|
Excerpted from Sailnet – Jeff/Super Moderator
When I worked in naval architect offices, we usually ran calculations for masts based on empirical formulas that have been around for a long time. Stability played a role but if I remember the formula correctly there was a simple surrogate formula that added increased load factor to the formula that compensated for higher stability. While today there are sophisticated computer programs to size spars and rigging, They really would not be necessary if you are simply replacing the spar on your 1960's era ( “racer cruiser”)
If I remember correctly Skene's had a pretty simple chapter on spar design.
As to making a decision between different spars, assuming that you are not changing your shroud attachment points or your spreader positions, the key numbers that you will want to pay attention to are the axial area of the spar, and its moment of inertia. Masts, especially in masthead rigs like ours, take enormous compressive loads and the axial area is the determinant of the axial load that the spar can take if in column. They also are subject to bending forces, and the moment of inertia refers to the stiffness of the spar, and so its likelihood of remaining in column.
For the same rig geometry, smaller dimensional spars are not usually lighter than bigger sectional spars since it takes more wall thickness to achieve the same necessary stiffness. Weight savings can only be achieved with smaller dimensional spars when the rig geometry is adjusted to reduce panel length so that the required stiffness can be reduced and perhaps spar tapering can be employed.
If you want to wipe out your beer supply and wear out your thinking chair you can also use the formulas from German Llyods.
Whatever you do, you are probably looking for a pretty conservative design. If worse came to worse, you should be able to determine the area and I (moment of inertia) of your old spar by looking up its dimensions and wall thickness at Dwyer or Kenyon, since most of those old spar shapes are still in production and use those numbers to make a judgment call on which spar section best suits your goals. (BTW within the constraints of conservatism likely to be employed in designing a spar for a cruising boat, fatigue should not be an issue since the safety factors are much higher than the sophisticated formulas used with high performance oriented computer aided design programs.)
Respectfully, Jeff
*********************
I think that aluminum spar design evolved from wooden spars at a time when the underbody design of boats were the limiting factor in their pointing abililty more than their rig design. Narrow spreader widths and narrow shroud bases would not have particularly helped the pointing ability of the boats of the day.
By the same token, the racing rules of that era over-penalized fractional rigs making the masthead rig the dominant rig of the era when spars were transitioning from wood to aluminum.
Comparatively speaking, masthead rigs operate at very much higher compressive load and that places a premium on stiff spars to take those loads without buckling. With the wide shroud bases and need for large cross sectional areas, and given the aluminum alloys available in the 1960's, a deck stepped mast with a two panel- single spreader configuration, with fore and aft lowers to reduce pumping was a very good choice.
But as underbodies became more efficient, allowing boats to point higher, rigs began to evolve as well. And with the advent of lower stretch sail cloths it became easier to design around higher aspect sail plans and expect more reliable shape holding. But that then placed a premium on somewhat contradictory objectives, precision control of spar bending and headstay tension, combined with narrow spreader/shroud base widths.
If the designers had stuck with two panel design but had narrowed the spreader/shroud base, the spar would have been subject to either a lot more weight, bigger stiffer sections and/or a lot more flexure which makes mastbend/headstay sag control far more difficult.
The logical solution was multi-panel design, which through the miracle of continuity reduces moment and deflection while permitting a narrow rig width, albeit at the price of complexity.
I come back to one of my frequent stated sentiments that good boat design produces a design that works well as a system. Your rig works well as a system with your boat's underbody.
If you could reduce the weight of your rig, your boat would be more stable and could carry more sail into a higher breeze which would improve the windspeed range of your larger headsails. That increased range could result in a small performance gain in changeable conditions.
Coupled with low stretch sail cloth, a lighter rig could also improve windward ability at that windspeed range where sail cloth stretch and leeway due to heel come into play. Taking advantage of the stability increase from a ligher mast, you might be able to increase the length of the mast a little resulting in a better light air performance and perhaps reduce the overlap on jib for increased ease of handling and efficiency.
But in the big picture, the gains would be small compared to the gains that would occur on a boat with a more efficient underbody where there could be big gains from a more efficient rig.
Respectfully, Jeff
**********************************
You need to run the numbers but, but in a general sense there are a wide range of choices that should be structurally sound. You should be able to taper the top of the spar which would be one of the bigger gains that you might achieve with a multi-spreader design. I should also point out that many of the better spar builders have pretty sophisticated design programs and will include the design of a suitable spar in the price of the spar.
Back in the 1960's and 1970's there were relatively few spar extruders. At the time that most American and Canadian spars came from the company that became Kenyon and from Dwyer. Both were mast fabricators as well as selling extrusions to other rigging shops.
Respectfully, Jeff
*********************************
DYNAMIC STABILITY
How stable should an offshore cruising boat be? Does it heel to much? Is it likely to be rolled over in a storm? If it does roll over, will it right itself quickly? Before we can answer these questions and evaluate the suitability of a boat for offshore use, we need to understand that what we normally call "stability" is really composed of two factors, static stability and dynamic stability.
Static Stability is familiar to most of us because it largely determines the angle of heel (roll) developed by a sailboat under constant wind conditions. Some of the roll can be reduced by changing the center of gravity (hiking out or moving ballast), reducing sail area, or running off slightly (avoid the wind). Under light to moderate conditions, the ideal cruising boat should carry enough sail to perform well and have enough static stability to avoid excessive heel.
The most important factors that increase static stability are heavy displacement, low center of gravity, and a center of buoyancy that shifts outboard quickly when the boat heels (strongly related to beam). Most cruising monohulls exhibit positive static stability out to heel angles of 130 degrees, with the highest righting moment occurring around 65 degrees. Multihulls peak higher and sooner than monohulls and capsize at lower angles.
Dynamic Stability controls how much the boat rolls in response to a transient wind gust or violent wave. The ideal cruising boat should resist these dynamic forces long enough for them to pass safely by. Reducing sail area will usually help reduce dynamic roll, and the boat can often be steered around the worst waves, but our ideal cruiser should have enough dynamic stability "built in" to survive an encounter with a strong gust or rogue wave without capsizing. If the worst does happen, and our ideal boat gets rolled 180 degrees, it should right itself quickly.
Heavy displacement helps dynamic stability, but the center of gravity is not much of a player and a large beam actually makes the response worse (beamy boats catch the wave early and give it more leverage and time to act on the hull). Once inverted, the increased static stability associated with beam becomes a liability since it keeps the boat inverted for a longer period of time. Light and beamy boats often have high Capsize Risk (see definitions). The most important factor in dynamic stability, however, is the boat’s roll moment of inertia. Without getting into much math, the roll moment of inertia is proportional to the square of the transverse distance between the boat and its center of gravity. The squared term makes the calculation very sensitive to how far heavy objects are from the center of gravity.
For example, a dingy with two people sitting fore and aft on the centerline has a smaller roll moment of inertia than the same dingy with the people sitting side by side. Both boats weight the same, have the same center of gravity, and the same center of buoyancy (same static stability), but moving the people off the centerline greatly increases the roll moment of inertia. Since the roll moment of inertia is proportional to the square of the distance from the center of gravity, deep ballast and long heavy masts have the most impact. A large roll moment of inertia is desirable for a cruising boat because it increases the total time and energy required to capsize the vessel. Boats with large moments of inertia have long roll periods and are highly resistant to rapid changes. Multihulls have a very large roll moment of inertia because the hulls are quite far from the center line.
Static or Dynamic Stability. Which is best? Can we have both? The trade off between static and dynamic stability forces us into a compromise situation where there is no single correct answer. Heavier boats have more static and dynamic stability, but less performance. Wide beam boats have high static stability, but they also have a higher capsize risk and more inverted stability. Wide beam is generally associated with lighter weight, higher performance boats, which will have a short roll period and low roll moment of inertia. High performance boats also typically have smaller section masts and less rigging. This reduces the weight aloft and increases static stability, but greatly reduces the moment of inertia. A heavy cruising boat with a deep bulb keel, heavy spars, lots of rigging, and a radar mounted above the spreaders will have a large roll moment of inertia, a long roll period, and be very resistant to wind gusts and waves.
The best we can do is to make our evaluations based on our expected use. A coastal cruiser, for example, may accept the dynamic stability penalties associated with wide beam. A blue water cruiser probably won’t. Similarly, carbon fiber spars may increase static stability (good for light air performance) but they will greatly reduce the roll moment of inertia (see example). While static stability will always be a critical sailboat parameter, the dynamic characteristics of a cruising boat should be understood since they can be very important under storm conditions.
Example
The following boats have similar LOA, Beam, Ballast / Disp ratio, and Draft. The "Racer" design has 50% less displacement, 50% longer righting arm (due to a flatter bottom and lower center of gravity), and a 66% lighter weight rig. Both boats are subjected to a constant 30,000 ft.lb. overturning moment, which is less than their maximum static righting moment. The simulation begins with an under damped condition which allows the overturning force to capsize the boat. The damping is then increased until the boat oscillates rather than capsizes, eventually damping out to a constant heel angle. The first case gives us the time to capsize, the second lets us measure the period of oscillation. Under static conditions, damping is largely determined by the rate that water is swept away by the keel as the boat rolls. The lateral area of the underbody normally controls damping (deep keels and centerboards help), however in a storm the keel may be in breaking water (froth) and the damping forces drop dramatically, allowing the boat to heel more.
RACER CRUISER
Disp., lb 16000 24000
Hull, lb 9300 13900
Ballast, lb 6400 9600
Mast and Rig, lb 300 500
Roll Period, sec 4.6 5.7
Static Stability
Righting Arm, ft 2.4 1.6
Max. Righting Moment, ft.lb 38347 38399
Heel at Max. Moment, deg. 62 64.5
Dynamic Stability
Moment of Inertia, lb.ft.sec^2 17304 26522
Time to heel 30 degrees, sec .9 1.1
Time to heel 60 degrees, sec 1.4 1.7
Time to heel 90 degrees,sec 2.0 2.5
Time to Capsize, sec 2.8 3.6
The first thing we notice is that the light weight racer has a much shorter roll period than the cruiser. Its tempting to claim that this indicates more static stability, however this is not completely accurate. Static stability does reduce the roll period, but so do other factors such as the roll moment of inertia. When we look at the actual values for static stability, both boats are about the same. Even though the racer ends up with a longer righting arm, the cruiser’s heavy displacement compensates for it since static stability is a function of both.
The big difference is in dynamic stability. The Cruiser has a 53% bigger roll moment of inertia, which greatly slows down its response to the overturning moment, resulting in the increased roll period. At 90 degrees heel, the cruiser lags the racer by 1/2 a second. At the point of capsize, this time difference has increased to .8 seconds. In a sever storm this could be the difference between an unpleasant knockdown and a life threatening capsize.
DEFINITIONS
DISP / LENGTH RATIO = disp/2240/(.01*lwl^3) Probably the most used and best understood boat evaluation factor. Low numbers (resulting from light weight and long waterlines ) are associated with high performance and quick response
SAIL AREA / DISP RATIO = sail area/(disp/64)^.666 This is a ratio of power to weight, calculated using a 100% jib. We want a cruiser with enough power to sail well but not so much sail that the crew is fatigued by constant sail changes or worried about having a fragile oversize rig.
BALLAST RATIO = weight of ballast / displacement
CAPSIZE RISK = beam/(disp/.9*64)^.333 A seaworthiness factor derived from the USYRU analysis of the 1979 FASTNET Race, funded by the Society of Navel Architects and Marine Engineers. The formula penalizes wide boats for their high inverted stability and light weight boats because of their violent response to large waves
ROLL PERIOD = Time in seconds to complete one cycle. The roll period can be measured by starting the boat rolling slightly (at the dock) and averaging the time for several cycles.
***********************************
Stability
Question: I recently had an interesting discussion about stability with a cruising yacht owner, and I thought this topic would be of real interest to any high latitude sailor. And I also suspect that you would have traversed this terrain long ago and have an opinion.
After the 1979 Fastnet race, the Joint Committee on Safety from Capsizing made the following recommendation: "The most significant contribution to the resistance to wave-induced capsize would be to increase the roll moment of inertia of yachts". For a sailing yacht, adding mass at the top of the mast would increase roll inertia more than adding mass anywhere else (hulls are normally designed to support a given keel weight and depth, and adding additional weight to the keel is not recommended).
At the same time, various regulatory agencies and yacht racing bodies have firm guidelines, even rules, to ensure the highest possible Angle of Vanishing Stability (also know as Limit of Positive Stability). For a monohull, removing that same mass that we placed at the top of the mast, would have a more beneficial effect on the LPS than shifting the same amount of mass anywhere else on the boat.
Unless I am overlooking something, there's contradictory advice here. To prepare a yacht to resist wave-induced capsize, do I favour an increase in roll inertia, or do I favour an increase in LPS? If I favour LPS, I would probably end up doing things that would diminish roll inertia (like keeping weight close to the deck).
Do you favor one approach more than the other, and why?
Answer: First off I should say that I’m no naval architect, so this question is getting pretty close to, or perhaps exceeding, the limits of my competence. Still, I will have a go and also talk a bit about our own thinking on stability as it relates to our boat and other boats we would be willing to go to sea in.
The contradiction you outline is a good example of the dangers of taking one conclusion of a long and complex report and trying to apply it to the incredibly complex and still only partially understood dynamics of sailboat capsize in breaking seas. Yes, it is true, although counter intuitive, that making the mast heavier actually increases a sailboat’s resistance to capsize—this is why dismasted boats are often repeatedly rolled in breaking waves. However, as you point out, increasing mast weight also reduces the boat's ability to recover from a capsize or knockdown. Like almost everything around boats it’s a compromise. The naval architect designing a boat needs to balance these two conflicting requirements to come up with the safest possible, but still practical, cruising design.
|
|
