# Stuck in the 20th century

So for our trip to Denmark next week, I had a question about tickets for local public transport.

Specifically, it wasn’t clear to me after reading their—Danish—web pages whether “tickets are valid for one trip” meant, for example, one bus ride, or one connected trip, which might involve changing busses and/or trains. So, for example, whether a trip with bus + train + bus would require one ticket or three.

Coming from Hamburg, the obvious answer to me seemed to be “one ticket”, but then the fact that they said that single “clip cards” “bruges som omstigningskort” confused me; that semeed to be “werden als Umstiegskarte gebraucht” = “are used as tickets for when you change [busses/trains]” to me.

So I thought I’d send them an email and ask.

But the contact information I found said that if you have inquiries about tickets and prices, you get to talk to a person: either walk up to the counter or phone them. No email address. *sigh* How 20th century.

So now I wonder whether I’ll give that a shot tomorrow (when things will be open again after the public holiday) or whether I’ll just ask at the counter at the railway station when I get there.

Another question I had was about the validity of round trips: that is, literally travelling in a (topological) circle where you pass one station more than once, or end where you start, but where it’s a single trip rather than a “go somewhere, stay a bit, and come back [possibly via an alternate route]” situation. One ticket, since it’s one trip? Or do you need to artificially break the trip into two parts somewhere and use two tickets? And how would the price be calculated? Specifically, I was thinking of going Lemvig–Thyborøn–Lemvig–Vemb–Holstebro[–Struer]–Lemvig, and wondered whether that would be one ticket, two, or three. I was kind of hoping for two: one for Lemvig–Thyborøn and then another ticket for the figure-6-shaped route T–V–H–L. But I could imagine having to “break” the second journey in, say, Vemb.

Or the other trip I had considered: Lemvig–Bækmarksbro by bus, then back to Lemvig by train (or vice versa, depending on how the connections end up). One ticket or two? In favour of “two”: you’re going “there and back”. In favour of “one”: the route you take back is rather than different than the way you go there, so you’re not simply doubling back and it could be considered a continuation of the first trip.

Relatedly, one thing I like about the local fare system is that it’s based on rings rather than zones. So while there are zones, the fare depends not on how many zones you travel through but on how far away the furthest zone you pass through is from the origin. (That furthest zone will often be, but need not be, the zone containing your destination.)

As an example, if you travel from Lemvig to Ramme by train, you go from zone 40 to the adjacent zone 43, so you need a ticket for two zones: straightforward enough. But if you take the bus to Fjaltring, you go from zone 40 through zone 37 to zone 43—but you still only need a ticket for two zones, because you’re never more than one zone away from Lemvig (you essentially go left and then down, while still staying inside the hypothetical “ring” formed by all zones that are immediately adjacent to Lemvig). And if you take either mode of transport to Bækmarksbro, you still pay only for two zones, whether by bus (40–37–43–42) or by train (40–43–42), since zone 42 “Bækmarksbro” is also adjacent to Lemvig (even if the two zones only touch at one point; I imagine it may be significant that a bus route crosses over that point).

An interesting consequence of this, though, is that the price for a trip can depend on the direction; for example, Lemvig–Holstebro–Struer seems to be 4 zones to me while Struer–Holstebro–Lemvig seems to be 3 zones to me. This is because Holstebro and the adjacent Linde zone are both adjacent to Struer, so they both count as “one zone away” for an origin in Struer, but they’re “behind one another” when coming from Lemvig, so they both count as increasing the number of zones from the origin when starting from there.

(If you want to follow along with those calculations at home, this document shows, for each possible origin zone, how many zones away every other zone in the fare area is, and this document shows the zone numbers and the routes of the busses and trains through the zones.)