Rigging Calculations for Allied Princess Ketch coming up odd

[svaletheia]

Hello,

I'm relatively new here (joined a while back, had some strange happenings in life around then, and am hopefully now back to 'normal' - whatever that is - for the next while).

Regardless, I've been running calculations for my Allied Princess ketch rigged boat per the Riggers Apprentice book and have noticed some VERY odd things about my current rigging situation.

For starters, here is what I have directly measured using a reasonably high quality digital caliper:

Twin forestays: 5/16"
Main shrouds, upper, and double lower: 1/4" according to my caliper, but rigger measured as 5/16" (and I measured across the widest part as well).
Main backstay, split around mizzen: 1/4" (same comment as above)
Mizzen shrouds, upper and double lower: 5/32"
Triatic? stay was not measured, but is present.

All are 1x19 SS of unknown composition.

Now for the tricky bits. According to the chart in Riggers Apprentice for RM30, the approximate RM30 for my boat (mid-line value) at 36' LOA and 27' LWL (at 30 degrees of heel its approximately 30' LWL I am told) is 30000 pound-feet. With a beam of 11 feet, chainplates nearly at the gunwales, and a safety factor of 1.5, that leaves a total force of 8182 pounds. Since this is a ketch, I understand that I apply 100% of these loads for mainmast calculations with an appropriate safety factor (2.25-2.75 seems usual?) and apply 100% of the same load to the mizzen, but with a reduced safety factor, closer to 1, given that the mizzen should only see the full load in extreme circumstances when its pretty much 'caught with its pants down' so to speak.

Running the numbers for the typical load percentages carried by a single-spreader design with twin lower shrouds, I get the safety-factor-adjusted load expectation of the cap shrouds at 9205 lbs.

Here is where things go a little sideways: 1/4" 1x19 SS, even 302 to be generous, has a breaking limit of 8200 lbs, according to Loos. 316 is worse, at 6900 lbs.
Now, 5/16" is 10600 lbs for 316, and 12,500 for 302, if I read the charts right.

So my questions are:

1. Is my rig likely undersized?
2. Did I calculate the RM forces properly and apply the theory to the ketch rig correctly?
3. If I'm going to replace all the standing wire rigging anyway, as a precaution, should I go with the 5/16" that I calculated or stick with what the rig has right now (its circumnavigated under the previous owner and the current rigging at least once)?

Bonus question:
4. Is the tension on the twin forestays supposed to be half as tight as the ordinary tension if there were a single forestay? My engineering theory tells me yes to maintain total tension on the mast, but my statics course was a long time ago and I'm not so sure we covered redundant member loading thoroughly. This is a really annoying part of my rig - how slack the forestays are which makes my leading edge of my genoa really sloppy. The rigger told me this was normal for twin forestay rigs and to just deal with it.

Many thanks!

[Brion Toss]

Hi and welcome back,
First, the "1.5" you mention is not a safety factor -- that comes later in the calcualations -- but the typical multiple of the load at 30 degrees of heel to the maximum load, typically at around 60 degrees. Your calculations' result is correct for the mainmast, in any event, so yes, the 9,000-ish lb load on the uppers is likely right, or right enough to select wire size.
No idea how you and the rigger could be off by a sixteenth, but this is something I hope you can clear up; if those uppers are really 1/4" they are probably too small. Any chance they might be 9/32"? This diameter would be better than 5/16" for the above numbers.
As for those jibstays, I am always wary of a "them're like that" argument, and this is no exception. It is indeed very difficult to get adequate tension up there, and if you keep the twin stays you'll want to come up at least one size on your backstay, even if it forms a wider angle to the mast than the jibstays. But it should be possible to prevent excessive sag on those stays with proper tuning, since as the loaded stay loads, it stretches the backstay, allowing the unloaded stay to shrink, casting off some of its load. But even then, since you can expect at least 4" of sag on the loaded stay, and since the unloaded stay is probably less than 4" away, you can be heir to the delights of hanks jumping to the other wire, among other things. So it doesn't really matter how well this rig can be tuned; switch to a single jibstay configuration. You'll have less weight aloft, less windage, less compression on the mast, a smaller backstay, less load on the hull, and less bother altogether. That's why this configuration was abandoned long ago, along with wire reel winches, twin running poles, and other technological experiments.
As for the mizzen, you scale it, not with a smaller safety factor, but with a smaller load factor, since, with few exceptions, there simply isn't enough sail area in the mizzen to generate anything like the maximum vessel righting moment with that sail, no matter how hard or unexpectedly the wind blows.
Fair leads,
Brion Toss

[svaletheia]

Brion,

Many thanks for the thoughtful and prompt response.

As for the 1/16" difference in measurement, yes, its surprising. 9/32" is, I believe, the 'spec' now that you mention it. The fix is simple, since I plan to replace the rigging anyway: thanks to your encouragement I'll just use 9/32 or 5/16ths moving forward. Would there be any negative consequences of slightly oversizing to the 5/16ths?

As for switching to a single forestay - I'd been considering roller furling, and am still truly on the fence about it, but for some reason I'd never thought of simply dropping down to a single forestay and remaining with the hank-ons. It would solve a number of problems I have with the current setup and I'm glad to know that the twin forestay "experiment" was not some fantastic seaworthy design I'm blindly turning my back on. Plus with a single forestay I can always convert to a roller after the fact much more easily.

Can I safely assume that I can run the same size wire (9/32 or 5/16, as the case may be) as the shrouds and backstay and be done with it, in this case?

Lastly, what is the right way to come up with an appropriate scaling factor for the mizzen? The main is about 266 ft^2 and the mizzen is ~94 ft^2, for a 35% size factor, but I assume that's not the whole story either. The mizzen is lower than the main, representing less angular force, but the rigging attaches at a slightly narrower part of the boat (maybe a 4.5 foot half-beam instead of a 5.5 foot, at that point), so it also has commensurately less leverage as well. Is there anything close to a "this will get you in the ballpark for wire sizing" kind of approach?

Again, many thanks.

[svaletheia]

Hi Brian, I completely understand being busy at this point.

Just wanted to run the idea of re-rigging to 5/16ths rather than 9/32nd (there seems to be no ability to contact either the original designer nor can I find consensus about what the proper wire size is amongst the owners) and go to a single forestay as you mentioned. I'm about to buy the materials and don't want to jeopardize my rig. On the other hand, if I can safely go that 1/32 larger, I would much rather do that since I'm hoping to take this boat into high latitudes in the not-too-distant future and if that does in fact give me the safety margin it seems to, it would be quite useful.

Much appreciation for your forum here.

[svaletheia]

Scratch that... 9/32 316SS (published values ~8700 lbs break strength) is shy of the max load factor calculated so cannot be reliably considered. I've therefore arrived at the conclusion that 5/16 is the closest line that has a strength above the calculated load factor.

Scaling the mizzen by sail area gives me a good estimate of the forces at < 40% versus the main. So I will use 3/16 on the mizzen, which is handy as it matches my lifelines.

[cstotland]

Since this post is a few years old, might be a bit late, but...consider..

By the time you were to hit the calculated loading on the sail plan, you'd have shortened sail. On my Princess, I reef by 20 kts, and if going above 25 kts, strike the main altogether. We've been hit full sail by 45kt squalls with no ill effect, on the stock, 30+ yr old wire. When we replaced the standing rigging last spring, I did upsize the main uppers to 9/32 from the measured and spec'd 1/4". Didn't seem that larger would help, since the forestay is only 1/4" and couldn't make that any larger without replacing the furler. (I did opt for dyform for the forestay).

Just a thought...

Cary Stotland
s/v C-Lover
AP II #128

[Brion Toss]

Originally Posted by cstotland

By the time you were to hit the calculated loading on the sail plan, you'd have shortened sail. On my Princess, I reef by 20 kts, and if going above 25 kts, strike the main altogether. We've been hit full sail by 45kt squalls with no ill effect, on the stock, 30+ yr old wire. When we replaced the standing rigging last spring, I did upsize the main uppers to 9/32 from the measured and spec'd 1/4". Didn't seem that larger would help, since the forestay is only 1/4" and couldn't make that any larger without replacing the furler. (I did opt for dyform for the forestay).

Just a thought...

8

Hello,
You seem to think that there is some overriding relationship between sail area and rig load. There is not. Rig load is relative to angle of heel, and it is possible, as many people have discovered on sailing's more exciting days, to achieve maximum rig load with minimum sail area. In fact, that's when it is most likely to happen.
You also seem to think that, because your old wire didn't break in a breeze, that it was all right. It almost certainly wasn't. Not at that age. How close to breaking do you think you got? How close do you think it is okay to get? Good thing you had a safety factor built in.
Fair leads,
Brion Toss