Well, I've come up with a new idea; calculate the centre of gravity of the structure and then put the front posts there.
Why...
This allows me to retain the same 'cantilever' design concept, which my friend is so keen on, but it also addresses the main 'flaw' in the design as it eliminates the tipping force in either direction. In theory I would then only need to secure it for wind, which is a smaller problem to deal with.
I'm still interested in maybe using those staddle stones, and haven't decided on fixings yet - either way, by placing the posts in a central position I can minimise the problem, and the risk.
So for those interested, I used the principal of leverage and 'moment arms' to find the CoG. And because I don't trust my calculations, I then checked the total moment on either side of the new calculated CoG to verify it was exactly equal on each side. To my amazement it was
Short version
So to cut a long story short, using spars of 1600mm in length, the CoG is 372mm from the rear post. If I drop from 13 spars down to 12 it shifts it even further back, to 357mm.
Here is the resulting design, dotted line the CoG at 372mm:
Long version
I've no idea if anybody finds this interesting or useful, but I thought it was a good thought experiment, if slightly ridiculous, and it had pragmatic application for me as it pretty much solved my problem (I think), so it might be handy for others too. So here are the details.
There are three components
1. Spars (100 x 50 x 1600), qty 13
2. Support rails (150 x 50 x 2000), qty 2
3. Posts (100 x 100 x 2300), qty 3
I didn't bother including density in the calculations as all components are the same material, and therefore I just worked from volume - the ratios are all the same and it eliminates one variable to mess around with, winner! So essentially I have set density at '1' to get mass. Although I suppose it might be interesting to put in the correct density and get the weight of the structure at some point. Anyway...
For the initial calculation of 'X' I set the arbitrary datum as the centre of the rear post, this eliminated a lot of messing around because it sets the moment arm at zero for two of the three components (because they are lying on the datum and hence moment is zero).
When calculating CoG I temporarily 'removed' the front posts - these will get added in later once I know where to put them (i.e. the position of the CoG). Essentially, this
simplified structure with just the 3 rear posts is what I am trying to 'balance'.
Initial calcs
result and calc check
Latest plan with the pergola
I plan to put the posts at 400mm from rear posts, not 372mm, this puts a little more weight on the rear posts and makes it more stable. I also have the diagonal braces which I deliberately didn't include in the CoG calcs, this adds a little more weight to the back again so makes things even more stable. Finally, the spars hang out 100mm at the back, which I also eliminated from the calcs. Because there are 13 spars this is the equivelent of 1.3m of additional timber extra at the very back of the structure, again moving CoG further backwards than calculated.
I will still have two groundscrews and a mixture of staddle stones and/or resin anchors on the other posts. So I'm pretty comfortable with this now, as I say, it only has to resist wind movement now so the fixings are doing less of a critical job than before.
Martin
