Journey times, and re-thinking filtered permeability

On a recent trip to the supermarket I happened to notice a driver turning into the car park at roughly the same time as me. Obviously this isn’t something you would normally dwell on, but in this particular instance I happened to notice the same driver entering the supermarket building itself some time later – when I already done a good deal of my own shopping.

What had happened? Well, I can park my ‘vehicle’ right by the entrance of the supermarket, something the driver wasn’t able to do.

Screen Shot 2016-02-08 at 11.24.42

They had obviously had to circulate around the car park, looking for a space, parking their car, and then walking all the way back to the supermarket entrance.

This set me to pondering on a bit of maths in an attempt to establish just how quick a car is at short trips, compared to cycling. You might think a car will ‘obviously’ be quicker at getting from A to B – after all, it just goes faster. But as my anecdote hints at, the basic problem this straightforward analysis overlooks is… parking.

Cars are big, and difficult to store. That means when you get to where you actually want to go to, you won’t actually be able to get there. By that I mean, it is very, very unlikely that you will be able to park your car right where you want to go to, either because someone else has got there first, or because there’s so much (induced) demand for parking where you are going to it has to be spread out over a large area (or on multiple levels), or because the area you are going to is somewhere that restricts parking altogether, because it’s not very nice when streets you want to visit are clogged up with cars that are either parked, or being driven around in search of parking spaces.

This isn’t the case with cycling; you will almost certainly be able to park exactly where you want to, especially if you have the kind of bike that has a built-in lock (the convenience of which I’ve written about before). So we have to factor in something ‘extra’ into the time taken to get from A to B by car – the time you are walking to or from your car, once you have parked it, to actually get to or from ‘B’.

So I came up with this rough little equation to establish the distances at which cycling time is approximately equal to driving time, adding in the extra walking time involved with driving. It equates cycling time (on the left) with driving + walking time (on the right).

Screen Shot 2016-02-07 at 23.42.11

  • is the actual distance from A to B;
  • SB is cycling speed;
  • SC is car (driving) speed;
  • DW is the walking distance, from parking stop to final destination; and
  • SW is walking speed.

Now we can plug in some values. If we take cycling speed to be 10mph, walking speed to be 3mph, and driving speed to be 20mph, we get the following –

Screen Shot 2016-02-07 at 23.53.38

And with a bit of rearranging, we arrive at –

Screen Shot 2016-02-07 at 23.55.19

What does this mean?

Well, it tells us that for our starting assumptions of speed (20 for driving, 10 for cycling, 3 for walking), cycling time is equal to driving (+ walking) time when the walking distances is 0.15 of the distance from A to B.

So – to take an example – let’s say I had to choose between cycling or driving for a short trip from A to B of 1 mile. In this case, if the walking distance from the parking to the destination is 240 metres (0.15 of 1 mile), then I can expect to arrive at the destination at exactly same time if I cycled or drove. If the walking distance is greater than 240m metres, then obviously the bike will be quicker.

For shorter trips the equation obviously tilts further in favour of cycling – for a trip of half a mile from A to B, you’d have to be able to park within about 100m of the actual destination for driving to match cycling.

How realistic is this? I think it’s fairly accurate, and if anything a little generous towards driving, for a couple of reasons –

  • 20mph is probably quite an optimistic average speed for driving in urban areas – it assumes no queues or congestion, and no traffic lights.
  • the equation doesn’t account for the extra driving time spent driving around looking for a parking space near the destination.
  • nor does it account for the actual ‘parking’ time; time spent shuffling your car in and out of a space.

To return to my supermarket example, I think the driver who entered car park at the same time as me probably had a walking trip of around 100m – a reasonable assumption based on the size of the car park. I’ve shown a typical ‘walk’ below, from the mid-point of the car park.

Screen Shot 2016-02-08 at 11.28.20

Of course the driver would have to have driven to this spot, and maybe a bit further, circulating around to look for it. That means if we both had to travel half a mile to get here, he would have gained nothing (in time, at least) by driving.

The equation tips further in favour of cycling when we examine ‘as the crow flies’ distance, rather than the actual travel distance, because driving – even somewhere as car-friendly and cycling-hostile as this town, Horsham – tends to involves longer routes than cycling. To take just one example –

Screen Shot 2016-02-08 at 11.42.02Here a short car trip to Sainsbury’s of nearly one mile is significantly longer than one by bike, principally because someone on a bike can use the short cut indicated by the red arrow, but someone driving can’t. The ‘crow flies’ distance here is around 600m; the cycling distance approximates to 900m, while the driving distance is a far less favourable 1400m.

The red arrow is actually an example of filtered permeability – a residential area which drivers can access with their motor vehicles, but can’t drive through. This makes it a pleasant area to live in, and has the side benefit of making cycling and walking trips more closely aligned with ‘crow flies’ distances, compared to driving.

This whole mathematical exercise got me thinking about filtered permeability in a different way. Essentially –

Filtered permeability only ‘punishes’ the kind of car trips that weren’t worth making in the first place.

Yes, filtered permeability will make your 0.5 mile car trip significantly longer, perhaps even twice as long. But that’s the kind of car trip it really doesn’t make sense to drive, because cycling will almost certainly be quicker over that distance, once we factor in the kind of details considered in the maths here. This is, in fact, precisely the case with the example I’ve used above. A car trip from A to B (Middleton Road to Sainsbury’s) would actually be costly in time terms, compared to cycling, even without any filtered permeability in place.

For longer car trips, however, of say 2-3 miles, the effect of filtered permeability is more negligible, perhaps adding only 5-10% to the overall journey time. So filtered permeability is only really a ‘problem’ for driving for those trips that are actually more time-consuming to make than going by bike, or even walking.

Now of course I fully acknowledge that cycling isn’t an option for most people in urban areas because of the hostility of road conditions – indeed, that’s pretty much what this blog is all about. So the kinds of comparisons here won’t work for most people, simply because they have to choose between walking and driving, and the equation here isn’t anything like as favourable as a cycling/driving comparison, because of the lower speed of walking.

This might explain why new ‘filtering’ schemes attract such a great deal of opposition in Britain; it’s because people are driving short trips of under a mile, and because the only realistic alternative is walking. Cycling is the missing piece of the puzzle, one that will unlock the benefits of ‘filtering’ and demonstrate just how inefficient short car trips in urban areas actually are, compared to the alternatives.

Of course to unlock that potential cycling has to enabled, and that means constructing environments that work for all users – protected routes on main roads, and genuinely quiet routes on residential streets, which will involve (ironically enough) filtered permeability. So this is something of a chicken and egg situation – the arguments in favour of filtered permeability rely partly on the benefits of a mode of transport that people aren’t currently prepared to use, and won’t be using until these kinds of schemes are in place.

But I think it is certainly helpful to consider just how painful driving is, in time terms, for short trips, when arguments and discussions about ‘filtered permeability’ are happening.

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36 Responses to Journey times, and re-thinking filtered permeability

  1. Danny Yee says:

    My commute to work is like that. Even if there were no traffic, driving would only be marginally faster than cycling, because of direct routes for cycling through central Oxford, and once you throw trying to find parking in there’s no comparison

  2. ORiordan says:

    I think this point is more applicable to the advantages of cycling for shopping rather than an argument for filtered permeability, but your equations and example are for a trip to a single destination.

    For a High Street with multiple destinations the advantages of cycling can be even greater. Taking my local High Street as an example, the majority of shops, cafes and restaurants are within a strip about 900m long. On a bike I can go from place to place to place and park the bike directly outside. In a car, a driver will either waste considerable time trying to do what a bike can do and go to multiple parking places, or keep the car parked in one place and spend a much longer time walking or, more likely, not bother visiting places that are too far away (that parking space being charged by time…)

    And shopkeepers still seem to think that providing better facilities for people on bikes will be the death of the high street…

  3. baoigheallain says:

    “This isn’t the case with cycling; you will almost certainly be able to park exactly where you want to,”

    Except if your journey terminates in Westminster where you can search for ten to fifteen minutes for somewhere to lock a bike; all the Sheffield stands are full with commuters’s bikes, there are no parking meters any more, and most buildings have “bikes locked to this railings will be removed” signage.

    It’s one of the reasons my Brompton has become my bike of choice for London centre trips; it comes with me and I save a large percentage of my trip’s whole time expended.

    Nevertheless, I agree with your good article. Cycling sure is the missing link in UK infra.

  4. Danny Yee says:

    Also, walking around and through car parks is often really unpleasant. Most of them force you to share space with cars for at least some of the way, and the multi-storey ones throw in dark, dingy stairwells or slow lifts as well. It amazes me that people who wouldn’t dream of walking 500 metres to the shops on reasonably pleasant residential streets regularly walk hundreds of metres around car parks without thinking twice about it.

  5. Clive Durdle says:

    Pucher city cycling discusses this, and interestingly includes the time spent at work to earn the money and pay the interest to buy the vehicle 🙂

  6. John says:

    Interesting article. Really highlights how our towns and urban environments are designed for cars, rather than to be efficient in terms of time by residents in moving around to undertake everyday local trips such as shopping, getting to school etc.

  7. Ollyver says:

    There is currently a proposal to close a residential London street to motors at one end. This was, unfortunately, branded as “for a cycle route”, and there are strong views on both sides. Apparently, it was actually at least partly proposed because local councillors were getting so many complaints from residents about through traffic, asking for the road to be closed.

    So which residents have strong views against the closure? Apparently those at the end with the closure, whose drive to the supermarket would now take 5 mins instead of 2. We stared in disbelief at the councillor explaining this: the alternative route from their houses is a 2 minute walk across a wildflower garden. I do not envy the councillors trying to reconcile the two sides!

  8. Tom says:

    I think the formula should be modified slightly if we assuming that the driver does not drive further the actual distance from A to B. It would then be
    \frac{D}{10} = \frac{D-D_W}{20} + \frac{D_W}{3}
    however this does not alter the result significantly and since we have made many assumptions it is probably not worth bothering.

    • Hmm, I think it might balance out. Sometimes the driver will find a parking spot short of the destination, sometimes they will have to drive some extra distance beyond it. But as you say it probably won’t make a significant difference to the outcome.

      • Tom says:

        Yes I think you are right about that. If we assume that that there is an equal chance of having an extra distance or no extra distance, then it would be D + D_W or D - D_W so the average would be your formula.

        • Jitensha Oni says:

          The problem is with D in the formula. It should be the Dd the distance you drive and Dc the distance you cycle. If Dd = Dc then the formula is correct, but Mark’s picture from Sainsburys’s clearly shows it isn’t (by a few metres) . In the limit, where the Dd-Dc is more than a few metres, 🙂 if you wanted to shop in the Market Place in Kingston upon Thames, Dd would be > Dc and Dw would be an additional distance. Which is why the numerous bike racks in Kngston are usually pretty much full in shopping hours.

  9. Notak says:

    Certainly agree that filtered permeability only “penalises” car journeys not worth making anyway, though I’d put the limit a bit higher: more like 2 or 3 miles than half. In fact, for half a mile it’s hardly worth getting on the bike, in terms of time over walking! But one thing you miss when discussing FP is that it also creates a much more pleasant environment and so is conducive to walking and cycling (and other street activities), especially when done so as to remove through traffic from a whole area rather than individual streets.

    • “In fact, for half a mile it’s hardly worth getting on the bike, in terms of time over walking!”

      Yep, for the same reason that bike beat car, walking beats cycling for short trips, unless I’m on my way somewhere else (although this will be exactly the same for drivers: for example one of the reasons people might do the school run by car is because they need to drive to work afterwards).

      On my bike I have to unlock bike at one end, possibly fix lights to it, attach pannier to bike, actual journey may be longer due to one-way system or no cycling route, find parking at end, get out lock, find keys, lock bike, remove pannier, remove lights if necessary. Reverse for way back. I don’t wear a helmet or hi viz for short journeys, but some people do. Not a big deal in the context of a longer journey, but it’s faff I can do without for a short one. I’ll actually trade a slightly longer journey time just for the ease of walking.

      • Tim says:

        This is why I rarely put my bike away during the day. And I never take the lights off at home, but if I did it would literally take about 5 seconds – just a click – to put them back on. I often wondered how it takes people 5 minutes (or whatever the time difference would have to be) to make a bike street-ready. Gosh, unlocking a lock, such a lengthy laborious task! Weird.

    • Tim says:

      I would always get on a bike to go a couple of hundred metres rather than choose to walk. It’s quicker *and* easier, and I’m lazy and impatient like that (despite running the odd marathon for fun – that’s different). I’m pretty sure cycling is at least twice as quick regardless of distance.

      Of course (and I think Mark has mentioned this before) it depends on the (in)convenience of getting a bike out, putting lights on it, whatever. In countries where cycling is more mature, they’re less likely to have to carry a heavy bike down three flights of stairs (for example) before they can get on the seat, and lights and locks tend to be built in.

      • “I’m pretty sure cycling is at least twice as quick regardless of distance.”

        That’s obviously untrue. You wouldn’t cycle next door, for instance. Nor to the one next to that. Nor the one next to that etc. At some point, the additional distance will be great enough to offset the extra work involved in using a bike. Quite where that is will depend on a number of things: where your bike is kept, where the cycle parking at the other end is, what accessories you have, what the road layout is etc.

        Our local is about 100m away, and my housemates beat me back home comfortably if I cycle (because I’ve cycled from somewhere else and gone straight to the pub).

        Nearest shop is about 500m away, and cycling probably is quicker, although as I mentioned, not being bothered with faff means I will usually walk it anyway. I’d say it’s marginal. Further than that distance I’ll normally cycle, unless I’ve a particular reason not to.

        (I actually do have dynamo lights, and they’re great. Except when the wires break, as has happened to me recently. Back-up solution is battery. Wouldn’t use integrated lock alone for security reasons).

        • Oh, and walking speed is also a factor. I’d understand why someone who walks with a stick has got a lower threshold for walked distance than someone who does 4mph consistently. Also relevant: whether you wear heels regularly or not (I don’t).

          • Notak says:

            And ease with which one walks, independent of speed. For people who find a bicycle a useful mobility aid it is, of course, worth cycling 500m. It might not even be possible to walk that distance but you might be able to cycle it.

  10. “This isn’t the case with cycling; you will almost certainly be able to park exactly where you want to, especially if you have the kind of bike that has a built-in lock”

    Aha-ha-ha-ha. Not where cycling is popular: and we are basing this on the idea that cycling should be more popular, right? 😉 Remind me to take you to the Grand Arcade cycle park at the CEoGB AGM, on a Saturday.

    And I wouldn’t trust a built-in lock for use in the UK, for anything other than a couple of minutes, ideally where I can see it, anymore than I would recommend people lock bikes to themselves only, rather than use a cycle stand.

    But it’s still easier than parking a car in Cambridge.

    • Personally, I’m reasonably happy to use my built-in lock for shopping, etc, when I’ll be leaving the bike for relatively short periods of time. That’s mainly because my bike is very heavy by UK standards, so to steal it you would essentially have to load it into a van!

      I’m also counting on the unfamiliarity of wheel locks to UK thieves – my guess is that a thief would hop on the bike in an attempt to ride it away, find they can’t, and then panic.

      And generally in Dutch cities there just is actually very little in the way of ‘cycle parking’ in shopping locations; people do just park their bikes in rows, then come back to them. It’s going to be more difficult to find a spot than the UK, certainly, but much easier than finding a car parking spot nearby! 🙂

      • “And generally in Dutch cities there just is actually very little in the way of ‘cycle parking’ in shopping locations; people do just park their bikes in rows, then come back to them.”

        I actually found this a bit unfair on pedestrians! Nowhere is safe from cycles when they can be self-supporting and parked anywhere! I did sometimes find I had to single file to get past bikes on pavements, and in those cases people in wheelchairs are going to have problems. I’d like to think that nobody would position permanent racks so ungenerously.

        Generally a great place to be a pedestrian: quiet, slow, few cars taking up large amounts of space or causing visibility issues. But I did struggle with the cycle parking practices, and it’s one of the few things about how the Dutch do cycle infrastructure that I’d not want to emulate.

        • Yes, ‘excess parking’ can be an annoyance on some streets – but (in my experience) these tend to be the ones that are still excessively dominated by motor traffic, where footways are just too narrow, or where there’s still plenty of car parking.

          That’s not to say it isn’t a problem, just that the ‘cycle parking issue’ is really still one about the way space is allocated on streets, even Dutch ones!

      • Corey says:

        I think there’s a psychological element to casual locking. Even in cities with high rates of bike theft, it’s generally the prevailing culture that determines what is and is not appropriate for securing bicycles. Here in the US, there tends to be a collective fear of bike theft that prevents acceptance of keeping bikes parked outside or parked with wheel locks.

        When I’ve tried to park my Dutch bike with only the built-in lock for a short run inside, that culturally ingrained fear makes me feel uncomfortable about the situation. I’ve even had non-cyclists express concern about my choice of bike security – they’re worried for me! The idea of keeping bikes parked outside overnight is especially taboo here.

        So I wish I could take a more convenient and casual approach. But there seems to be quite a bit of pushback in a non-cycling culture.

        • Cambridge has certainly got a cycle culture, but there are also high rates of theft. While it’s not necessarily unusual for people to lock bikes to themselves (integrated locks less common here) I can’t say it’s something I’d advise, and most people do lock to cycle parking (or lampposts, fences, tree guards, street signs etc) if available.

      • HivemindX says:

        This was exactly my thought. I wouldn’t be at all happy to leave my bike using only a wheel lock. If lots of people started doing this I imagine supermarkets are going to get pretty unhappy with their entryway being crowded with bikes. How many could reasonably be left if the position in the picture before they start to block access?

        In general I agree with the point. Parking is a mess and when I arrive in the city centre on my bike I am in a FAR better position to find a more convenient and cheaper place to leave my bike. Lots of shopping centres I go have bicycle parking in convenient locations. However there are also lots that don’t, they either have bicycle parking hidden away somewhere in the depths of the car park or you end up cycling around the entire place to discover they don’t have any.

        Ironically I’ve heard people complain about how hard it is to park cars at commercial centres and then go on to say that it is wasteful to have bicycle parking whenever that space could better be used to squeeze in an extra car space or two.

    • neil says:

      The frame locks do have sockets for plug in cables or chains, so you can easily lock _to_ something if you want. Of course that means finding a bike rack, lamp post, whatever.

  11. On filtered permeability, I find people rarely make the same complaints when you have a development which is deliberately dead-end in order to avoid through-traffic, than when you take away a route that already existed, even if the result is the same. On a development where through-traffic is excluded it’s a positively saleable feature!

  12. CRGardenJoe says:

    Interesting post and formula. In the U.S, there is usually a bike rack that is not always logically or conveniently located (at my gym, the bike rack is at the far end of a sidwalk away from the curb cut by the door, situated to require me to cycle past the door on the way to the rack–when there is the same empty rock edge to the building that would allow the rack to be right by the curb cut, and it could be placed so a biker would rarely cross the paths of pedestrians going to the door). So there often is some walk time even when you ride your bike to a store or business. Still, because the racks are always closer than the majority of parking places in the parking lot (we don’t have “car parks” here, I guess our cars are too uptight to play), the basic premise of your post is still accurate. I add about 15 minutes to a 15-minute trip by riding my bike to work–but save at least a 5-minute trudge up a hill from the parking lot, so I’m only adding 10 minutes to my actual travel time. And, of course, the whole trip is far more pleasant because I’m in the world rather than encased in a traveling metal cage.

  13. congokid says:

    “choose between walking and driving, and the equation here isn’t anything like as favourable as a cycling/driving comparison, because of the lower speed of walking”

    The other benefit cycling offers is being able to let the bike carry the weight of the shopping, rather than your arms.

    My nearest supermarket is equidistant by bike and car, just about half a mile away, but on the bike I have the option of a quiet riverside route that is shared with pedestrians, many with dogs, but which is a pleasure to use compared with the often busy road which is a rat run for motorists as well as a bus route.

    As it happens, Google maps suggests the journey takes the same time by bike or car – 3 minutes.

    Before the riverside route was created – previously it had been industrial land closed off to the public – I went by car to the store. To avoid the hassle of driving, I restricted myself to big weekend shops, and I’m sure I also often created big shops simply to justify driving, but I hated it so much that eventually I switched most of my shopping online, first from Tesco and later Ocado.

    Then my car was stolen, not to be replaced, and my shopping experience was transformed when I started going by bike. The hassle of big shops and parking woes were banished and I happily make trips not only to the nearest supermarket, taking in the great riverside vistas along the way, but also others in the area, returning home to offload in between if necessary.

    Even mundane grocery shopping is a joy compared with the chore it used to be.

    I don’t think anyone has mentioned it here yet, but is there any organised lobbying of supermarket groups for improved cycle parking provision – or, even better, safe, dedicated transport infrastructure to approach them? I’m sure they can’t be blind or deaf to the growing heap of data on how more cycling boosts retail business. Those with enormous car parks could really benefit by turning over much of that space to bikes and attracting cycling customers.

  14. Highwayman says:

    I like your article. With a few tweaks hear and there, you can submit this as an opinion column in your local newspaper.

    You make use of your algebraic formula correctly and take time to define your variables. Too many writers forget to do that (or maybe too many editors strike such details from final copy). Still, for those of us taught in a foreign school system (such as America’s public “educamation” system), it would do well that you included all the steps in the algebraic exercise you walked us through. I can decipher the leaps of algebra well enough, thank-you, but still it did take me about 10 minutes for me to check your algebra before continuing reading your article.

    I might use your article, or more likely, just your formula in whatever deliberations I might involve myself.


  15. Ovalone says:

    i think one thing that doesn’t help with most supermarkets is actually accessing the cycle parking – often you either have to behave like a car (ie ride a long loop down a vehicle feeder lane (with no breaks allowing you to turn off and then through a the car park) or make an illegal manoeuvre to behave like a pedestrian (eg cycling on the pavement area). I’ve never seen a UK supermarket with a logical arrival route for cyclists.

    • Notak says:

      I can’t imagine anyone objecting (with any degree of seriousness) to cycling on the pavement round a supermarket, as long as it’s done respectfully. After all, that’s where the cycle parking is!

  16. Right now our group of residents: FumeFreeStreets ( is trying to use the argument of journey times (albeit without the formula!) and also environmental and community impact to persuade residents/visitors/all of the benefits of supporting filtered permeability in London Fields/Hackney.
    We’d appreciate support for Option 1 in our local council’s consultation if you can spare about 3 minutes:

  17. I timed a trip I can make on bicycle and another I can make in a car to the nearest grocery store. It’s 870 metres away by bike and by car it’s about a kilometre, give or take about 150 metres of driving distance. On a bike I can do the cycling assuming 20 km/h in about 3 minutes (if a stop sign was replaced by a yield/give way sign), by car it takes at least 3 minutes, often more due to a traffic light (though that could be a roundabout) and a couple minutes more due to parking. Assuming I can use a wheel lock, I don’t have to fiddle with a U lock and cable on a bicycle, making the park bike process a few seconds long process.

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