# placement and spacing of frames

Discussion in 'Boat Design' started by alanrockwood, Jul 3, 2011.

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### alanrockwoodSenior Member

Suppose the spacing of frames is 1 meter apart. How does one handle the placement of frames with respect to the two ends of the boat? Is the spacing from one end of the boat to the closest frame taken to be one half meter (i.e. 1/2 of the frame spacing), or is it taken to be one meter (i.e. 1 of frame spacing) or, or is it some other value? That is my main question at in this post. My uninformed opinion is that the right spacing would be one half meter (i.e. 1/2 of the frame spacing.)

A second question: If one has a scantling rule for frame spacing (let us say from Gerr), does one use that number strictly, or does one try to make a minor adjustment so that an integral number of equally spaced frames will fit into the length of the boat? My uninformed opinion would be that one would adjust the spacing downward (i.e. number of frames upward) so that an integral number of equally spaced frames would fit into the boat.

Thanks.

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### PARYacht Designer/Builder

If using a scantling rule, you're best advised to stay as close as possible to the rule, given you don't understand the math behind the rule. This said, Geer clearly states you can adjust the spacing and dimensions of structural elements using his scantling rules, though there are limitations. In creasing spacing or decreasing dimensions should be done with the caution, that you're increasing point, local and global loading situations.

You question about frame spacing in the ends of the boat needs much more definition, as we frankly haven';t a clue what you're talking about. Are these ring frames, bent frames, sawn frames? Boat shape, build type, materials employed, etc., etc., etc.
As a rule you'd start you 1 m spacing directly aft of the bow and continue until you run out of boat. This is true unless you have circumstances that require additional stiffness or strength in certain areas (such as impact and slamming loads in the fore foot, or the planning patch aft, etc.).

An equal number of frames aren't necessary and is often the case. Structural elements are placed where they're needed, some moving fore or aft of an equally spaced location, for the convenience of the accommodations, engine or other equipment installation, etc. In other words if you have a bullhead for the aft wall of the cabin falling 120 mm aft of the evenly spaced frame location, then move the frame to the bulkhead, so you can employ both in the same location. This saves weight, improves strength and makes life easier. Adjusting frame spacing down ward from Geer's rule will just make the boat necessarily heavy. Geer's scantling rules are not going to produce a light boat anyway, so if the logical frame spacing in your project comes up one short of Geer's recommendations, you'll be fine.

Lastly, this assumes you have some clue as to the engineering concepts behind the building method and how the structural elements interplay with each other. If you're guessing, which it appears you might be (not an intentional dig at you, just an observation based on your questions) then stay close to Geer's recommendations. The result will be a wholesome and well founded build.

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### alanrockwoodSenior Member

No offense taken PAR. I am in a learning phase, sketching out hypothetical designs. I am not planning to build my hypothetical designs.

Regarding Gerr's recommendations, that is what I am basing my thoughts on. I have worked part way through his book. However, the information in the book is not quite complete, which is one reason I am asking questions of those who are (hopefully) more knowledgeable than I am. For example, Gerr's book does not answer the question I posed for this thread on the positioning of the frames.

Regarding unequal spacing of frames, your comment about adjusting the frames in response to other elements of the boat design is interesting. In general though, based on general considerations one must expect that uneven spacing (or more correctly I should probably say "deviations from optimal spacing") is likely to lead to weak areas in a hull. For example, offsetting a single frame from its natural coordinates will leave an area of weaker strength, i.e. the longer span that resulted from the shift in frame. There would also be a stronger area, i.e. the area where the frames are closer together. However, the weaker area would be the more important in terms of likelyhood of failure.

By the way, has anyone done a study to determine what the optimal spacing profile is for frame placement in a simple hull? If so, is it evenly spaced. My guess (only a guess) is that it would likely be some kind of uneven spacing, whith evenly spaced framed being used in practical designs mainly because it is easier to design, or perhaps out unchallenged tradition. I haven't defined "simple hull", but it would probably be something like a hull with a uniform cross section over it full length, or some other relatively simple and well-defined geometry, perhaps with some kind of tapered ends.

Speaking of a simple hull, I am reminded of the farmer who asked the physicist for advice on improving the egg yield of the chicken operation on the farm. The physicist went a way for a month and came back with a theory based on a model based on an abstraction that started with the phrase "consider the spherical chicken...."

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I must say, I do despair when I read posts like this.

So, you’re uninformed opining and guessing leads you to make firm conclusions:

Or,
you do know, based upon your own reasoning, in which case, why case ask if you already know?

I mean no disrespect, but either you do know or you don’t. If you don’t, say so, and don’t offer spurious conclusions with no engineering based rationale.

So, back to the question:

It is very simple.

It is weight versus cost. On slow speed boats it is cost, on high speed boats it is weight...and then those inbetween mix it up!

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### AlikSenior Member

For frame spacing of small craft, we do this way:

- Define general arrangement of boat
- Define accommodation and watertight bulkheads that would be used as structural
- Split distance between those bulkheads into even spaces
- Verify spacing taken by structural calculations, adjust if required
- Play with longitudinal stiffeners and finalize the structural concept

Directive spacing is the worst thing one can do for small boat. Put the frames where You need them first, and as often as required from scantlings.

The only reason for having frames more often at ends was construction technique. Form point of view of design loads, it is not always necessary.

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### CaptBillCaptBill

But chickens are built with their frame spacing set on the Golden Section....which goes like this..

Measure LOA, multiply that by .618 (30'x0.618 = 18.54)

Now you have 18.54 and 11.46 (30-18.54)

Now you have your main bulkhead spacing (18.54 from bow, 11.46 from stern).

THEN..do the same thing all over again with the two divisions (18.54 and 11.46)

18.54 x .618 = 11.45772 (notice the close match to 11.46)

and again....

11.45772 x .618 = 7.0808

7.0808 x .618 = 4.3759

This is what makes an egg so strong relative to its thin shell.

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### alanrockwoodSenior Member

Let's clear up a few things. I am a neophyte in terms of boat design. I am not a neophyte in terms of physical theory or mathematics. My background in those areas is probably at least equal to yours. I have, for example, published nearly one hundred peer reviewed scientific papers in a variety of disciplines, ranging from physics to instrumentation design to analytical chemistry to clinical chemistry to medicine.

It seems your big issue is with my assertion that placing frames at a non-optimal spacing is likely to lead to weak areas in the frame. It suspect that this is actually a rather non-controversial point for most engineers or scientists. However, to discuss it in detail, this is a conclusion that can be reached on quite general principles.

"Optimal" means, a best possible result. It is a rigorous mathematical result that any deviation from optimal results can, at best, result in a second equally optimal condition, i.e. one that is as good as but no better than the first. (Here I am talking about global optimization. Locally optimal conditions are a little different in some respects, but most of the considerations are the same, provided one restricts deviations of variable around the locally optimal condition.)

In almost all cases deviation from an optimal design is going to result in a sub-optimal design, which in the context of the present discussion means one using the same number of frames, but placed differently from the optimal placement, resulting in a reduced strength.

Now, consider the nth frame member, which in the optimal design is placed at coordinate xno, where the subscript n refers to the nth frame member and the subscript o refers to the optimal location of that frame member. Let us assume that the strength (shall we say the point that exceed the elastic limit of any part of the structure for a given force profile?) is a continuous function of the coordinates of the frame members. (One could generalize this to discontinuous functions as well, but let's not venture into that territory. This case would change some of the mathematical details, but not the general considerations.)

Let us further assume that the strength function is twice-differentiable, at least in the local space where all the coordinates are near their optimal coordinates. Under these conditions any change in the position of xno will result in either an unchanged strength or a reduced strength. In most cases it will be a reduced strength. One can put this rigorously as

partial derivative of S with respect to xn = 0

S strength (defined above as yield strength), which is a function of the coordinates of all the frame members, and the derivative is evaluated with all frame members in their optimal positions, etc. There is also a second derivative condition that one would apply to assure that the locally extreme value of the function is a maximum and not a minimum.

All this is very general and is covered in basic calculus courses.

What this means of course is that if you vary the position of the frame members away from an optimal position it will weaken the hull. One does not even need to know the details of functional form of the strength function, except to constrain it in certain very mild ways, such as the differentiability of the function. For example, one would not need to know if the decrease in strength were a quadratic function in the displacements away from the optimal position, or a third order function, or fourth order, or whatever

In most physical problems the loss of "optimality" (my terminology) will be a second order function of the displacement of the variables from optimal values. This is not a requirement, but it is the usual case for physical systems. In certain highly optimized designs in certain types of problems the loss of optimality may be a higher order function. For example, taking an example from my own professional background, in time of flight mass spectrometry one can correct the flight time so that various orders of derivatives of the flight time as a function of kinetic energy are all zero up to a certain derivative order. However, in most physical or engineering problems optimizations are not carried beyond setting the first derivative to be zero.

What does this mean as far as boat strength is concerned when one moves a frame member away from the optimal position? It means that, unless hull strength is extremely different from most physical systems, small deviations from optimal will produce a design that is nearly optimal, but with the loss of optimality will likely be proportional to the second power of the deviation, or in other words, small deviations won't matter much, but large deviations are dramatically worse.

Note that all this can be concluded from very general considerations and will be valid unless the strength properties of boats are vastly different from most optimization problems in physical systems.

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### alanrockwoodSenior Member

Alik,

Thanks for the comments. Can you clarify some terminology for me? What do you mean by "Directive spacing"?

On the placement of frames near the ends, if I can make a leap of interpretation, one would consider the end of the boat to be at least as strong as one of the interior frame locations, and therefore there is no need to place the first and last frames any closer to the ends of the boats than they would be to the other frames. Is that a reasonable "plain English" interpretation of the concept?

CaptBill,

I like your analysis (chuckle), but are you sure you haven't omitted a factor of pi somewhere?

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### AlikSenior Member

Directive spacing is spacing defined directly by scantling rules, say frame spacing depending on length of boat. This is old style and not used in most of todays structural calculations.

This depends on design loads. Say, for ABS sailing yacht rule the design load for bottom plating of bow overhang is 0.8h at fwd end of LOA, and 1.2h at 0.05LWL to 0.35LWL, where h is design head. So once for bow overhang design load is smaller, why that area should be associated with smaller spacing?

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### alanrockwoodSenior Member

My conceptual (and probably wrong) reason for spacing the terminal frames (relative to the end of the boat) are based on a concept of continuation, i.e. if I were to make the boat longer then half-spacing at the end would allow the pattern to continue with the same spacing. (I am probably not explaining the thought process very well.) It was based on the idea (probably wrong) that the end of the boat would resemble the mid-point between frame members more that it would resemble a frame member itself. If one can consider the end of the boat to be at least the equivalent of a frame member as far as strength considerations are concerned then it would seem to not be necessary to reduce that distance.

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### alanrockwoodSenior Member

By the way, in very rule-of-thumb terms, how do typical scantling rules compare to first principles designs? Are they (scantling rules) generally extremely conservative?

Also, do scantling rules very often give a wrong (by this I mean unsafe) result?

I presume that they tend to be very conservative compared to a first principles calculation and seldom produce an unsafe result, but I would like to hear informed opinion on this.

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### AlikSenior Member

I suggest You get the following books/rules:
- start from Larsson, Eliasson 'Principles of yacht Design' where basic principles of structural design for small craft are explained (with samples from ABS and ISO12215);
- ISO12215-5 that is today's standard for structural design of small pleasure craft (available for purchase from iso.org);
- Rules for small and special craft of other classification societies, say GL, LR, DNV - most of them are in free access now, but more complicated compared to previous ones;

Look at principles involved in structural calculations; I am sure with Your maths-based approach this is best way to study.

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### CaptBillCaptBill

That's just it... the physical system in play here is fluid dynamics. Look at a breaking wave. What you have is a PERFECT fibonacci spiral. The Golden section is there, like it or not. We must conform to it...it won't change to suit our chosen frame spacings. Therefore embracing it is embracing the realities of that which exists.

Want to test it in another physical system to see (hear) it in action? Pluck a guitar string (open, no fingers on the fretboad). Now lightly touch the string at the center (from nut to bridge). What happens? Thud...It absorbs all the energy and stops resonating completely. Now pick it again and measure exactly .618xlength and touch there. You just found the harmonic center, which instead of going deat (thud) you get a nice harmonic ring one octave higher. The string is still resonating. The energy still 'flows'. This is a natural process that you can use to your advantage when determining your frame spacing. Notice that ALL guitar fretboards ring harmonically at this.618 ratio.

What you want is your MAIN bulkhead centered so that it falls at this same harmonic point, just like a guitar fretboard does. Now the hull will will be balanced harmonicly and will pass the energy efficiently in both directions vs. a 'thud' in one or the other

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### AlikSenior Member

The problem of using first principles for structural design of boats is that one needs definition of design loads. The Rules define those loads; after that one can use a) first principles or b) formulas from rulebook to define thickness, section modulus, etc.

Problem is that the design loads in different Rules can be 3 times different; sometimes applying first principles to them would cause poor result. Say, design loads of GL for wet deck of catamarans is much higher compared to ISO and LR; but rest of design loads (bottom, side) are smaller. For general strength of cats, loads applied in ISO are much higher compared to LR and GL. Definitely the loads are associated with structural methods used in particular Rule.

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### alanrockwoodSenior Member

A few weeks ago I downloaded a PhD thesis on comparison of various scantling rules. It was written by someone in Italy. I don't recall his name. I have not tried to read it.

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