I want to query the Overpass Api to find out the distance of special relations (railways). The request is fine, and returns me all relation, way and node objects I'm interested in. Example for Hamburg:
[out:json];(rel(53.55224324163863, 10.006766589408304, 53.55314275836137, 10.008081410591696)["route"="train"];>;);out body;
In Overpass, each relation object has members defining this relation. For way objects you can resolve the lat/lon of its node attributes and calculate the distance for that way. If you sum up all the way distances it seems to be reasonable.
However, there are members from that relation of the type node (most of the time, they have a role of "stop") which seem to represent the right order of stops from that relation. But instead being in between the members, they are roughly at the end.
If I try to look the stops up inside the ways, they are not all present. How am I supposed to calculate the distance between two particular stops?
There seems to be a misconception about relations. Relation members don't necessarily have to be sorted. Consequently you might have to sort the members yourself, if necessary at all.
You can take a look at JOSM which has a neat sorting algorithm for various types of relations. But I don't think it is able to place members with the role stop at the correct position. This isn't always possible because a way doesn't necessarily have to be split at each node with the stop role. This also means a single way can contain more than one node with a stop role, making it impossible to sort the relation members correctly. Unless you do some pre-processing for splitting each way accordingly.
For calculating the distance between each stop it seems unnecessary to sort the elements. Just follow the way by iterating over all each nodes and check for each node if it has a stop role in the corresponding relation. When reaching the end of the way continue with the one which shares the same node at its start or end and which is also member of the relation.