The strange reason why trains in Switzerland are not allowed to have 256 axles

In Switzerland, trains can have up to 255 axles. They are also allowed to have more than 257 axles. From this you might infer that trains are allowed to have 256 axles, to which we say this: Are you trying to get us all killed?

“Um das ungewollte Freimelden von Streckenabschnitten durch das Rückstellen der Achszähler auf null und dadurch Zugsgefährdungen zu vermeiden”, explains a document from the Historical Railways of Switzerland (HECH). “Darf die efficacious Gesamtachszahl eines Zuges nicht 256 Achsen betragen.”

If your reading of the Swiss regulations is not up to par, this roughly translates to:

“In order to avoid unintentional clearing of route sections by resetting axle counters to zero and thus putting trains at risk, the effective total number of axles of a train must not be 256 axles. “

So why is this the case? As noted above, the problem is with the train axle counting. Along the railway track, detectors are placed to count the number of wheels traveling along it. These are fairly simple detectors, but which play an important role: indicating to railway operators whether this section of track is free or occupied by a train.

As mathematician, author and mathematics communicator Matt Parker explains in his book Humble Pi: a comedy of mathematical errors, the problem is that the country does not use enough binary digits in its counting system.

“Unfortunately, they record the number of wheels using an 8-digit binary number, and when that number reaches 11111111, it changes to 00000000,” Parker writes. “All trains that bring the count down to exactly zero move undetected, like ghost trains.”

In binary, which uses only zeros and ones, 254 is represented by 11111110, 255 by 11111111, and 256 by 100000000, adding a new binary digit. Since the Swiss rail system is not able to use 9 digits, this means that the count is reset to 00000000, and a train with precisely 256 axles would not appear to be there at all.

Having trains occupy sections of track without being registered could lead to accidents, for example if two trains were allowed on the track at the same time, risking crashes. Rather than updating the system, which could involve replacing hardware, the country opted to prevent trains from having exactly 256 axles (although of course any multiple of 256 would also cause the problem).