Abstruse CSB Theory
CSB source book summary of the Abstruse CSB Theory Thread, which is for people who are actually interested in the way the spreadsheets used to sort out CSB fulcrum placement go about their business. There is no doubt this is a minority interest and can tend to confuse. Therefore, for those just wanting to know where to put their CSB fulcrums, this is distinctly NOT compulsory reading.Relationship between Axle weights and CofG
The thread starts with 4 posts which bring out the fact that, while it is simple to calculate where a locos Centre of Gravity (CofG) is from the weight carried on each axle, for a sprung chassis you cannot easily reverse the calculation. That is, you can't easily work out from actual location of the CofG what weight will be carried by each axle. To do so requires that you know a great deal about the characteristics of the springs. Much of the discussion that follows stems from this simple truth.A worked CSB Example for a symmetrical 6 coupled chassis 7’0” between the wheels
This starts with a post from John Bateson concerning his calculation of a set of CSB fulcrum points which produced a highly volatile solution, not like the robust outcomes I was claiming. This is followed by a series of posts that discussed the fact that there is always more than one possible solution and that he had chosen an extreme one. 3 more stable possibilities are provided. Each solution has slightly different characteristics. One post contains a diagram
which I still find useful to help visualise these differences, and determine which solution to choose. Justification and Development of Fulcrum placement calculation software
The latter two thirds of the thread is taken up with a discussion of the numerical methods used by the spread sheets to calculate fulcrum positions. The original Roger Wyatt spread sheet goes about it in a way that isn’t immediately intuitive, and a lot of the discussion here was around determining if it was in fact valid. This led to Alan Turner writing a new spread sheet, using a totally different method, which magically turns out to give the same answers. That is at least when considering the fulcrum point placement, which was the whole point after all. There is still stuff about the weight distribution which we will eventually come back to. In defence of the CSB Spread Sheet
This was the only set piece posting in the midst of the discussion, in which I finally managed to explain the circumstances in which the Roger Wyatt methods was an applicable and effective tool. I'm not sure Alan was ever fully convinced.
The practical upshot is that we now have two different methods for approaching the same job, implemented as spreadsheets. These have different characteristics giving you a choice of which one you feel most comfortable with. The results are the same. While copies of Alan's spread sheet are contained within the thread, anybody wanting a copy should download the most recent versions from theCLAG website