Deck-Stepped Mast or Keel Stepped

Discussion in 'Boat Design' started by Southern Cross, Feb 6, 2014.

  1. Southern Cross
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    Southern Cross Senior Member

    The new Volvo 65's went with a deck stepped mast.

    When designing an ocean racer, what are the main reasons, besides saving interior space, a shorter length of spar for choosing either one? Rake? Sail shape? Are Carbon spars ever keel stepped? Is it simply that the material, carbon, makes it all possible?

    And ... would it be ill advised to try to convert a keel stepped to a deck stepped given the necessary structural modifications were in place? What if the spar was aluminum? Could it be made in a smaller diameter if mounted on the deck?

    Just curious.
     
  2. philSweet
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    philSweet Senior Member

    Modern sails don't need as much mast bending as the old ones?

    Possibly transportation issues, or a perceived safety issue, being able to clear a deck stepped mast more easily after breakage. Personally, I always figured I got windage-free support from the below-decks portion. Less stay windage. That might be less of a boon as masts continue to get skinnier. Having a mast that will stand up with the rigging off is a convenience, but having to seal the darn thing each time isn't.

    I wonder if it is easier to transport the hull this way, since the hull has more reinforcements.
     
  3. Eric Sponberg
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    Eric Sponberg Senior Member

    SC, whether a mast is stepped on deck or on the keel is immaterial to the material used to build it. A keel-stepped mast is always stronger than a deck-stepped mast, on the order of +50%, because of the fixity provided by the deck partners. Therefore, if it is inherently stronger, it may also be a slightly smaller cross-section, and therefore lighter, than a deck-stepped mast. Although, a true detailed comparison may need to be made because the keel-stepped mast is longer.

    A deck-stepped mast is easier to bend because of the lack of fixity at the deck, and that is usually important to top-notch sailors--they like to bend the mast all over the place to alter mainsail shape. This is harder to do with the keel stepped mast.

    Changing the design of the rig for the step is rarely done, usually because that's the way the boat is built, both methods of stepping work just fine, and there is usually little need to change. It involves some pricey reconstruction inside the boat. But if a change is done, it is more common that a deck-stepped mast would change to a keel-stepped mast than the other way around. The reason to do that is to increase the strength of the rig which is important to cruising sailors venturing offshore. A deck stepped mast is much more commonly found on trailer sailers whose rigs are erected and taken down frequently.

    As Phil Sweet mentioned, there may be practical issues as well that figured into the decision to go with deck-stepped masts--transportation, safety of the boat and crew if damage results. Although, in my opinion, it has always been axiomatic in boat design that in dire straits, a deck-stepped mast is almost assuredly going to totally go over the side, whereas a keel-stepped mast usually breaks well above deck, leaving a remnant aboard from which to set a jury rig.

    That's my 2 cents worth.

    Eric
     
  4. FAST FRED
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    FAST FRED Senior Member

    ocean racer, what are the main reasons, besides saving interior space,

    Easier to jury rig a deck stepped mast with short pieces of the old spar.
     
  5. Eric Sponberg
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    Eric Sponberg Senior Member

    On a typical ocean racer like a Volvo class boat, there is hardly any interior to worry about--i.e. it's pretty open, so the space occupied by the mast is not really an issue.

    Most stayed rig dismastings are caused by a failure in one part of the rigging. If something up high lets go, then there might be a broken remnant of the mast left on deck, whether deck-stepped or keel-stepped. If something in the lower shrouds or stays lets go, then a deck-stepped mast generally goes totally over the side, whereas a keel-stepped mast will break between the deck and the first set of spreaders, leaving a piece of mast still standing. Most of the time, when spars fall over the side, they are very difficult to retrieve because of their weight and it being really awkward to do so. So the damaged spars are cut away and discarded so they won't punch holes in the hull, leaving little else on board. With a keel-stepped mast, it is more likely that something of the mast remains that is available for jury rigging.

    Eric
     
  6. PAR
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    PAR Yacht Designer/Builder

    Agreed in all Eric has mentioned. I do think a significant amount of weight can be saved with the below deck portion of the mast missing, as in a deck stepped arrangement. Possibly enough to make a designer consider it, though I'll bet tuning is the major reason for this decision. I've lost deck stepped masts previously and it's the best you can do, to cut away the remnants, before it holes the boat or tears off a rudder, then any value in keeping portions of it for a jury rig.
     
  7. tom28571
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    tom28571 Senior Member

    Eric,

    While I understand that a keel stepped mast is inherently stronger in many respects, the figure 50% is surprising. What element or elements of strength do your mean? On a boat small enough to allow fore and aft control at the partners, a keel stepped mast should be as bendable, or perhaps more so than a deck stepped one.
     
  8. Eric Sponberg
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    Eric Sponberg Senior Member

    Hi Tom,

    In Euler's column buckling equation from engineering principles, the critical buckling load, P, is given as:

    P = C x (PI^2 x E x I)/L^2

    Where, in consistent units:
    PI = 3.14159
    E = modulus of elasticity of the material the column (mast) is made of
    I = moment of inertia of the column cross-section
    L = length of the unsupported column
    C = a coefficient based on the end fixity,
    C = 1 for pinned ends (both ends)
    C = 4 for fixed ends (both ends)
    C = intermediate values for other end conditions such as fixed at one end and pinned at the other, such as a mast, where a keel-stepped mast is considered fixed at the lower end, but the upper ends of the shrouds are considered a pinned end. The precise value is a matter of experience and practice, depending on what kind of designer you are and what sort of risks you like to take. Real life conditions are not perfect, and that is why the coefficients are not cast in stone.

    Safely, one considers a deck-stepped mast to have C = 1.0. For a keel-stepped mast, you could conceivably use a value of C = 2.0, although this might be optimistic, so perhaps it is maybe around 1.5 to 2.0.

    Therefore, if the load at which a deck-stepped mast will buckle (which you don't want to have happen, of course) is at a load P using a C coefficient of 1.0, then the very same mast, with the same rigging arrangement, but stepped on the keel, would have a critical buckling load 50% greater (C = 1.5), due solely to the fixety of the step.

    If the mast can be moved fore and aft at the partners for bend control, then it really doesn't have end fixity, so using a C = 1.5 would be inappropriate. Actually, it would be more like a deck-stepped mast that, in fact, has a longer unsupported length, and conceivably could be considered weaker than a deck-stepped mast because the longer length would lower the critical buckling load, and by a lot because P is an inverse function of L^2. A little bit of extra length has a powerful reduction effect on P.

    By the same token, shortening the length on any panel has a powerful strengthening effect, which is why it is common in sailboat design to pile on the numbers of spreaders. The spreaders are considered pinned connections (usually), and by adding more spreaders, you decrease the panel length and buckling strength goes way up. Play your design cards right and you can reduce the mast section by a size or two, which reduces weight aloft and mast windage. You can take that to the extreme where the extra weight and windage of wires and spreaders becomes deleterious, but you get the picture.

    Interestingly, B&R rigs (Bergstrom and Ridder) which don't have any backstays, do, in fact, have reverse diagonals that drop from the tips of the spreaders and attach to the mast lower down near the next lower set of spreaders or the deck. The reverse diagonals tend to make the spreader connections fixed points, so C goes up to 4 (or at least goes pretty far in that direction) and the mast can be made a lot skinnier as a result--lower mast form drag and less weight aloft. It also opens up the space for improving the shape of the mainsail, which now does not have to be confined to the triangle formed between the mast and where the backstay would have been. The mainsail can be made more elliptical or square-topped, as we see so often these days, because such shapes are more efficient (more lift, less induced drag). So, those are benefits all around just by adding a few bits of wire to strengthen the mast by giving the spreader connections more fixity.

    That's probably a whole lot more information than you were expecting, but I hope that helps.

    Eric
     
  9. tom28571
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    tom28571 Senior Member

    Yes, a lot to digest on Sunday morning Eric. Luckily, I don't really design sailboat masts and just use accepted practice on the smaller boats. I did have a failure on a wing mast because twist in the mast under load was not adequately considered in building the diamonds. The mast burst, with half going over the side, and the repair was hurried and hectic to get to a race on time.
     
  10. steel42
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    steel42 Junior Member

    I'm interested that you use Euler buckling as your criteria for mast design. I'm sure that you know vastly more about this than me, but in my mind the horizontal loads (sail forces) would be dominant, so standard beam bending equations would be of more importance. Effects of spreaders and lower/intermediate shrouds ignored for simplicity!

    For the keel-stepped we in effect have a fixed-pinned beam, and for the deck stepped a pinned-pinned. Maximum stress is identical for these beams, Wl/8Z. For deck stepped it would occur at the midpoint, and for keel-stepped it would occur at the deck attachment. I've attached a graph (left) showing surface stress in totally arbitrary units with keel stepped (blue) and deck stepped (yellow) masts, with identical variables apart from the fixing (masts mounted horizontally with deck along y-axis).

    Deflection is another matter. Clearly keel stepped would deflect less, and I have always thought that this was the argument behind keel stepping - not so much a strength issue (relevant to cruising) but a stiffness issue (relevant to racing). Another graph attached (right) to demonstrate this (with distorted axes).

    So, where is my understanding flawed? Are keel stepped masts really 'stronger' in an ultimate failure sense, or is it just a stiffness issue as I assumed?
     

    Attached Files:

  11. Southern Cross
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    Southern Cross Senior Member

    I apologize for being absent from this post. I hadn't received any email notifications. Thank you all for the replies.
     
  12. philSweet
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    philSweet Senior Member

    steel42,

    If the two masts are stayed identically, then there is a boundary condition at the point of stay attachment where both must have the same leeward deflection when experiencing a given compression. This is due to the stress/strain of the stay wires. Also, the mast isn't really fixed at the partners, it is just a much shorter panel down to the keel, so the stress doesn't rise to its full value compared to a truly fixed base.

    Keep in mind that the Euler formula provides the critical load at the point of divergence. It says nothing about what the stresses are after the buckled condition settles out.
     
  13. TANSL
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    TANSL Senior Member

    If I understand what you mean, I would add that all the formulas that are used to ship scantlings are valid up to what you call "the point of divergence." For example, the formulas which define the bending of a beam, are only valid while the material is subjected to a stress lower than its elastic limit. From that moment the formulas no longer apply. Euler's formula, as all others, is what it is, can be used for certain things, and nothing else. But it is absolutely right to apply for the buckling of a strut. Beyond the collapse, the story changes, of course.
     
  14. steel42
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    steel42 Junior Member

    I take your point about the maximum stress value not falling at the partners. However, if the keel-stepped base does not behave as a true fixed end then stresses will be increased elsewhere surely?

    I'm still not entirely sure why you choose to use the Euler (buckling) formula. In my mind, rigs fail through bending due to lateral forces from sails or impact with the water, not from buckling. Don't get me wrong, I'm sure you're correct, I just can't quite see why!
     

  15. daiquiri
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    daiquiri Engineering and Design

    Euler's equation is a very simple tool for evaluating the main parameters involved in buckling, so Eric has rightly used it to show what happens in two cases. Your graphs are also a good tool for visual comprehension of the effects, but they won't tell you why do those lines look the way they do and what values you should tweak in order to increase the maximum load, like Euler's eq. will.

    As for the lateral forces acting on the mast, they can indeed change the value of the admissible axial load. In order to take it into account the concept of eccentricity has to be introduced. The eccentricity is the offset of the compression force from the principal axis of the beam. The mast bends under the aerodynamic forces, the amount of displacement due to bending at the stays-to-mast attachments is estimated, which is then used as the estimate of eccentricity of the compression force (which is the sum of the stays tensions) in the Secant formula (for example). But that's an unnecessary complication at this stage of discussion, irrelevant to the matter of deck-stepped vs. keel-stepped mast.

    As both Eric and PAR have noted, racers don't like stiff masts. They want to be able tune the rig on the go and in all directions, so flexibility is actually wanted. And that's where a deck-stepped mast is more versatile than a keel-stepped one, due to a higher virtual unsupported length and a possibility of rake tuning.

    Cheers
     
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