Joel N. Weber II
Engineer
I'm trying to get a better understanding of what factors affect the shortest headways that can be achieved on a single track. Assume we're talking about a double or quad tracked railroad, so opposite direction traffic doesn't get in the way, and assume all the trains are stopping at the same stations as all the other trains, so we don't need to worry about express trains passing local trains. Also assume we aren't dealing with any stub end terminals; all the station tracks we're talking about are through tracks.
The MBTA's North South Rail Link study talks about building 1050 foot long platforms at some stations, and I assume that wouldn't necessarily include the locomotive, so it seems reasonable to assume that a passenger train might be a bit less than 1/5 of a mile long.
If the signal system knows only the positions of the trains and not their velocities, and the particular railroad were set up so that each block is 1/8 of a mile long, then a single train would normally be occupying two or three blocks at any given time. (Is 1/8 of a mile long a vaguely reasonable block size for a railroad that wants the closest possible spacing between trains? And do any of the PTC systems pay attention to train velocity to be able to space trains more closely?)
If we lived in an alternate universe where trains could accelerate to their top speed from a dead stop instantly, and could come to a complete stop instantly, that would suggest that if the blocks are 1/8 of a mile long enough, the distance from the front of one train to the front of the next train would be 3/8 mile.
But we don't live in that alternate universe, so presumably you also need to add to that spacing the stopping distance at whatever speed the trains are going with whatever grade the trains are dealing with.
And the stopping distance will increase with speed. On the other hand, if you had trains that could stop instantaneously, increasing the speed would increase the number of trains per hour you could get through the track. Somewhere, there's an optimal top speed that will maximize the number of trains per hour on the track.
And then there's also the factor that if a train is approaching a platform, it probably won't be operating at its top speed as it gets close to the platform, and that will increase the time from one train to the next.
One of the other things I'm trying to understand is that it seems to me that if track from one station to the next were infinitely expensive, and tracks at the station are infinitely cheap, you want each track linking the stations to connect to two tracks at the platform. If the reverse were true, you'd want only one track at the platform for each track linking the stations. The proposals I've seen for Boston's North South Rail Link seem to assume that you want one platform track for each track that links the stations, and I wish I better understood whether that's the best approach and why; but while you need to look at the headways that would be achieved with the two options, the relative cost of constructing a track from one station to the next vs the cost of constructing another track at a station is hard to determine accurately from what I can see.
The MBTA's North South Rail Link study talks about building 1050 foot long platforms at some stations, and I assume that wouldn't necessarily include the locomotive, so it seems reasonable to assume that a passenger train might be a bit less than 1/5 of a mile long.
If the signal system knows only the positions of the trains and not their velocities, and the particular railroad were set up so that each block is 1/8 of a mile long, then a single train would normally be occupying two or three blocks at any given time. (Is 1/8 of a mile long a vaguely reasonable block size for a railroad that wants the closest possible spacing between trains? And do any of the PTC systems pay attention to train velocity to be able to space trains more closely?)
If we lived in an alternate universe where trains could accelerate to their top speed from a dead stop instantly, and could come to a complete stop instantly, that would suggest that if the blocks are 1/8 of a mile long enough, the distance from the front of one train to the front of the next train would be 3/8 mile.
But we don't live in that alternate universe, so presumably you also need to add to that spacing the stopping distance at whatever speed the trains are going with whatever grade the trains are dealing with.
And the stopping distance will increase with speed. On the other hand, if you had trains that could stop instantaneously, increasing the speed would increase the number of trains per hour you could get through the track. Somewhere, there's an optimal top speed that will maximize the number of trains per hour on the track.
And then there's also the factor that if a train is approaching a platform, it probably won't be operating at its top speed as it gets close to the platform, and that will increase the time from one train to the next.
One of the other things I'm trying to understand is that it seems to me that if track from one station to the next were infinitely expensive, and tracks at the station are infinitely cheap, you want each track linking the stations to connect to two tracks at the platform. If the reverse were true, you'd want only one track at the platform for each track linking the stations. The proposals I've seen for Boston's North South Rail Link seem to assume that you want one platform track for each track that links the stations, and I wish I better understood whether that's the best approach and why; but while you need to look at the headways that would be achieved with the two options, the relative cost of constructing a track from one station to the next vs the cost of constructing another track at a station is hard to determine accurately from what I can see.
