I'm a bit late to the draw here. I started typing this earlier and just came back to finish it. Looks like a nice job on the line you made up today. A few points below; bottom line I am concerned the 3/16 amsteel used is not as strong as the original wire in this application.
Size the backstay to be least as strong as the original, after derating the new one to account for the differences between dyneema and steel. Hayn shows the breaking strength of 3/16" 1x19 316 Stainless wire as 4000lbs - reference here:
https://hayn.com/tech/wire_breaking_strength.html . If the original was 304 stainless wire, breaking strength is even higher at 4800lbs. If 5/32, strength is 2800lbs (316 stainless) or 3335lbs (304 stainless)
Derating factors for Dyneema might include (but are not necessarily limited to, 'cause there's a lawyer in the house...):
1. Strength loss due to UV exposure
2. Strength loss due to wear and abrasion (internal to the line, or external) over time (e.g. for dyneema in a cascade rubbing on rings, or around pulleys, or wear between fibers as load is cycled on a backstay)
3. Strength loss due to stress concentration in splices or as the line bends around pulleys, low-friction rings, or other terminations and, more generally, small radii (knots, pulleys, low friction rings, etc...)
4. Fatigue. At cursory inspection, Dyneema appears to have similar fatigue characteristics to steel. For the sake of this example, I'm going to assume dyneema is comparable to steel.
#1: 50% strength loss after 5 years due to UV exposure. Source: Eurofibers PDF showing % strength remaining in an 8mm dyneema line after some months of UV exposure. See page 12 here:
https://issuu.com/eurofibers/docs/name8f0d44.
#2: Assume 10% due to wear and abrasion; I haven't been able to find good data for this. It's more than zero, probably less than 50%. How sporty do you want to be? The Netherlands
tugboat line test data here is a good source for info, but doesn't directly address internal abrasion.
#3: Assume 15%; though it can be up to 50% when wrapped around a bend of diameter equal to the line diameter. If using low friction rings instead of pulleys in a cascade, this factor may be greater than 15%. If the splice bury is not tapered very carefully, this factor is about 15% according to
test data from L-36.com Let's assume 15% for the standing portion of the backstay.
#4: Assume 0%
Total strength loss is then (1-.50)*(1-.10)*(1-.15) = .5*.9*.85 = 38% rated breaking strength after 5 years. If sizing a dyneema backstay, make sure it is at least 2.5x the breaking strength of the steel wire. That way after a year or two in the sun & salt
your backstay is still as strong as the original steel wire was.
Original SS Strength Dyneema BS
5/32 316SS 2,800 lb 7,000 lb
5/32 304SS 3,335 lb 8,338 lb
3/16 316SS 4,000 lb 10,000 lb
3/16 304SS 4,800 lb 12,000 lb
If the original wire is 3/16" 316SS, I recommend using dyneema with no less than 10,000 lb breaking strength.
New England Ropes lists breaking strength for their 1/4" (6mm) SK-78 at 9,700lb (close, and maybe close enough). 5/16" (8mm) SK-78 is 14,500lb. Using NE SK-78 instead of amsteel might be the difference between 6mm and 8mm in this application. If the original wire is 5/32, breaking strength per Hayn is 2800lb, and 2.5x that is 7000lb which also requires 6mm SK-78 from New England. Per your email, the 1/4" Amsteel is also above 7000lb breaking strength.
For reference, 3/16" Amsteel SK-78 with initial breaking strength of 4,900 lbs is about equivalent to 1/8" 316SS wire after a year or two in the sun. I would not sail with a 3/16 dyneema backstay.
Sanity check:
The dyneema tugboat tow lines tested after 1 or 2 years of use fail at 50-60% their original strength.
Colligo marine says to size Dyneema to be 2-5x the strength of the original wire. Their sizing is driven by stiffness and creep characteristics, but it's another data point that confirms the "at least" ~2.5x strength recommendation above.
For what it's worth, my boat has a nitronic stainless rod for the backstay, and 7x19 wire going through pulleys in a 24:1 cascade. The nitronic rod is smaller diameter than equivalent strength 7x19 wire, so presents a smaller aero cross-section for lower drag. It should last 10+ years, and I don't have to worry about mainsail battens chafing dyneema over time. The backstay purchase is set at 24:1 for less line in the cockpit, and to make it harder to inadvertently break the forestay. If you're using rings instead of pulleys in your cascade, the math says there's enough friction to make going beyond a certain ratio basically pointless beyond some ratio which, if I remember correctly, is around 20:1 (i.e. 48:1 isn't easier to pull than 24:1). Use pulleys in your cascade to make it more efficient. Best bang for your buck is to use pulleys on the 'control line' side of the cascade, as they're smaller, lighter and cheaper and give similar benefit.
It's possible (difficult, but possible) to break the forestay by pulling a 48:1 backstay cascade with one hand. You don't want your crew accidentally breaking your forestay on a windy day. Without a mechanical 'safety' that limits the load, the only indications that loads are too high on the forestay are:
a) It's hard to pull the backstay control line (which isn't the case with a 48:1 cascade, unless it has a ton of friction...in which case, might as well reduce friction and got to a 24:1)
b) Cracking sounds from the hull and deck
c) The 'twang' of a separating forestay
Consider a 24:1 backstay purchase with pulleys at each location. It'll require pulling only half the line (less spaghetti factory in your cockpit), with similar force. You can still nearly break the forestay with an enthusiastic, double-handed pull on the backstay line. I can share a parts list if interested. Selden makes some nice, reasonably lightweight, and cost effective pulleys. Check these out:
First:
Second:
Third (or the Harken equivalent wire block):
Lower pulley for the third cascade (or the Harken equivalent)
Regards,
Manolis