Optimal stop spacing and travel distance
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).
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 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.
 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.
 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%
26th May, 2014 01:20:55
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EAP Women's Trophy with Adam Cassidy; Associate and Affiliate Cricket Podcast
There were three tournaments of note at the beginning of May. Europe Division Three, won by Belgium, not without a scare, and the ACC Premier League, won by Afghanistan are reviewed in depth with Andrew Nixon (@andrewnixon79). As are the Ireland-Sri Lanka and Scotland-England matches. Then Adam Cassidy (@butchy77) from the ICC East-Asia Pacific office joins Russell Degnan (@idlesummers) to discuss the EAP Women's Trophy, preparations for the Asian Games, what next for PNG and his book An Ocean of Cricket. There is news of tournaments in Africa, tours to Ireland, and trouble in Bulgaria and the USA. And we discuss a little sporting history and the politics of exclusion.
Direct Download Running Time 1:12min. Music from Martin Solveig, "Big in Japan"
The associate and affiliate cricket podcast is an attempt to expand coverage of associate tournaments by obtaining local knowledge of the relevant nations. If you have or intend to go to a tournament at associate level - men's women's, ICC, unaffiliated - then please get in touch in the comments or by email.
24th May, 2014 17:13:59
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Monday Melbourne: CCC, May 2014
Returning to the beginning. Taken May 2014
20th May, 2014 22:08:09
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The Gastronomic Pub Crawl of South Melbourne; The Limerick Arms
364 Clarendon Street, South Melbourne
(Corner Clarendon and Park Street)
Until recently, the Limerick Arms was the pub you found on local shop-a-dockets offering two-for-one meals. It made the place seem cheap, an impression enhanced by the basic bistro, pool table, copious tv screens covering multiple sports, and the proximity to the glinting stainless steel and glass frontage of Honey.
It is cheap, but in a good way for meals, being priced well south of $20. The pot pie caught my fancy, of chicken and vegetable with a lot more of the former. The chips were thick and crusty, but perhaps needing a few minutes more, while the salad was oily. The steak my companion ordered was similarly accompanied, and the main of similarly good standard.
The crowd at the Limerick varies from quiet to rowdy depending on the night, but wiith plenty of sport on offer in the next month, it might be worth visiting more often than I do.
The Short: For watching sports and playing pool
20th May, 2014 21:40:27
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Monday Melbourne: CCXCIX, May 2014
Southbank in fog. Taken May 2014
13th May, 2014 23:04:11
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Mode Choice and Rational Commuting
Amongst the various comments about the proposed Metro line and the new station at Fishermans Bend, certain forms of analysis stood out, not for their accuracy, but their falling back on cliched understandings of travel, and the limitations of simple analysis in complex areas.
There are issues with the new proposal, mostly around the absence of long-term strategic planning in favour of project lists, which is not a new complaint.
There are fewer issues with a station at Montague, notwithstanding the commentary suggesting otherwise. Jason Murphy is normally very good, but his use of coverage diagrams merely highlights their limitations. Coverage is only as valuable as the service being connected to, the services that service connects to, their frequency and the line speed. Moreover, residential coverage is meaningless in the context of an area with several major destinations (the conference and exhibition centre, and South Wharf) and the expectations of significant future employment. What matters is the way that area connects as a destination. A connection to South Yarra and Southern Cross is potentially very useful; if debatably similar to the proposed (if unlikely) connection to Newport and Flinders Street.
The complaint of both Daniel Bowen and Tony Morton that residents would not use the station to connect from the light rail is in a similar vein: correct but basically irrelevant, if the stop is considered as a destination.
But they highlight a more general transport problem that is worth noting and explaining:
Public transport has big trade-offs for short trips
This often comes under the problem of the last mile, whereby a trip that ends at a transport hub needs a short connector that is hard to serve efficiently. But the problem of serving the last mile is true generally for short trips.
Consider someone within the residential area of the proposed Montague station, working in the CBD. In general, the potential user won't be either next to the residential station or working at a station in the loop. For the sake of argument we'll put them 400m from each.
As a walk, it is 3km into the centre of the CBD, or around 30 minutes. A trip to Docklands would be shorter, other parts of the CBD potentially longer.
As a train trip is is two walks of 400m (or 8 minutes), two trips through the station and onto underground platforms (2-4 minutes), waiting for the train (2-5 minutes), and a 2km trip on the train to Southern Cross (3 minutes). Somewhere between 15 and 20 minutes, most of which is spent walking and waiting.
On any transport, the walking distance can be shortened by reducing stop spacing. But here again, there is a trade-off in travel time as the stops add minutes, and the transport spends more time accelerating and decelerating at lower speeds. A tram with a 200m stopping distance would quarter the walk on average (2 minutes) but stop six times (5 minutes), and take 6 minutes to make the trip at the lower speed. Making the trip, including wait time, between 13 and 18 minutes.
In his piece on Fishermans Bend Alan Davies sourced a graphic showing walking lengths very substantially by mode in Melbourne. Most likely, this reflects two things: firstly, that stopping patterns are shorter for buses, and therefore the walk is naturally reduced; and secondly, that, although the environment has some effect on preferred walking distance, commuters are largely rational with respect to walking distance and time. Train journeys are longer, and walking is more efficient than the poor connections available in suburban Melbourne (on which, more later).
That being the case, the "rule of thumb" noted by Jarrett Walker of stop spacing between 400 and 800 metres is flawed. If we assume for rational commuters trying to minimise time, for a given trip length, there is an optimal stop spacing where walk time is offset by the speed of the transport. Because commuters go vastly different lengths this distance actually varies, and is often substantially longer than 800m. Though as a future post will show, this is complex; for large metropolitan areas, connections matter, a lot.
But on a short segment such as to Fishermans Bend, where most CBD/Docklands or local trips will be between one and four kilometres, there is no time advantage to having a heavy rail line with stops a kilometre apart through the area. The maximum possible trip is a mere 7km, which just barely goes past 1km as an optimal spacing. Stop spacing of a kilometre is double the optimal length for most of those trips. Yet on heavy-rail, any further shortening of those stops is impossible, and would both: effectively make the service a very expensive light-rail line; and were there a Newport connection, significantly slow suburban passengers.
The graphs below show the various trade-offs, although they slightly over-simplify the longer stopping lengths as at some point it becomes quicker to just walk, and wait-time is eliminated.  Notice too, that the optimal stopping distance is, as expected, between 400 and 800m for trips in this range.
There may be a future capacity issue in Fishermans Bend, given the projected population, and there would be a case for a station in Wirraway that connects to local transport in the event the South Morang-Newport connection occurred. But the future residents of the suburb will be much better served by efficient (and substantially cheaper) light-rail/tram lines. The vast majority of their trips (and the only ones reliably performed by public transport now) are too short to gain anything from services better designed for much longer journeys.
 Some assumptions need to be noted: 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. It reflects averages; the transport time and waiting time will vary, obviously.
10th May, 2014 19:40:19
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The Gastronomic Pub Crawl of Fitzroy; The Napier Hotel
210 Napier Street, Fitzroy
(Corner Napier and Moor Street)
A pub that barely needs any introduction. The Napier Hotel has retained the cluttered front bar and sprawling eating spaces for as long as I can recall. Photos indicate that the clutter is a steady accumulation of years of history rather than a modern affection, and it is a popular place for both regulars and semi-regulars for a decent meal and interior warmth on classic pub furniture. Upstairs gives way to an art gallery befitting its place in the centre of Fitzroy's gritty - not entirely gentrified heart.
Burgers or roo are the specialties and we had one of each; the later sliced onto a parma in place of ham. That gae the parma a particularly rich taste, though not too filling, which was the concern. In any case, the salad and fries are merely adequate and not to the same standard as the parma itself, so there are options to leave a plate unfinished. That is perhaps unsurprising, given the price is reasonable, and reflective of the Napier's standing as an institution.
The Short: For cold nights and lazy cooks
10th May, 2014 16:33:41
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