Forces on mast by sails yet again

Here is a side and top view of the sail. mast and stays. The mast is 15m high.

 

Hi Deepsix -

Simplistic maybe. My rough calculations led me to 1500 to 2000kg's and that would be for 20m/s wind.

the mast - Stays connect about 3m200 directly astern, and mast is 3.9m to the stay anchor. Angle to the aft stays from the forestay is about 134 deg so the two aft stays are about 96 deg apart.

Thanks Yades, looks like a usefull paper. I'm working on the calculations now to see kow it compares with my previous ones.

 

There will be lower stays, same as what you see in the sketch, but they will be disconnected most of the time. They are the storm jib and it's stay's. Will only be connect when the wind becomes too wild for the main sail

 

Have you had a look here?
http://www.boatdesign.net/forums/downloads.php?do=cat&id=5

 

It does not matter about the wind speed. The peak load in the mast is a function of displacement. At some point with a 15m mast and corresponding sail plan you will get a gust that will be sufficient to lift the windward hull. If you do not design for this condition then the cross beam will yield or shatter depending on material. Could result in an interesting attitude of the hulls. One trying to go east while the other is trying to go west.

Likewise it is difficult to order the wind to stay below 20m/s until you have the lower stays connected. In the interim the mast will buckle if this is you design condition. I have seen bullets come over a hill when sailing close to a windward shore that knocked a 24ft trailer yacht down and drag it sideways until it was completely swamped. Totally unexpected things can happen. Under these circumstances you do not have time to fiddle with things.

Rick W.

 

Yip, that beam breaking would be a FU to say the least. If there is one thing that may NEVER break it is the cross beams.

I plan to have some release under drag if the forces exceeds a specific load on the sails. One cannot control the wind speed or gusts, but I think it would be better if it can let sail out should such an unexpected bullet hits. I agree, there may not be time to do something about it. The racing guys didn't agree about the dragged cleat release but I think it will have it's place.

The calculations above is just to give me an idea of the loads to expect. I'm not sure if they are correct which is what I'm double checking now.

 

Using Yades link

http://www.hiswasymposium.com/pdf/2004/R.Janssen.pdf

I calculated the max compression force as 1586kg. Seems I wasn't too far out initially. If the weight isn't going to become too much I will design the beam for 2000kg instead.

I'm getting other software that one can use to calculate the structural strength with for carbon and GPR structures.

 

The paper discusses mast design software. The only formula provided for compression load is the Skene method. If you used this I cannot see how you arrived at your figure. It will be way too low.

Rick W.

 

Well, you said the peak load in the mast is a function of displacement. I used two thirds the boat's weight since it would be leaning on one hull and the wind pushed the vessel over to 30 deg. These forces are pushing the mast in only one direction and that's down onto the beam.

I'd gladly look at the Skene method as well. I'll google for it.

Something's up with my google... up to nuggets all day long

 

Another hint...

have a look at this calculator....rather interesting......
http://www.barefootsworld.net/windwalker/aftmastsailingcalc.html#menubar

Furthermore, there is also the E. G. Van De Stadt empirical method wich is (or at least was) extensively used for spars compression calculation...it is referred to also in the book "Technical Yacht Design - by A. G. Hammitt" very interesting .....
Will shortly try to outlined the main points....simple but smart....

YADES

 

Hi Yades, I've read so many articles on masts forces and up to now I must say that it looks more like nobody is really sure what they are doing !

Nice link - i'm going to play with it a bit. Thanks.

I'm thinking there are so many sailing activities going about I'm surprised no one came up with some kind of rule of thumb. Seems every one just follows someone who went before them...

Just reviewed four comparative calculations for a specific mast - they all vary, and it seems they suggest that they are not too sure either.

It seems the solution would be to get a gross idea of the loads and forces, and just design it accordingly and allow for some safety factor.

 

On the little trimaran I've built I've found the mast upright to work better despite the more angle in the forestay. The sail is larger than with the mast at an angle and the aft stays is simpler to implement.

As in Brian Eilands article this link also suggests the mast is at 10 deg foreward. Is there a specific reason whay it is leaned foreward ? other than an attempt to keep the forestay(s) as vertical as possible ?

 

Fanie, very simply put, mast compression happens like this;

1. Wind load causes yacht to heel
2. Righting moment develops
3. Righting moment opposes wind load
4. Mast rigging connects righting moment and wind load
5. Tension in the rigging causes compression in the mast
6. Compression increases further down the mast with max compression at heel.

To calculate the necessary section size to accommodate compression loads Euler's strut theory/formula is used to get the moment of inertias of the section to be used.

To use Euler's strut formula for the mast inertia, you need the following;

1. End condition of the mast, eg. fixed at base and pinned at head (keel stepped) of pinned to and bottom (deck stepped)
2. LOA
3. RM at 30 degrees (righting moment)
4. Number of spreaders
5. Number of lower shrouds
6. CPW (chain plate width)
7. Height above the deck
8. Panel lengths (between deck and spreader and mast head)
9. Safety factor to be used

With all the above, you can safely calculated the fore / aft and athwartship inertias of the mast section to be used.

As for forces on the sails itself, there are quite a few forces at work and all can be calculated.
However, it is much easier and simple to calculate the lift force and the drag force (which are simple formulas) and to plot it to scale (see sketch attached) in the directions it acts and the heeling force (Fh) and the driving force (Fr) can be measured to scale to reveal the magnitude of these forces...

Having said this, aspect ratio of the sail plan plays an important part in sailing.

A hight aspect ratio sail of the same area is more effective than it's low aspect ratio counterpart in terms of the driving force it can produce, particularly if the mast diameter is small. It can be that a high aspect ratio sail plan produces more driving force and yet less heeling force, the latter offsetting the larger heeling lever common to high aspect ratio sail plans.

If sailing downwind, maximum driving force comes from maximum sail area, and aspect ratio is not very significant.
However, sailing to windward, high lift-drag ratios are sought after....

 

Very nice, thanks Wynand ! Getting there slowly.

I am keeping the sail setup as basic as I can. Remember I plan to use only one sail as main sail so far. I also have a few experiments to do still, and was actually hoping to try a few things this weekend but things aren't working out as planned.

I'll have to compromise on the aspect ratio of the sail since I'm using the same sail all round. I am adding a storm jib which I hope I may never have to use, and I may add another small one later aft of the aft mast but that would be only to balance the sail forces if required.

I have had another look at the beam of the cat. The structural beam requirements on a 7m BOA vs 8m BOA ia quite a bit. I suspect that Frosty would be somewhat disappointed if I reduce width - space where beer could be stacked is compromised.

Here is another question. I know there is an optimum minimum distance between the hulls for a 10m cat, and is to eliminate interference between the hulls from water displaced, but beside that.

If I have a 7m wide cat and an 8m wide cat, same LOA, what would significantly be different between them if they are on the same water ? Besides the reduced cabin size and you have to walk further to the bathroom... ?

 

One more thing on sails - won't a few long thin vertical sails give you more windward speed than one big sail ?