Deutsche Bahn use a fairly reasonable and systematic numbering scheme for designating their locomotives. Numbers are of the form xxx yyy-z, where xxx is the Baureihe (Class) and yyy the serial number. z is a checksum.
The three-digit class numbers work like this:
- 0xx -- steam locomotives
- 01x and 02x -- tender engines for express passenger trains
- 02x and 03x -- tender engines for passenger trains
- 04x and 05x -- tender engines for freight trains
- 06x and 07x -- tank engines for passenger trains
- 08x and 091 through 096 -- tank engines for freight trains and shunting
- 097 -- rack locomotives
- 098 -- old locomotives for local trains
- 099 -- narrow-gauge locomotives
- 1xx -- electric locomotives
- 10x and 11x -- passenger service
- 12x and 13x -- universal locomotives
- 14x and 15x -- freight service
- 16x -- electric shunters
- 17x -- locomotives incompatible with 15 kV / 16-2/3 Hz AC
- 18x -- multisystem locomotives
- 2xx -- diesel locomotives
- 20x through 28x -- road diesels
- 29x -- diesel shunters
- 3xx -- small shunters
- 31x -- power class I (up to 29.4 kW)
- 32x -- power class II (29.4 - 110.3 kW)
- 33x -- power class III (110.3 kW - 480 kW)
- 38x -- battery-powered
- 4xx -- EMUs
- 40x -- high speed
- 42x -- commuter AC
- 47x and 48x -- commuter DC
- 5xx -- battery-powered EMUs
- 6xx -- DMUs
- 60x and 61x -- long-distance
- 62x through 69x -- short-distance
- 7xx -- service and maintenance vehicles and rail buses
- 70x through 78x -- service and maintenance
- 79x -- rail buses
- 8xx -- motorless EMU trailers
- 9xx -- motorless trailers for DMUs and 7xx-series vehicles
The second and third digit for 8xx and 9xx trailers are always the same as on the corresponding 4xx, 5xx, 6xx or 7xx MU.
The three-digit serial number is 001 for the first vehicle in a series. Vehicles of the same physical class may be classified under two different classes because, obviously, the serial numbers only allow for a maximum of 999 vehicles per class.
To obtain the checksum that goes after the dash:
- Replace the second, fourth and sixth digit in the number with the doubled digit; i.e. 110 184 becomes 120 288 and 111 049 becomes 121 0418
- Compute the sideways sum, i.e. 21 for 100 184 and 17 for 121 0418
- Subtract the last digit of this result from 10 unless it's 0; thus, the complete numbers are 110 184-9 and 111 049-3.
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