Birds Mouth Spars

[Bob Ketterling]

I am planning to build hollow spars for the Gannet I am building and I have reread the article in Wooden Boat 149 and I still have a question. The plans give dimensions for solid spars; do I need to change the diameter if I build them hollow using the birds’ mouth method? The plans don't specify the type of wood to use and I would probably use Douglas Fir for the hollow ones.

[Bob Cleek]

Nope. Hollow or solid, the dimensions should be as the designer intended.

[Keith Wilson]

With all respect, Bob is dead wrong on this one, and I can go over the math in detail if you like. A hollow spar of the same diameter as the solid one will be weaker and more flexible. Exactly how much weaker and more flexible depends on size and wall thickness. This may be acceptably strong, but making it a little larger in diameter will give you the same (or greater) strength and stiffness with considerably less weight than a solid spar. Off the cuff, for a reasonable ratio of wall thickness to diameter - say around 0.15-0.2 to 1 (like a 3" spar with a 1/2" wall) - the diameter should increase maybe 10 to 20%. It partly depends on the type of wood - fir is heavier and stronger than spruce; you can use a thinner wall. Another factor is the type of use; is weight or strength more important? It's not hard to run rough numbers; what size of mast are you talking about?

[StevenBauer]

http://www.pragdata.com/philboat/birdsmouth.GIF

The wood in the center of the spar adds little strength. How little, I'm not sure. smile.gif Iain's specs probably are for spruce, so with the added strength of the fir you could keep to the original dimentions.

Steven

[Bob Cleek]

I'm with Steve on this one, Keith. If there is any greater strength to a solid spar, I doubt it is enough to make much of a difference. Lighter, yes, but stronger or more flexible, I'm not so sure. In any event, I've never noticed that solid spars were any smaller proportionately than hollow ones. Like I said, use the designer's dimensions, and... if the designer said either solid or hollow, that's the way I'd go.

[Billy Bones]

http://www.carlsondesign.com/

At the bottom of the linked page are two mast calculating programs which should tell you all you need to know.

While I cannot speak to scantlings hollow v solid, I can say that I recall two or is it three mast failures due to insufficient size, each in Caledonia Yawls. Hence I might round upward in scantling size. A quarter inch can make a LOT of difference in this situation.

good luck.

[bheys]

I assume the Gannet and Fulmar have similar spar dimensions. Oughtred specifies a hollow mast and yard for the Fulmar. However his spars are not bird's mouth and have a rather thick section and small hollow area. I used the bird's mouth method with the same outer diameter and a section width appropriate to Doug Fir. These spars seem stout. Oddly enough, he spec'd a solid and rectangular cross-section boom. This spar proved to be inadequate as it would develop a disconcerting arch in stronger winds. I ended up building a new boom useing bird's mouth. It is a round, tapered at each end and about 9" longer. Despite the added mid-boom diameter it feels as light or lighter and is much more stiff.

[Bruce Hooke]

From Skene's Elements of Yacht Design:


Mr. Skene worked out an example illustrating the advantage of a hollow spar: Two spars are compared. Each is made of spruce and is 10 feet long. Each is designed for the same strength, 8500 pounds. One is hollow, the other solid. The hollow one has an outside diameter of 4 inches and in inside diameter of 3 inches. Its weight is only 11 1/2 pounds. Now for the contrast: the solid one is only 3/8" smaller with a diameter of 3 5/8", but it weighs 21 1/2 pounds, or about twice as much!There is no question that (assuming we are not making other changes like the type of wood used), a hollow spar does need to be a little larger than a solid spar to get the same strength, but that in the end the hollow spar will still be MUCH lighter than the solid one. However, the change in size is not large -- about 10% in the above example, which is a number I've heard frequently in this context before.

Using a stronger wood does allow for some reduction in scantlings, which offsets to some degree the change from solid to hollow, but this effect is small -- a 10% increase in the strength of the wood means a 3% reduction in diameter, if my quick running of the numbers is right. NOTE: I was checking the basic formula for an unstayed mast -- stayed masts may be a little different on this count.

Since stiffness varies as the cube of the depth of a beam while strength increases as the square of the depth of the beam, I expect that our slightly larger hollow spar will be stiffer than its comparible solid spar that matches the hollow spar in strength. A hollow spar the same diameter as a solid spar will be a little less stiff. I did not run the numbers to figure out exactly how much.

While the safe route is to simply follow the designer's specs and not build a hollow spar unless the designer provided dimesions, plenty of people appear to have deveated from this rule and not come to a bad end.

[Don Maurer]

All theory aside, I built a birds mouth mast for my Tammie Norrie out of douglas fir. The staves were 1/2" thick. I used the same diameter specified in the plans. The strength of the mast is more than adequate. It is an unstayed mast with solid cores from the foot to about 6" above the mast partner and about 6" down at the top for a dumb sheave.

[Bob Ketterling]

Thanks for all the comments. I am not sure if this will advance the argument but the dimensions of the spars are as follows:
· Mast – 14’ 6” long – it tapers from 2” to 2 and 12/16 to 2 and 1/16
· Yard –10 long –it tapers form 2” to 1 and 2/16
· Boom – 8’ 3” long – it is a rectangle as Bruce descried and varies from 2X1 ½ to 2 ¾ by 1 ½ to 1 ½ by 1/12

[ion barnes]

i have been following the other thread regarding hollow oar shaft and went so far as to ask Joel Herzel for a copy of his article "Building A Hollow Shaft Spoon Blade Oar".

His postscript two years later says "I've continued to tinker with the oars in an attempt to make them as stiff as possible without increasing the weight. The lastest pair were made of Sitka spruce. At the same time, I increased the diameter to 2-1/8" (the originals were 1-3/4" dia.) and made the wall slightly thinner. Each stave was initially milled to 9/32" X 13/16". the amount of taper cut into each is still 3/8", so they taper in width to 7/16" for the narrow ones and 1-3/16" for the wide ones. After glue up, and the shaft is planed and sanded, the wall thickness averages about 1/4".

He also says that he feels that the blocking he added at the ends and in the way of the oarlock position made a truss in effect that further stiffened the shaft.

[Keith Wilson]

OK, a little math. Stiffness in bending is proportional to the moment of inertia of the section. Look here. (http://www.engineersedge.com/beam_bending/beam_bending1.htm)

Moment of inertia of a round tube is I = (π/12)*(OD^4-ID^4). Here’s a calculator (http://www.engineersedge.com/calculators/section_square_case_12.htm) to find the section properties of round tubes. (For a solid bar, set the ID = 0 )

A 2.75” dia. solid bar has a moment of inertia of 2.77 in^4 with a cross sectional area of 6 in^2. A spar of equivalent stiffness with a ½” wall would be about 2.9” in diameter with a cross-sectional area of 3.8 – in other words, just as stiff with 63% of the weight. A 3” OD with a 3/8 wall is about equivalent as well, but with half the weight of a solid spar. However, if the wall gets too thin you have to worry about localized failure, buckling or cracking, and 3/8 is pretty thin IMHO. Skene’s example is similar: I for the hollow tube is 8.57 in^4, I for the solid one 8.46. This of course assumes that they are made of the same material – you can look up the elastic modulus for Douglas Fir and Spruce if you like.

Anyway to sum up – if you want to make the spar hollow, make it a little bigger in diameter. It will be a lot lighter for equivalent strength and stiffness.

[Rick Clark]

Well gentlemen here I go again, on not off the shelf in building. Years ago I could not afford to buy a new mast and boom for this sloop I bought cheap.
I was tinkering with the thoughts of a 1/2" plywood mast built like a truss in homes.

So I build a diamond shape mast 24'long free standing. ! 10" sides tapering to 4" , with diamond shape spacers to fit every 16" and layered foam blocks in between the spacers and then fiber glassed it. Talk about stiff and light, yes everyone at the marina poked fun and I just took the ribbing and sailed off for a week that was 20 years ago and the mast and boom and gaff are still in good working order.

I had some friends pull the boat over from the top off the mast 100' of rope to see how well it would float I then crawled out the length and could not sink the mast more the a foot under water.

Like I've said before it take a little tinker to get what you need. Larger dia. is always better for stiffness, take a look at the wall thickness of pipe and check the flex of different ones to give you an idea off what your looking fore. :cool:

[ 12-01-2005, 11:47 AM: Message edited by: Rick Clark ]

[Bob Ketterling]

Thanks for all the thought and commentary. There are a couple of specification I should have added, the sail plan is a gunter sloop and the sail area is 118 square feet. I would rather make the spars a little heavier than risk breakage and I like to keep things relatively simple. How do you think it would work if I added a ¼ inch to the diameter of each spar and kept the wall thickness of all three at ½ inch?

[Keith Wilson]

FWIW, that's what I'd do if it were my boat. They'll be lighter, stronger and stiffer. Don't forget to put in plugs at areas of high stress - at the mast partner and the place where the jaws of the yard usually go.

Another advantage of birdsmouth spars is that it's easy to use cheaper wood and just cut out the knots. You don't need a long clear stick. Staggered scarf joints in the staves affect the strength not at all. The last one I made was about that size, and came from the local lumberyard's best 2x8; it cost maybe $25.

[ 12-02-2005, 09:38 AM: Message edited by: Keith Wilson ]

[Ozzie]

Regarding the relative strength of hollow unstayed masts, if the wall thickness equals 20% of the diameter then the diameter should be increased about 5% for the same bending stress experienced by the solid mast.

There are two common types of bird mouth designs. The first has the bird mouth cut symmetrically. This type is easy to cut on the table saw but little 'ears' are left on the outside of the spar which need to be planed off. The formula for sizing this type of spar is as follows:

w = 0.4142D - 0.1213t,
where w = stave width, D = spar diameter, and T = stave thickness.

The second common type of birdmouth design has the birdmouth offset toward the inner face of the stave. If the peak of the birdmouth is positioned properly, the outside of the spar is a clean octagon with no 'ears'. In this case, the width of the stave is: w = 0.4142D. Thus the diameter is not dependent on the thickness of the stave. Offset birdmouth staves are most easily cut on the router table using a special cutter sold by Lee Valley (Veritas) in Canada.

The relation between the bending stress in an unstayed hollow mast and a solid mast of the same diameter is roughly as follows:

Sh/Ss = 1/(1 - (1 - 2t/D)^4), where: Sh = bending stress in hollow mast, Ss = stress in solid mast, t = stave thickness, and d = mast outside diameter.

For example, if D = 73mm and t = 14.6mm, then Sh/Ss = 1.149. If a hollow mast with the same strength as the solid mast is required, then: Dh = Ds(Sh/Ss)^0.33 while keeping t constant.

For the example above, Dh = Ds(1.149)^0.33 = 73 x 1.047 = 76.5mm

[Ozzie]

Further to the above messy maths, if I knew how to add graphics it would all be a lot simpler.

In the meantime, if you want the complete story email me at marshal@grapevine.net.au

Or maybe somebody could describe how to attach an image to a reply.

[emichaels]

Originally posted by StevenBauer:
http://www.pragdata.com/philboat/birdsmouth.GIF

The wood in the center of the spar adds little strength. How little, I'm not sure. smile.gif Iain's specs probably are for spruce, so with the added strength of the fir you could keep to the original dimentions.

StevenSteven is correct about the wood in the center adding little strength. In a static momonet the wood adds a great deal of strength but as the mast starts to develope a bending moment then the wood in the center actually works to weaken the side of the mast in tension. The force vectors pivot about the wood in the center.

In addition in the real world,the grain orientation of the wood will play a huge part in the tension strength of both general spar designs.

Ozzie got it right.

[ 01-04-2006, 07:49 AM: Message edited by: emichaels ]

[Lewisboats]

Originally posted by Ozzie:
Further to the above messy maths, if I knew how to add graphics it would all be a lot simpler.

In the meantime, if you want the complete story email me at marshal@grapevine.net.au

Or maybe somebody could describe how to attach an image to a reply.If you can publish the image to a web site, or server, then you can hit the 'image' button and stick in the address pointing to the image. example:

{IMG}http://www.angelfire.com/ego/lewisboatworks/Images/GuppyII/images/Transomntempgunnel.JPG{/IMG}
(I changed the brackets so you could see what the line would look like, the brackes are square in the actual insert. I would end up looking like this:

http://www.angelfire.com/ego/lewisboatworks/Images/GuppyII/images/Transomntempgunnel.JPG

Steve

edit: Wow! sorry about the size. There...Fixed it.

[ 01-04-2006, 09:37 PM: Message edited by: Lewisboats ]

[emichaels]

Hey Steve, you need to build a bigger boat man, theres still floor showing on the sides. :D

Just kiddin,

What design is that boat ??

Eric

[Billy Bones]

And when did Dewalt start making motorcycles?!?

[Lewisboats]

Originally posted by emichaels:
Hey Steve, you need to build a bigger boat man, theres still floor showing on the sides. :D

Just kiddin,

What design is that boat ??

EricI work with one eye open on one side, roll it sideways and work with the other eye open on the other side. Keeps things in perspective but ya gotta remember which eye to use on which side. tongue.gif
Its called GuppyII...A stretched version of Guppy (Below) It runs about 11.5 ft long, room for one to cruise and beach camp or bunk on board.

http://www.angelfire.com/ego/lewisboatworks/Images/GuppyII/thumbnails/GuppyMed.GIF

That's my DeWalt sponsored Racing chariot ;) :D

And I really only wanted to show off my clamp collection...Isn't it spectacular?

[ 01-04-2006, 09:27 PM: Message edited by: Lewisboats ]