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How to do load calculations

2K views 19 replies 14 participants last post by  nhsail 
#1 ·
Are there any engineers on this forum that would like to answer a question for me

How would you perform the load calculations necessary to design a sailboat?

I would like to see a sample or two.

For example:

How would you work out the numbers as to how many and how big the keel bolts need to be?

How about the tang size and bolt pattern on a mast tang.

How about deciding on if you need double or single spreaders on a mast.

If these are too hard maybe show the math for a simpler one and a general description of the process for the hard ones.


I have no immediate project just a curiosity..
 
#2 ·
Are there any engineers on this forum that would like to answer a question for me

How would you perform the load calculations necessary to design a sailboat?

I would like to see a sample or two.

For example:

How would you work out the numbers as to how many and how big the keel bolts need to be?

How about the tang size and bolt pattern on a mast tang.

How about deciding on if you need double or single spreaders on a mast.

If these are too hard maybe show the math for a simpler one and a general description of the process for the hard ones.

I have no immediate project just a curiosity..
David--

We can tell you but...then we'd have to kill you.

None of the questions you've asked are particularly demanding but, absent a knowledge of Statics, Dynamics, Fluid Flow and Strength of Materials, the answers wouldn't be very useful to a lay person.

Regarding Keel bolts, one has to evaluate the possible bending moments about the keel base/hull interface, a basic "baseplate design" problem. The crush strength of the base of the keel stub is the determining factor as far as the number, position and size of bolts. The more salient issue is developing the loading profile of the keel for determining the moments, taking into account the keel's weight (less buoyancy effects) and forces developed as the keel moves through the water, essentially pushing the water aside, as the hull rotates in the transverse direction about its longitudinal axis. For that one needs an understanding of the Bernoulli effects of incompressible hydrodynamic flow, taking into account the period of oscillation of the hull's rotation which gives one the relative velocity of the water flow against the keel as the result of such motion. If you get any of that, let me know...

Alternately, I refer you to "Skene's Elements of Yacht Design"...
 
#10 ·
A lot depends on whether you want to be a handbook engineer (a la Skene's) or a real engineer who understands the underlying equations to avoid applying them incorrectly. It is more than the math - it is choosing the correct math.

None of the questions you've asked are particularly demanding but, absent a knowledge of Statics, Dynamics, Fluid Flow and Strength of Materials, the answers wouldn't be very useful to a lay person.
Correct. There are also engineering design courses that--in a good program--talk about failure modes. There are math classes including numerical analysis that addresses discontinuities in equations where the numbers don't really mean anything. Then there are integrating courses like machine design that show how all the foundational elements are combined to answer real world questions.

I remember our first class assignment in machine design that was a simple blanking plate on a 18" oil pipe. It was a group project and we started running numbers and we were coming up with some ridiculously small sizes for the bolts. By this time we had all spent a work term in a shipyard and a term at sea so we KNEW the bolts were bigger. The upperclassman were rolling on the floor because they knew what was coming. The professor walked us all through the thought process and where we had neglected really important elements of design.

If I recall correctly the class was second semester sophomore year. It certainly is now ( Curriculum at Webb | Engineering, Ship Design & More ). So to answer your questions takes two years of full-time academic study plus some practicum.

It isn't the equations that make answering your question hard. It is the prerequisites to pick the right equations and factors for the specific application that make things hard. Most engineers can look at the curriculum I linked to above and show how each course builds on what you learned earlier.
 
#3 · (Edited)
For the keel (bolts)-
For simplicity and 'initial estimation', the keel attachment would be a 'cantilever'** (root) subject to beam formulas requiring 1/4th (!!!!) the normal stress levels (shear and 'bending moments', etc.) of a simple beam - a known 'civil engineering' structural requirement.
You'd imaginarily (on paper, etc.) take the intended design, pull the boat over from the top of the mast (boat now imaginarily heeling over at about 45° and with a full estimated 'full load' being carried by the hull) and then calculate the stress-strain reactions (according to 'cantilever' beam formulas, or 'finite element analysis' etc.) of its (torque) 'moment' (= center of mass of the keel 'times' the distance of it center of mass to attachment point). You'd then investigate the tensile loads in shear, bending stress, etc. of all the components and their 'reactions' (stress) and deflections (strain) .... and then apply the appropriate customary/scantling 'factors of safety' - multiply the near finalized entire substructure connection strength requirements by a minimum of 3 times for an offshore design, or by minimum of 2 times for a 'coastal' design, or by 1.5 times for an inshore design.
If you were a large scale 'major' builder/designer (ie. a very vulnerable 'deep pockets' entity), you'd probably at least build a subsection keel joint system and physically test (statically and dynamically) to failure to see if 'the numbers' agree to where failure occurs (without and without) the applicable safety factors applied.
This would require the total evaluation of not only the keel bolts but also the structural 'attachment' and 'reaction' points to ensure that not only the bolts would not fail; but also, all the mating and support parts of the keel root structure.

I don't know what you precisely mean by mast 'tang'. However all structural mast attachments would be subject to the same '~45° over' analysis and then safety factors applied. Then, a prudent designer would have the connection physically tested for static/dynamic loads, especially for those shapes, etc that are 'statically and dynamically indeterminate'.
Double or single spreaders would depend on the elasticity and rigidity --- geometric Moment of Inertia (cubed) of the components under load, and a calculation of the 'deflection' of the 'stiffness' of the mast and rigging under calculated maximum expected sail loading, and the calculated 'combined moment arm / reactions' of the boat over at ~45° ....... plus applied factors of safety. This is usually already done by the spar manufacturer. The designer usually then just 'checks' / verifies the application to his/her hull design (weights, developed moment arms, etc. when the boat is over at ~45° and of course with the added 'factors of safety' applied.
In spar design, the 'worst' and 'easiest' mode of failure is by 'buckling failure' - a very exceedingly complex failure mode involving the possible generation of 'infinite' forces by mathematical 'anomalies' set off by 'deflection' of the spar and compression acting along the long axis of the spar. The primary function of 'spreaders' is to enhance 'stiffness' so that the 'sideways' deflection and the potential of buckling failure remains 'small' (the reason why one should set rig tensions by a gage rather than by eyeball).

The designer, of course, then adds his/her own experience of what historically worked and what didn't work during the further exhaustive refinement process/calculations. Most of the 'math' involved would be primarily plane / spherical trigonometry in 'free-body' (x,y,z direction) diagrams, etc. of each individual connection/interface/load bearing point or surface. A lot of this is done automatically by computer programs involved with 'finite element analysis'. The designer's extensive experience would be the final judgement factor in the actual design selection.

** https://en.wikipedia.org/wiki/Cantilever

HAHAHA ... your original questions would be similar to someone contacting a large chemical manufacturer, such a DuPont or BASF: "Gentlemen, Kindly reply with all your information about 'chemistry'". OR ... "Dear Boing Aircraft Company, please explain why the wings don't fall of your 787 airplanes. ... ." ;-)
 
#4 ·
"Quote"
HAHAHA ... your original questions would be similar to someone contacting a large chemical manufacturer, such a DuPont or BASF: "Gentlemen, Kindly reply with all your information about 'chemistry'". OR ... "Dear Boing Aircraft Company, please explain why the wings don't fall of your 787 airplanes. ... ." ;-)

Yea, but if there's a forum with all that information you're good to Go. I'm sure someone like Bob Perry would share a lot if you bought a couple of carbon cutters from him.:laugh
 
#5 ·
No idea about the keel, but the mast design is strait out of Brion Toss' 'The Complete Riggers Apprentice.'

The reality though is few boat parts are calculated from first principle. It can be done of course, but it is far cheaper and easier to just build what has worked. If you built a keel design for a xxx42' and now change the keel to a xxx44 with a scaled up keel, you are probably just going to reuse the attachment method that was so successful on the 42'. Iterate this by a few thousand designs over the years and there is a huge body of knowledge about what works, what doesn't, and what was needed to fix those that didn't.

It's only in the event of very high performance where those calculations get done, which is part of why performance is so expensive.

Look at mast tangs as an example. Any aluminium section that is stiff enough to handle the loads of sailing can pretty much just be riveted into and that's also strong enough to handle the tension loads. I don't know this because of math, but because all aluminium rigs to this point have been done this way and are going fine.

Switch to a tapered carbon extrusion and you may have a problem, because you need to figure out how much extra material you need at the attachments to handle the loads. So the first carbon rig designs were crazy expensive to figure this stuff out. Now days however builders have a pretty good idea how much extra material is necessary, so they don't have to go back to first principle and design it from scratch...

'Your mast looks a lot like the Farr 40' rig, and they used X very successfully, so if we do that on yours you'll be fine.

Unless you care about removing every last ounce of weight, in which case a full laminate study is required, and the cost of building may only be half the cost of the new rig, with the rest dedicated to the design.
 
#7 ·
I used to have plant guys come up to me and ask "where can I take a class to do your job?"

I would answer "6 years in the Virginia Tech engineering department and 35 years of experience in the plant and lab." I think they had something simpler in mind.

I'm betting it would take a 3 credit course, assuming some college background, to explain the process and understand the questions, without even getting to the calculations. That would take years more.
 
#9 ·
Are there any engineers on this forum that would like to answer a question for me

How would you perform the load calculations necessary to design a sailboat?

I would like to see a sample or two.

For example:

How would you work out the numbers as to how many and how big the keel bolts need to be?

How about the tang size and bolt pattern on a mast tang.

How about deciding on if you need double or single spreaders on a mast.

If these are too hard maybe show the math for a simpler one and a general description of the process for the hard ones.

I have no immediate project just a curiosity..
Visit and post the question here for more useful replies:

Boat Design Forums
 
#15 ·
If you were referring to my "scale-up" comment, there is really very little relationship to a half model. I suspect that would nearly always be a mistake. Somethings are linear, some less, some exponential, and then there are the interactions. That is where understanding the underlying science is vital, to know what scales up how. For example, it is generally understood that the energy required goes up about with the 4th power of WL. What does that tell you about shroud loads? Well, it's not obvious, because the dynamic forces go up in a different manner.
 
#16 ·
Any engineer that told you how to do what you are asking would be either negligent or incompetent, or in a few cases both, and some of them are professionally licensed and liable for their suggestions.

You can go and look up on the internet all sorts of formula; the value of the education is knowing which, when and why, and as noted above what the non specified issues are.

Do it for example building a simple truss, and you can figure out what your static load suggests for a given span, then you check the building codes, and then you make it the right size based on practice and available materials, and then perhaps you pay the structural engineer to look it over and correct your mistakes.

regarding either question in addition to some of the above:
What are appropriate safety factors for:
material strength variation in raw stock (bolts, materials the bolts are bedded in or bolted through? mast and rigging material?)
fabrication: sectional variation, voids, nicks, perforations
aging: mechanical fatigue and corrosion?

what is your design life target in years/cycles?
What are the dynamic loads and do you have static creep issues?
Will this boat ever go aground and balance on the keel, at what angle/speed?
Will it ever sail through/off a wave and drop ?

(I'm an electronics engineer, who took mechanics and material 40 yrs ago, and realizes how little I knew then or remember now)
 
#17 ·
I tend to think the liquid forces are more critical than supporting the weight. If the keel is very wide, the side load against the water when a gust hits is pretty significant. I say this because my boat has a light keel, but yet seems to respond to gusts very well. The wind hits, and the heel slowly increases. That means the force of the water against the keel is greater than the weight.

As far as the mast, a second consideration is what you want the mast to do. You can design a very flexible mast, which requires a lot of support, but also bends easily so that it is self compensating for the wind. Or you can design the mast to be totally self supporting. Most will fall somewhere in between, but you need to figure what you are going for first.
 
#18 ·
I do have the education and credentials to say without any doubt that you cannot scale up structural designs. For instance you can make a paper model of the empire state building, but that would be a terrible structural theory to apply to the real thing.
 
#19 ·
Such scaling is done all the time .... but not for magnitudes greater/larger, .... just 50%, 100%, sometimes 200% increase in job/size/etc. and then the scale up is quickly rechecked and recalculated based on the already on file scrutinized/reviewed/checked/rechecked calculations of the OLD design.
The Chemical Engineering, etc. folks have a novel 'rule of thumb' for initial estimating costs for such scale ups ---- "the rule of two-thirds": Cost of original 'times' the scale up factor to the 2/3rds power --- something twice as large will only 'cost' ~1.6 times the cost of the original.
 
#20 ·
Scaling for size tends to follow Square Cubed law, strength goes up as square of scale factor, mass as cube.

Which is why grasshoppers can outjump elephants.

In any structural endeavor you have a lot of factors that a few good humiliating engineering school problem sessions will open your eyes too...
 
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