Having a bit of a dreadful time...

Well let me start with a funny bit; This mass produced, west minster chime, mantle clock that I have just serviced took one day to do. The following morning I sat watching it ticking away nicely on my mantlepiece with cup of tea in hand. When it started to chime the fourth quarter. Merrily it chimed away - ding dong ding dong, ding dong ding dong, etc to the tune of the great clock in Elizabeth tower on the palace of westminster. When all of a sudden it went - dingdingdongdongdingdingdingdongdong! Really fast! It made me jump out of my skin. So I pounced on it to arrest which ever gear train had suddenly set itself free. After a little scrutiny I discovered the culprit; The little piece of spring steel that holds the fly to its arbor on the strike train had fallen out. So when the strike released of its warn, it raced through as fast as it could. It is remarkable the differance it makes. Having no fly. On the negative side of things I am finding it difficult sourcing a mainspring for the chime side. I bought a new 22x.40x45mm which I am sure should do the job, but I am incorrect, it is not up to it. It drives the train with reluctancy and only when fully wound. So I have been led to ask 'What are the equations of determining correct spring thickness x length for a given barrel..? The answer as you might have guessed is not easy. I am not a great mathemetician and I need hands on help overcoming this hurdle. Until then it is a case of trial and error and me loosing out on profits. :( You really have to be 100% thorough when servicing a clock. If you cut a corner it will bite you in the ass. Clocks are not friendly things. They don't like being touched.