flat vs convex surfaces

In a surface under distributed load, a zero curvature form has significantly higher stress and therefore strain within the surface. In the simplest example, consider a hemisphere supporting a pressure difference. The forces all resolve to compression or tension within the msterial. Trivially easy to support. Replace it with a flat plate and suddenly the forces resolve to high shear loads with the surface.

 

Well put. So, to get a sense of proportions: what would the curve of resistance to load look like in the range of angles from zero degrees for a flat surface up to an angle of 90 degrees for a fully developed hemisphere? Would this be like a sigmoid curve? Extending from this, how much thicker needs a flat surface be to have a comparable resistance to load at the lower angles of curve development? Then I presume the question is how the increase of thickness of the panels can be prevented with internal stringers, if these offer weight advantages for a comparable resistance to load? Are there any rules of thumb here?

 

That would largely depend on the size of the boat. Small boat design in driven by stiffness. As the boat gets bigger, strength becomes driving property. Can you explain what you mean by "resistance to load"? Also, keep in mind that designing a boat, or any other structure, requires a global approach and understanding. What is the goal or the function of this design? If you are simply trying to compare a flat panel to a curved one, there are many engineering textbooks or online calculators that will give you values. Otherwise, if you want to design a hull built of only flat panels, it would depend on how many panels you divide the whole surface into. A 100 foot hull built with panels of no more that 1 foot square would be fairly similar to a hull with fair lines. If the panels were 20 feet square, not so much.

 

This is very helpful, thank you. The intent is a hull with only flat panels. In the extreme, this would be a simplistic rectangular cross section beam with cutouts in the top panel. I wanted first an appreciation of what flat cost vs curved panels. A better term to use is probably "resistance to buckling".

I found these publications:
Proceedings of the Annual Stability Conference Structural Stability Research Council Pittsburgh, Pennsylvania, May 10-14, 2011 Stability of cylindrical steel panels under uniform axial compression. K.L. Tran1 , L. Davaine

K. L. Tran, Cyril Douthe, Karam Sab, J. Dallot, L. Davaine. Buckling of stiffened curved panels under uniform axial compression. Journal of Constructional Steel Research, 2014, 103, pp 140-147. ff10.1016/j.jcsr.2014.07.004ff. ffhal-01073382

Both compare with flat panels. The math is above what I am comfortable with but the lesson I took is that resistance to buckling is asymptotic to the degree of curvature. Also the important effect of defects went counter my naive engineering intuition.

So, the original query can be reduced to how to stiffen a rectangular cross sectioned hull (where Rob used bulkheads, frames and flat in-panel diagonal stiffeners).

 

That's impossible unless you make a shoebox hull. I assume you're referring to developable panels, not flat panels. In that case, most panels will have curvature, at least lengthwise (unless you use very small panels).
On the other hand, it's very hard to find panels that have buckling problems, so that shouldn't be a concern for panels, but it should be for stiffeners.

 

If a brick shaped hull is part of the SOR (Statement of Requirements, in case you hadn't seen the acronym till now) then it still depends on size.

A boat's hull manages multiple loads that vary not just in magnitude, but also in nature.
A hull must resist puncture. A load on the smallest area.
It must handle local water loads. Pounding waves from driving into a wake, for example.
And then global forces. Like when a hull is suspended between two large waves whose wavelength equals the hulls length. All the support is at the bow and stern, with the middle basically hsnging in the air.
It must also be buildable. The NA may determine through art, experience, and calculation that all these demands might best be served by a very thin skin on complex framing. But if that skin is too thin to actually weld or lay up, it still won't work.
So. The smallest boats are governed by puncture resistance and material manufacturing limitations. A one person HDPE corracle that can survive landing on a rocky shore or bumping into a dock doesn't really need any other framing. The thinnest you could make the HDPE skin for that limitation covers all the other issues.
On the other a large ship has a paper thin skin, compared to it's size. The forces that threaten are global forces effecting the ship as a whole. That vessel has large complex framing that requires serious engineering.

So what size did you have in mind?

 

It depends on what type of structure you are designing. Frames, stringers, etc. are not stiffeners, they are the structure. The plating keeps the water out and transfer loads (water pressure, slamming, force from docking, etc.) to the framing. Smaller boats can be of monocoque structural design in which there may be no framing, or just some stringers or bulkheads to spread out a local force. As DogCavalry, if you scaled down a ship to say 20 feet, the plating would be like aluminum foil thickness.

 

I think there is a serious mistake here. Stiffeners are also structure, they are part of the structure that resists the loads on the hull. Without them the structure might not be strong enough to withstand the loads on it.
A very small boat may indeed have no frames but will always have stiffeners of some kind, either as individual pieces or as "natural" stiffeners (chines, for example, central keel, gunwale, ....).

 

Stiffness by configuration w/o extra material. Something that is really lacking in flat plates.

 

The other day I landed on a forum for latin literature seeking a spellcheck on a latin saying that I altered to support a message in a presentation. The forum was littered with threads seeking advice on latin expressions for tattoos. It was delightful to read the erudite discussions among latin scholars eager to find the right latin words to cover the OP's requests. In this thread I feel like the uncut heavy metal rocker looking for a flashy tattoo in latin in time for the next gig.

The motivation for this thread is watching YouTube videos on the construction of 40+ foot cruising catamarans and trimaran in aluminum, fiberglass and carbon. No wonder that the staggering amount of skilled labor and burden on quality control pushes the production to south east Asia. I also saw a Norwegian builder using robot welding on below 20 foot aluminum boats. There was no mention on how much manual welding and mending was still necessary but it was hard to believe the contention that programing the robot only took a day for each model. I also saw the construction of a 60+ foot brick barge prototype in HDPE but found not trace if the barge ever splashed. And 3D printing these sizes has not taken off.

So the question is how far can one push the traditional shapes of a 40+ cruising cat to keep manual labor to a minimum. I understand that building the body of a boat is only about half the labor, but still. So, how to compromise while maximizing straight, flat and perpendicular. For example, going for a shunting drua-like design eliminates the need for rocker; the loss of light wind efficiency may be worth a simplistic brick shaped bottom; a plain rectangular wedge for a bow ? etc... This no-curve bias will dictate its own design spiral.

 

It's an interesting thought experiment, but aside from the most niche of applications, the massive efficiency loss in proplusion would outweigh the minor labour savings. Probably by lunchtime on launch day.

 

Drua hulls shunt, but have near enough semi circular hulls below the water, a lot of rocker and 4 different bow shapes per boat.

A flat, unrockered hull has less wetted surface than a rockered, round one. But it does not need the weight (and build hassle) of fitted floors, nor the added topside height to get headroom. In a lot of boats, the unrockered, flat hull will be faster in the light.

Water likes to travel in straight lines. Failing that, gentle curves. These (not "plain rectangular wedges") are required for brick sections to transform to pointed bows and sterns. These are the waterline shapes of the village suitable boats we are building. In limited testing, they work well, and are easy to build with flat panels.

A data point or 3: The prototype 24m, 3 ton cargo proa hulls, 2 x telescoping masts, rudders and beams and it's 8.5m tender are built from infused, uncored flat panels and right angle shapes where possible (bricks transforming gently to pointed ends). It took 2 slow old guys 2 years to build, having weekends and holidays off and usually working 8 hour days. Because it was a new design and build technique, there was a lot of chat. Because we liked to experiment, there were a lot of samples built, tested and busted. We didn't get it quite finished (fortunately, as it had to go into 2 x 12m container for shipping to Fiji), and the finish is agricultural, but I'd say between 1/3 and 1/2 of the time could have been saved if plans existed and were followed. So 50 x 40 hours x 2 = 4,000 hours, which could be 2-3,000 with plans and motivated workers. We are waiting for MSAF approval for the boat, then expect to build several of them, so I should get a better idea of the hours.

Attached is the video that should have been in my last post. 2 x 315W panels (less than 1 hp), a converted to electric petrol outboard with a too small prop, no batteries. 3 large people on a 6m barge hull with ski tip bow. Just after high tide, so maybe 0.5-1 knots of tide. 4 knots by gps across the tide earlier in the day.

The next iteration, which the students have just started, is a catamaran with low bridgedeck. Empty, it is self draining; driver only, the rear of the bridge deck is immersed, becomes a planing/lifting surface; with 8 people on board, it becomes a barge, but with conventional pointed bows either side of a ski tip front on the bridge deck.

 

Building a hull takes a lot less time than the rest, unless is maybe and open small fishing boat. Further, the market value of a boat built with flat panels will be close to nothing. It would be less than the time and material put into it. Aesthetics are one of the most important aspects of a boat's value.

 

The rough rule of thumb is ;
1/3 shell
1/3 fit out
1/3 rig (standing and running) and sails

Edit. Rig you can update
Fit out you can refurbish
Hull and deck your stuck with.

 

1/3 of what, are you refering to cost, weight, time of construction, etc.?