Balancing the sail plan and board position

Hi,

I am amateur sailor currently designing a dinghy. This is my first attempt at doing this so I am leaning heavily on books. I am currently am using 'Yacht & Small Craft Design' by Gordon Trower as my primary reference book.

In this book it suggests that a basic way to create a dinghy that is balanced is first to find the (CLP) Centroid of Lateral Plane (hull) and the (CSP) Centroid of the Sail Plan and create a design where the CSP 'leads' the CLP by 5% (dinghy) of the waterline length.

Is this correct?

As when I draw the outline of my proposed sail plan and find the centroid this positions the board a very long way back in the boat using this basic rule. The only difference I have made is to find the Centroid of the complete sail including roach, where as the book suggests just the basic triangles, but only for ease. I have done this by the simple device of cutting out my plains and using gravity and a plumb line to find the intersecting points.

Is this where I have gone wrong.

This basic way of balance the boat in the design process also doesn't seem to agree with the basic principal that the center of force of the sail plan (combined) on a sloop rig ( jib & main ) is 30-35% of the cord length and the center of lateral resistance is roughly a small percentage in front of the board when you combine the forces of the hull and the board together.

Can anyone help me out here in a none techy way.

 

If you're looking for a none "techy" way then you have to use imperial study of well known existing designs, develop your own "lead" estimates and take a fairly educated guess, based on your studies.

The concept and use of lead, is a portion of yacht design that is surrounded with all sorts of black magic and shrouded in less then equateable formulas. Frankly, the best designers have enough experience to place it close enough, to have an option of fine tuning it when constructed. There are many things that can affect the amount of lead you provide a specific underwater area/sail plan combination. So, a simple answer isn't to be.

Several mathematicians have attempted formulas, none work particularly well. Some designers have offered suggestions for different rigs, but none work with reasonable reliability. The real test is what you've learned and observed, from your own work and that of others.

I don't know your rig, nor your hull form, but 5% seems a bit light. You're in luck, as a dinghy can be balanced with the skippers butt. If you have a moderate to high aspect ratio, modern, fractional Bermudian rig, with large roach and similarly high aspect appendages on a scantly immersed hull form, then I suspect you'll want a wee bit more lead.

The lead amount is a percentage of the LWL. In other words, divide the LWL by 10. This represents the scale (marked in 10% increments) you'll use to offer up the lead for the CE. Hanging strings and using push pins is a pretty easy way to introduce considerable error into your work. Very simple geometry will solve you're problems, once you make the decision on how much lead you'd like to use. This type of geometry is well covered in elementary school.

 

Thanks for the reply PAR.

The boat is a skiff type. With a high aspect rig with a 45% - 65% sail area split between jib and Main. Fine entry to the hull and flat planning surface aft.

I have found the centroids of the sail plan triangles using geometry and also the plumb line method and the results a very similar ( as close as dam it at this stage ). I then used the plumb line method on the whole sail plan including the reasonably large roached main. This as you would expect positioned the centroid further aft and slightly higher.

The question really was... given that the concept of lead requires the sail plan centroid to 'lead' the hull centroid by a percentage, and given the results above, is it right that with this sort of sail plan the board would be so far back in the boat. We are talking 2/3rds back from the stem!

My own experience tells me this is not the norm. But the methods I have used and the information I have is telling other wise. I don't think the methods for working out the Centroids are at fault (http://en.wikipedia.org/wiki/Center_of_mass). But I am interested in what others think so I can confirm or deny my results.

Thanks

 

As I suggested, many things can affect the amount of lead, but your question seems to stem around whether you've placed the rig too far aft on the hull, which consequently moves the appendages aft. I don't generally design in this fashion, usually having a fair idea where everything is going to live as I'm developing the hull. The hull I'll use will be rig dependant and not as well suited for a different rig or one that is located very far from my initial ideas for the design.

What percentage of LWL is the mast centerline aft of the stem?

 

Hi PAR,

I thought to make matters easier I'd attach a couple of pdf's. The design is made more complex by the fact that I want to be able to sail the boat singlehanded. With the main only and smaller assy kite.

As you can see from the attachments the sail plain centroids do not lead the hull centroid. But there is an element of balance between the estimated center of force of the sails and the presumed center of lateral resistance (this is not marked) but I am estimating it to be just in front of the board.

 

Hi UK9,
I wouldn't go above 5% lead for the Cheruby-skiff type thing you are designing. You will only sail the boat flat, unlike a yacht, so bigger values will not help restore balance in a breeze. Also, because it is really just a fairly crude rule of thumb, including the (large) roach does not really help the accuracy of the 'calculation' all that much, so I would just stick to the CSP of the triangles. Finally, when calculating the CLP I wouldn't include the hull, just the daggerboard and rudder. This is because your hull is likely to be very flat (and very shallow draft) so will not give much grip.
But basically you have it right. The design looks good, but I'd be tempted to move the dagger board forward half a chord, especially if your assy has a long pole.

 

Thanks for the advice PI Design. Are you saying that I have roughly got it right for both mast positions including the singlehander? Or just the Main & Jib version?

 

To my eye the board looks looks a little far back in single handed mode (or the rig is too far forward). What are you using to design it?

 

I just took a quick look at your sail layout, it appears to me you have your CSP too far aft. The centroid of the triangular jib will occur at one third of the way up from the bottom edge (the same is true of a triangle main too). You show a line at 35% way back from leading edge but I do not see a point on the jib that shows the centroid of the jib. Forgive me if I am misunderstanding your drawing, but it appears you are not "weighting" the total sail area far enough forward because you are using that 35% line, instead of a point.

Typically you would find the centroid of each area, and then multiply the centroid location from some reference point (usually the front of the boat) times the sail area of each sail, add them together and then divide by the total sail area. If you do not have the centroid located accurately then your answer will be wrong of course.

If you are assuming the center of lift on the sail occurs at the 35% cord point (not a good assumption on a fabric sail IMHO) you can modify the "centroid" location forward to the .35 mean aerodynamic chord point and then try again.

But I think the dagger board location appears too far aft because by my eye anyway, the CSP appears to far aft. Check your assumptions on your centroid locations.

Nice looking sail plan btw.

 

Yes I think you may be right. I was beginning to come that conclusion myself.

The design is a collaboration. The hull shape has been designed by a friend in the Southern Hemisphere. I am doing the rest.

Are you basically saying not to take to much notice of the 'Centroid' lead approach and to balance the boat on the centers of force / resistance?

 

The traditional way of "balancing" the design to put the center of force of the sails slightly ahead of the center of lateral resistance on the hull/centerboard/rudder (anywhere for 3 to 10 % of WL-5% is good) This is done by simply finding the centroid of each of the areas and assume that the aerodynamic force and hydrodynamic force act at the centroid of each of these areas. For traditional designs this works "close enough" and the forces are not real large so any unbalance can be adjusted or trimmed out during trials. It is a good place to start, but keep in mind you want to have some adjustment in your mast step location and mast rake to fine tune the balance. You could also trim the centerboard and/or rudder size, but this is a more permanent "adjustment"

FYI the reality is more complex than that. The aerodynamic center occurs about one third of the way back from the leading edge of the mean aerodynamic cord of the sail for an actual foil shaped sail. For uncontrolled sail shapes the max camber occurs further aft (from 35 to 50%) and even changes as you flatten the sail or adjust the twist. Typically in a "relaxed" sail shifts the aerodynamic center aft, a taught close hauled and flattened sail that is fully battened is forward of the centroid. So the centroid is not a bad approximation for the sails, and a reasonable place to start for a "typical" trimmed sail.

The hull profile in the water can be anywhere in the center third of the WLL I would guess depending on hull shape, hard or soft chines, bow and stern shapes, angle of heel, etc. A foil shaped centerboard and rudder, especially high aspect ratio ones, will have the hydrodynamic center at about a third of the way back from the leading edge of the the foil surface. The combined effect will depend on how large each of these surfaces are and again the centroid is not a bad place to start.

With the center of force of the sails slightly ahead of the center of lateral resistance for the hull you would have a light feel to the tiller. It would feel stable and "normal" with the feed-back through the tiller. If the center of force on the sails was slightly aft of the center of lateral resistance it would feel "unbalanced" and holding a heading would be more difficult.

 

Thanks Petros, that has helped fill in a few gaps in my understanding. I will go and recheck my calculations and assumptions. This may take a while LOL!

The sail plan is fully battened btw.

 

Hi UK9

Those drawings look really interesting, I have been considering a singlehanded skiff type boat for some time now. Would you be prepaired to give us a little more info on your boat? Is it going to be a one-off or will plans be for sale?

 

It's currently a one off but I dare say the plans could make there way to you at some point in the future.

A pic of the hull shape.
©David Lee

 

Oh yes, thats what im looking for. Cant wait to hear more, when you are ready of course.