Estimating strength and stiffness of a carbon-wrapped 2-piece wooden mast

This "p".

 

Hi @rxcomposite,
You timber numbers are way off!
ISO 12225-5 Table F1 has mechanical properties of typical wood species, these are 80% of the mean value for small clear specimens.
Here is an approximate match up:

Sail Pressure Calculations
I use an air density at 21 degrees C or 1.2 kg/m^2
Skene and others use 1 lb/sq.ft (48 Pa) which equates to 17.4 Knots or 32 km/hr, this is not important here, you can do as you please.
Your "Force" calculation confuses me, for your sail area (8.6 m^2) and wind speed (9 kts) I calculate 13 Pa and 111 N.

Skene's "Elements of Yacht Design" goes through the design of an unsupported solid wooden mast (page 119):

d=(16*PL/Pi/f)^(1/3)​

where

d = Diameter
P = Load (total pressure on the sail)
L = Length of the mast
f = Extreme fiber stress​

Some observations of his calculations is that he uses a safety factor of 4.0 and the MOR for "green" Spruce.
I can rationalise the high safety factor due to wind gusts and the low MOR for high wood moisture content.
Extreme fiber stress and MOR (Modulus of Rupture) imply bending/flexural strength.
Also he does not bother with a detailed estimate of the mast moment, other than M=PL/2.

Regards AlanX

 

Those were downloaded. Your numbers does not mean anything yet as it is not the one used in the formula. I need "G", modulus of rigidity/shear modulus for preliminary sizing.

 

What good is a safety factor of 4? The mast remain unbroken but the boat has capsized. 2 seems a good number. some use 1.8 in mast design.

 

That is according to your calculations. No need to get confused. Pascal is a unit of measure for pressure. Force is Weight.

 

Hi @rxcomposite,

Perhaps you should share your "preliminary sizing" formula.

Regards AlanX

 

That is what I am afraid of. It seems you shoot first and ask question later. And I haven't posted yet the spreadsheet.

Would it be "peer reviewed" or a professor grading a student thesis?

There maybe several approaches. The one I am working on is carbon fiber driveshaft using filament winding of hoop, axial, and helical winding by Stan Peters, WD Humphrey and RF Foral. Procedure is very similar to what is being discussed. Multi layered composite with different properties. The inset in post $23 is the one which address exactly the method in free standing mast only that it deals with homogenous material. I have a working spreadsheet for that, not the multi.

 

@rxcomposite,
No surprise.
regards AlanX

 

@laukejas,

I have finished my calculations for the design of a composite and possibly hollow masts.
It is not a simple process with five failure mode (excluding point load or puncture failure).
What the calculations indicates is that to take advantage of MOE and MOR of E-Glass or Carbon FRP, then wood does not make a good core.
Anyway, for @laukejas questions:

So, my question is, with such a complicated combination of factors, what is the best way to estimate the strength and stiffness of the mast? Right now, the wall thickness I chose for Birdsmouth (14mm) assumes no carbon fiber tubing. Obviously, this tubing will add a lot of strength and stiffness, meaning I could save considerable weight by making mast walls thinner. Currently my CAD says the mast will weigh 6.6 kg (14.5 lbs)... That is not counting the epoxy and paint.

Question is, how much can I thin it down to get a similar strength and stiffness that I would have if I were to use no carbon fiber tubing?​

Above:

• "strength" means design moment
• "stiffness" means deflection but I will use relative stiffness or E*I
• and minimising weight per metre is the objective.

The design moment or "strength" of all mast are the same or 1383 Nm
The design moment is estimated as SailArea*WindPresure*MastLength/2.

As we have been given a mast length above the deck of 5.5 m and a sail area of 8.6 m^2 we can use Skene's Spar Rules to determine if the given unreinforced mast dimensions (OD 68 mm and ID 42 mm) are suitable for use as an unstayed mast.

Let us assume the wooden core is Stika Spruce, Skene's Spar Rules suggest not at OD 91 mm for a solid wooden mast.

Therefore we do need reinforce the mast with either E-Glass or Carbon FRP:

• For 30% v/v W/R E-Glass the skin thickness needs to be 5.2 mm.
• For 30% v/v U/D HS Carbon the skin thickness needs to be 1.3 mm.

For the carbon fiber skinned mast:

• the section modulus is 7,376 mm^3
• the relative stiffness (I*E) is 0.0185 Nm^6
• the weight is 1.42 kg/m (+7.8 kg excluding the mast foot and assuming no mast taper).

The equivalent solid mast would be:

• the section modulus is 72,521 mm^3
• the relative stiffness (I*E) is 0.0246 Nm^6 (133%)
• the weight is 2.46 kg/m (+13.5 kg excluding the mast foot and assuming no mast taper).

The equivalent extreme hollow mast would be:

• the section modulus is 72,521 mm^3
• the relative stiffness (I*E) is 0.0582 Nm^6 (315%)
• the weight is 0.53 kg/m (+2.9 kg excluding the mast foot and assuming no mast taper).
• But the mast outside diameter is now 214.4 mm!
• And the wall thickness is 2.1 mm!

So with regard to making the mast diameter as small as possible using carbon fiber you could go down to:

• Outside diameter 38.3 mm
• Skin/core diameter 23.8 mm
• Weight is 1.14 kg/m (+6.28 kg excluding the mast foot and assuming no mast taper).
• Relative stiffness (I*E) is 0.00647 Nm^6 (35%)

I think this answers the above questions.

Note: I have used ISO 12215-5:2019(E) parameters where applicable.

Regards AlanX

 

"strength" is a material property...not a moment!

 

Shouldn't we take into account, according to this, the position of the sail center?

 

@TANSL,

Strength is in inverted commas, I obviously know I have interpreted it as a load/moment.
I have clearly understood what Laukejas is asking for rather than the narrow interpretation of a material property.

The centre of pressure is approximately 50% of the mast length above the deck.
The exact centre of pressure (and load distribution) of a sail is unknown.
Unless you are saying you know where it (or its distribution) is!

Regards AlanX

 

And why not with respect to the water line or the center of drift of the submerged area?
I suppose that when you say this it is because you have very strong reasons for saying so, because you have studied this problem in depth. But I had never heard this statement until now and it seems to me, honestly, that although it is an "approximation", it is a very crude approximation. I am sure, although you seem to be the expert here, that a formula can be given for the value of that moment that is much more adjusted to reality than the one suggested by you.
When the wind blows strong it is normal for the skipper to reef the sails. This is a typical case that is studied among the loading conditions to which a rig can be subjected. Is your formula still valid for those cases? Thank you, you always have to appreciate the explanations of the experts.

 

@TANSL,

Fair questions:

I am estimating the required mast section modulus (the moment on the mast at the partners or the deck) rather than moment between the CE/CLR.

Basis for the 50% estimate:

• The centre of effort for a typical (right angle) triangular sail is sometimes stated as 39% of the sail hoist, here is just first one I found:
  refer 3.2 Transverse sail forces 3.2.1 Monohulls, "(I-4-2) Guidelines for Design and Construction of Large Modern Yacht Rigs" by Germanischer Lloyd SE.
• The height of he gooseneck is somewhere between (but not limited to) 600 mm to 900 mm above the partners or deck.
• So the relative moment arm is approximately (39%+0.6m/5.5m) or 50% for this (5.5 m long) mast.

By the way I did not invent this formula, refer page 196 of "Designing Power and Sail" by Arthur Edmunds, among others.

Can you point to the standard for:

"When the wind blows strong it is normal for the skipper to reef the sails. This is a typical case that is studied among the loading conditions to which a rig can be subjected." ​

AlanX

 

The Germanisher Lloyd's no longer exists. Could you cite a reference to any regulatory body that does exist?

Regardless of whether there is a norm that says that, which there is, doesn't it seem normal to you that this calculation has to be made?