Pearson 10M Standing Rigging Calculation

Standing Rigging Calculation

Standing Rigging Calculation Back to Rigging

By appearances the 10M is a very heavily rigged 33 footer. Here are the OEM wire sizes for the standing rigging:

10M OEM Rigging
Wire Headstay Backstay Upper Shroud Lower Shroud		Size 3/8" 3/8" 5/16" 9/32"

So is the rigging over-sized on the 10M? I ran the numbers for the 10M by methods from three sources starting with David Gerr's book "The Nature of Boats." By Gerr's methods the OEM wire sizes seem large by two sizes all around. But there are a few factors he describes that need to be accounted for. Shroud base width is the distance between the chainplates. This distance, along with the mast length, determines the shroud angle. A wider shroud angle means lower loads on the shrouds. Gerr says his estimation formulas are good for typical boats with Shroud base width that is greater than 20% (1/5) of the mast height (deck to headstay). On the 10M this distance is a little small at 18.4% (17.6% for tall rig). Gerr also says his formulas are meant for typical boats with shroud angles over 10 degrees. The 10M angles are slightly less at about 9.5 (this is related to the Shroud base width). These variations will increase load on the shrouds and require up-sizing to compensate. My guess is Gerr would recommend one size larger all around based on the slightly small shroud base width. He did not discuss safety factors but I think his method is intended to fit into the common standard of 2.5 to 3.0.

From David Gerr "The Nature of Boats" pp. 291-296

Std Tall

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.

USYRA stability data for the 10M
US Sailing AVS Calculator
Graham Radford Yacht Design, STABILITY DISCUSSION
More info on sailboat design ratios

From David Gerr "The Nature of Boats" pp. 291-296
	Std	Tall
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

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

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

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.