How can we get more stretch from a bridle?
More length. Yes, but there will also be losses from friction. In the left center (below) illustration the stretch would be 5 feet in 50 feet, given the assumptions about line size and stretch, but it is only 4.5 feet because some force is subtracted by friction over the bow.
Double around a low friction ring (left illustration). The problem here is that we lose a lot of tension going around the ring. They are only 70-75% efficient in a 90 degree bend (testing). Stretch goes down to 3 feet and a new chafe point is introduced. What if we use a thinner line (center right illustration) to increase stretch? The safety factor stays the same and stretch goes up to 3.4 feet. The only way the doubly method comes even close is by using pulleys, and it is still less efficient.
What about energy absorbed by friction? Yes, that is valid, but work is still force through a distance and the damping distance is still reduced. The same effect would be had by using one size larger rope, and without the chafe risk.
In fact, there is fourth case, (left), where the stretch increases to 8.4 feet, using a 0.5:1 purchase. In stead of rigging the bow as a 2:1 purchase, a line runs forward, but on the side deck a reverse purchase is rigged, so that the forward line moves twice as far as the side line stretches. Complicated, though.
