# Is there a map or resource that represents the distance in terms of time instead of Km or Miles?

Based on this question I started wondering if there is a world map (or local maps) that reflect the distance between points in terms of time to travel and not Km or Miles.

I know such resource is not easy and it depends on a lot of variables. It will also show a completely different world. But I think it can be very useful to choose destinations and start high-level travel planning.

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Great question, at first I thought air-travel time would probably scale with distance, but maybe not. This isn't what you want but it's in that direction: bioval.jrc.ec.europa.eu/products/gam/index.htm – SpaceDog Nov 29 '13 at 10:46
isn't what google maps already does? Select two points and choose how you wanna reach the end-point from the start-point (walking, public transportation etc) – Geeo Nov 29 '13 at 10:59
@Geeo, not exactly. That's just a route on a map. I really mean a map where distance from A to B is in travelling hours and not Kms. For instance Lisbon and Madrid are 600Km away, and 1 hour away by plane. Lisbon and Coruna are 600Km away but the quickest conection takes around 5 hours. That means the maps would represent Coruna 5x more distant than Madrid. – nsn Nov 29 '13 at 11:06
@SpaceDog In principle yes, that makes sense, but there are a lot more variables than can be considered. If you take to the limit the map will vary depending on your departure point. – nsn Nov 29 '13 at 11:10
Won't it depend a lot of what modes of travel you consider? eg if Private Jet is allowed, then everywhere is pretty linear other than distance to nearest small airport, while if you limit to Public Transport it'll look rather different to limiting to car, while cycling is different again! – Gagravarr Nov 29 '13 at 11:20

Such a map is impossible, or at least it cannot be consistent. It might be possible on a 3D map.

Mathematically, I think this is because you cannot form a consistent metric based on travel distance since it cannot always satisfy the triangle inequality.

For example, imagine you have a mountainous natural reserve with a resort town in the middle, and around it there are 3 cities. The cities are linked by fast highways or train lines that encircle the nature reserve, so traveling between the cities takes only 1 hour. Each city also has a slow, winding road over which the resort can be reached in 2 hours.

On your map, the resort has to be twice as far away from each of the cities as they are from each other - but still be located in their middle! That's simply not geometrically possible.

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Not true. You could use contours to show time, rather than the traditional height. This emulates the 3D requirement on a 2D plane. – RedSirius Nov 29 '13 at 13:50
However, there remains the problem that going A>B might be quicker than going B>A. E.g. up/down a cliff. – RedSirius Nov 29 '13 at 13:52
@RedSirius not only up/down a cliff.. also in air-travel, with/against jet stream... – Heidel Ber Gensis Nov 29 '13 at 16:36
Here is an example, which I think addresses the question quite nicely (but only for NYC in the 19th century…): mnn.com/green-tech/transportation/stories/… The next step would be to generalize this sort of things in an interactive map. Getting all the data you need is a major challenge and processing it quickly enough would not be trivial either. – Relaxed Nov 29 '13 at 17:18
Travel time mostly does satisfy the triangle inequality: the time to go from A to C is at most the time to go from A via B to C, which is the time to go from A to B plus the time to go from B to C. Your counter-example respects the triangle inequality, it's just not in the middle of the segment in the travel-time space. One reasonable models where the triangle inequality isn't respected is with scheduled transportation, if the quickest route from A to C is via B there's no good connection at B. – Gilles Nov 29 '13 at 20:17

Interesting question! It is not necessarily an impossible task to create an informative visualization that will satisfy your information need. Yes if you limit yourself to old-fashioned 2d plotting, but in the world of Hans Rosling and d3.js a lot becomes possible, as long as you have the data. It might be impossible today, due to obscurity most of that data is currently hidden. With the same way of thinking I asked a question on quora. I wanted to know what an average drive-through speed is of a given highway/road/route. Once you have that data you can easily represent distances in terms of time.

In answer given, Inrix traffic is mentioned. Unfortunately, INRIX is limited to the US only and I didn't find their core data yet. So for now I am afraid that there isn't a generic approach globally. That will remain until more and more data becomes open data.

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It's been done, and here it is:

Courtesy Uchida, H. and Nelson, A. Agglomeration Index: Towards a New Measure of Urban Concentration, who came up with this for the World Bank’s World Development Report 2009. Large version here.

Now the major caveat that this map is done with a very simplified model: a city of at least 50,000 people is bright yellow, and as the distance from all cities increases, the color changes to red (24 hours from a major city) and then black (10 days). The white lines are major cargo shipping routes, which is useful if you're a container, but less so if you're a human.

So this doesn't actually account for roads, flight routes, etc, it just approximates them by assuming that lots of people = lots of transport options. Fortunately this is mostly true, although it's not hard to find bugs: eg. coastal Greenland and most of Papua New Guinea is actually fairly easily accessed by plane, whereas much of the Sahara is not, and traveling in India isn't as easy or quick as traveling in (say) central Europe.

(Edit: Oops, just realized SpaceDog already posted this in a comment several days ago. But IMHO it's worth a full answer!)

For travel time maps that uses actual connectivity information, but only work in some cities, check out TriptropNYC (pretty, but very slow and NYC only), Transit Time NYC (rougher approximations, fast, again NYC only) and Mapnificent (lots of cities, but only shows a 'boundary' of how far you can get in X minutes).

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it also doesn't indicate travel time at all. It merely maps population density and assumes that travel between any 2 points on the map with similar population density takes roughly the same time. Which would have a train ride between Amsterdam and Rotterdam (40 minutes or so) take the same as an aircraft trip between Amsterdam and Cape Town (10 hours or so). – jwenting Dec 5 '13 at 7:14

It isn't a printed thing you can hang on a wall, but Microsoft's Streets and Trips has an interesting feature that can give you something really close.

Given a starting point (and assuming an automobile), it can draw a polygon of all points that are a specified number of minutes away. If I were to give it my address and say 60 minutes, it would calculate the distance along every possible route from that point, then connect the dots to make a polygon of that time. As travel times are always between two points, you would really need to approximate time to travel in such a fashion.

Trying to get a paper version of this would require a single starting point in any event. As such, you'd have to find a visualization for each point that you might want to start from in order to color code appropriately. Because this doesn't lend itself to the economies of printing, you can safely assume the thing isn't available for purchase. That said, it doesn't mean you couldn't build it and print it yourself using a tool like this.

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Isochrone maps for a bunch of European cities:

http://emptypipes.org/2015/05/20/europe-isochrone-map/

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