases, capacity decreases — an obvious point. If average speed increases, everything else remaining the same, capacity decreases — not that obvious. That’s because when average speed increases, braking distance increases more than proportionately.  Stability is about margins and buffers between trains. The idea is to prevent delays from getting amplified, so that there are no negative effects on the running of other trains. Finally, heterogeneity is about speed of trains running on the same track. If this difference is large, everything else remaining the same, more capacity will be consumed. This is not a problem IR alone faces. It’s an issue for all railway networks. In 2004, the International Union of Railways (IUR) prepared a code for measuring capacity. Because of the use of French, IUR is abbreviated as UIC and this code is known as UIC Code 406. That listing of the elements of the number of trains, average speed, stability and heterogeneity is from this code.
 
Here is a quote from this Code. “A unique, true definition of capacity is impossible... Given the various consequences of capacity-relevant constraints, a generally applicable definition is not appropriate.” A section, or block section, is a stretch of track between two railway stations. Any “average” distance between two railway stations is misleading. If both stations are within a city or urban network, it can be as low as 1 km. But outside urban networks, the distance can be 10 or 15 km.  A block section is thus 10 or 15 km in length. However, there is a slight problem in understanding a block section from that perspective. More accurately, a block section is that part of the track between two block stations into which no train can enter the first station in that block until a “line clear” has been obtained from the block station at the end of the block. That is, a block section is really defined from a signalling angle.  With conventional signalling, perhaps a block section is 10 km long. But with automatic signalling, that same stretch of 10 km can be divided into multiple block sections. 
 

TRACK CHANGE Most people in the Indian Railways will say they use Scott’s formula and then say they don’t use it because it is too rigid and theoretical. Photo: iSTOCK

In 2015, IR brought out a white paper that mentioned 1,219 sections in the network. It said 40 per cent (492 out of 1,219) of sections have a capacity of more than 100 per cent. That’s overall. Along the high-density network (loosely, those between metros), 65 per cent have a capacity of more than 100 per cent.  Sometimes, capacity is more than 150 per cent. Most of the network is now broad gauge. Let’s say 60,000 km is broad gauge; 60,000 divided by 1,219 is almost 50 km. Clearly, this “section” cannot be the same as a “block section”.  It is too long to be a block section. This “section” consists of several block sections and is roughly the distance between two junctions, not two stations.  This takes us to the more important question: If capacity is difficult to measure, how does IR quantify it? There will be a mention of Scott’s formula, which goes something like this. During a 24-hour period, there are 1,440 minutes.  Take away the time required for maintenance, say, 120 minutes. This leaves 1,320 minutes. Add running time taken by the slowest train to pass that section to time required to prepare that section (meaning signalling and stuff) for the train to pass. Divide 1,320 by this number. Now multiply the result by 70 per cent. This is known as efficiency factor. It scales down capacity available, because time distribution of trains isn’t uniform and some time is lost. This kind of Scott’s formula is applied to “block sections”, not “sections”.
 
Most people in the IR will tell you they use Scott’s formula and then tell you they don’t use it, because it is too rigid and theoretical. It can’t take into account issues such as type of signalling, mixed traffic, infrastructure at junctions and loops. Therefore, rules of thumb, deviations from the transparent template of Scott’s formula are used.  For a given block section, you draw time along one axis and distance along the other and plot all passenger trains.  Wherever there are free paths, insert goods trains. Insert maintenance blocks and whatever else is required. This method, known as the master chart method, thus gives the number of trains that can pass through a block section.  Plug in the actual number of trains and you get capacity utilisation. This sounds much more confusing and complicated than Scott’s formula, as indeed it is.  But then, every discipline has its own jargon and we don’t work for the Indian Railway Traffic Service (IRTS).  However, no IRTS officer I have asked has been able to answer my question:  Why is Scott’s formula mentioned in Indian discussions on capacity utilisation but not in the international? Who is Scott? (Perhaps some reader will write in with the answer.) I suspect it might have something to do with the 1922-23 Scott and Budden Committee on revision of Indian Railway statistics, but I can’t vouch for this.

The author is chairman, Economic Advisory Council to the Prime Minister. Views are personal