Square rig variation

I am planning to build a variation on a square rig where yards are fixed to the mast for rotation, but raise and lower in tracks on the mast.
Mast rotation is used to control sail angle on all yards simultaneously. Reefing and furling is achieved by lowering some or all of the sail and yards. The bottom of each sail is connected to the yard below, forming in effect a single sail rig, allowing a single halyard to raise and lower all sail and yards on the mast. Refer to attached (Crayon?) sketches (not to scale).

This is to be installed as a biplane rig on a cruising cat, each sail approx 40 square metres (eventually - I've only just started building the boat...).

I am currently considering options for controlling the mast angle, so would like to be able to estimate typical and maximum torque produced by the sail about the mast.
This parameter is similar to “pitching moment” used in aircraft design, but finding a value for given windspeed and angle is taking me out of my aerodynamic depth.

Assume for the purposes of calculation all sails rectangular and identical up the mast with a foot of 3 metres. Yards are symmetrical about the mast, and sail is simple single layer fabric.

Torque will be produced by sail drag and lift forces in varying proportions as sail angle of attack changes. I can find some data for lift and drag coefficients, but very little for the location of the centre of lift and centre of drag.


My question is then, can the torque force on the mast be simply approximated and if so how? Any info most welcome.


Feel free to post comments on other design aspects as well, but be aware that I'm not aiming to produce the worlds most efficient sail here, just an effective rig thats fun to play with and cheap to build (but with less damn strings than a junk rig ).

For anyone interested, I've attached a short pdf I wrote on the reasoning behind the rig.

Thanks in advance,
George

 

Autodafe;

To get the torque on the mast when braced hard on the wind use the moment coefficient about the 1/4 cord point, which is commonly given for most airfoils (or a constant camber section such as you have), and the lift to work out the center of effort.

On a more serious matter however, having all the yard braced to the same angle will be very inefficient due to the wind velocity gradient from the surface to the masthead. The lower yards will need to be braced further around than the upper yards to maintain a consistant AOA across the sail.

 

Thanks jehardiman,
I had heard the 1/4 chord was used, and it's good to have confirmation that that's for sails as well. I'll see what numbers it gives me.

I had considered the windshear issue, but looking at graphs of windshear over open water at different wind speeds it didn't seem worth a lot of effort to put twist in the sail. There is a lot of difference between 0m and 2m off the water, and not much between 5m and 15m. AoA over the top two thirds of the sail will be within +/- a few degrees in pretty much all conditions, which is close enough for me.

 

Oh no, look at any tallship sailing, youll notice that is quite a lot of twist!

Regards
Richard

 

Except Maltese Falcon


I'll put a spreadsheet together when I get some time to check what AoA I get up the mast on various headings.

 

Neat. The construction problems for an equivalent self-tacking fore-and-aft rig (variant of the Balestron) would be harder to solve but a square rigger is balanced laterally so it should be easier. A cross between a junk and the Maltese Falcon. Here are some additional points -

You might have problems getting the hardware you need unless you have access to a machine shop. If you change the rails on the mast to a "C" section perhaps you will be able to use standard sail track, and the "T" shaped runners for the booms will be easier to make. The hardware will have to be overbuilt as it could be disasterous if a boom were to jam.

Not only is the rig not self-tacking, but the aerodynamic forces on the mast will try to rotate the sail normal to the wind, like a Raleigh disk. The torque to counter that may be quite high in a decent wind, which may make it difficult to set the sails quickly if the wind or the heading is changing, except for downwind. However, this torque is in the right direction to help with the wind velocity gradient.

I know you’re not particularly concerned with performance, but I think the sail efficiency should be high, approaching that of an aero wing. Provided the flexible leading edge does not flutter so you can set it to a low angle of attack, masking of the leeward sail by the windward sail should not be a problem on most points of sail.

The halliard tension to ensure that will be considerable. That could be a problem; I'm not sure how this rig will behave in high winds with the halliard slackened off for reefing.

When pointing close to the wind it will act like a biplane; typically the lift of the second wing is about 70% of the first, if the separation is about the same as the chord, and this improves as the separation is greater, as it is with your design.

 

Thanks for the kind words Terry

Using channel instead of rail on the mast is not a bad idea. I've been wondering for a while which is least likely to jam.

Re-reading the post I made earlier I see I was refering to velocity gradient as windshear. Whoops

I hadn't thought of the problem with having a slack luff during reefing... I guess I could put a brake on the halyard and use a winched downhaul during reefing, but that would be a bit of a pain.

Maybe a stiffish boltrope would help? I'm currently putting a 15' cat together to act as a prototyping platform and I'll have to play around with that in strong wind.

 

Sail twist calculator

Ok, I've put together a calculator for AoA twist with wind gradient.
I haven't protected the sheet so feel free to check the equations and let me know if you find any problems.

Wind gradient based on two theoretical sources, given in separate sheets in the file.

If anyone has a stash of real world data I could use, please let me know

The results match my expectations pretty well. Total twist over my sail span perhaps up to 10 degrees in some conditions, but less than 5 degrees over the top two thirds of the mast. A couple of degrees each side of optimal I can live with, but it would be important for anyone trying to build a competitive racer.

 

Sail Torque

Back on my first question:
I'm now happy with calculating lift, drag and moment around the quarter chord point - I'm thinking of using CL 1.3, CD 0.2 and CM 0.1 at stall of 16degrees for maximum torque.

But what happens after the sail stalls? As I understand it, initially the stall moves from the back edge, and lift moves forward as total lift reduces, so quarter chord approximations are probably still ok up to the point where the foil is fully stalled.

Once the sail is fully stalled can I assume that CL=0 and centre of pressure reverts to the centre of area?

 

I don't agree with the values for apparent wind speed from which the angles are derived but I got similar shear values from my own calculation using the Ruggles formula. Thanks for that information by the way, new one to me. With the sail profile you propose most of the drive will come from the upper sails as is usually the case for a square rigger so efficiency should be optimised for that portion of the sail if it cannot be optimised throughout.

Alas, my knowledge of aerodynamic theory is insufficient to take me further with you on your journey, so I do not know how the sail will behave in the stalled condition before alpha reaches 90 deg, at which point the center of pressure is clearly centered by symmetry alone. The only practical experience I have of deliberately stalled airfoils dates back to childhood experiments with model planes which used entirely different profiles so what little I remember is of no use to you.

One thing occurs to me; the sail will be thrashing around under stall conditions, so any attempt to predict CL, and perhaps torque as well in these conditions, using theory developed to describe air flow behavior over a rigid surface, is probably doomed. Perhaps tests on scale models is a better tool.

 

You may have a point there

 

I have been assuming that you’re aware of the Maltese falcon thread but here it is in case you are not- http://www.boatdesign.net/forums/sailboats/maltese-falcon-hit-miss-12459.html -it has some references to worthwhile technical sites and great pics. The depth of the yard curve for the MF is 12% I believe. This would be an included angle of about 27 deg which looks close to your sketches.

More thoughts on reefing: it should be possible to reef with the sails trimmed normally. They will not flutter in that condition and the lowest sail section -the one being reefed- should collapse as the wind is spilled out of it, when its upper yard is lowered. You will need to pull each yard down separately as you lower sail, but no doubt you are already aware of that.

On the design of the yards, there will likely be a lot of unbalanced vertical force on them. The Maltese Falcon has a system of bracing wires and this link to a page on the site of Brian Eiland shows the braces on another dynarig boat- http://www.runningtideyachts.com/dynarig/ -I’m not sure how much problems the use of bracing wires would cause you but if you go with an unbraced design the sliding runners will need a fair amount of vertical depth.



I was thinking about a telescopic rigid wing sail a year or so back but I couldn’t solve the design challenges. It was for a smaller boat (I’m starting to become notorious on the forum as the pesky wee tiny boat man I suspect), and you have given me another idea; it is a shameless ripoff of yours. The rotating mast will be telescopic and a yard will be attached to the top of each section forming a Tee. Like your design each sail section can be permanently attached to the yards above and below it and simply brailled when reefed. It should be quite practical, even easy for a small boat (each mast section will have to be raised by pulling up its yard manually) and it escapes many of the challenges you still face. The lower rig will be subjected to more wind shear than yours but it should be easier for me to introduce mast twist. Thank you for the idea and for helping me to get a long-stalled project going again!

 

Thanks,

Yes I've been through the Maltese falcon thread. As you say some good stuff there, although I always end up wanting more detail

Feel free to ripoff as much as you want, I'm not a huge fan of IP protection for small changes to existing ideas.
Good luck with your project, it sounds intriguing and I'd love to seem some pictures when you get to that stage
Designing and building a telescoping mast sounds intimidating to me, but it does avoid all the sliding yard problems I'm going to have And with the advantage of lowering airdraft and CoG when reefed.

With regards to my yards, I'd like to keep it as simple as possible, but if required bracing wires cause no particular grief.
I was planning to have slides with a fair amount of vertical depth, to reduce the chance of jamming as well as provide vertical rigidity to the yards. I don't expect that to be able to take the whole sail tension though. I'm hoping that the luff and leech boltropes will carry the main load to the topyard and boom. Top yard is then supported by halyard and boom heavily re-inforced. When reefed the lowered yards would be lashed to the boom.
I'll see if this theory works on my scale model.

I am aiming for the 12% mentioned for MF, but it has occurred to me that by shifting the point on the yard that I attach the sail, and having flexible battens I can adjust sail camber according to conditions if I want. This will be a little tricky on the tops'l as it is connected to the yard at more than two points, but shouldn't be too difficult.

 

Here's a sketch of what I had in mind: perhaps it can help you? It works out well for my car-topper sailboat as it folds compactly. Something I have also been looking for!

 

Thanks for the sketch!
Using Al tube construction should be quite straight forward.