paperboat design competition

[Hans Lassen]

Dear forumites,

with all that knowledge available here, I wonder if some of you would be willing to give advice on how to best design a paperboat under the following rules:

"Constraints
Mass of empty ship < = 10 g
Ratio length/breadth > = 2
Midship section coefficient < = 0.95
Waterplane coefficient < = 0.85
Waterline, angle of entrance < = 30°


The boat should be built completely out of paper; any type of glue may be used.
The design should allow evenly distributed loading.
Stiffeners, appendages etc. outside the hull and exposed to water on both sides will not be taken into account for evaluation of the main characteristics.
Participants are asked to 'christen' their boats and to label them properly."

I found this competition under www.paperboat.de (http://www.paperboat.de) (there's an English translation, too) and was very much intrigued by it.The idea is to build a paper boat of less than 10 grams that can carry as much weight as possible (the weight being added in the form of lead pellets). I want to participate with a few of my students. We are thinking about a wide double ender hull with outriggers to balance the loaded boat. For the body we will probably use extra lightweight paper for airfreight (?) letters. Any help would be greatly appreciated!

[ 03-04-2003, 01:47 PM: Message edited by: Hans Lassen ]

[Mrleft8]

What is the definition of "Paper"?

[Paul Scheuer]

A little over the 10 g limit, but it illustrates a few things relative to "paper" boats:

This kind of stuff is really fun.

Double-ended designs are simpler to execute.

Outriggers and extreem beam are not required if the plan includes a reasonably stable hull.

The example is 200 lbs with a maximum tested payload of 1800 lb. built to a "stretch limo-" variation of a normal canoe.

Corrugated or honeycomb structures provide better strength for the weight involved.
http://www.imagestation.com/picture/sraid19/pf88b57e109f2924679d943d0b6a61621/fdc77883.jpg

[ 03-05-2003, 01:44 PM: Message edited by: Paul Scheuer ]

[Bruce Hooke]

Well, it seems like the basic issue is how to contain the maximum amount of volume with the smallest amount of material, and thus weight. The ideal shape to achieve that end would be a half of a sphere, but, of course, the rules will not let you use that shape. So, one approach would be to modify a half-sphere just enough so that it fits within the rules. So, squeeze it down so that it is twice as long as it is wide, make the ends just pointed enough so that it meets the waterline entry angle rule, and make sure this puts you within the waterplane coefficient rule. The one rule that seems less relevant to me is the Midship section coefficient because this is trying to stop you from making something with a rectangular midsection, and a rectangular midsection is not the best way to maximize the volume to surface area ratio anyway. Also, a curved bottom is much stronger than a flat bottom and flat sides.

As far as the constuction goes, my suspicion is that simpler may be better -- in other words put almost all the material into the skin of the craft, rather than into lots of fancy ribs and bracing. You may just need some sort of cross-brace at the midpoint (maybe a "bulkhead") to keep the sides from collapsing in. Also, I would make sure that the weights, when added, don't all want to run to the center because then the whole thing might want to fold up like a jackknife. In general, I would think in terms of failure modes and how to prevent them...

I am not familiar with how paper is put together and waterproofed to make a boat but if there is room for various approaches here this seems to me like it might be a key area. You might need to do some experimenting to find the lightest way to keep the boat waterproof long enough for it to get through the test, because it would, I think, be very easy to add a lot of extra weight via the waterproofing...

Good luck and have fun!

[Hans Lassen]

Thank you for the input! Here are three examples of the winning entries of last year's competition. It's not going to be easy to beat 3 kg :rolleyes: ... but we'll try hard!
As to the definition of paper: I guess anything you can write on and fold? I think the stiffeners will require the most work for the grey cells - where to put them, and how to make them with the best ratio of strength/weight. http://www.imagestation.com/picture/sraid53/pec04d085d0e9a497fac1842426159613/fc8b85f2.jpg http://www.imagestation.com/picture/sraid53/p2b4ff237fd481dbdb830d16179e7e549/fc8b85f4.jpg http://www.imagestation.com/picture/sraid53/pdc7d0e4b7d63c6bfe259d3b8e1ea4a1a/fc8b85f5.jpg

The restraints we face seem to be the limits of the flare of the ship's sides. I understand the waterproofing is added after the weighing - i'll enquire which stuff thy are going to use.

[Don Maurer]

Get yourself a copy of the Carene 40 and Carene 50 hull design programs. You can download them free off the internet. They allow you to build a hull using flat sheets of material and calculates the panels for you. They also give a wealth of information as well as letting you try many iterations of your design. The new version of the program is available at http://www.sailcut.com/

[Bruce Hooke]

Well, I have to admit that I'm rather surprised by all the flat surfaces on these craft. I would have thought that curved surfaces would have done better in terms of containing the weight. It may have something to do with the difficulty of making a curved shape out of a sheet material. Actually, in thinking about it now I'm also realizing that the advantages of curved surfaces are probably largely lost when you are dealing with such a thin skin. So, the major factors might be how deep the craft can settle into the water without the sides collapsing in on themselves or simply dropping below the surface of the water. It would be interesting to know how the winners failed when they did fail...Did the bottom drop out, the sides colapse in, water come over the sides,...

Another point to consider is the paper used. Japanese paper (and other similar papers) with long fibers are MUCH stronger than average office paper.

[George Roberts]

"any type of glue may be used."

I like that part. I would abuse the rules as much as possible.

Get a glue that expands as it cures and make curved hollow ribs from it. Use a non expanding glue to fasten the paper on the inside.

I guess that someone could compute the volume of water that 3kgs of lead shot displaces. (lots of tough thinking) Must be 3kgs of water about 3 liters. These are big boats.

How much paper is 10g. Must be a lot.

[TomRobb]

I'd have guessed that your biggest problem is panel stiffness. If insufficient, it'll fold up like a wad of toilet paper.
Why not laminated strips - papier mache - to whatever shape gives the best load carrier that fits the numbers, and thickness (honeycomb paper between inner & outer skins will add stiffness all out of proportion to its weight) to the design limit weight?
Sounds pretty straight forward w/ that design program.
And, yes, abuse the rules - isn't that the point? :D

[ 03-06-2003, 01:01 PM: Message edited by: TomRobb ]

[Paul Scheuer]

Anyone else planning to enter? Deadline is March 31, 2003.

[htom]

One kilogram is about 62 cubic inches of fresh water.

I'd go for a flat bottomed pram shape, with the flat bottom being one side of a triangular beam running the length of the boat, and a thwart or two that were passed through the center of that beam bracing the gunwales (which would curve inwards like those of Bolger's Nymph.) His Ruben's Nymph might be a good starting point.

[John Bell]

The problem with a pram shape is the rules don't allow it. It is required to be pointy on one end.

[John Shin]

I think Bruce has the right approach - designing to overcome the failure mode(s) will dictate the shape. He has identified three obvious ones: the weight of the lead breakes the bottom, the pressure head of the water collapses the boat, or the boat simply becomes overloaded and water comes over the sides. The last one can be easily solved for any given target payload by supplying the needed volume. The other two will make or break the design.

The hull can be thought of as a membrane (thin wall) that must hold the outside pressure of the water. The weight of the lead pellets (I am assuming they are reasonably close to spheres) could be used to create balancing force from the inside. If the forces on the two side of the membrane are kept balanced, the paper needs only to be strong enough to support the small spans between pellets.

A problem with this approach is that the lead pellets are much denser than water - over eleven times as dense. Adjusted for the space between the balls I get about eight times as dense. That means as the lead is loaded, the water on the outside is rising faster than the level of the lead. Also, as the lead continues to be loaded the force at the bottom of the boat continues to increase.

Perhaps the answer is a double hull with a shallow vee bottom. The lead will rest on the outer hull. The inner one one is to make the lead stack against the outer hull in a layer. The shape should be such that the volume of the space for the lead is 1/8th the submerged volume for any waterline (so the levels of water and lead remain the same). Most of the lead would have to fit against the shallow vee bottom as any of them against a near-vertical side would create the problems we are trying to overcome.

That leaves the problem of how to make a double-hulled, shallow-vee bottomed, paper boat that meets all the rules.

[John Bell]

The biggest challenge as I see it is building a structurally sound hull with ~3500 cc of volume out of only 10 grams of paper and adhesive. Ten grams isn't much, it's less than 1/2 oz, 0.3527 oz to be exact. So whatever you come up with better be efficient!

One idea to cheat the rules may be to have a shape that deforms to make more volume out of the avialible surface area as lead shot is added.

[John Shin]

Am I missing something? My dictionary shows 28.35 grams to an ounce. 3500/28.35 = 123 oz and change. If that is right, an 8-1/2 X 11 sheet of 15# paper should weigh 0.85g, and we should be able to use over eleven sheets of it. Of course the glue would use a lot of that weight.

Idea for structural panels: Fit a sheet of paper against a form to hold it in the desired final shape. On another sheet of paper draw circles, say 1/4" diameter and 1/8" apart in staggered rows so the effect is that of a honeycomb. Cut out and remove the circles. Apply a thin coat of glue and apply the perforated sheet to the sheet on the form. Continue making honeycomb sheets and applying them until the desired thickness is achieved, being careful to match the holes. Now apply an unperforated sheet. The resulting panel should be much stiffer than any single paper and quite light.

[John Shin]

No, Paul, I don't plan to enter, but I wish I had the time. To those who do, be sure to let the rest of us know what you come up with. It's a very interesting problem.

[John Bell]

When I get to a lab tommorrow, I'll weigh some paper to give you an idea of relative weights. I just weighed ten sheets of about 35# inkjet paper on a spring scale here at my home and found they weighed about 2 oz total.

FYI, the basis weight of paper is the weight of a 500 sheet ream of C (17x22) sized sheets. A 500 sheet ream of A sized sheets would therefore be one-fourth that amount. By my figuring, a single sheet of 15 lb paper would weigh 15/4/500 = 0.0075 lbs = 3.4 grams.

Looking at the pictures of the boats on the website, they all appear to be made out of ultralight glassine type papers, probably with a high linen (flax) content for strength.

It also appears the winning boat did deform some since it carried about 200 more grams that it was calculated to be able to carry.

THere were some who designed much larger boats, with theoretical capacities around 7kg, but they failed at fairly low loads. The first decision you need to make is how heavy do you need to go to win, then design the most structurally sound boat you can to carry that load and nothing more. It doesn't make sense to design for 7 kg if the boat folds up with 1 kg. The ideal design would fail just as the water was coming in over the rail when it swamped!

[George Roberts]

I would suggest that you make lots of boats and do a lot of testing.

Make the boats in pairs. Test one keep one.

It looks like the two most important issues are:

1) use the right material. As others mentioned thin tough paper is best.

2) be lucky. The 10% differences between the top boats is luck as much as anything else. One poor glue joint, or a bit of imbalance in the loading and the engineering goes bad.

[John Bell]

I just weighed some regular copy paper on a laboratory balance. The paper was 20# G-P Spectrum; the average weight was 4.535 grams per sheet, which is exactly what it's supposed to be.

20 lbs / 4 / 500 sheets = 0.01 lbs = 4.535 grams

[ 03-07-2003, 08:55 AM: Message edited by: John Bell ]

[John Shin]

Ah Ha! I was using a ream of A-size paper. Now my figures match your's, John Bell. Thanks

[ 03-07-2003, 08:24 AM: Message edited by: John Shin ]

[htom]

If the pram had a very deep thin cutwater -- perhaps one sheet thick -- that extended the bow so that the angle was less than 30 degrees ... ah, that bit about appendages not being measured.

[Hans Lassen]

You guys are great - wish I had some of your dedication as colleagues in the physics department :D . Will experiment over the weekend, using VERY light paper. Will have to find glue that isn't too heavy either. The idea about the "expected deformation" is perhaps really where the solution lies... But anyway, we'll enter the competion to win, of course, but we're not going to crumble on the floor, weeping, if we sink with flying colours ;) . My students asked me to thank you very much. I'll keep you posted. Additional input is always welcome.
I love this. smile.gif

[Wild Dingo]

Orrr... you could go to the paper models of the Stevenson Vacationer and Weekenders here (http://www.byyb.org/byyb/model/)
and play around with them??... change the paper used the arrangements etc?? better than just a box? ...fun experiment and from my hoons viewpoint one heck of a fun way to spend a couple of days muckin about!! :D

Best of luck with it mates! :cool:

[htom]

Perhaps a lightweight "ring frame", set horizontally, to contain the incoming weights.