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Monday Melbourne: CCCV, July 2014
Russell Degnan

Flinders Lane. Taken July 2014

Melbourne 22nd July, 2014 21:38:25   [#] [0 comments] 

Monday Melbourne: CCCIV, July 2014
Russell Degnan

VCA. Taken June 2014

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Monday Melbourne: CCCIII, July 2014
Russell Degnan

Winter's morning sunlight. Taken June 2014

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Monday Melbourne: CCCII, June 2014
Russell Degnan

Federation Bells. Taken May 2014

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Monday Melbourne: CCCI, June 2014
Russell Degnan

Fitzroy Gardens in the rain. Taken May 2014

Melbourne 3rd June, 2014 00:42:32   [#] [0 comments] 

Optimal stop spacing and travel distance
Russell Degnan

In my previous post on stop spacing I made the point that for short trips - particularly the last mile shortening stop spacing counter-acts the benefits of shorter walks because the transport slows down. Efficiency and speed is currently under-rated - in comparison to connectivity and frequency - in transport discussions (at least in Melbourne). It shouldn't be, for two reasons: speed is the primary determiner of the route and travel method chosen; and faster transit leads to faster turn-arounds and therefore fewer trains and drivers for the same frequency. A 20% improvement in travel speed doesn't increase capacity (that remains throughput) but it would have massive implications for recurring costs.

In this post I'll discuss trips of varying lengths, in order to make a simple but important point: in a walk-transit-walk environment optimal stop spacing is a function of travel distance. A secondary point will also be made, with caveats: that for many systems, particularly in Melbourne, stop spacing is much too close. (A point made in relation to trams in Melbourne by Jarrett Walker)

Firstly a few assumptions. Adjusting them may make some small differences - and if anyone wants the spreadsheet I did this on, just ask - but less than you might think. For the sake or argument I am assuming a grid with even density, so average walking distance is equal to stop spacing at both ends of the journey: half the users will walk less than half stop spacing, half will walk more than half, with those in the centre of the grid traversing half in both a N-S and E-W direction. The transport in question has a 1m/s2 acceleration and deceleration time, with intersections ignored (ie. light-rail, either grade separated or gated), a 40 second stop penalty, 5 minute waiting average, and a walking speed of 5km/h. Graphs will reflect averages; walking, transport and waiting time will vary, obviously.

But to emphasise, again, adjusting these numbers makes very little difference to optimal stop spacing: waiting time is a constant, and only matters if someone can walk the distance faster - ie. for very short trips. Otherwise walking and transport speed are minimised at the point where transit speed is not compromised by frequent stops: the major factor in determining optimal stop spacing is the distance being travelled on transit (given a particular walking speed)[1].

Optimal stop spacing in a walking only environment

Below is the journey speed for a 4km trip, given the assumptions above. There are two things worth noting. Firstly, that optimal stop spacing is 850m, which is outside the generally accepted range for short-ish trips of this kind. Secondly, that the cost of sub-optimal spacing is much higher on the short side. A 400m stop spacing is of a piece with a 1700m stop spacing, and the cost of reducing it further much higher.

There is an important, and unresolved tension then, between two conceptions of walking to transit: is the commuter rational, and therefore willing to walk whatever distance affords them the fastest trip, where speed is all that matters; or are they unwilling or unable (speaking here of the general population, not the mobility impaired - and of a decent walking environment, as that can be fixed) to walk further, even if it meant faster transit? This graph from VISTA data (courtesy Alan Davies), would indicate that people are willing to walk reasonable distances for trains (which on average have longer travel distances), but may merely indicate that many train stations are further apart. Similarly, while there is a significant clustering effect around train lines in Melbourne, that is in part because the stop spacing is short, and therefore geared for short walks.

The graph below shows the optimal stop spacing for various trip lengths. The levelling out at 2km is a function of the maximum travel speed of the transit, but shows that except for very short trips the optimal stop spacing is in excess of 1km, and growing. Keeping in mind the previous point that longer is better than shorter, a large percentage of commuters in Melbourne are suffering excessively long travel times.

Optimal stop spacing with a connecting transport

While Melbourne has an high percentage of walking only access to trains, this is probably a reflection of both poor local connections, and the short stop spacing that allows extensive walk-up access at the expense of travel speed. I'll cover the relative speed of Melbourne public transport in a future post. In large cities, with long commutes, feeder systems allow for a slightly different stop spacing arrangement, because they can cover for shorter trips, and allow the train system to focus on longer trips at higher speed.

In the following graphs, a feeder system, travelling at an average speed of 30k/h[2] with a 400m stop spacing takes passengers between stops with a 5min wait for a connecting service. The difference this makes to a 20km trip can be seen below:

Again two points are worth taking from this graph. The first is that a significantly longer stop spacing is optimal when there is a connecting service. The second is that the margin of error for the stop spacing on the long distance service is much higher. Anything from a 3km to 8km stop spacing gives a broadly similar transit speed because the service is mostly running at full speed. This is important, because transit must, of necessity, serve trips of different lengths. If the speed is broadly similar regardless of the stop spacing then (provided the basic minimum stop spacing is achieved) transit agencies can place stations in major centres to maximise connectivity.

The graph for optimal stopping distance across all commute lengths shows how much further out the stops can be with a good connecting service.

This conclusion is in some ways obvious: naturally transit can go much faster if it doesn't stop, and naturally systems that interact will work better. But it leads to several important points:

  • It is better to have stop spacing too long than too short, because the time penalty is significant.
  • Transit for long trips and short trips is not interchangeable. This is particularly true if transit designed for long trips has better frequencies, as it will out-compete local transit, making it redundant.
  • A system that allows bleed between the roles of different transit will be sub-optimal. Part of long term planning should be to optimise the system for efficient travel by reorganising stops and connections.

Needless to say this has important implications for Melbourne's public transport system.

[1] Here I have assumed walking is a constant, but note that even at very slow speeds (1km/h) the optimal stop spacing for a 10km trip is 650m, compared to 1300m for a walking speed of 5km/h.

[2] This would be an unusually fast service given that level of stop spacing, and most likely, a street running route. Halving this to 15km/h reduces optimal stop spacing for the rapid transit service by around 15%

Planning 26th May, 2014 01:20:55   [#] [2 comments] 


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