Wow, talk about a smoke screen. I have read this post over and over and can’t see the message. I must be really dumb. If you’re saying that 10:1 scope is less likely to drag than 5:1 then I agree, obviously that is correct. But that’s like saying is a Volvo boat going to get there before my boat? Well, obviously.
Oh, never mind. ��
No smoke screen. The math gets complicated, because the effect of the chain catenary is a function of the weight of chain out. In fact, the formulas are not that complex, but there are many variables. It's really to much to post in a forum. It's more like a chapter, with graphs.
As a rule, as the water gets deeper, there is more chain, and thus the catenary is more effective. Over 20 feet, catenary works very well even in strong winds; it's hard to lift that much chain if the scope is at least 7:1. Under 5 feet chain doesn't work differently than chain once the wind hits 25 knots; it lifts off the bottom in under 15 knots. In between, it is, well, in between. I've spent a LOT of hours on the bow with a load cell, and a lot of hours diving, checking theory against data.
What is critical is the angle at the bottom.
Less than about 10 degrees, not much change, more than 10 degrees anchor holding drops off (except for Fortress, which drops very slowly). Finally, all anchors are more vulnerable to weakening due to yawing when the chain is off the bottom, which is probably the actual cause of most dragging of well-set anchors.
I do a lot of anchoring testing. This spring I did a series of test on riding sails (3 designs). Rode types, kellets and yawing. Just yesterday I was testing several variations on bridles, though that was probably trimaran-specific. It is not a simple topic, though most of the time you can just chuck the anchor and 5:1 scope and all is well. But optimizing is complicated. You could say to same of sailing, of course. That Volvo crew could make any boat go faster!