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KeelHaulin

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Again; nice writup Giulietta. I was wondering about the difference between rake and pre-bend. When you measure pre-bend is that in addition to the rake? So first you measure the rake and then you put additional pre-bend on the mast?

I also have a question regarding the wedging at the cabin roof for a keel stepped mast. "Spartite" was installed at the partners so I can't remove and replace wedges. Can I add rake and bend with the Spartite in place or would trying to rake the mast at this point only result in bending? The mast already has a factory taper and pre-bend IIRC; it's a tall rig, the I is 52'. Visually I don't see much rake; but there is bend above the upper spreaders.

KeelHaulin

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guilietta said:
The rule is simple each 1mm of stretch means 5% of the breaking load, and that is valid for ANY CABLE IN A SHROUD, no matter what the diameter is!!!

Careful... I did some basic calcs on this and yes; for an equivalent diameter and equivalent length the linear stretch is roughly proportional to tensile stress regardless of diameter. BUT if the smaller diameter shroud is smaller in length (which it should be) then the amount of pre-load you apply per mm of stretch is increased. That's because strain = change in length / original length.

Example:

Let's say you have a 50' mast with 7/16 upper shrouds. The calculations I did suggest that you would need 5.98 mm of stretch applied to them to get ~1600 lbs of pre-load.

In the same example; if the shrouds were 1/4" you would also need to stretch them 5.98mm to achieve 540 lbs of pre-load.

But; if you have a shorter mast (as you should) with 1/4" wire the stretch required to get 540lbs of pre-load will be less. If the mast is 30' tall the stretch required will be 3.6mm to get the same 540 lbs of pre-load. If it were tightened to 5.98mm it would have roughly 900 lbs of pre-load or 25% of break load.

So; while the rule-of-thumb is probably OK for a rough tune I would say that if you apply it to taller rigs it will result in shroud tensions that are on the loose side; and on shorter rigs it will result in shroud tensions that are a bit too tight.

Thanks for the additional info on rake VS bend. I understand it now; and now I'm not sure if the mast actually has rake or not. I'll do some measuring and adjusting according to your excellent procedures.

KeelHaulin

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From the web, Young's Modulus for 1x19 wire rope is 107.5 kN/mm^2.

Using the table of breaking loads for different diameters of AISI-316 wire rope as given in the book "Principles of Yacht Design" I got the following table for wire stretch for a 2000mm wire loaded to 5% of breaking load:

diameter(mm)____breaking strength(kN)___delta L(mm)

3_______________7.7__________________1.01
4______________13.8__________________1.02
5______________21.6__________________1.02
6______________30.o__________________0.99
7______________40.9__________________0.99
8______________53.5__________________0.99
10_____________69.1__________________0.82
11_____________83.5__________________0.82
12____________120.2__________________0.99
14____________160.1__________________0.97

This practically confirms what Alex is saying.

regards
Right; I said the same thing. If the shroud length is constant; the amount of stretch required is the same. But you can't apply this universally to all shrouds because different boats have different lengths of rigging wire. If you plug in 4000 mm for your base length; the delta L will double to get the proper tension. Since that's true you can't use the 1mm/5% rule to get exact tension. If I tighten an intermediate 1/4" shroud using that rule the tension will likely be ~40-50% of breaking load because the shroud lenth is much shorter than the upper shroud; which goes from the masthead to the deck.

Giu-

I'll get back to you with the data; I am aboard my boat tonight using a different computer. I should still have the spreadsheat I was doing the calc's on; but if not I will make up a new one. I was just using the modulus for 316 stainless and an approximate breaking strength for each size. Please don't use those numbers I posted as "actual"; I was only trying to make the point that stretch is also dependent on wire length (and this is independent of the max strength of each wire diameter).

KeelHaulin

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OK; here is the way to solve for stretch at 15% breaking strength. It's a simple derivation; it really only uses two well known engineering equations to solve it.

Strain is defined using the greek symbol epsillon; I'm using E

Strain is defined as:

E = dL / Lo

Change in length is dL; Lo is the Original Length.

For elastic conditions; we can use the definition of Young's Modulus to determine how much extension (strain) exists in a length of wire for a given amount of force applied.

Young's Modulus - E = Applied Stress / Strain = S/E = S/(dL/Lo)

Young's Modulus is a material specific constant measured by a testing applied force vs extension.

For type 316 Stainless; E = 28,000 kPSI

We can solve this for the change in length; dL

dL = Lo * (S/E)

The only real "variable" in this equation is Lo. For all wire diameters we want the same amount of stress (15% of breaking) so we can say that S is a constant.

Let's calculate S for some different wire diameters to prove it's relatively constant:

S = (F/Ao) - "F" is the tension force in the wire; Ao is the original cross sectional area of the wire.

(Breaking strengths taken from loosco.com for 1x19 type 316 wire)

For 7/16 wire - S = 15% * (20,000#)/(Pi * (7/32")^2) = 15% * 133,040 PSI = 19,956 PSI

For 1/4" wire - S = 15% * (6900#)/(Pi * (1/8")^2) = 15% * 140,560 PSI = 21,084 PSI (within 5%)

For 5/16 wire - S = 15% * (10,600#)/(Pi * (5/32")^2) = 15% * 138,200 PSI = 20,730 PSI (within 4%)

Using Young's Modulus for type 316; the 15% breaking load equation becomes:

dL = Lo * (20,600 PSI) / (28,000 kPSI) = Lo * .000736.

Use inches or mm for the shroud length; multiply by .000736 and get the length you need to stretch the cable.

For a shroud 55' long: dL = 660" * .000736 = 0.485"

For a shroud 20' long: dL = 240" * .000736 = 0.177"

It's -fairly- independent of wire diameter; but clearly dependent on length! You could use this for type 316; (but of course the standard disclaimer applies); and it does not take into account deflection of the rig or hull when you tighten the shrouds. Again; you should use an appropriate tension gauge to determine the actual rig tension.

KeelHaulin

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I note that American's frequently use the # sign. Can you explain what it means?

What would you use to measure the 0.485" (say) in the 55' shroud to ensure that you don't tension it more than 15% of breaking strength?
# for American "Engineering Notation" is Pounds. It can be either LBF or LBM; it's just a shrot-hand for Pounds because it's called the "pound" symbol.

To measure the 15% tension I'd just use a standard Loos Gauge. Although the calculation predicts 0.485" extension I would not bet my life on it. Young's Modulus is a theoretical constant for the material and it is calculated based on lab results under ideal conditions (perfect sample, solid section, etc.). If the theoretical is within 20% of the actual tension in LBF I'd call it a good comparison; but that's not as close as you would get with a Loos Gauge.

If you wanted to measure the extension I would put a pair of calipers on the open body turnbuckle and measure the distance between the threaded ends. That's a direct measure of the amount of elongation you are putting into the shroud.

KeelHaulin

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I think we need to know what type of boat you are sailing to determine if the problems you describe can be associated with the rig or not. Some issues with broaching or helm balance are more associated with the sailplan or a particular hull design and without knowing these things I can't say whether or not it is due to improper adjustment of your rig.

KeelHaulin

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Seems to me that your boat is similar in design to the J-105; in rated area and size, etc. I can't say for sure about the sailing properties because it appears that Elans are primarily sold/sailed in Europe. The listings on Yachtworld only show them available in Europe/UK. That's why I hesitate to say exactly what the problem is.

If I were betting; I'd say that the problem is due to the high SA/D ratio and that the boat is getting overpowered earlier than a heavier boat or a boat with less sail area. The J-105 fleet racers say that they are a beast in heavy wind and they are always cranking the backstay up and spilling the traveler down to keep the boat on it's feet; of course they are pushing it to the limits when racing in their fleet. These tactics also require a crew who is constantly trimming and "rail meat" to help stabilize the boat.

Again; I'd try reefing it down good and then see how the boat performs. You'd be amazed that when you reduce sail area; your leeway reduces, the boat stands up and is able to sail at a more optimal angle of heel and can actually go faster. Your pointing might be a bit reduced depending on sail shape but hey if the boat goes faster and is easier to control you are going to make your destination more quickly and with less struggle.

KeelHaulin

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I used to build a system that used a 1/4" cable 800 feet long. Proper tension on that system was to stretch the cable 8 FEET!
Yes; that was why I did the calculation on page 3 to show what theoretical length would be needed to stretch a cable to 15% break strength. It's dependent on the pre-tensioned length of the wire (and type of metal); not diameter.

15% break strength on an 800' (type 316) cable would be to stretch it approx. 6 feet. (Not accounting for thermal expansion or weight); so depending on the type of wire you were probably at about 20% break strength or a bit higher.

Giu's rule-of-thumb will put approximately 20% breaking strength into the shroud if you stretch 1mm per meter of cable. So a mark at 1 meter should move up 1mm on a scale attached to the shroud swage. For 10% breaking strength stretch 1mm per 2 meter length measurement.

KeelHaulin

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Keel, I am not going to argue this anymore.
Was not trying to argue anything Giu; I was simply trying to add some information to your excellent post of how to adjust your rig tension.

Since there was confusion on what your post was saying I tried to determine why it would be 1mm extension for 1 meter or 2 meters; but it is off by ~50%. The calculation is correct; so it must be a problem with the published breaking strengths. So I was doing some more research on 316 stainless and it turns out that the published breaking strengths must not be actual ultimate breaking loads; they seem to have a safety factor of 2 built in. The 15% breaking strength calculations I did earlier were based on the published breaking loads; while the Selden formula is based on the true Utimate Tensile Strength of stainless wire (actual failure strength).

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