Re: [bolger] Re: Bird's mouth ratios

I'd subscribe to a short course on beam theory for the
ennumerate if it were 
on offer somewhere. 

The usual way is to look at skeene, or whatever. Its
like asking what theory do you use to choose a window
header. Two more inches than the span in feet is
typical, but it is not great theory, unless you really
feel the required safety factor needs to increase as
well.

 
Can an unstayed mast be treated as a simple case of a
cantilevered beam? 
(relatively simple case - if memory serves, Galileo
didn't quite get it 

Getting the right number is less a mater of the beam,
than the condition, what load do you choose? For
cruising boats we did the full nock over loads with
trimarans, but I haven't actually calculated a mono
load.

right, and he was a brighter than average fellow.) 
 
Tensioning the luff obviously introduces a compression
load, but perhaps this 
load is so trivial compared to the bending load that
it can be neglected? 
 

Right I mean you are in the tons per square in area
for the compresion loads, in practice the harware will
break long before the spar.

>>>In the case of a hollow, unstayed mast, would

fitting rigid diaphragms at 
intervals (e.g. like bamboo) permit a lighter spar for
a given 
strength/stiffness?

yes it could, but I don't think this would be in a
case where the collapsing of the walls is a
likelyhood. We have been talking about 20% walls,
that would be like 4-6" walls in my tri that currently
has 1/4" ply "walls". It could be done in a spar with
say foiled ply wing sections.

>>>(There must be an accepted term better suited than

>>>Does anyone know how engineers deal with span-wise

loadings of a cantilever, 
as opposed to end loading? 
 
Boeing's wing designers must calculate this out to
umpteen significant 
digits.

Joseph Norwood covers it in one of his books

Right, but you can get a homebuilt aircraft certified
by pilling sacks of sand on it.

______________________________________________________________________
Music, Movies, Sports, Games!http://entertainment.yahoo.ca

See below:

--- In bolger@y..., wmrpage@a... wrote:
snip
> I'd subscribe to a short course on beam theory for the ennumerate if
it were
> on offer somewhere.
>
Somebody should, but it should be someone who's been thru it more
recently than me. Lots of good info in Machinery's Handbook, but short
on theory.
> Can an unstayed mast be treated as a simple case of a cantilevered
beam?
I should think so, if partners are set up so as not to gouge or waken
mast.
> (relatively simple case - if memory serves, Galileo didn't quite get
it right, and he was a brighter than average fellow.)
>
Yah, but he didn't have all those people to work it out first. It's
pretty obvious stuff once someone has explained it all the one time.

> Tensioning the luff obviously introduces a compression load, but
perhaps this
> load is so trivial compared to the bending load that it can be
neglected?
>
Yup.
> In the case of a hollow, unstayed mast, would fitting rigid
diaphragms at
> intervals (e.g. like bamboo) permit a lighter spar for a given
> strength/stiffness? (There must be an accepted term better suited
than
> "diaphragm" for this concept. "Bulkhead" doesn't seem appropriate;
"web" is
> rather ambiguous. Help! My vocabulary has deserted me!)
>
If the mast was thin walled so that local buckling was a problem, and
you used these bulkheads close together, it might help quite a bit.
Maybe foam of some type in the middle of the mast?
> Does anyone know how engineers deal with span-wise loadings of a
cantilever,
> as opposed to end loading?
I used to. Formulas in Machinery's Handbook, theory in Timoshenko.
>
> Boeing's wing designers must calculate this out to umpteen
significant
> digits.

Nah, they just let the computer do it, I bet, then I'll guess some
old guy in the back room checks to make sure it's close.

>At the partners, a mast must (unless deliberately
sacrificial)
> sustain the load necessary to overcome the righting moment of the
boat plus
> whatever factor of safety (a.k.a. "factor of ignorance") is
necessary to
> compensate for inertial effects, material variances, etc., etc., ad
> infinitum. At masthead, at least in a "jib headed" sail, the load
must
> diminish to little more than the windage of the spar itself, opening
up some
> small possibilites of less material, weight aloft and aerodynamic
> interference at the cost of considerable labor and planning.

I don't know how sophisticated you have to be for this. If you do a
straight taper, you could probably go down to an inch or two on a
small boat, particularly if no halyard is used. Our Brick mast is
something like an inch dia on top and seems plenty strong. It does
flex a bit, but that might be a good thing.
>
> Ciao for Niao,
> Bill in MN
> (idly contemplating (Do^4-Di^4)/Do v. (Do^5-Di^5)/Do and wondering
what the
> implications are.)
I left out the constants, but one thing it means is that a small
increase in thickness increases stiffness more than strength. If you
made a mast out of aluminum soda can sections carefully welded end to
end, it would be pretty stiff but not strong, even if you filled it
with foam to keep it from buckling. The foam would make a huge
difference, though. You seem to have a good handle on the material.

In a message dated 4/5/02 3:31:31 PM Central Daylight Time,
lincolnr@...writes:

> As far as strength, beam theory is a well developed
> subject and it's very clear that a slightly larger, hollow beam can be
> as strong as a solid one and lighter at the same time.

I'd subscribe to a short course on beam theory for the ennumerate if it were
on offer somewhere.

Can an unstayed mast be treated as a simple case of a cantilevered beam?
(relatively simple case - if memory serves, Galileo didn't quite get it
right, and he was a brighter than average fellow.)

Tensioning the luff obviously introduces a compression load, but perhaps this
load is so trivial compared to the bending load that it can be neglected?

In the case of a hollow, unstayed mast, would fitting rigid diaphragms at
intervals (e.g. like bamboo) permit a lighter spar for a given
strength/stiffness? (There must be an accepted term better suited than
"diaphragm" for this concept. "Bulkhead" doesn't seem appropriate; "web" is
rather ambiguous. Help! My vocabulary has deserted me!)

Does anyone know how engineers deal with span-wise loadings of a cantilever,
as opposed to end loading?

Boeing's wing designers must calculate this out to umpteen significant
digits. At the partners, a mast must (unless deliberately sacrificial)
sustain the load necessary to overcome the righting moment of the boat plus
whatever factor of safety (a.k.a. "factor of ignorance") is necessary to
compensate for inertial effects, material variances, etc., etc., ad
infinitum. At masthead, at least in a "jib headed" sail, the load must
diminish to little more than the windage of the spar itself, opening up some
small possibilites of less material, weight aloft and aerodynamic
interference at the cost of considerable labor and planning.

Ciao for Niao,
Bill in MN
(idly contemplating (Do^4-Di^4)/Do v. (Do^5-Di^5)/Do and wondering what the
implications are.)

[Non-text portions of this message have been removed]

Hi Richard, I should have noted that end grain epoxy joints have
little or no strength under stress. The lower the ratio for the scarph
joints the lower the ultimate strength of the joint because you are
approaching end grain joining. As to why "we still stagger the
scarphs", I don't worry about staggering scarphs. I think they should
be symetrically placed if possible. I believe it is a belt and
suspender approach. In the article I quoted, Bud McIntosh shows a
common approach to wooden mast repair that is essentially 4 scarf
joints in a bunch. Yes two adjacent scarphs (or one for that matter)
result in a stiff section of the mast. I don't believe unstayed masts
as a class are very bendy anyways. I can't imagine the slight
additional stiffness making a bit of difference. I scarfed a batten
for drawing lines and it sure did make a difference there.
Bob Chamberland

--- In bolger@y..., "rlspell2000" <richard@s...> wrote:
> Accepting that we are assuming that epoxy wood flour joints are
> stronger than the wood, why do we still scraph 12-1? Why not, say, 8-
> 1? 4-1?
>
> Also, why do we still stagger the scarphs? If the joint is stronger
> than the wood, putting two scarphs next to each other should have you
> a strong spot, no?
>
>

Glued wood is stronger than the surrounding crossgrain
wood, not than end to end, Scarphs need to be
proportional to the woodgrain runout.

--- rlspell2000 <richard@...> wrote:

<HR>
<html><body>

<tt>
Accepting that we are assuming that epoxy wood flour
joints are 
stronger than the wood, why do we still scraph 12-1?
Why not, say, 8- 

______________________________________________________________________
Music, Movies, Sports, Games!http://entertainment.yahoo.ca

The direction of the joint is very important. If you try to glue
across end grain, you are looking at very high stress. If the joint is
along the grain, then it only has to be stronger than the wood when
stressed across the grain, which isn't very strong. However, I've
often heard that 8:1 is considered adequate. On very light balsa wood,
with Titebond glue put on correctly on a tight joint, 0:1 is adequate!
I suspect the appropriate angle depends to a great extent on the wood.

The joint may be stronger than the wood, but it represents a
discontinuity. Do you really want a hard or soft spot in your mast?

I suppose if you had very well matched wood and a well made joint with
a thin glue line this wouldn't be a big deal.

Someone else was suggesting experiments. THese would have to be very
careful to be valid, and one would have to be very careful about how
far to extend use of the results. It would be necessary to have a good
theory and some experience in order to have some idea how far to trust
these results. I suspect, tho I'm not positive, that Forest Products
Labs or whatever they are called has already done this work, probably
even in relation to T-88 epoxy.

--- In bolger@y..., "rlspell2000" <richard@s...> wrote:
> Accepting that we are assuming that epoxy wood flour joints are
> stronger than the wood, why do we still scraph 12-1? Why not, say,
8-
> 1? 4-1?
>
> Also, why do we still stagger the scarphs? If the joint is stronger
> than the wood, putting two scarphs next to each other should have
you
> a strong spot, no?
>
> --- In bolger@y..., "rdchamberland" <cha62759@t...> wrote:
snip

Accepting that we are assuming that epoxy wood flour joints are
stronger than the wood, why do we still scraph 12-1? Why not, say, 8-
1? 4-1?

Also, why do we still stagger the scarphs? If the joint is stronger
than the wood, putting two scarphs next to each other should have you
a strong spot, no?

--- In bolger@y..., "rdchamberland" <cha62759@t...> wrote:
> You are up against the question of faith. When we use epoxy we are
> accepting the manufacturers conclusions from his testing as to the
> strength or tenacity of his product. Accepting that epoxy glues are
> stronger than the adjacent wood fibres (and will not let go) which
is
> what all of the manufacturers we deal with say I believe then
there's
> little difference in terms of strength in a spar built with the
bird's
> mouth technique or of staves as has been sketched by David. You have
> roughly the same amount of wood fibres providing the structure of
the
> mast. In either case you need a wall thickness of 20%. It is easier
to
> get that with less wood in the birdsmouth but not by much.
> Bob
>
>
> --- In bolger@y..., Sakari Aaltonen <sakari@a...> wrote:
> >
> > But how can the builder--say, myself--decide? Is there any
evidence
> > other than hearsay that shows a hollow mast built according to the
> > various bird's-mouth diagrams is as strong as a solid one?
> >
> > Out of curiosity: which Bolger boats are *required* to have hollow
> > masts?
> >
> >
> > Sakari Aaltonen

See below

--- In bolger@y..., "rdchamberland" <cha62759@t...> wrote:
> You are up against the question of faith. When we use epoxy we are
> accepting the manufacturers conclusions from his testing as to the
> strength or tenacity of his product.

No need for faith here. Glue two blocks of wood together and try to
tear them apart. If you've done it right the wood fails first. Of
course I'm not talking about gluing to end grain, but that's another
story.

snip
> little difference in terms of strength in a spar built with the
bird's
> mouth technique or of staves as has been sketched by David. You have
> roughly the same amount of wood fibres providing the structure of
the
> mast. In either case you need a wall thickness of 20%. It is easier
to
> get that with less wood in the birdsmouth but not by much.
snip
Actually, the amount of wood fibers is FAR from the only factor. You
could up the diameter a little more and use 10% wall and it would
probably be stronger, but now we have to be a little careful due to
buckling properties and a lot will depend on the section, quality of
wood, etc., although I suspect that 10% is still pretty conservative.
Harder to build, of course. Diameter is very important. If the fibers
are further from the center, they don't have to take as much stress to
provide the same strength, or else you can use less of them. FOr a
stayed mast, stiffness is probably more critical than strength as the
failure mode is probably in buckling as a column. THis means a thinner
wall might be best, particularly if you don't do the bendy mast
thing. Thin walls will get you in trouble due to local buckling of the
wall, as when you stand on a Coke can and poke it with your finger.
(You really can stand on one if you are a light person and hold
steady. This is something I remember from years ago when I was
lighter and they hadn't gotten rid of quite as much aluminum, tho)

If you didn't care about windage, mechanical damage, or water
resistance, you could make a strong and very stiff solid balsa mast
that was lighter and much larger than a normal one. Of course the
fittings would be a problem and it would be more than twice the
diameter.

I suspect that this decision, like most, will have to be somewhat
subjective. However, it's possible to educate yourself about the
factors somewhat. With different wall thicknesses, you can change the
weight savings. As far as strength, beam theory is a well developed
subject and it's very clear that a slightly larger, hollow beam can be
as strong as a solid one and lighter at the same time. If you have a
round mast with a round hole, as I recall the strength is proportional
to: (Do^4-Di^4)/Do
The stiffness would be proportional to(Do^5-Di^5)/Do
where Do is outside dia of mast, Di is inside dia of mast. Hope I
haven't misremembered here. The above implies that the material on the
outside of the mast has the most stress. If you look in Machinery's
Handbook you can find a condensed summary of all this, tho it's
probably possible to draw the wrong conclusions if you don't
understand the engineering behind it. If you want to get theoretical,
consult Timoshenko (sp?) Strength of Materials, but that may be
overkill. THe above assumes that local loads do not crush the mast and
that wall thickness is sufficient to prevent buckling. Use a plug
inside where the fasteners or partners are, and don't go really thin
on the walls and these factors should not be a problem. Timoshenko's
buckling criteria are not valid here as the material is not isotropic
(i.e. the same in all directions).

--- In bolger@y..., Sakari Aaltonen <sakari@a...> wrote:
> Porky wrote
> > Your question about the "break even" point in the work involved
with
> > a hollow mast is meaningless. If a mast is required to be hollow
to
> > save weight aloft, to allow the mast to be raised without
elaborate
> > gear, or for some other substantial engineering reason, you build
it
> > hollow. The labor involved is a requirement of the design. If
there
> > is no objective need for a hollow mast, the option is the
builder's
> > and the break even point is whatever that person decides it is.
>
> But how can the builder--say, myself--decide? Is there any evidence
> other than hearsay that shows a hollow mast built according to the
> various bird's-mouth diagrams is as strong as a solid one?
>
> Out of curiosity: which Bolger boats are *required* to have hollow
> masts?
>
>
> Sakari Aaltonen

You are up against the question of faith. When we use epoxy we are
accepting the manufacturers conclusions from his testing as to the
strength or tenacity of his product. Accepting that epoxy glues are
stronger than the adjacent wood fibres (and will not let go) which is
what all of the manufacturers we deal with say I believe then there's
little difference in terms of strength in a spar built with the bird's
mouth technique or of staves as has been sketched by David. You have
roughly the same amount of wood fibres providing the structure of the
mast. In either case you need a wall thickness of 20%. It is easier to
get that with less wood in the birdsmouth but not by much.
Bob

--- In bolger@y..., Sakari Aaltonen <sakari@a...> wrote:
>
> But how can the builder--say, myself--decide? Is there any evidence
> other than hearsay that shows a hollow mast built according to the
> various bird's-mouth diagrams is as strong as a solid one?
>
> Out of curiosity: which Bolger boats are *required* to have hollow
> masts?
>
>
> Sakari Aaltonen

Porky wrote

>
> Your question about the "break even" point in the work involved with
> a hollow mast is meaningless. If a mast is required to be hollow to
> save weight aloft, to allow the mast to be raised without elaborate
> gear, or for some other substantial engineering reason, you build it
> hollow. The labor involved is a requirement of the design. If there
> is no objective need for a hollow mast, the option is the builder's
> and the break even point is whatever that person decides it is.

But how can the builder--say, myself--decide? Is there any evidence
other than hearsay that shows a hollow mast built according to the
various bird's-mouth diagrams is as strong as a solid one?

Out of curiosity: which Bolger boats are *required* to have hollow
masts?

Sakari Aaltonen

Sakari,

The rule of thumb thickness for the walls of a round wooden mast is
20% of the diameter, so the hollow portion would be 60% of the
diameter. You are therefore substantially correct in your estimate.

Your question about the "break even" point in the work involved with
a hollow mast is meaningless. If a mast is required to be hollow to
save weight aloft, to allow the mast to be raised without elaborate
gear, or for some other substantial engineering reason, you build it
hollow. The labor involved is a requirement of the design. If there
is no objective need for a hollow mast, the option is the builder's
and the break even point is whatever that person decides it is.

Personally, for the spar you describe, I think metal tubing (aluminum
or steel, depending on the strength and weight you need) would be a
reasonable and easily fabricated alternative,

porky

--- In bolger@y..., Sakari Aaltonen <sakari@a...> wrote:
> Birds-mouth diagrams seem to make the (the diameter of the) hole
> in the middle about half of the total thickness. So the area of
> the hole would be a quarter, which is the weight savings, that
> is, 25%.
>
> A mast I'm thinking of making is 50mm (2") thick and 3m (10')
> long. If solid, it would weigh about 3.5kg (8 lbs). The birds-
> mouth weight savings would be 0.9kg (2 lbs).
>
> 3.5kg vs. 2.9kg (8 lbs vs. 6 lbs) is not much of a difference,
> it seems.
>
> Of course, the bigger the mast, the bigger the weight savings.
> Is there a break-even point where the lighter mast justifies
> the extra work?
>
> Or is my calculation wrong?
>
>
> Sakari Aaltonen

Birds-mouth diagrams seem to make the (the diameter of the) hole
in the middle about half of the total thickness. So the area of
the hole would be a quarter, which is the weight savings, that
is, 25%.

A mast I'm thinking of making is 50mm (2") thick and 3m (10')
long. If solid, it would weigh about 3.5kg (8 lbs). The birds-
mouth weight savings would be 0.9kg (2 lbs).

3.5kg vs. 2.9kg (8 lbs vs. 6 lbs) is not much of a difference,
it seems.

Of course, the bigger the mast, the bigger the weight savings.
Is there a break-even point where the lighter mast justifies
the extra work?

Or is my calculation wrong?

Sakari Aaltonen

This will probably have been answered as I get further into today's
mail, but here is John's (JBoatguy) comments to me on the subject,
reference a cartopper mast. He is the one with the article in
Boatbuilder on the subject.

Harry

The numbers for birdsmouth are posted on the Bolger message board in the
Files under 'How To tips'.

You can go for a 20% of mast diameter thickness, as I did, and get a
mast
slightly lighter, but possibly not quite as strong as, a solid stick,
depending on stock. (Bolger calls for a 2" stick if it is to be made
round).
I haven't had any trouble with mine, but I would still recommend that
you
consider going for a 15% of diameter wall thickness, and then up the
overall
diameter by 10%, to 2.2". That works out to .88" width (7/8"), by .33"
(11/32) thickness for each stave, for an eight stave birdsmouth mast.
You'll
get a thinner wall for a lighter mast, with just as much strength as a
solid
3" stick. And I do think the lighter mast makes a difference in
Cartopper
with its relatively narrow bottom.

If you do opt for a 15% wall, by all means build a plug to extend up
past any
mast base fittings, cleats and whatnot, you may want to screw on. The
weight
is minimal, and low, and won't make the a difference. Make the plug
birdsmouth style, from staves longer than you need the plug to be. Then
taper the extra length of the staves--but from the birdsmouth
face!--right
down to a point. Don't taper the plug itself as you put it together.
The
tapered staves will stand straight up like little pointy fingers,
dissipating
the mast's cross sectional area slowly.

To be honest, in such a small mast you may not need to worry about
stress
concentration, but why take a chance? If it's an eight stave mast, the
inside comes out octagonal, and an eight stave plug, properly sized,
will fit
in like a glove after a few swipes with a plane. Measure across the
inside
of your test fit mast, and divide by 2.4 to find the stave width for
your
eight stave plug. Build the plug before gluing up the mast, then glue
up the
plug, fit it into your test fit mast, mark everything so it goes
together the
same way, then glue up the mast, with the plug inside, in one step.
With
glue slathered all over the outside of the plug, and using the plug as a
'rolling pin' to roll up your staves around, mast glue up is an easy,
one man
operation. If you're using epoxy (by all means use epoxy, the slow set
up,
and the fact that it's slippery when wet, will make glue up and
straightening
much easier) then all you need to do is spiral up a wrap of hand tight,
waxed
twine around the mast as a clamp. The whole thing will take ten
minutes.
Make sure the mast is straight!

--- In bolger@y..., David Ryan <david@c...> wrote:

> FBBB --
>
> What is the preferred wall thickness to spar diameter ratio? I
> thought we had it in our files, but I can't find it.
>
> YIBB,
>
> David
>
> C.E.P.
> 415 W.46th Street
> New York, New York 10036
>http://www.crumblingempire.com
> (212) 247-0296

Referring to Woodenboat #60 and the article by Sam Manning on building
spars: He gives an example of a hollow 6" spar made up of 4 staves. He
specifies that the wall thickness at the inner corners of the mast be
1 fifth the diameter. As it happens 1 1/2 inch material would meet
this specification. This works out to 1.2" wall thickness for a 6"
spar. Would a birds mouth constructed mast be different? Not likely.
You might want to look up this article. Scarfing by the way is not
difficult especially if you have a router and/or a power plane. It
requires a simple jig.
Bob Chamberland

FBBB --

What is the preferred wall thickness to spar diameter ratio? I
thought we had it in our files, but I can't find it.

YIBB,

David

C.E.P.
415 W.46th Street
New York, New York 10036
http://www.crumblingempire.com
(212) 247-0296

Re: [bolger] Re: Bird&#39;s mouth ratios

Re: [bolger] Re: Bird's mouth ratios