mast design question...

[mastquestion]

I did a cursory check and could not find answer in prior posts.

Why is the mast allowed to have a lighter section if the mast passes through the deck and is stepped on the keel as opposed to being stepped on the deck?

Thanks for any help on this.

[SailDesign]

For the same reason that you can bounce on a diving board that is resting on two supports, but not on a seesaw ;-)
Think of the deck as an added support at some distance up the mast from its base. Tha tis exactly what it is, so the mast itself can be lighter. In engineering terms this is the difference between a simply supported beam and a constrained beam.
Steve

[mastquestion]

thanks for the response, a few more q's

Why can you not treat the connection at the deck as some level of fixity? Is it because of inadequate backing structure in the deck itself? (assume of course there is a compression strut under the mast from deck to bottom of hull).

So if keel stepped, then fixity is assumed at the base, with a pinned support at the deck, so some of the rigidity from the fixed base at keel restrains rotation somewhat at the deck? Just want to understand this a bit better, thanks for help.

I'm thinking about a vertical lifting keel in a design, with keel trunk under the mast designed as compression strut to support a deck stepped mast, and was wondering about specs requiring higher section properties for deck stepped mast. Perhaps if the trunk could support moment transfer as well, then mast could be deck stepped assuming a fixed base. Then you'd have shorter span as well as fixity?

[Eric W. Sponberg]

To achieve fixity at the deck on a deck-stepped mast, you would have to have a pretty heavy socket or heel fitting to achieve that rigidity. It is hard to do in a very short height.

You have it basically right. In a keel-stepped design, the combination of the depth of bury between the deck and the keel, and a hard clamp around the mast prevents rotation and so achieves fixity at deck level. Since fixity at the deck is inherently stronger and stiffer than the "pinned" connection of a deck stepped mast, the mast section can necessarily be smaller.

For your keel trunk is to support moment transfer from the mast, you have to connect the mast to the keel trunk in a rigid connection. This may mean extending part of the keel trunk structure up above the deck, or extending the mast down into a socket in the trunk.

Lars Bergstrom developed the Bergstrom rig which has highly swept spreaders and shrouds that take the place of the backstay. He put one of these rigs on "Route 66", as well as on some of the "Child" designs, I believe ("Tuesday's Child", "Thursday's Child", and "Hunter's Child", but I'd have to check). An additional feature of this boat's deck-stepped mast was the support tubes, made of carbon fiber, one each side and I think one on the centerline, that mounted on the deck and came to a clamp about 6' above the deck. These support tubes effectively made a rigid connection to the mast at the clamp height, so the mast section could be even smaller than on a normally deck stepped or keel-stepped mast. It was like moving the partners 6' above the deck. Of course, you had to make and mount the carbon tubes. The overall cost and weight of the rig was about the same as a normally rigged boat, but the center of gravity of all that weight, because of the lighter mast section, was a lot lower. The boat's stability was greater as a result.

Eric

[mastquestion]

Eric,
Thanks for response, appreciate the time. Can't the mast rotate at the deck level though (see attached diagram) in a keel stepped mast as well?

[gggGuest]

Originally Posted by mastquestion

Can't the mast rotate at the deck level though (see attached diagram) in a keel stepped mast as well?

Yes, but it won't bend as much with the deck level support as it would without.

[Eric W. Sponberg]

The keel-stepped mast will rotate ever so slightly but it cannot rotate nearly as much as a deck stepped design.

In classical engineering, the compression load on a mast follows Euler column theory in which P is the critical buckling load, that is, the load at which the mast is sure to collapse:

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

Where
E = the modulus of elasticity (Young's Modulus)
I = moment of inertia of the cross-section of the column or mast
L = length of the longest unsupported section of the mast
C = coefficient between 1 and 4, theoretically

If C = 1, then the end connection of the column is defined as pinned, as in a deck-stepped mast. It is free to rotate. If C = 4, the end connection is defined as perfectly fixed and does not rotate at all, as in a keel-stepped mast. However, in real life, fixity is never perfect, and C is rarely more than 2.

So what you try to achieve is as much fixity as possible so that critical buckling load is very high, higher than what you think the mast will ever see. For two masts made of the same material (aluminum, say, E = 10x10^6 psi) and the same cross-section (so the I is the same), right away you can see just on the basis of the coefficient, C, a keel stepped mast (C = 2 realistically) is at least twice as strong as a deck stepped mast (C = 1). Therefore, if a deck-stepped design is strong enough with its value for I, whatever it is, then a keel stepped mast, because it is inherently twice as strong, can have an I that is only half as large. This does not mean that the mast section itself is only half as big because I is a function of the dimensions to the 3rd power (either section breadth^3 or section length^3, or both if both change).

Eric

[mastquestion]

Originally Posted by Eric W. Sponberg

The keel-stepped mast will rotate ever so slightly but it cannot rotate nearly as much as a deck stepped design.

In classical engineering, the compression load on a mast follows Euler column theory in which P is the critical buckling load, that is, the load at which the mast is sure to collapse:

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

Where
E = the modulus of elasticity (Young's Modulus)
I = moment of inertia of the cross-section of the column or mast
L = length of the longest unsupported section of the mast
C = coefficient between 1 and 4, theoretically

If C = 1, then the end connection of the column is defined as pinned, as in a deck-stepped mast. It is free to rotate. If C = 4, the end connection is defined as perfectly fixed and does not rotate at all, as in a keel-stepped mast. However, in real life, fixity is never perfect, and C is rarely more than 2.

So what you try to achieve is as much fixity as possible so that critical buckling load is very high, higher than what you think the mast will ever see. For two masts made of the same material (aluminum, say, E = 10x10^6 psi) and the same cross-section (so the I is the same), right away you can see just on the basis of the coefficient, C, a keel stepped mast (C = 2 realistically) is at least twice as strong as a deck stepped mast (C = 1). Therefore, if a deck-stepped design is strong enough with its value for I, whatever it is, then a keel stepped mast, because it is inherently twice as strong, can have an I that is only half as large. This does not mean that the mast section itself is only half as big because I is a function of the dimensions to the 3rd power (either section breadth^3 or section length^3, or both if both change).

Eric

Eric,
Thanks again for the info. I guess you partly answered me, and I didn't state question clearly enough. I am a structures guy and was basically unclear about the assumed fixity for this case- I know every industry has their assumptions on behavior and was unclear about mast design assumptions- I should have asked what the assumed buckling length is for keel vs. deck-stepped masts and why. I understand the reduction in buckling length for the keel vs. deck-step, but just how much and why. I'm guessing it might be because current criteria seems to work pretty well under typical conditions and safety factors? Engineering judgement? It seems unlikely there were ever physical tests conducted for verification, given the expense required.

[Eric W. Sponberg]

As one goes through the engineering for a rig, there are specific sizes of mast sections that are found in mast catalogues, so you already know the moments of inertia for a bunch of sections. Therefore, I and E are known values. You also know the load, P, which is dependent on the righting moment of the boat, and there are various ways to figure out the total, and the compression in the mast tube at any given height. The only thing left is L, which you determine by the geometry of the rig at hand. You have to decide early on how many spreaders you are going to use; it may be one or two sets, or perhaps two or three, or maybe three or four, maybe four or five. The more spreaders you have, the more fixed points you have (each spreader set is considered pretty much a fixed point) and the more spreader sets you have, the shorter the panel lengths, L, the unknown in the equation for critical buckling load. You want to get the most L out of a given E and I, so you can optimize the rig accordingly. Of course, the cost of the rig rises with complexity (more spreaders), so that becomes a factor as well.

You have to work out the engineering of the mast for each panel, depending on the number of spreaders you have for a given mast height. You have to do this in the transverse direction and in the longitudinal direction. Spreader sets are used for the transverse engineering, and the stays (and inner stays and check stays/running backstays) determine the panel lengths in the longitudinal direction. Therefore, you are checking loads against I for each panel length both transversely and longitudinally.

In aluminum mast sections, there is no way to taper the section as you go up the rig, except in the last panel. Wedge sections are sometimes cut out of the sides of the mast and the front side rewelded to the after side to make the section smaller. Correspondingly, I gets smaller, and weight and windage aloft reduce. This is typical on racing boats, but not common on cruising boats. One can see the advantages of carbon fiber masts where the thickness of the laminate (therefore I and weight) reduce the higher up the rig. Generally, the loads are less at the top of the rig, and they increase panel by panel coming down the rig. A carbon laminate can be tapered, but an aluminum mast section cannot, at least, not easily.

So the answer to your question is, every rig is worked out individually following the above general procedures.

It is extremely rare that rigs are tested, at least at full scale. I do recall some tests done back in the early 1980s that LeFeill masts did to test a mast to destruction on an actual sailboat. Interesting at the time. Rigs are generally pretty easy to engineer because the loads are easily identified and the geometry of the structural parts are pretty simple. Therefore, testing is not really required. In the America's Cup or in grand prix racing, the rigs are usually carbon fiber and are modelled with finite element engineering. But that is because the owners/syndicates are trying to eliminate every last possible ounce of extra weight and to keep safety factors to a minimum. As a result, you sometime tend to see failures more frequently in high-profile races, and that's because those people are just really sailing right at the edge.

Eric

[mastquestion]

Thanks Eric,
Appreciate the explanations, and your time.

[jonsailor]

Eric has done a good job at explaining a lot of the main points.

I worked in Australias largest spar company for 10 years and along with an aeronautical engineer, we developed our own engineering package which was mostly explained by Eric. We then went into a lot more inputs from shroud angles and spreader sweep which was incorporated into the design inputs to give a very accurate result. Many of our masts were engineered at the second panel moments so that we sleeved the bottom to allow for halyard slots and extra gooseneck loads etc while the top panel is reduced with tapers.
Most Spar companies (larger ones) will offer a free engineering service with a quotation. The best individual mast engineer I know is probably Chris Mitchel from NZ who will evaluate your rig on a professional basis. As with all engineering, the main inportance is the inputs of criteria into the equation. One of the most important is the righting moment of the yacht (how stiff) which can be a little hard to achieve from the "backyard" design.

Keep up the good posts Eric..
cheers
Jon www.sayerdesign.com

[catsketcher]

Hello all,

Is there are rule of thumb for compression at the heel of a mast and stability? It seems that a designer should know what the maximum compression loading should be to better engineer the rest of the boat. This is especially the case for catamarans where the crossbeam design is pretty important in the whole design.

Does the mast compression have many dynamic loading variations like when driving to windward and afer you have fallen of a wave? Do you ask the rig designer each time and then multiply by a fudge factor or is there some consensus. I reverse engineered about 10 catamaran's mast beams and had a wide variation of seemingly successful designs. Some would have failed if half a displacement load had been applied on the mast step and others were 6 times stronger. What do Jon and Eric do when designing mast steps and the like? Then again Jon's early boats used concrete engineering so I am sure this was pretty easy

cheers

Phil Thompson

www.foldingcats.com
info@foldingcats.com

[Eric W. Sponberg]

Originally Posted by catsketcher

Hello all,

Is there are rule of thumb for compression at the heel of a mast and stability? It seems that a designer should know what the maximum compression loading should be to better engineer the rest of the boat. This is especially the case for catamarans where the crossbeam design is pretty important in the whole design.

Does the mast compression have many dynamic loading variations like when driving to windward and afer you have fallen of a wave? Do you ask the rig designer each time and then multiply by a fudge factor or is there some consensus. I reverse engineered about 10 catamaran's mast beams and had a wide variation of seemingly successful designs. Some would have failed if half a displacement load had been applied on the mast step and others were 6 times stronger. What do Jon and Eric do when designing mast steps and the like? Then again Jon's early boats used concrete engineering so I am sure this was pretty easy

cheers

Phil Thompson

There is not really any "rule of thumb" because generally the loads are pretty easy to identify, and they all come from the righting moment of the boat. Typically what I and many designers do is assume that the wind loading on the sails is equal and opposite to the righting moment of the boat. This moment is assumed to come from a distributed load along the mast multiplied by the center of its area above the waterline or above the CLR, depending on how you like to design. "Skene's Elements of Yacht Design" by Francis Kinney (therefore what used to be standard practice by Sparkman and Stephens) assumed that this distributed load along the mast was uniform, i.e. a constant value up the mast. Other designers such as myself assume that the load is larger at the top of the mast, smaller at the bottom. In my case, the top half of the mast is uniformly loaded, and the bottom half of the mast has an increasing distribution from zero at deck level to the same value at mid-height as the upper half of the mast. To summarize, then, the lower half of the mast is a triangular load distribution, and the upper half is a uniform distribution. The total moment of these two distributions (center of its distribution for each area to the waterline) is equal and opposite to the righting moment of the boat.

I hope that's clear. This is a live load. Therefore, you need some factor of safety on top of that somewhere in the analysis, either an allowable stress under live load, or multiply your live load by some FoS and calculate back to the yield stress, ultimate stress, or buckling stress, whichever is appropriate. Typical factors of safety may be anywhere from 1.1 to 4.0. My personal belief is that if you have to use a FoS over 5.0, you don't know enough about the problem to engineer it properly. FoS over 5 and you are overbuilding.

So to answer your question, there is a fairly well defined procedure for identifying the loads, therefore we don't need to rely on a "rule of thumb".

Yes, there are dynamic loadings that have to be accounted for. When you get to the grand prix level of design, there are more sophisticated programs that will calculated dynamic motion of the boat, which will translate back into acceleration loads on the rig. These then become identified live loads and you can engineer the rig accordingly. At this point, more detailed engineering will involve finite element analysis to correctly size the mast section, spreaders, shrouds, and stays.

Compression in a stayed rig increases from the top of the mast going down. Each set of spreaders adds compression; halyards add compression, so again, the loads are fairly easily identified and you can calculate the compression at the bottom of the mast and design the mast step accordingly.

Eric

[catsketcher]

Thanks Eric,

I had been using a similar but simpler method to work out compression loading. I have always been interested in dynamic loads and FOS. With my other hat on (I write for a multihull magazine in Australia sometimes) I had the opportunity to ask these sort of questions to Nigel Irens and Peter Ullrich (built the tri B and Q for Ellen Macarthur) and many others besides.

The interesting thing was that in the end it does come down to some sort of empirical feel. When asked about finely tuned engineering Peter Ullrich said that the Sydney - Hobart boats are not fully engineered because no one really knows the absolutely full load conditions these boats go through when falling off a wave (for example). He prefers to rely on a fair bit of experience because the computer may miss something.

Even someone as clever as Nigel Irens can get it a little wrong when pushing the envelope really hard. In the last Route du Rhum he had carbon/carbon nomex/carbon tris ripping apart. So for Ellen's tri he and Peter Ulrich moved away from carbon nomex and even went to the technique of connecting the inner and outer skins every few metres to produce a rip stop effect. Balsa was used in high shear areas.

In terms of mast compression I wanted to make sure there was nothing I was doing that was silly. What would be really good is to put a load cell under the mast and go sailing. It would be fun to see the values I get out sailing to give some data back for the computer.

In the end though the mast and mast step are really being designed for very rare conditions so even though I may get data, unless I really flog the boat I won't get very interesting data anyway. Still, any leads on cheap compression load cells for a 7 metre cat? I would be very happy to go sailing and make the data public. Should there not be a bit of a load cell group to get good data from our boats to give the engineers some real meat to their models. As a science teacher in my other life I really like the idea of theory and experiment going hand in hand. It would be nice to narrow those FOS down a little.

cheers

Phil Thompson

[waikikin]

Phil, theres a company in taren point that has something like that- they weighed a couple of engines for us a year or 3 back, dunno about cheap though, they "charged us" a carton(he he) but to own the gear may be quite different$.I met you when you had the twiggy, I used to sail with Ian,Gladys & Matt on "Glad Tidings" in times past.Best regards from Jeff.