What resources would you recommend if someone wanted to run the numbers themselves for some rigging puzzles?
You replace your standing rigging with synthetic and figure you could shorten the keel a couple inches and have the same stability. How would you calculate that?
You are comparing two boats and want to calculate the margin of safety that the two builders used based on observed rigging.
You are thinking of replacing your chain-plates with titanium, how much smaller can you make them considering that titanium is several times stronger than steel.
You use a load cell to measure the force required to banana a boat with the for-stay and back stay. How do you calculate is that is the right amount of stiffness or if the boat has lost structural integrity?
In every case the answer is ask a navel architect.
But if such a person is not available or you want to check their work how would you make the calculations yourself?
Such 'numbers' arent directly ascertainable as each 'architect' uses and applies additional 'safety factors' to the structure. The applied safety factors (increasing the strength or geometrical shape/amount of material, etc.) are based on a 'historical average' of what worked, what didnt work, how LONG in time the component has been in service, etc. .... and usually are arrived at or are reported by underwriters or insurance carriers --- called 'historical scantlings'. Especially in a 'boat' where there are repetitive applied or cyclical stress is applied, how 'strong' (tensile or compressive stress) a material is comparatively insignificant when fatigue (embrittlement, etc.) is probably the predominant failure mode; and where good design for fatigue and the special properties that lessen fatigue failure is more important than 'strength'.
I wouldnt go so far as to say 'ask a naval architect' either, as marine structure does fail, and fail more often than 'static' design. I'd rather delve into the material sciences that govern all the 'weirdness' (of shape/geometry, of materials morphology, etc.) that controls 'dynamic' applications. The 'ultimate' is of course to dynamically and destructively test in exacting/same conditions in order to understand and to develop 'time or cyclical' under dynamic loading constraints so to better apply the 'correct' safety factor.
As regards 'titanium', unobtainium, and impossiblephorus ... the jury is still out as titanium, etc. has not been in service all that long especially in marine design so that engineers and designers are SURE that the long term effects in service are 'all that well understood'. 300 series stainless, when most of our current boats were designed (and that includes their rigging) had not come to the 'evolution of knowledge' that it has today .... about 40 years after the fact; and, builders still use this vulnerable material - vulnerable to fatigue, crevice corrosion, etc. etc. and improvement is by simply by 'bumping up' the amount of safety factor and the 'geometry' of the component 'may' work, or 'may not' work. The applied safety factors are to cover 'unforseen and unpredictable untowards effects' --- dont mess with it, let it 'evolve', naturally, and by the reports by the insurance carriers who advise of such scantling failures in marine service, including your insurance carriers recommendations to 'its time to replace'.
Youre definitely not going to improve by building or changing to 'stronger', its much much more complicated than that.
It takes a wee bit more than a cookbook/handbook and list of 'material strengths', it takes design and materials 'evolution'. Imagine the cost of a boat if all the metal structure was 'titanium', even if we dont know all the long term effects of titanium - called the cost of diminishing returns.
If you really want to be 'sure', build a new one and dynamically test it until total failure under the exact expected conditions, understand correctly & completely the failure, and then make small changes so that you 'slowly evolve' into 'better'; rather than, changing the whole set of underlying circumstances that puts you back firmly to 'square one' in the constantly evolving design process.
Lastly, if your 'redesign fails', and wasnt 'approved' by your insurance carrier or you cant prove that the redesign completely and under all conditions was 'better', guess who is going to pay for and be ultimately responsible for all that includes the catastrophic failure caused by your 'redesign'?