Forces on mast by sails yet again

[Fanie]

Hi guys,

Sorry to yet again start another one of these, I have however not found any practical answers on some of the old(er) threads regarding this, or I have missed it.

I don't want to bore you to death by trying to find formulas and so on either.

What I want to know is the force one can expect per square meter on a sail at a given wind speed.

So lets say the sail area is 50m^2 and the windspeed is 20m/s what force would be pushing against the sail ?

Has anyone measured or attempted to measure this before ?

Considering if I'm using an aft mast setup and the main sail is as a jib it would be safe to say the force on the sail would be about the force down on the mast, and plus the weight of the mast it would be the beam load.

If for example the wind load per square meter of sail is 10kg at 20m/s on a 50m^2 sail, then the total sail force is about 500kg plus the weight of the mast say 200kg then the beam should be able to carry 700kg plus a safety factor - at that wind speed.

I don't know if a 20m/s wind will load a square meter of sail with 10kg - which is what I hope to find out from you guys !

If I can find the wind force per square meter, I can design the mast, the beam and the auto tacking strip for it amongst other things.

Your help appreciated. Thanks in advance.

[Fanie]

Come to think of it, the force per square meter should be known factor. Times the wind speed should give you the force.

Any idea ?

[deepsix]

Im no expert, but as I understand it there are fairly standard sail force coefficients used by NA's, Im not sure if there is something suitable for your sail plan. Look on amazon.com for C. A. Marchaj - maybe sail performance or aero-hydrodynamics of sailing, maybe someone will recomend one.

As I understand it the sail force is not that important in designing the mast and rigging, these loads are all related to the righting moment. The wind speed, sail area and sail force coefficient merely determine when the maximum righting moment is reached and you must shorten sail.

You can get a resonable idea of the loads involved by just using basic trig, or you can use freeship to produce control curves and then calculate stability curves and righting moments.

Have you tried this? http://www.wb-sails.fi/news/SailPowerCalc/SailPowerCalc.htm

[Fanie]

This looks interesting...

http://glwww.mst.dk/udgiv/publications/2000/87-7944-019-3/html/bil07_eng.htm

Thanks Deepsix, will have a look.

[MikeJohns]

Fanie
If you want a very basic approach the important consideration is the righting moment. The heeling moment from the sail (acting at the center of area) cannot exceed the force required to reach the maximum righting moment of the vessel. Work out the division of forces amongst the sails and find your maximum rigging loads accordingly. You will have to make a call on which sails will blow out and which will heel the boat given a 10 second hurricane.

You should to consider these 'bullets' hitting the vessel in all sail combinations.

[Fanie]

I have found some information as well as a graph that implies the force per sqare feet at so many miles per hour wind - not a linear graph.

You would have to decide at which wind speed you want to switch to a storm sail so you won't cause damages to the rig.

Now to find a conversion for these old units - wish the US would come to the table with their units :o

The righting movement of the boat as well as the forces of the sails will be taken into consideration, thanks Mike. Amazing how quicly numbers add up when you start calculating these forces. Currently exceeding by quite a bit to what I expected initially.

[deepsix]

It sounds like you are describing this

Lift(N) = ½ ( D * Area(M2) * Coeff of lift * Speed2(M/s) )

Where D is the density of the fluid, about 1.2 in air. Coefficient of lift(Cl) is highly variable dependant on sail planform and section shapes ect, around 1.0-1.5 is the general ballpark, but it can be very different.

This shows that all things equal the forces produced by a sail increases with the square of wind speed. So when the wind speed doubles, the force produced quadruples.

Calculating the forces produced by the sail is quite complicated because it varies according to many factors, aspect, section shape, angle of attack, windspeed ect. These factors can change depending on the course you are sailing and how your sails are trimmed, so one Cl is only valid for a small set of circumstances. The amount of force that is translated into driving and heeling moments is also variable.

You must design to the maximum righting moment of your boat, this effectivley limits the maximum force that the sail exert on the rig, because the heeling moment cannot exceed the maximum righting moment or else you will capsize.

It might me easiest to design to one of the scantlings rules, here is part of a draft of ISO 12215 for small craft, Im not sure if there may me something more applicable, maybe someone will suggest something else.
http://www.nmma.org/certification/local/downloads/documents/WD_12215-9__E_-2004-03-02.pdf

[Fanie]

Hi Deepsix,

That formula is to determine the lift, also used on aeroplane wings.

In this case I want the head on full wind force pressing against the sail. Just the pure unprocessed brutal force.

It seems there can be quite a bit of force from the sails. I'm surprized nobody in the 'old' days used these sails as catapults before. You could throw a bomb further with it than you could by hand.

[Fanie]

The local guy here who can make carbon fibre or fiberglass masts is away for a week. I must get an idea what stiffness and load rating one should expect for different sizes as well as the weight for the materials.

My rough calculations indicates the mast could be around 160 to 180kg ! and the beam carrying the mast should be able to carry up to 1500kg to 2000kg !

Can this be ? Did I move a decimal point somewhere ?

[Fanie]

Anyone have any idea ? This forum is supposed to be packed with experts.

[Rick Willoughby]

Mast compression load will be slightly less than the total displacement unless you overtension the stays. This is based on chainplates mounted on the outside of each hull. If you bring them inboard then compression load will increase.

Mast section will depend on the number of stays (fewer the better from sail handling point of view). Usually two sets are enough. Surprise me if the mast weighs more than 10kg per meter if in aluminium so you would expect much lighter with CF.

Rick W.

[Fanie]

Hi Rick,

Thanks, youve always been very helpfull all along.

There will be only three stays - two aft and one foreward which is also the stay where the sail furls onto.

If the mast is going to be around 10kg/m I'll be very happy - it will make some other mechanical issues a lot less complicated. I have calculated it slightly heavier, but it is still within what I expected.

If I use the total displacement to determine the mast compression - which is 2600kg's - per hull (gulp) - it comes to quite a bit. This is 5 tonnes !

This will require some super structure to support :eek: Have I misunderstood you on this ?

[deepsix]

That might be a little simplistic, how far from the stern will your mast be?

[Rick Willoughby]

Fanie
I made an assumption that you will have side stays. Eliminating these may increase the compression load. It will certainly increase the mast bending if you do not have lower stays. Your original weight estimate may be close to the mark.

The compression is very nearly the total displacement if you have side stays so if that is 5t then that is the compression load you need to resolve in the cross beam.

The torsional load through the cross beam is also substantial and needs to be resolved.

Rick W.

[yades]

Anyone have any idea ? This forum is supposed to be packed with experts.

Why dont you try out this HISWA 2004 paper....it looks rather interesting ...and it has perhaps some few keen answers to your issue...

cheers

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

[Fanie]

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

[Fanie]

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.

[Fanie]

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

[deepsix]

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

[Rick Willoughby]

Hi Deepsix -

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

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.

[Fanie]

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.

[Fanie]

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.

[Rick Willoughby]

Using Yades link

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

.............

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.

[Fanie]

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 :o

[yades]

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 :cool:

[Fanie]

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 ! :D

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.

[Fanie]

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 ?

[Wynand N]

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.


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....

[Fanie]

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... ? :D

[Fanie]

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

[yades]

Just to add a further technical contribution on the issue (with a resulting compression load value !!...)which I believe being of good interest to many keen speculators on this subject......

Cheers...

YADES :cool:

[charmc]

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

"It is well known that higher aspect sails produce greater lift when close hauled." "What's the Ideal Sailing Rig?" Michael Kasten, Kasten Marine Design

Yes. Think schooner, as in Bluenose, America.

[charmc]

There are limits, though. Too high and thin (too high an aspect ratio) and they will stall at low "angle of attack". In other words, they will be great when pointed well up, but not efficient at other points further off the wind. Not versatile. I think AR of 3 -4 is considered best for all around use.

[Fanie]

I hate these compromises. One would think that after all these years and years of sailing experience you guys would have come up with some kind of golden rule to what works and what doesn't. Instead everyone blunders ahead and this theory and then this formula... I think I mentioned this before.

Eh YADES !! The pdf you uploaded is just about spot on with my size cat. Same mast length, same boat size, couldn't ask for a better calculated example :D Only thing I don't like is the 6000kg mast loading ;) That is quite a bit of loading, considering that is the weight of 6 toyota carolla 1600's eh !

[MikeJohns]

Fanie
The lack of exact definition is because anything to do with fluids and dynamics is basically indeterminate. Thats why we use static loads and then a factor of safety to allow for indeterminate loads. The FOS is then refined through observation. It is only with dead static loads that we can design absolute to specific numbers and know it will last.


The most up to date rule from any society for rig design is from Germanisher Lloyd, (it is a public domain document) attached. As the knowledge and particularly materials and design move on the newer guides are more applicable.

GL as underwriters suggest that a vessels rig be designed to this spec. So they are putting their rule where their money is, as to speak :)

Hopefully it will help you along with the others contributions.
Cheers

[yades]

I'm pleased to read on your reply that the example is just fitting yr situation....... That' s because I made some ......realistic assumptions..... as stated on the enclosed paper, for the evaluation of mcl, based on the infos gathered from your previous threads...........However, bear in mind reason for such a high compression load is mainly due to a no-spreaders rig arrangement and also due to a deck-stepped mast.....:cool:

[Rick Willoughby]

I hate these compromises. One would think that after all these years and years of sailing experience you guys would have come up with some kind of golden rule to what works and what doesn't. Instead everyone blunders ahead and this theory and then this formula... I think I mentioned this before.

Eh YADES !! The pdf you uploaded is just about spot on with my size cat. Same mast length, same boat size, couldn't ask for a better calculated example :D Only thing I don't like is the 6000kg mast loading ;) That is quite a bit of loading, considering that is the weight of 6 toyota carolla 1600's eh !

Fanie
If you want to reduce mast compression then reduce displacement. If you get it to displace one toyota corolla rather than 6 then you only need to allow for one corolla of compression.

Poor design results in failures and why you see boats set to sea and then make a quick retreat as things start to fall apart.

Yades result is close to my original number provided in one of the very earlier posts on this thread, #11. My calculation did not have any safety factor apart from a small one based on my mostly conservative simplifying assumptions.

Rick W.

[Richard Atkin]

Fanie you want to have your cake and eat it too. And you want the icing to be thicker and you want candles too :P

Quote: "won't a few long thin vertical sails give you more windward speed than one big sail ?"

The way I see it, one big sail (long and thin) will give more windward speed than several smaller ones, but will also give you more heeling force and bigger rigging loads.

[Richard Atkin]

Sorry Fanie, I haven't been keeping up with all your threads. Have you decided on a boat length yet?

[Western grace]

Hi Fanie,

Am not a expert but have a 57' heavy offshore cutter. The righing moment of the hull is the firts thing to look at. Walk the docks and you can see fast differents in size of rigs.

Look at it this way. your rig should be strong enough to witstand a knockdown. A tender vessel will lay over a lot easier than a stiff vessel thus a tender vessel needs a lot les rig than a stiffer one. so you start with getting the righting moment than calculate forces. just doing the math on sail area is sitting you up for disaster.

good luck

John Van Strien
Sv Western Grace

[Fanie]

Thanks for your comments, all is taken in consideration. I still have some things to work through before making any final decissions on boat length, sail or sails sizes and so on. So many compromizes... in the 'old' days things were much more simple, not even to mention time. Since this is an expensive exercise I'd like to do it more or less right the first time.

Thanks for the goog luck John, I'll take it :D

[Western grace]

Fanie,

As you are starting out be carefull. building a boat is very expensive even when building a proven design. If you go and build a unproven design you set your self up for failure. having come to a large building process can only recommend buying a baot or finshing a well done project. have seen many go down with the project that is financial.

John

[BigCat]

If you are trying to understand the relationship between wind speed and pressure, it is calculated with Martin's formula, which is the square of the wind speed in miles per hour x .004 = pounds per square foot.

[FAST FRED]

A very rough rule is the sails will produce 1 lb/sq/ft of pressure at 17K.

FF