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· Wood costs of building a boat
· The problem of bending boards
· Simple Formulas and a Handy Table for Bending Stuff
· Comments from Yahoo Boatbuilder Group Members on bending wood.
· Why Large Polytarp Sails face Difficulties
The cost of boatbuilding is central to my so-called research. I liken amateur boatbuilding to the US getting to the Moon in 1969. They were greatly constrained by weight considerations, and to lesser extent by cost considerations. Home boatbuilders are constrained by cost and effort. The analogy may be silly ... but it keeps me happy ... very happy. You could once find a link to Michalak's essay, Boat Costs, at the bottom of this page at Links, ect. Recently, I have not found it on the web. I have a backup copy but cannot distribute without verifying that permission to do so is granted.
The cost of wood ranges from 30% to 60% of the cost of the entire boat. I think. Budget boats often have a higher fractional wood cost because cheap wood is not really that cheap. On the other hand, cheap masts, sails, rigging, and surface protection can be very cheap.
Shown below is a chart of the cost of wood versus thickness for various low-cost wood options. Since marine ply made from northern softwoods can be purchased for only about twice the cost the alternatives, we have to consider it as suitable for a "cheap" boat. The ubiquitous 1.5 inch (e.g. "2x4") board may have the most promise in low cost boatbuilding. At less than $1 per pound these thick boards might make cheap ballast, more expensive than water, but much easier to construct and maintain, perhaps. If placed at the bottom of a flat hull, the difference in mass density between the materials is not very significant.
Keep in mind that I have yet to convince myself that home construction lumber has any suitability as material for the hull of a boat that is intended to last. That is the spirit of this entire website. It's amateur science ... but it's real science. Don't look for practical boatbuilding tips. Instead, look for ways to contribute with your own investigations.
I obtained this data from a local Lumber yard (Carters), as well as two or three sources on the internet. The local lumberyard had the best prices in every category.
Here I introduce a simple model for the bending of wood without the use of steam or chemicals. This is a "model" because all equations, graphs, and tables are just a "model" of reality. See Plato's Allegory of the Cave. The model is "simple" because it is restricted to the so-called "elastic" limit of gentle bending, because I assume that the thickness of the wood is small compared with the other lengths, that the bending is an exact arc of a circle. Above all, the model is "simple" because wood is complicated. I developed this model and posted it on the internet to see what others thought. Their comments cause me to believe that this is a bad model, in spite of the fact that the math is right. The problem is that wood is like people; nobody's perfect, any board that is not "perfect" will not will not exactly obey these equations. The model does seem to work with plywood ... or so they say.
This section is divided into two parts:
The first section states a simple formula and concludes with a useful table that anybody can use quickly.
The section section derives the formula and shows how I obtained reasonable values for the factor "P", which can only be obtained from real-life experience with bending wood.
I would greatly appreciate any data anybody wishes to contribute: If you tell me your "rule" for bending wood, I think I can incorporate your data into this discussion. I am also interested in knowing how close people are willing to come to this breaking point.
Click here to see comments from boatbuilders. They ALL say that these tables and charts are not reliable.
These variables are the boards thickness, "T", the deflection of the board, "y", and a parameter I call "z", which is approximately equal to the length. The picture to the below and to the right shows these three parameters
When you are gently bending wood to form a boat, there are actually two lengths to think about. The figure to the right (above) depicts the length of the board before it is bent as "s", and the length along the axis of the boat, "x". My parameter "z" is between these lengths and has the advantage of permitting simple clean formulas. Simple but nasty-looking trig formulas can be used to replace "z" by "s" or "x".
The formula is:
Ymax = 0.005 P z2/T
I had to include one more parameter, "P", which is the maximum possible strain on the wood, in "percent". My best guess is that the estimated breaking point occurs at at a strain of 0.004 = 0.4% (P = 0.4). Of course nobody would want to bend the wood this far.
Example: Suppose you wanted to build a 22 ft boat using bottom planks that are 1.5 inches thick. From the figure, we would be bending about 11 ft of board. We must convert 1.5 inches to 1.5/12 =0.125 ft. Taking P = 0.4, we have:
Ymax = 0.002 z2/T [Estimated Breaking Point]
Ymax = 0.002 (11 ft)2 / (0.125 ft) = 1.94 ft [Estimated Breaking Point]
Personally, I would not want to bend wood to within a factor of 4 of this limit. So I would go to about 6 inches. Does anybody agree or disagree?
The above formulas work for any consistent set of units. Hence, if you a bending wood for a small model boat, and the wood is 11 cm long and 0.125 cm thick, the maximum deflection is 1.94 cm. Sometimes it's nice to use inconsistent units. I like to measure wood thickness in inches and all the other dimensions in feet. Hence the following formula:
Ymax (feet) = 0.024 (Z-ft)2/(T-in) [Estimated Breaking Point]
Taking the previous example of an 11-ft board that is 1.5 inches thick, we get the same answer: Ymax = .024 x 11 x 11 / 1.5 = 1.94 ft.
Handy Table: We can get the same result from the following table, which I made from the formula above (at P = 0.4). The table does not show a 1.5 inch thick plank that is 11 ft lont. But the average results for 10 ft and 12 ft is 1.95 ft.
|
Estimated Ymax (in feet) at rupture in feet for various board lengths and thicknesses. The maximum strain is taken to be 0.004. As stated before, with low cost planks, I would dived all values of Ymax shown below by a factor of perhaps 4. |
||||||
|
|
Thickness of board |
|||||
|
|
0.25 in |
0.375 in |
0.5 in |
0.75 in |
1in |
1.5 in |
|
Length |
|
|
|
|
|
|
|
1 ft |
.096 |
0.064 |
0.048 |
0.024 |
0.02 |
0.016 |
|
2 ft |
0.38 |
0.26 |
0.19 |
0.13 |
0.10 |
0.06 |
|
3 ft |
0.86 |
0.58 |
0.43 |
0.29 |
0.22 |
0.14 |
|
4 ft |
1.54 |
1.02 |
0.77 |
0.51 |
0.38 |
0.26 |
|
5 ft |
2.40 |
1.60 |
1.20 |
0.80 |
0.60 |
0.40 |
|
6 ft |
3.46 |
2.30 |
1.73 |
1.15 |
0.86 |
0.58 |
|
7 ft |
4.70 |
3.14 |
2.35 |
1.57 |
1.18 |
0.78 |
|
8 ft |
6.14 |
4.10 |
3.07 |
2.05 |
1.54 |
1.02 |
|
9 ft |
7.78 |
5.18 |
3.89 |
2.59 |
1.94 |
1.30 |
|
10 ft |
9.60 |
6.40 |
4.80 |
3.20 |
2.40 |
1.60 |
|
12 ft |
13.82 |
9.22 |
6.91 |
4.61 |
3.46 |
2.30 |
|
14 ft |
18.82 |
12.54 |
9.41 |
6.27 |
4.70 |
3.14 |
|
16 ft |
24.58 |
16.38 |
12.29 |
8.19 |
6.14 |
4.10 |
|
18ft |
31.10 |
20.74 |
15.55 |
10.37 |
7.78 |
5.18 |
|
20 ft |
38.40 |
25.60 |
19.20 |
12.80 |
9.60 |
6.40 |
This "derivation"of
the basic formula assumes a knowledge of calculus, and is little more
than the basic equations and figures involved:
Solve for y to get, y = (0.5M)(z2/T), where .01P = M = dL/L is the maximum strain. Actually, the formula for the change in length dL/L = T/R may overestimate the actual strain. I have assumed no strain on one side of the wood. This is reasonable because many boatbuilders will not optimize the location of zero strain by subjecting the wood to the right amount of tension or compression.
I once bent quarter inch thick piece of clear pine lath to near the breaking point. The deflection was .75 in and z was 6 in. Hence the maximum strain was (2)(.25)(.75)/36 = .01, or about 1%. I know I was near the breaking point because the board snapped on a prior attempt. I also bent it around a single point, so the maximum radius of curvature was less than the z2/2y
The table below shows data for Douglas fir. As I understand the chart, the only modulus of elacticity (strain/stress) is 1550k psi. For the ultimate strength parallel to the grain, I take the minimum of 12300 psi and 6500 psi. This yields a strain of 6500/1550000 = .004, or 0.4%.
|
Strength value |
Douglas fir |
|
Density at 12% moisture content [pounds per cubic foot] |
32.5 |
|
Static bending: fibre stress at proportional limit [pounds/sq. inch] |
6700 |
|
Static bending: modulus of rupture [pounds/sq. inch] |
12 300 |
|
Static bending: modulus of elasticity [thousand pounds/sq. inch] |
1550 k |
|
Compression parallel to grain: fibre stress at proportional limit [pounds/sq. inch] |
4850 |
|
Compression parallel to grain: maximum crushing strength [pounds/sq. inch ] |
6500 |
|
Compression perpendicular to grain [pounds/sq. inch] |
1100 |
|
Shearing strength parallel to grain [pounds/sq] |
1000 |
|
Hardness [load required in pounds] |
640 |
|
Tension strength parallel to grain [= modulus of rupture ] |
12300 |
|
Tension strength perpendicular to grain [pounds/sq. inch] |
130 |
This is a wonderful site that may not stay up too long. He quotes the following table from "Boatbuilding Manual 3rd edition" by Robt. M. Steward (1987).
|
Plywood thickness |
Minimum Radius (across grain) |
Minimum Radius |
|
1/4 |
24 |
60 |
|
5/16 |
24 |
72 |
|
3/8 |
36 |
96 |
|
1/2 |
72 |
144 |
|
5/8 |
96 |
192 |
|
3/4 |
144 |
240 |
Using Excel to convert these into strains (T/R), I then graphed the results:
LC wrote: It's important to know how clear the grain is.
NM wrote: Formulas
should work fine for plywood but solid wood is highly variable.
Moisture content, ring density, reaction wood, shakes, how it was
dried, how it was milled etc can throw off mechanical properties you
find in any table. Experimental stress analysis is your best option
or use a large factor of safety. Read Bruce Hoadley's books. I do
applaud your efforts though.............Now to answer your question
(How much can you bend wood?)...Until it breaks.
MC
wrote: Formulas should work fine for
plywood but solid wood is highly variable. Moisture content, ring
density, reaction wood, shakes, how it was dried, how it was milled
etc can throw off mechanical properties you find in any table.
Experimental stress analysis is your best option or use a large
factor of safety. Read Bruce Hoadley's books. I do applaud your
efforts though.
My response: There is a problem with experimental stress analysis. Since a planked boat can have over 10 planks, we must multiply the chances of 1 plank breaking by about 10 to get the chances of failure in the boat. If you want that probability to be less than 1 in 100 (pretty risky sailing!) then you need to test about 1000 planks. No thanks.
WCS wrote: Anhydrous
ammonia can be used to make extreme bends in wood. I've seen photos
of square pieces of wood tied in a knot. If the link below won't
work, try googling ' bending wood anhydrous ammonia 'for more
information.
http://www.allbusiness.com/furniture-related/office-furniture-including/644819-1\.html
My response: It just never ends. Now I have something new to investigate. Don't local corn and bean farmers use this type of ammonia?
If you like the science of boatbuilding, you MUST visit Jim Michalak's website. The aforementioned link may not work, and I don't know where to get his essays any more. You might have to scroll down to the bottom to reach his index. His essays are much better than mine for the simple reason that Jim has lots of practical advice and he knows his stuff. Some of my favorite Michalak essays are
o Boat Costs
o Sail-Area Math
o Ballanced Lug Jiffy Reef
o Ballast: water Calculations 1 Calculations 2 Calculations 3
o Knockdown Recovery: Part 1 Part 2
Duckworks
Magazine The
Online Magazine for Amateur Boatbuilders
Short
and long
essays about Phil
Bolger, who greatly influenced both Jim Michalak, as well as the
home boatbuilding community at large.
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I always need more information: You may email comments to guy.vandegrift@wright.edu
