It certainly takes quite strong wind to drag our chain out straight (and I mean strongish by our standards eg a longish 40+ knot
gust in moderate nominal 20 knot
type conditions has never been long enough, as far as I have observed).
I think forces from waves are less than many think also. I have tried to get some idea of the magnitude of those but is a complicated dynamic thing (haven't looked on his site for a long time but I recall
Alain Fraysee said words to the effect it is all too hard and too many variables). The examples I tried working through used foredeck accelerations based on Marchaj's "Seaworthiness" which are for boats underway (so higher) and a pitching angle of 20 degrees which I would suspect means an untenable anchorage.
The force to accelerate the chain is not really significant - one has to remember it is accelerated most at the bow roller and not at all at the point it hits the sea bed
and the acceration direction varies according to where one is on the cable. What impulse loads from waves on the boat are I have not looked at but as long as anchored bow to waves (which would, of course, be normal unless one has a stern anchor out which would not seem a sensible thing to do if the sea conditions were concerning) I suspect these are quite low.
There are actually some plus's in that if the bow pitches up 20 degrees AND no chain is lifted off the bottom then the catenary deepens so the forces in the chain from the catenary reduce - by over 12% if the water depth
is 15m, cable length to point it hits the bottom is 50m and pitching 20 degrees. If chain is lifted from the bottom then the reduction is not so great dependant on how much is lifted, but if water depth
is 15m, and all the pitching height is lifted from the sea bed
with 20 degree pitching there is still a slight reduction in catenary forces.
In all that the lines of the boat make a big difference to the magnitude of the cable loads as do its longitudinal mass moment of inertia (in that it affects pitching angle), any tendency to resonant pitching and the boat's length.