Elliptic vs Rectangular Daggerboards

[kerinin]

I'm in the process of designing a 16-foot catamaran (more on that here if anyone's interested) and I'm about to turn my attention to the daggerboards and rudders. From some experience reading about airplane wings, I seem to remember that elliptic wing planforms have the lowest drag, but I haven't seen many elliptic daggerboards (feel free to correct me if this impression is mistaken).

I was talking with a friend who knows a lot more about this subject than myself and he mentioned that part of the reason elliptic planforms are efficient has to do with the way the trailing vortices interact; clearly this doesn't come into play with sailboats. Has anyone else heard anything along these lines?

The other reason I can see for not using elliptic planforms is that compared to rectangular planforms the center of lift is closer to the root, which would seem to be detrimental in a sailboat where the torque of the daggerboard is fairly important in resisting the force of the sail.

Are there other reasons people don't use elliptic daggerboards more often I haven't considered?

[CTMD]

The main reasin people use rectangular boards is they are easy to build and have a constant section so they "fill" the dagger board case in any possition. If you build eliptical boards and then pull them up down wind they'll rattle around causing drag and depending on how far up you pull them you may end up with a fire hose through the slot.

[Rick Willoughby]

The shape of the lift distribution alters the induced drag. An elliptical distribution results in lower induced drag than other profiles. It does not necessarily relate to the planar form of the foil. The same thing can be achieved by altering the section over the span. Irrespective you still have the problem of sealing the case when operating with partially inserted board.

The main factor in reducing induced drag is the foil aspect ratio.

If you want to read more then look for Oswald efficiency or span efficiency.

Rick W

[Doug Lord]

I think the best thing you can do -if you're not limited by rules-is give the foil as much span(depth) as possible. I've read that in order to get elliptical loading the shape pretty much has to be rectangular-maybe slightly tapered(because of the tip vortices's).
Of more importance than generally recognized is the tip shape for this kind of board. As I understand it, the trailing edge of the board should be longer than the leading edge with the angle from the leading edge( for a rectangular planform) close to 40-45 degrees down to the trailing edge.
Good Luck-I'm following your progress closely...

[Ad Hoc]

kerinin

It is a very complex interaction (beyond this website to discuss/debate easily), but you are correct in regards to the vortex system. Since one of Helmholtz's laws of vortices is that a vortex line must be closed, it cannot end in the fluid.

It leads, again short circuiting, to the horseshoe vortex. Because for a given angle of incidence, alpha, a lift force on the foil implies that the pressure on the lower, or under surface, must exceed that on the upper surface. In other words, fluid must escape around from one surface to the other. It does this by outwards to the ends on the lower surface and and inwards and to the centre on the upper surface. This means at the trailing edge the two flows are discontinuous, so the vortices are swept downstream. To cut short, in theory the tip vortices are joined to the starting vortex, but far downstream, to complete the vortex ring and uphold the law.

Again, cutting a long story short. Once the induced velocities (and hence induced drag) and energy systems have been resolved via angles of incidence and lift coeff's (since work is done against the induced drag and manifests itself as kinetic energy of the tip vortex), one arrives at the relationships of angle of incidence or attack, being directly proportional to the CL coeff's and also the aspect ratios. It is shown, in many text books, that the slope of the lift curve decreases as aspect ratio decreases, which leads anyone to assume that a high aspect ratio is best. But practical limitations dominate on ARs over 4. In order to attain a high lift force for a limited span, the plan area of the foil can be increased with sweepback and with a reduction of chord along the span, ie an elliptical type of shape. Otherwise the local bending moments and hence strength become very suspect. Why do you think elliptical shapes rarely occur in nature, if ever, in ARs above 4?

Ive had to read over some of my old foil theory to remind myself, it has been years since i have done this in any real depth. But i think that is the nub of it, as you say all because of the vortex system and then the practical limitations of a foil to satisfy the vortex laws.

Not sure if this really answer easily for you?..complex concepts to grasp, i don't remmeber much of it myself anymore.

[Jimbo1490]

I've often wondered why you don't see tip 'fences' on the foils of boats. It seem that you can have your cake and eat it too (rectangular tip vs elliptical shaped). Works for airplanes, after all (Whitcomb winglets)

Jimbo

[Ad Hoc]

There has been, look at the wing keels of the Australia II that won the America's cup boat. Doing two jobs, fence and a little lifting.

But as with everything in design, not always applicable across the board. Each set of design requirements must be viewed on its own merits, not just "ooo, that looks good, works for them, must work for me" basis. If that were the case, everything would look the same, neh! Understanding the mechanics of what and why aids in ascertaining if XXX is applicable for you or not.

[Rick Willoughby]

Originally Posted by Jimbo1490

I've often wondered why you don't see tip 'fences' on the foils of boats. It seem that you can have your cake and eat it too (rectangular tip vs elliptical shaped). Works for airplanes, after all (Whitcomb winglets)

Jimbo

Google Ben Lexan - wing keel:
http://en.wikipedia.org/wiki/Australia_II

Like most things pros and cons. Get more lift with a given draft. Also can increase draft when heeled. More complex to build. Cannot be lifted out of case.

Rick W

[rwatson]

If you would like to introduce another idea into the mix, check out

http://www.thestar.com/Business/article/213475

for a "whale" fin idea . You might get some inspiration there. At least you would be able to get the board out of the case

[kerinin]

Those whale things are really cool - I remember reading about them when they first announced them a few years back.

Those might work well for a rudder - my recollection is that the bumps delay flow separation at high angles of attack, and you probably wouldn't want to have leeway angles high enough to benefit from that right?

[Eric Sponberg]

Originally Posted by kerinin

I'm in the process of designing a 16-foot catamaran (more on that here if anyone's interested) and I'm about to turn my attention to the daggerboards and rudders. From some experience reading about airplane wings, I seem to remember that elliptic wing planforms have the lowest drag, but I haven't seen many elliptic daggerboards (feel free to correct me if this impression is mistaken).

I was talking with a friend who knows a lot more about this subject than myself and he mentioned that part of the reason elliptic planforms are efficient has to do with the way the trailing vortices interact; clearly this doesn't come into play with sailboats. Has anyone else heard anything along these lines?

The other reason I can see for not using elliptic planforms is that compared to rectangular planforms the center of lift is closer to the root, which would seem to be detrimental in a sailboat where the torque of the daggerboard is fairly important in resisting the force of the sail.

Are there other reasons people don't use elliptic daggerboards more often I haven't considered?

Referring to the underlined sections above: You can find many elliptically shaped daggerboards on sailboats. Look in any catalog of boats, such as Sail Magazine Boat and Equipment Directory, and you see them all over the place.

Also, Doug Lord is correct in his description that the trailing edge should be longer than the leading edge. Many boats have this backwards with the trailing edge being shorter.

Elliptical lift distribution is the goal because it creates a uniform downwash which, in turn, minimizes the tip vortex to its smallest possible size. The downwash and the resulting tip vortex are the very manifestation of, the definition of, induced drag. You cannot eliminate induced drag because it is the natural creation of lift, but you can change induced drag up or down. An elliptical planform comes very close to creating an elliptical lift distribution. You can also closely approximate an elliptical lift distribution with a twisted rectangular planform. This is why in America's Cup, Volvo, and other Grand Prix classes you are seeing square-topped mainsails--to maximize lift and minimize induced drag--i.e. tip vortex.

The remarkable thing about all this is that the phenomenon of downwash, induced drag, and elliptical lift distribution was figured out, purely in his head and without the benefit of experiment, by aerodynamicist Frederick Lanchester in England in 1897 and published 10 years later in 1907. You can read all about this in C.A. Marchaj's book, Aero-Hydrodynamics of Sailing. This is a must-read book for all who dabble in sailing yacht design.

I quote some of Marchaj's work in my article on free-standing masts which you can see at the link below, and I show a picture from the book of a model sailboat in a wind tunnel and what a tip vortex on a sailing yacht rig looks like.

http://www.sponbergyachtdesign.com/StateoftheArt.htm

Eric

[Ad Hoc]

Eric

Not heard of the work done by the Brit in 1897, thanks for the info; i must look for that. I'm sure it is a good read.