Centerboard design

[MastMonkey]

A couple quick questions:

Does rounding the trailing edge of a foil near the tip reduce or increase tip vortex?

When does an endplate become beneficial? Are there any rules of thumb for the design of endplates?

[Tim B]

Do you mean rounding in section or planform? Rounding the "aft corner" in planform will increase induced drag. Rounding the trailing edge in section probably isn't good, but I doubt you'll notice a difference excep on super-high-performance boats, and even then...

Endplates (in the old-fashioned sense) are not at all beneficial, except under very specific circumstances, for which they are hard to design. Winglets and other appendages also need very careful design, and can (but are by no means guaranteed to) give an advantage. For the amateur, however, the extra design is probably prohibitive, and you might as well gain advantage by increasing the span a bit.

Keep it simple. A single or double taper design, with the leading-edge corner rounded a little and th trailing edge straight is a good place to start.

Good luck,

Tim B.

[gonzo]

Dinghies that use a metal plate as a centerboard benefit from rounding the bottom edge. I don't have specific data, but no winning boats have a square bottom edge.

[MastMonkey]

Originally Posted by Tim B

Do you mean rounding in section or planform? Rounding the "aft corner" in planform will increase induced drag. Rounding the trailing edge in section probably isn't good, but I doubt you'll notice a difference excep on super-high-performance boats, and even then...

Endplates (in the old-fashioned sense) are not at all beneficial, except under very specific circumstances, for which they are hard to design. Winglets and other appendages also need very careful design, and can (but are by no means guaranteed to) give an advantage. For the amateur, however, the extra design is probably prohibitive, and you might as well gain advantage by increasing the span a bit.

Keep it simple. A single or double taper design, with the leading-edge corner rounded a little and th trailing edge straight is a good place to start.

Good luck,

Tim B.

Originally Posted by gonzo

Dinghies that use a metal plate as a centerboard benefit from rounding the bottom edge. I don't have specific data, but no winning boats have a square bottom edge.

I was referring to plan form, but both your post made me consider that it can also be tapered toward the tip or have the bottom edge rounded. The centerboard is 11" wide and approximately 2.5' long shaped as a NACA 0012 foil from pieces of cedar. I am planning to give the leading edge an elliptical profile in planform, but was uncertain about the trailing edge. On some designs it is also rounded at the tip, but on many boats now. I wondered about the difference.

Gonzo: Do you mean the board should be taped to a point?

[Tim B]

Tapering to a point is unlikely to be helpful. It is also vulnerable in contact with the bottom, and on dinghies, can be dangerous.

For the tip I would draw a line stream-wise about 3" from the tip, and draw a smooth curve which is tangent to the leading edge, and stream-wise at the trailing edge. Something like http://farm4.static.flickr.com/3153/...e9d65dc80e.jpg

Square corners at the tip cause flow separation and secondary vortices, so ideally you want the tip to be smoothly tapered and rounded in spanwise section, as in the image above. That should give you a reasonably good board.

Tim B.

[PAR]

Thee has been some debate over this issue for years. Rounding the trailing edge will usually setup a harmonic that causes the appendage to hum at speed. One camp will have you bevel the trailing edge unevenly, much like that of a chisel, which is effective at removing the sympathetic vortices. Others will have you grind the trailing edge to a point, which may work as well, if leaving you with a very delicate edge to maintain, though I don't have personal experience with this. I prefer to back cut the trailing edge, assuming it's of sufficient thickness, so there's a "V" shaped depression or just squared off with crisp edges, with easier to maintain.

[MastMonkey]

Is it worth it to fiberglass the board? Does this add anything in terms of rigidity? Or is it principally to protect the wood from water intrusion?

[PAR]

You'll need a fairly substantial weight of fabrics to significantly stiffen a board, so no, it's for waterproofing and abrasion resistance mostly.

On the leading edge of centerboards and the trailing edge of daggers, you can greatly improve the impact resistance with an epoxy saturated line (I use single braid polyester), set in a shallow groove, cut on the centerline. Of course this is faired in, but it'll absorb impact with little damage, saving the wooden board. Personally, if I can avoid a wooden board I do, preferring inert materials that don't rot, swell or need sheathings.

[MalSmith]

Originally Posted by MastMonkey

A couple quick questions:

Does rounding the trailing edge of a foil near the tip reduce or increase tip vortex?

When does an endplate become beneficial? Are there any rules of thumb for the design of endplates?

Assuming you use a constant section shape for the full length (span) of the centerboard, the theory is that minimum induced drag is achieved by having and elliptical planform (semi elliptical in the case of a centerboard). It's not the elliptical shape that is important so much as the elliptical distribution of the planform area along the span. This in turn is because the ideal lift distribution for minimum induced drag is elliptical. Note that if you vary the section shape along the span, or have any twist in the foil, the ideal planform shape will be something other than elliptical, but the intention is always to achieve an elliptical lift distribution.

Because an elliptical planform is difficult to build, straight tapers or rounded tips are often used to approximate an elliptical distribution of area.

Whether you round or taper the leading or trailing edge of the centerboard should not matter that much, except that it will change the effective rake of the centerboard. Raking the centerboard forward or aft creates spanwise flow, which effects the upwash angle along the span and alters the loading distribution. Consequently, an aft raked foils needs to be tapered more, and a forward raked foil needs to be tapered less.

Endplates decrease the induced drag by increasing the effective span. The effective increase in span is equal to width (span) of the endplate. End plates should only be used if there is some reason (structural, environmental or rule based) why you can't just increase the span. If you can just increase the span, you benefit from the lift produced by the added planform area. End plates do not add any lift, yet you still have the added from and frictional drag of the end plate itself. So if you use end plates the additional efficiency they provide must outweigh the additional drag they create.

There is good info on all this in C. A. Marchaj "Sailing Theory and Practice".

[Tim B]

Do not confuse elliptic loading with elliptic planform. Whilst elliptic loading will give you minimum induced drag, the tip has a distinct effect on vortex roll-up, and thus is critical if you really want to optimise the foil for minimum induced drag. For yachts with centreboards, elliptic planform often forces a significant area penalty, which will impact on other requirements (eg. draft, space in the boat due to board length etc.).

Sweep (what you refer to as rake) does not create "spanwise flow", as the span is still defined as the direction normal to the inflow velocity in the plane of the wing (ie. vertically for centreboards). The relationship between sweep and taper is complex, and is not usually considered for boats, as the effects are relatively small, when compared to the effects that moving area has on the balance of the yacht.

Endplates do not add benefit without SIGNIFICANT design work, even then they only offer limited benefits. Increasing the area (preferably by increasing span) will give more advantage.

Hoerner's Fluid dynamic lift and fluid dynamic drag are unquestionably the best references for info on the effect of planform and loading.

Tim B.

[PAR]

End plates on a centerboard can't work, except in the fully lowered position. Rectangular plan forms offer additional area at the tip and though they can generate more tip disturbance, the benefits of the additional area can usually over come the more efficient, but less area elliptical board.

[MastMonkey]

Originally Posted by MalSmith

Assuming you use a constant section shape for the full length (span) of the centerboard, the theory is that minimum induced drag is achieved by having and elliptical planform (semi elliptical in the case of a centerboard). It's not the elliptical shape that is important so much as the elliptical distribution of the planform area along the span. This in turn is because the ideal lift distribution for minimum induced drag is elliptical. Note that if you vary the section shape along the span, or have any twist in the foil, the ideal planform shape will be something other than elliptical, but the intention is always to achieve an elliptical lift distribution.

Because an elliptical planform is difficult to build, straight tapers or rounded tips are often used to approximate an elliptical distribution of area.

Whether you round or taper the leading or trailing edge of the centerboard should not matter that much, except that it will change the effective rake of the centerboard. Raking the centerboard forward or aft creates spanwise flow, which effects the upwash angle along the span and alters the loading distribution. Consequently, an aft raked foils needs to be tapered more, and a forward raked foil needs to be tapered less.

Endplates decrease the induced drag by increasing the effective span. The effective increase in span is equal to width (span) of the endplate. End plates should only be used if there is some reason (structural, environmental or rule based) why you can't just increase the span. If you can just increase the span, you benefit from the lift produced by the added planform area. End plates do not add any lift, yet you still have the added from and frictional drag of the end plate itself. So if you use end plates the additional efficiency they provide must outweigh the additional drag they create.

There is good info on all this in C. A. Marchaj "Sailing Theory and Practice".

Originally Posted by Tim B

Do not confuse elliptic loading with elliptic planform. Whilst elliptic loading will give you minimum induced drag, the tip has a distinct effect on vortex roll-up, and thus is critical if you really want to optimise the foil for minimum induced drag. For yachts with centreboards, elliptic planform often forces a significant area penalty, which will impact on other requirements (eg. draft, space in the boat due to board length etc.).

Sweep (what you refer to as rake) does not create "spanwise flow", as the span is still defined as the direction normal to the inflow velocity in the plane of the wing (ie. vertically for centreboards). The relationship between sweep and taper is complex, and is not usually considered for boats, as the effects are relatively small, when compared to the effects that moving area has on the balance of the yacht.

Endplates do not add benefit without SIGNIFICANT design work, even then they only offer limited benefits. Increasing the area (preferably by increasing span) will give more advantage.

Hoerner's Fluid dynamic lift and fluid dynamic drag are unquestionably the best references for info on the effect of planform and loading.

Tim B.

Originally Posted by PAR

You'll need a fairly substantial weight of fabrics to significantly stiffen a board, so no, it's for waterproofing and abrasion resistance mostly.

On the leading edge of centerboards and the trailing edge of daggers, you can greatly improve the impact resistance with an epoxy saturated line (I use single braid polyester), set in a shallow groove, cut on the centerline. Of course this is faired in, but it'll absorb impact with little damage, saving the wooden board. Personally, if I can avoid a wooden board I do, preferring inert materials that don't rot, swell or need sheathings.

Originally Posted by PAR

End plates on a centerboard can't work, except in the fully lowered position. Rectangular plan forms offer additional area at the tip and though they can generate more tip disturbance, the benefits of the additional area can usually over come the more efficient, but less area elliptical board.

Thank you all for your very informative replies. It will take me a while until I can understand it fully, but I think I get the gist. I was intending to create an elliptical planform, but knowing what I do now, it seems I would probably not gain any advantage for the additional amount of work or would possibly suffer a performance penalty. I am going to stick with a straight forward rectangular board. I plan on running glass tape along the trailing edge to provide some damage resistance. I am curious what other materials are used to build rudders and centerboards. I am building both out of wood because that is what I am familiar with and it is for a wooden boat. I would guess that metal and composite are the preferred materials but are these easy for a home builder to use? Out of curiosity why would the section be varied along the length of the board in some cases? My interest in endplate design was to try and improve the angle at which the rudder might stall at, but again it doesn't seem like there is any real advantage there. I get a little carried away thinking about performance and end up making more work for my self.

[Tim B]

Composites are not as hard to use as people think. They can be messy though. Dependent on the structural results you want, there are a few methods: wet lay-up, vacuum bagging, resin infusion and pre-preg. Roughly in order of complexity and performance. Vacuum bagging is slightly easier than resin infusion, and gains a lot over wet-layup. There is plenty of info on the web about vac-bagging, so I won't repeat it all here. Essentially it is wet-layup that is put in a bag which then has the air sucked out of it.

Rudders and centreboards can be made from pretty much anything you like. Hardwoods are fine, aluminium is used quite often, particularly in rectangular foils which can be built from an extrusion with a tip-cap. Foam and glass/carbon is also pretty common, and gives more freedom over shape than aluminium, usually at the same, or lower, weight.

Varying the section along the span of a foil is usually due to structural constraints (ie. a constant thickness spar with a tapered planform). On aircraft it is done to meet required stall characteristics (root should stall first), but these constraints don't apply to yachts.

Hope this helps,

Tim B.

[Petros]

Putting an end plate on the rudder will make the rudder stall easier. Generally the higher the aspect ratio of the surface, the lower the angle it will stall. IT will produce more effective and efficient lift (less induced drag), but it will stall at a lower angle of attack. The end plate has the effect of making it a higher aspect ratio, and unless there is a depth limitation of some sort, it is far better and easier just to make it higher aspect ratio than building an end plate for the rudder. Same is true with the keel as well.

You always want rudders to be relatively low aspect ratio to make it more stall resistant, and it will be effective through a larger swing of the tiller.

[Tim B]

Sorry, Petros, you're contradicting yourself, and I don't agree with your final assertion.

There is no substitute for span, span increases the rudder depth, which helps the ventilation characteristics at large angles of attack, and reduces CDi at low angles. This is all good. Low aspect ratio foils will stall later, but come with lower dCl/dAlpha, so you gain nothing unless you have specific constraints on rudder size.

As you turn, you change both yaw angle and yaw rate, which reduces the effective angle of attack on the rudder. So although the rudder is at 30deg to the centreline, it may be at 10deg to the flow. Consequently, turning the rudder smoothly to initiate a tack can keep the foil operating at CLmax; and that's good sailing practice, trying to make up for poor sailing practice with fluid dynamics is a very bad (even dangerous) idea.

Tim B.