Standing Rigging Calculation |
10M OEM Rigging | |||
Wire Headstay Backstay Upper Shroud Lower Shroud | Size 3/8" 3/8" 5/16" 9/32" | ||
From David Gerr "The Nature of Boats" pp. 291-296 | ||
deck to headstay (I) | 44 | 46 |
mast width | 5.87 | 6.13 |
mast for/aft | 8.21 | 8.59 |
wall thickness | 0.17 | 0.18 |
shroud base width as % of I | 0.184 | 0.176 |
upper shroud angle | 9.9 | 9.6 |
lower shroud angle | 9.6 | 9.1 |
Standing Rigging | ||
displacement | 13,000 | 13,000 |
total shroud breaking strength (1.2 * disp) | 15,600 | 15,600 |
upper shroud load (40%) | 6,240 | 6,240 |
upper shroud wire size | 9/32 | 9/32 |
lower shroud load (60%) | 9,360 | 9,360 |
lower shroud wire size | 9/32 | 9/32 |
The next two methods are basically the same but use slightly differnt load levels for the shrouds. Both are based on the this formula:
Shroud Load = RM30 * 1.5 / 1/2beam
RM30 is the righting moment at 30 degrees heel
1/2beam is half of the shroud base width
I don't have a direct figure for RM30 but I do have IMS measurement data for the 10M and can extrapolate a pretty good approximation. The IMS data shows a righting moment at 25 degrees of heel as 716 lbs/degree or 17,900 lbs. The righting curve is fairly straight line from 0 to 35 or so and the rate is actually decreasing so using the 716 lbs/degree will give a slightly high value at 30 degrees which is nicely conservative. So 716 * 30 gives an RM30 of about 21,500 lbs. This is the figure I used in the formulas below. Unlike the Gerr formula the RM30 formula accounts for shroud base width. But without mast height I suppose this is only partly covering the shroud angle issue?
From Brion Toss "The Riggers Apprentice" pp 137 | ||
RM30 | 21,500 | |
1/2 beam | 4.05 | |
shroud load | 7,963 | |
wire capacity with safety factor 2.5 | 19,907 | |
Upper Shroud Capacity (40% total load) | 7,963 | |
upper shroud wire size | 1/4 | |
Lower Shroud Capacity (25% total load) | 4,977 | |
lower shroud wire size | 7/32 | |
RM30 = righting moment at 30 degrees heel. Aproximated from IMS data on RM25 (=17,900) 1/2 beam = 1/2 of shroud base distance (distance between chainplates) shroud load = RM30 * 1.5 / 1/2 beam |
From Richard Henderson "Understanding Rigs and Rigging" pp 117-120 |
||
RM30 | 21,500 | |
1/2 beam | 4.05 | |
shroud load | 7,963 | |
wire capacity with safety factor 2.5 | 19,907 | |
Upper Shroud Capacity (45% total load) | 8,958 | |
upper shroud wire size | 9/32 | |
Lower Shroud Capacity (32.5% total load) | 6,470 | |
lower shroud wire size | 1/4 | |
RM30 = righting moment at 30 degrees heel. Aproximated from IMS data on RM25 (=17,900) 1/2 beam = 1/2 of shroud base distance (distance between chainplates) shroud load = RM30 * 1.5 / 1/2 beam |
In the Toss method 25% load was used for each lower shroud to match his example. Gerr and Toss both note that the lowers get more load than that and when there is more than one each should be capable of handling the full load. And both say having lowers at least the same size as uppers is a good idea. But have you ever seen a boat so rigged?
Those methods give a guide to sizing the wire for the 10M. The Gerr method seems to go a bit smaller but all of them are smaller than the OEM rigging on the 10M. The numbers in the Toss and Henderson calculations were for a 2.5 safety factor. The standard seems to be 2.5 to 3.0. Working the 10M rigging figures backwards can give the safety factor Pearson applied to the 10M. Taking the total capacity of the upper and lower shrouds compared to the shroud load calculated using the RM30 formula gives a safety factor of 4.2. That's a little high because it's using the combined capacity of the lowers and reality will have them loaded differently. Taking 70% of the lower shroud capacity gives a safety factor of 3.4. Taking the upper and a single lower of 5/16" gives a safety factor of 3.1. But these are for breaking strength of the wire. Staying within elastic limits gives safety factors of 2.5, 2 and 1.9 respectively.
10M OEM Rigging | ||
OEM wire capacity (5/16 upper + 9/32 lowers) | 33,100 | |
safety factor (based on RM30 load) | 4.2 | |
Upper Shroud Capacity (% total load) | 38% | |
upper shroud wire size | 5/16 | |
Lower Shroud Capacity (% total load) | 62% | |
lower shroud wire size | 9/32 |
What does all this mean? Maybe the 10M is not so over-rigged as it appears. Or maybe a lot of other boats are under-rigged? I need to do some more study and number crunching.
1x19 Wire Rope Specifications | ||||||
Wire 5/32 3/16 7/32 1/4 9/32 5/16 3/8 7/16 1/2 |
Strength 3,300 4,700 6,300 8,200 10,300 12,500 17,500 22,500 30,000 |
E-Limit 1,980 2,820 3,780 4,920 6,180 7,500 10,500 13,500 18,000 |
Weight 5.5 7.7 10.2 13.5 17.0 21.0 29.4 41.0 52.1 | |||
Strength is breaking strength of wire.
E-Limit is the elastic limit of the wire. Loading beyond that point will cause permanent deformation. It is estimated at 60% of the breaking strength. See Brion Toss "Riggers Apprentice" p. 137. Weight is per 100 feet of wire. |