Foil Shaped - Sectional Areas Curve

[mcollins07]

I am designing a sailing dingy which will fit on the bow of my 37’ sailboat, so there are a number of constraints on the design. The Lwl is about 104”. Bmax can be up to 64”. The prismatic coefficient is expected to be about 0.70. The construction will be lightweight, foam/fgrp sandwich. I would like to make the dingy sail as well as possible but also usable with an outboard, thus a transom is used. The bow is a pentagon shape in station view. Has two chines, in addition to keel curve and sheer curve.

I attempted to fit the hull geometry to a Curve of Areas (Sectional Areas Curve) as suggested by Skene. I also had the idea to use foil shaped chine curves. Any lift from hull shape would be great. I found that neither the foil shaped chine curves nor the Skene Curve of Areas seemed to work well for this dingy. But through this experience I now have the idea to use a foil shaped curve for the Sectional Areas Curve. Then fitting the hull geometry to the Sectional Areas curve.

So this is my question. Is a foil shaped curve appropriate for a Sectional Areas Curve for this light weight sailing dingy? Has anyone else used this idea for sailing hulls?

[sorenfdk]

A foil-shaped curve is a very bad idea (and I'm not too sure about the foil-shaped chine curves). The sectional area curve (SAC) should be shaped more or less like a bell.
And remember that the prismatic coefficient (CP) is not the only thing that you can derive from the SAC - the longitudinal center of bouyancy (LCB) is much more important because if you don't get that right, the value of the CP doesn't matter.

[Asleep Helmsman]

A little off topic, why foam and glass instead of wood strip planks and glass.

[messabout]

Don't get overly technical with your little boat. It is very small and it will have its' own performance characteristics by virtue of the small size. In fact an obscenely simple little boat such as the PD racer will deliver all the benefits that you need from it. The downside of such as the PDR is that it is butt ugly and will almost surely be the object of derision at the yacht club. Never mind that it might very well outsail the high zoot pram for which some kids father paid five grand.

[mcollins07]

Thank you all for your response.

Soren
I gave the expected Cp to indicate the Froude Number or Speed/Length ratio regime that I am concerned with. According to Skene’s Elements of Yacht Design (by Francis Kinney, 5th ed.) pg.284 (as reported in this forum, I have an older version) there is an optimum Cp for a particular speed/length ratio. And Fn = 0.30 x (speed length ratio) p. 73 Larsson & Eliasson Principles of Yacht Design. So Fn ~= 2.0 is where I’m anticipating operation.

This boat is intended to be a semi-planing dingy. The forces in this regime are making a transition in direction relative to the hull, as I understand it. In displacement mode the forces are more normal to the hull, relative to planing mode where the direction of force moves to a smaller angle relative to the hull.

Also, based on my analysis, displacement hull designs result in a bell shaped type of SAC. However, a semi-planing hull design might have the aft end of the bell shape truncated. A semi-planing hull would have a fuller aft section. Any reasons this should not be the case?

Often aerodynamic concepts for aircraft will not apply to hydrodynamics because the Froude number is relatively so very low for the hydrodynamics of sail boats. Because this semi-planing regime is different from the displacement regime leads me to think that a different shaped SAC (other than the Sine/trochoidal curve) might be more appropriate in this regime. A foil shape came to mind simply because it is related to lower resistance in higher Froude number conditions. The aft section of a foil curve would need to be truncated also for it to be applicable. Perhaps there is a transition from sine/trochoidal cruve to a different shaped SAC based on Froude number.


Asleep Helmsman
A good friend, Charlie Jones in Port Lavaca Tx, makes excellent very light boats of similar size with marine ply and stitch & glue methods. Based on what I’ve seen him do, it would be a reasonable approach.

I happen to feel like I can get a wider range of desirable material properties with the foam sandwich construction methods, and I’m comfortable working with fiberglass. So, at least for now, I plan on using foam sandwich techniques for a strong light weight boat.


Messabout
You are right about the PD Racer, I am a fan of that boat. However, it is not exactly what I want. Also, I enjoy getting technical and seeing what I can learn. If you are interested, based on my analysis, the SAC on the PD Racer design follows the Skene SAC curve very closely.

[Asleep Helmsman]

I grew up in Texas. I miss the Gulf Coast.

Talk to West Systems. They have reams of data on boat construction.

[sorenfdk]

Originally Posted by mcollins07

According to Skene’s...

Skene's is a very old book... Yacht design has come a long way since it was written/revised.

Originally Posted by mcollins07

So Fn ~= 2.0 is where I’m anticipating operation.

I think you're a little optimistic here. You shouldn't design for top speed, but for average speed.

Originally Posted by mcollins07

This boat is intended to be a semi-planing dingy. The forces in this regime are making a transition in direction relative to the hull, as I understand it. In displacement mode the forces are more normal to the hull, relative to planing mode where the direction of force moves to a smaller angle relative to the hull.

As messabout said: Don't get overly technical - it is after all just a dinghy.

Originally Posted by mcollins07

Also, based on my analysis, displacement hull designs result in a bell shaped type of SAC. However, a semi-planing hull design might have the aft end of the bell shape truncated. A semi-planing hull would have a fuller aft section. Any reasons this should not be the case?

No.

Originally Posted by mcollins07

...the sine/trochoidal curve...

Forget about the sine/trochoidal curve! As I said above, Skene's is a very old book - nobody uses the sine/trochoidal curve any more!

Originally Posted by mcollins07

A foil shape came to mind simply because it is related to lower resistance in higher Froude number conditions.

But the SAC doesn't define the shape of the hull. It defines the distribution of volume.

[mcollins07]

Originally Posted by sorenfdk

Skene's is a very old book... Yacht design has come a long way since it was written/revised.

Forget about the sine/trochoidal curve! As I said above, Skene's is a very old book - nobody uses the sine/trochoidal curve any more!

The Sears-Haak curve seems to be very similar to Skene's Sine/Trochoidal.

Which curves do you use for SAC's ?
What is the basis for these SAC curves equations?

[mcollins07]

The foil curves represent some of what we have learned about 2-dimensional models of fluid dynamics. These 2-D models are for relatively high Froude numbers and can show pressure distributions. The Sectional Areas Curves represent some of what we have learned about 3-dimensional models of fluid dynamics. These 3-D models are for relatively low Froude numbers.

So, we have knowledge and experience with 2-D models for high Froude numbers, and knowledge and experience with 3-D models for low Froude numbers. Can we make the mathematical link between the two models, for use in the transitional Froude number regime?

Perhaps the link is the pressure distribution. How can we show pressure distributions related to the Sectional Areas Curve short of ab-initio computational fluid dynamic models?


Ok guys! I know, you thought I was getting too technical before. You must really see this as jumping off the deep end. But I thought there might be someone out there interested in such a conversation.

Also, If I’m going to the trouble to build a dingy, I might was well learn all that I can about hull design from it. If this model can be achieved, a dingy is a good place to test it. Every time I used the dingy, I’d be aware of the model, and how it performed under various loads and conditions.

[sorenfdk]

Originally Posted by mcollins07

The Sears-Haak curve seems to be very similar to Skene's Sine/Trochoidal.

Which curves do you use for SAC's ?
What is the basis for these SAC curves equations?

Yes - the Sears-Haak curve looks just like a good curve of areas. I have no idea whether it really is that.

We don't use SACs that can be mathematically expressed. We used to do it many years ago, where we used an expression given by George Hazen in some SNAME-paper (I have forgotten the title).

[sorenfdk]

Originally Posted by mcollins07

The foil curves represent some of what we have learned about 2-dimensional models of fluid dynamics. These 2-D models are for relatively high Froude numbers and can show pressure distributions. The Sectional Areas Curves represent some of what we have learned about 3-dimensional models of fluid dynamics. These 3-D models are for relatively low Froude numbers.

So, we have knowledge and experience with 2-D models for high Froude numbers, and knowledge and experience with 3-D models for low Froude numbers. Can we make the mathematical link between the two models, for use in the transitional Froude number regime?

Perhaps the link is the pressure distribution. How can we show pressure distributions related to the Sectional Areas Curve short of ab-initio computational fluid dynamic models?


Ok guys! I know, you thought I was getting too technical before. You must really see this as jumping off the deep end. But I thought there might be someone out there interested in such a conversation.

Also, If I’m going to the trouble to build a dingy, I might was well learn all that I can about hull design from it. If this model can be achieved, a dingy is a good place to test it. Every time I used the dingy, I’d be aware of the model, and how it performed under various loads and conditions.

You shouldn't forget that the flow around a hull is always 3-D!

[mcollins07]

Soren,
Yes thanks for your help. Eric Sponberg also just explained to me in another thread that SAC is not really used much in designing semi-planing hulls, or in the regime that I'm concerned with.

The fact that the flow around a hull is always 3-D is the "why" for my intrest in the SAC. The SAC gives us a veiw of a 3-D aspect in a 2-D curve. so it condenses the information somewhat for analysis purposes.

Through more analysis experience and perhaps some theory, I hope to obtain a means to compare semi-planing hull designs through the use of their SAC. The little experience that I have so far, looking at the SAC for different semi-planing designs is ineresting, and appears that it will give insight to performance. At this point, the analysis is intuitive, similar to looking at chine lines and estimating performance. But perhaps there is more to be discerned. Clearly this is a tangent to the currently accepted practices, thus low priority for now. Thanks for your guidance.

~ Michael







I

[Leo Lazauskas]

Originally Posted by mcollins07

Soren,
Yes thanks for your help. Eric Sponberg also just explained to me in another thread that SAC is not really used much in designing semi-planing hulls, or in the regime that I'm concerned with.

The fact that the flow around a hull is always 3-D is the "why" for my intrest in the SAC. The SAC gives us a veiw of a 3-D aspect in a 2-D curve. so it condenses the information somewhat for analysis purposes.

The attached draft of a paper on slender body theory and applications by E.O. Tuck might help.

Good luck!
Leo.

[mcollins07]

Leo,
You are amazing!

The draft is very useful.

Thank you.

~ Michael

[mcollins07]

Top Speer (tspeer) gives an equation for the sectional areas curve, which includes Cp, in his paper:
http://www.basiliscus.com/CSYSpaper.pdf
page 10.

Does anyone know the orgins of this equation or any history of its development?