Will L wrote:Hallow Russ, I'm probably thinking of you here.
Coincidentally, Will, I added a new section to the CSB page yesterday on CofG placement. (It will need further amplification in due course.)
Although it is quite simple to derive the CofG position from a set of known or nominated axle weights, for example those plugged into the spreadsheet, I have struggled to derive the converse relationship in the 3-axle case, namely what a set/sets of axle weights would or could be from a nominated CofG position. I thought it should be possible, but I can't isolate the variables in the resolved moment equations, and I think the situation is indeterminate. (In fact I think I have proved it is indeterminate, unless I'm missing something obvious.) I suspect a reverse iterative method could be fruitful, but it's longwinded. The 2-axle case is simple, and the 4-axle case may be partially solvable by symmetry (I haven't tried that yet), but the nasty one is the 3-axle case. Btw, this problem is not specific to CSBs.
It would be useful to give the CofG position on the spreadsheet from the nominated static axle weights*, since it is only the actual implementation of that position in a constructed model that will realise those intended nominated weights. I think we are all aware of the importance of accurate balance - what we don't have a collective handle on yet is the effect(s) of CofG positioning errors. Intuition says that such errors should have slightly less effect on an 8-coupled than on a 6-coupled, but intuition and springs is a dangerous combination, particularly with CSBs. I'll try simulating your O4 leading axle de-loading.
It's a refreshing change to know that at least some people here are interested in this sort of thing.
I'm not particularly enamoured of full-length CSBs for 2-4-0s, but I've been running some simulations on an intentionally de-loaded uncoupled axle. Initial conclusions are that CofG placement and implementation are very critical if porpoising is to be avoided and the coupled axle loads are to remain reasonably equal.
* I'll give it a try later.