All-plywood birdsmouth hollow mast

[Aharon]

The plans for the Werzsko dinghy I am building Werzko 4.5 - 15' ply stitch-n-glue sail dinghy call for a 20’ (6.300 mm) mast. According to plans its approximate section is 57 x 73mm (2 ¼” x 2 ¾”), 2mm thick walled, Luff groove aluminum alloy mast, with a “required transverse moment of inertia” of 14cm4.
Looking for affordable, diy ways of getting a staff and boom, I learned about birdsmouth construction. While “lurking” and learning around, here and in other forums, I came about this:

“Here’s a simple calculator (http://www.engineersedge.com/calcula...re_case_12.htm) for the moment of inertia and section modulus of round tubes; you can put in zero for the ID of a solid mast.
This assumes that you don’t make the wall very thin; the failure mode is different in that case.
If you play around with it, you’ll find that the larger diameter and thinner the wall, the lighter the weight for a given strength. For example, a 4-1/2” diameter mast with a 3/16” wall has the same section modulus as a 3” solid, but 35% of the weight. That’s way too thin a wall in wood, I think; I expect it would fail by splitting along the grain unless perhaps you could find a way to make a hollow plywood tube.” (In woodboats by Mr. Wilson. Maybe he even cohabitates in this here noteworthy forum).

I think I have a solution to the problem posed by Mr. Wilson, and I will make my first mast like this, unless you say I am crazy.
3 stripes (1.2” wide) from a 240 (78.5”), ½” marine plywood board scarf jointed make one 20’ stave (1.2” wide). 24 needed for 8 staves and a 3" diameter mast.
The mast will be cylindrical (no taper, as in “kiss”). Two opposing staves to be protected with tape, to allow a two-part mast for insertion of hard points and anti-moisture treatment.
Once planed and sanded, a first 10 cm wide strip cut from a 3.00 mm “aviation marine-grade plywood” sheet is glued in an upward helicoidal fashion, clockwise. The “step” of the winding is kept regular at 10 cm. A second stripe is then glued side-by-side with the first one. Then the same process is made, but this time counter-clockwise. The whole mast is tied (several methods available), excess resin squeezed out, then put in a straight jig to let the glue set.
I believe the resulting “plywood tube” would be very strong and light. What do you think?
Any need for an external fiberglass "condom"?

[PAR]

You method creates more issues then it solves. Plywood is a silly material for a spar for obvious engineering reasons and precisely why you don't see it used in mast construction.

A molded mast on the other hand, from thin veneers, oriented where the loads will be, could be an alternative, if much more labor and material consuming method.

[Aharon]

Thank you PAR for your comments, I respect them a lot.
As a last attempt at this, suppose I used 1/2" thick pine for the staves, and then did the twin, ultra-thin plywood outer layers as proposed: would I get "the best of two worlds", that is, the lightness of a hollow mast, and the structural strenght of the aviation plywood?

[gonzo]

Plywood is a bad choice for a mast, unless you are going to fiberglass over it. If you are using 1/2" for that mast section, there is no need for plywood outside.

[PAR]

Plywood is a bad choice for the mast because 1/2 the grain orientation is facing the wrong way, which places it in the "along for the ride" category, which is (again) silly in a spar, where maximum fiber orientation, per pound is the goal. The reason we use Sitka and white spruce for spars is their very high weight to strength ratio. Plywood is quite strong, but also quite heavy in comparison.

You can't just guess at stave thicknesses Aharon. The stave dimensions need to be application specific, which several "qualifiers" added in to insure it's strong enough, for the application and material choices.

It's actually a fairly simple set of engineering problems, unless you're going weird (rig) on us. If you want general birdsmouth dimensions I can provide them (for free too), but I'll need to know the boat's approximate full up weight (crew, fuel, engine, cooler full of beer, etc.), the general dimensions of the boat, the amount of sail area, the type of rig (be specific) and how it's stayed, how will the boat be used (racing, cruising, deep water, coastal), etc.

[Aharon]

Wow PAR, this is very generous from you – thanks! Although I used the “karkuretor” mentioned to arrive at the stave thickness (the 3” OD was pure guesswork), I am thankful rather than offended, because I know I must sound as “green” and inexperienced as I really am. A double 3mm ply, counter-oriented helicoidal outer "casing" seemed a good idea to add strenght without adding much weight. Oh, well!
The boat is an S&G dinghy designed by Radoslaw Werzsko (www.dinghy.pl) and the plans are offered for free. The version I’ve chosen (4.5) has a LOA of 15’, beam of 162cm (63” ¾), hull height (sorry, don’t know the maritime term) is 50.5 cm (about 20”) without daggerboard. The overall weight (with me, son and beers) will be around 300 Kg.
The plans call for a 20’ (6.300 mm) Luff grooved aluminum alloy mast, approximate section of 57 x 73mm (2 ¼” x 2 ¾”), 2mm thick walled, , with a “required transverse moment of inertia” of 14cm4.
Sailing rig is the "bermuda sloop" - mainsail @ 8.5 sq.m. and jib @ 3.5 sq.m. 3 stays, one aft and two tied to the sides.
The tension points are the hound, which is located 1800mm (6’) down from the top of the mast; the spreaders, located 12.8’ from the top of the mast; Perhaps the masthead cage (which was “fitted into the spar” in the original aluminum version) could be carved out of a harder wood, and glued there as a finishing piece?
The use will be coastal.
If I missed any necessary information, please be patient (I can see you are) and let me know. Any help will be much appreciated.
Aharon

[TeddyDiver]

Originally Posted by Aharon

That’s way too thin a wall in wood, I think; I expect it would fail by splitting along the grain

You think wrong.. the problem with too thin walls is buckling, no matter what's the material. Common solution against this to happen are transversal walls or frames inside the tube (like in bamboo)
BR Teddy

[PAR]

Assuming the fractional rig, staying as described and a 20% wall thickness for an 8 stave birdsmouth mast: a light racing spar would be 2 5/8" (67 mm) at the base with a continuous taper to the 2" (51 mm) masthead. This is a light stick and will break if tested in high winds. It'll weight about 12 pounds (5.4 kilo). A less competitive stick, but still in the racer category would be 2 3/4" (70 mm) heel with a 2 1/8" (54 mm) head and weighs about 13.25 pounds (6 kilo). A moderately light cruising mast would be 2 15/16" (75 mm) at the hell and 2 1/4" (57 mm) at the masthead and weighs about 15 pounds (6.8 kilo). This would be a good all around stick, capable of heavy weather sailing, but if you want nearly bullet proof then a 3" (76 mm) heel and a 2 3/8" (60 mm) head would work well too at 16 pounds (7.3 kilo). This is using white spruce and again a 20% wall thickness. If using Sitka spruce, then the weights will be about 7% more and if Douglas fir, then a hefty 26% more in mast weight, though it's also a fair bit stronger too.

[Aharon]

This is the roadmap I was looking for. Thank you, PAR. You have just made a grandfather very, very happy!

[jknight]

Sorry for bumping a forum from several months ago...

@PAR
I'm interested in these calculations - can you point me somewhere that will outline the basics?

For Instance, I snapped the 10' mast on a lug-rigged shellback dinghy this weekend. The mast was made by someone trying to make a lightweight boat as a design project and was undersized.
The Hull weighs 60 lbs (foam/glass). The Daggerboard, rudder, and rigging weigh 15 lbs. And I can see having as much as 400 lbs in passengers / gear while under sail (max)... let's round up to 220kg total mass.

The standard sail area is 54 sq-ft, and it's a lug rig with a 10' mast. The mast is stepped through the forward thwart 1-foot from it's base. What moment should I expect the mast to resist?

I'm a mechanical engineer, so I know you're going to tell me a more-detailed version of F=ma... but some of those details elude me.

I plan to make a birds-mouth mast. 2" bottom OD, tapered (to 1.25?) out of either 1/4" or 3/8" boards. Analyzing this for strength is something I can do - if I knew more about the loads expected.

[Chuck Losness]

Here is a link to a calculator for determining the size of birds month masts.
http://www.duckworksmagazine.com/04/...outh/index.cfm
Also, Eric Sponberg has shared his engineering analysis for free standing masts. It is available on his website.

[jknight]

thank you for the links...
The calculators on Duckworks site are helpful - and I can image they'd be invaluable if I didn't have access to the power of a CAD suite.

I read over Eric Sponberg's site, but didn't see any guidance to calculate my own.

For a given geometry, I can calculate strength, but for to test if it's "strong enough" I'll need to know expected loading under maximum conditions. I'm assuming the answer is a combination of the force required to tip the loaded boat over, and any down-haul on the boom. I should be able to work from that, but I am hoping a NA would chime in and teach me something quickly.

[Chuck Losness]

Mast design is based on the righting moment of the boat. That is the maximum load that can be placed on a mast and you design from that plus a safety factor for the type of rig being used. There are books like Skene's and Lars that layout the design process for stayed rigs. Eric Sponberg has posted his analysis on this forum but I don't remember the thread so I have attached it for you. Maybe he will chime in here.
Good Luck