Calculating Boom Modulus...

[davef]

Greetings,

I am trying work through the sectional requirments for my sailboat boom and am once again having difficulty.

I am using the calculations provided by Larsson and Eliasson in Principles of Yacht Design (Page 197). To calculate the required vertical section modulus of the boom they provide an equation:

SM=600*RM*(E-D1) / (Sigma *HA)

Where RM = righting moment at 30 degrees (given as 53000 Nm)
E = Main sail foot length (4700mm)
D1 = length to Vang connection 1700mm
Sigma = Yield Strength of boom (not sure)
HA = Distance from waterline to center of effort on the sail. (not given - assumed to be around 7800mm)

I am trying to get their example (the YD-40 rig) to work and cannot get the answers they are providing. Once I get their equation to work I will substitute in my values.

a) What is a reasonable yield strength for an aluminum boom. I cannot find a reference for that?

b) Assuming that it is around 310MPa (310 Newtons/mm^2) I still cannot get any values that are reasonably close to what is provided in the book.

They are providing a vertical modulus of around 72*10^3mm. I am getting 1/2 of that so I must have some mistake????


Does anyone see my mistake?

[Raggi_Thor]

Most aluminium alloys known today and used to structural applications have the maximum yield strength of about 600 MPa, so maybe you are a bit conservative?

[Dutch Peter]

Ragnar,

Are you not confused with the max. tensile strenght?

Davef,

It's better to calculate with the minimum values of a material and than indeed with the yield, or 0.2% proof stress.
For alu 6000 series (extrusion material) that's about 215 - 260 N/mm^2, depending on composition.

Getting back on the equation, using 215 MPa and taking into acount your astimate of 7800 mm for the HA, your getting pretty close to the correct answer!

Good luck,

[Raggi_Thor]

Oops, I did a (too) quick lookup in a table, Yes you are right.

[davef]

Dutch Peter and Raggi Thor...

Thank you... that was indeed my mistake. I am very appreciative of your assistance. I have found the book "Principles of Yacht Design" to be very very helpful but one suggestion I would have would be for them to provide more sample equations instead of just giving the answers. This is particularly difficult for those of us who are working in english units since sometime the equations they present have hidden conversion factors. For example, in the equation above, the 600 is also taking into account that the righting moment is is Nm where as all the other length dimensions are in mm. When I convert this to english units it is easy to make a dramatic mistake.

As long as I have the attention of two experiened people I wanted to ask another question of you.

I am a pure amature with very little sailing experience and no previous design experience. We have designed a small 20 ft day sailing sloop. She has a retractable keel and displaces around 1400lbs.

In computing the 30 degree righting moment, therefore, the biggest contributor is my assumption on how many "passengers" I elect to include in the equation. This has a very dramatic affect on what type of section I need for my mast and boom.

For example, if I assume 2 people on the high side of the boat at 30 degree heel, I get IX = .85 and IY = 1.28 respectively. If I go to 4 - people on the high side at a 30 degree heel I get IX 1.093 and IY 1.642.

Just this difference takes me across several different mast extrusion profiles (I am looking at masts from Dwyer Spar).

The boat has a fairly large cockpit and will actually hold up to 5 people but I just can't imagine ever sailing in a condition where I had all 5 on one side of the boat.

The boat will only be used for inland lake sailing and since I am not experienced I don't expect to do much heavy weather sailing, although you can never tell.

I don't want to overdesign the mast terribly, but I certainly don't want it to fail either.

Do you have any advice?

If you look at Dwyer Mast

http://www.dwyermast.com/families.as...cat1Name=Masts

I am looking at the DM6 Profile. Does this seem to make sense?

Any advice on a Boom profile?

Thanks very much in advance.

Dave

[Dutch Peter]

The question is, will the boat heel to 30 degrees with 4 people on the high side?!!! How did you calculate the RM?
It's better not to compair the calculations for a 15 mtr boat with a 6 mtr boat. Stability calculations for such a small boat are very much influenced by persons onboard compaired to a larger craft. And subsequently everything related is also influenced.
Look for a boat of similar lenght and similar sailarea and copy that boom section.
Not scientific, but a lot is done in the boating world like that.

Hope this helps, I'll look for more info for you, got some more "design books"

[davef]

Peter... The book does not seem to take into account if the boat is capable of experiencing a wind that would heel the craft to 30 degrees with four people on the high side. PYD seems to simply assume that the boat had done so and then compute the loading on the mast that would result from the moment of the keel, the center of boyancy and the people.

I have attached some crude rig drawings of my boat along with the calculations for the rig... perhaps you can find some errors.

Regarding your suggestion to find a similar boat and copy it; that would be fine, however I have not found someone with a similar boat who will tell me what section they are using. I guess I could try to find a boat and measure the section but have not done that yet.

Unfortunately it is winter here (and darn cold out as well) and all the nearby boats are packed up so I can't easily run out and measure a mast. I am trying to get the rig on order within the next couple of weeks...

All of the spar manufacturers that I have talked to are reluctant to make a recommendation because of concerns about liability. They want me to tell them what section to use.

[Dutch Peter]

Dave,

I'll look at it tonight

[Raggi_Thor]

I agree with Peter (again :-).
It's better to compare your mast with other boat's masts.
For exampe the Yngling, 600kg + 3Crew, has a mast that weigh approx 1.4kg/m.
You don't have to go out in cold :-)
http://www.proctormasts.co.uk/dinghy...p?section=3525
Here you can find examples for ather classes as well.

[davef]

Raggi,

Thank you very much! THis is very interesting information. Are you familiar with any of these boats that would have roughtly similar specifications to my craft?

The following are a few basic dimensions - I hope I didn't mix up the translation to metric!

Dave

LOA 6096 mm
LWL 5689.6 mm
DISPLACEMENT 0.5940 M^3
SAIL AREA 19.3 M^2

PRISMATIC COEFFICIENT 0.5531
LOA/MAX BEAM 2.78
LWL/DRAFT 4.67
LWL/DISPLACEMENT 6.77
LOA / LWL 1.07
FREEBOARD FORWARD / FREEBOARD AFT 1.26
FREEBOARD FORWARD / LENGTH RATIO 0.13
BALLEST RATIO 0.27
SAIL AREA / DISPLACEMENT 27.32

[davef]

Oh, Incidently, here is a picture of my boat... Hard to believe someone could get this far without having designed the mast eh?

[Raggi_Thor]

Well, I thought the Yngling was close enough.
It's about the same weight, maybe less beam but a little more ballast.

[Dutch Peter]

Dave,

Didn't get around to it last night. It's gone be an other day.
Sorry.

[davef]

Raggi,

Thanks for pointing that out. I had missed that you had already mentioned the Yngling. That is a pretty little boat. I have never seen one here (but then again I am 3000 miles from the nearest ocean here). I beleive there is a small fleet of Solings in Milwaukee which is not far from here.

I took a closer look and perhaps have a bit more confidence now in my calculations:

When I compare my boat with the Yngling I find:

The LOA are roughly equal.
My boat has a much broader beam .
My boat is carrying a good deal more sail – 19.3m^2 versus 14m^2
They are both fractional rigs but my boat has no back-stay
The displacements are very similar
The Yngling has more ballest

When I compare my calculations versus the mast section that the Yngling is carrying I find my calculations are calling for a stiffer mast section (by about 20%): Given the greater sail area and the back stay on the Yngling I think I feel a bit better about my calculations. Perhaps they are a bit too conservative. I'm still not positive...

My calculations Yngling
Ix = 40cm^4 Ix = 29cm^4
Iy = 60cm^4 Iy = 43cm^4

[Dutch Peter]

Dave,

I think I found the fault in your calculations, where did you get the Rightning Moment from? Did you make a stability curve?