Keel/bulb Replacement on Beneteau First 235

NACA Foils using Rhino Grasshopper, from an SA forum discussion, December, 2016 (ProaSailor)

Images posted to SA threads were lost on the forum when DropBox dropped support for that sort of hosting, so I'm posting my original images here in the context of that thread.

Part 1: Shaping the Keel/Bulb (this page) - Part 2: Attaching the Keel/Bulb


Using a NACA 0012 section and not including the bulb, I get 1,617.66 cubic inches = 662.76 lbs.


Using NACA 64-012A, volume is 1559.28 cubic inches = 638.8 lbs. beiley_f235_lead_keel_64-012A.3dm


For the bulb, I decided to try a "surface of revolution" using the profile as drawn. Looked pretty good but, after subtracting the intersected fin, the volume/weight was less than the specified 265 lbs. So I scaled the bulb horizontally (only in the Y direction, width not length) until the weight was correct. Combined total weight is 903.8 lbs.


In this diagram, "COA" is 'Center Of Area' of the cross-section, not the surface.
"COV" is 'Center Of Volume", AKA 'Center Of Gravity (COG)', located ~24" below the hull while the bulb draws 44.2".

Curiously, the combined fin+bulb uses "only" 1.27 cubic feet of lead.
Yeah, Bens, Grasshopper is WAY COOL! Love it. As to decreased density, give me a number? Easily fixed by scaling the bulb slightly wider, eh?


Compared to 707.9 for pure lead? ~98.2% - so for this shape, we need 18 lbs. more in the bulb... Here you go, in green. COV (COG) lowered slightly.

This change took more time in Photoshop than Grasshopper. ;-) Updated Rhino file, same link as before: beiley_f235_keel_bulb_64-012A.3dm


Clearly NOT the bottom of the keel/bulb. Or did you mean the bottom of the fin? Probably the center of the bulb but I didn't count on that.
Do you have Rhino? The .3dm file I linked to has all these horizontal lines from the PDF, at six inch intervals except for the first one at three inches. They are where I located the scaled NACA cross sections for lofting. For the center axis of the bulb, I started a horizontal line from the tail and it's VERY CLOSE to the 42" line - so close, in fact, that it was a mistake for me not to use the 42" line. I see the error now (it's not even horizontal!); oops, really should redo that... it's done in Rhino, not Grasshopper.
While I'm at it, I should also do a better job creating that bottom bulb profile curve that I revolved to get the initial bulb surface. Picking arbitrary points along that curve to interpolate (as I did) really isn't kosher. Pretty close though.


OK, I fixed the skewed bulb axis on this version at the 42" mark. And I redrew the bulb profile curve, again by interpolating arbitrary points picked off the PDF; not ideal but I was more careful this time and believe it's better. beiley_f235_keel_bulb_64-012A_2016Dec21a.3dm


Until now, the bulb profile curve I drew was defined in the PDF and plotted manually. From now on, the only things preserved from the PDF are bulb LOA (30") and vertical thickness (~6").

I've spent quite a few hours this morning reading and digesting Tom Speer's comments on bulb design and creating Grasshopper code to model it. WHEW! Every sentence he writes is loaded with meaningful information. Fun and very clean results ("kosher" CAD methodology!). It has opened a big can of worms an infinite number of possibilities in terms of shape control and I've barely begun to explore the possibilities.

Some of the bulb tails are so pointy that Grasshopper fails to create a "Closed Brep" (solid), which of course breaks what follows. Those are likely too pointy to be practical anyway but it takes extra time figuring out why the code breaks, tweaking a NACA foil end point ever so slightly to avoid the error, etc.

The NACA 0020 foil he mentions is a family of configurable curves ("Max camber position", etc.) that I haven't touched yet.

One of Tom's suggestions is to "to place the maximum thickness near the trailng edge of the keel", moving maximum cross sectional area aft where the fin is thinner. Another one is "taking airfoil coordinates to the 3/2 power (and scaling to the original thickness)" - a perfect job for Grasshopper.

Here is what I came up with; the result is passed to earlier code (not shown) that scales the bulb width to achieve desired weight.

I have included seven different NACA foil data sets (so far) to choose from:

The "Power" slider is set to 3/2 ("1.5") and applied to the "Y" coordinate, which has the effect of dramatically shrinking bulb diameter (the revolved NACA curve) while subtly modifying its shape.

The "Scale" slider here ("4.879") is then used to return bulb diameter to ~6".

What I discovered (and this is where Grasshopper is SO COOL!) is that adjusting "Power" to less than one INCREASES the diameter of the bulb, so "Scale" can be set to "1" - effectively ignored - or you can use any combination of the two sliders that result in a ~6" diameter bulb. The effects are immediately visible.

The purple shapes below are what I posted earlier, the rest use this new method. In the middle, you can see how a new one (in gray) is smaller in front, revealing the original shape (purple) and larger further aft, hiding the original.

Taking a break...


As this hi-res screen shot of the PDF shows. If they aren't exactly the same, the fin would either poke out or leave a gap at the nose of the bulb.


Yes, agreed, thank you. What's interesting is that the ends get smaller "faster" than the middle? In other words, the 3/2 power affects smaller 'Y' values (close to zero) more than large 'Y' values (close to one) - I think? My math skills and confidence has eroded over the decades.
Here is a NACA 64-012A to the 1.25 power; bulb width is 10.77". f235_keel_bulb_64-012A_2016Dec22a.3dm

P.S. 12 metre, thanks for the confirmation.


Here is a NACA 0012 to the 1.25 power, raised 1/2" with thickness increased from 6" to 7", keeping draft at 45". Bulb width is 9.5".

Note that I haven't bothered yet to shorten the fin 1/2" so it protrudes slightly - will fix that.

Wonder what Tom Speer would do...? The longer "roof" he mentioned would help (extending max cross section for a greater portion of the length), will look again at how he did that.

The fin without a bulb suggested above by 12 meter is worth a look. What's the budget again?


Did you look at the CAD file? View ONLY the layer named 'NACA 66-021'.
This is an evolving Grasshopper tool for exploration and creative design with many options including NACA foil profile curve and scaling features. No shape yet claimed to be ideal. Experiments in progress from the Rhino Grasshopper world.

The extremely pointy tails are an unresolved dilemma...?

Layer 'NACA 66-021' below, from above, but only 6" bulb thickness (height) instead of 7" (obtained by raising the bulb axis 1/2"):


Look, I'm not speculating on or advocating for any particular optimum shape. The shapes I'm playing with are:

  1. derived from the original profile drawn by Leif Beiley and posted as a PDF and/or
  2. advice on bulb design from the esteemed Tom Speer, whose credentials are impeccable and whose work I have long admired.

I didn't quite understand what he was talking about at first but figured it out, implemented it correctly in GH (Grasshopper) on the first try and then verified my understanding of the effects of his "3/2 power" advice by consensus and affirmation here.

I've distilled it as best I can in this bit of Grasshopper code (below):

What this shows is a panel labeled "NACA 66-021" containing X and Y coordinates for that particular foil shape, as fractions between zero and one, obtained as a .dat file from here:

Without getting into the weeds of GH too far, the 'Split' component parses the coordinates and the 'Item' component separates them as 'X' and 'Y' values that are passed to the 'Pt (Point)' component, generating a list of points that are passed to 'IntCrv' (interpolated curve). Finally, the 'Scale NU' component allows the curve(s) to be scaled only in 'Y'.

The 'Pow (Power)' component modifies the 'Y' value before it is passed to 'Pt (Point)'. Connecting three sliders to the 'B' input (the exponent value) results in three sets of points and three separate curves.

The middle curve with 'Power/exponent' set to "1" is the unmodified NACA shape. The bottom curve is the result of the bottom slider, setting the exponent to "1.238". The top curve results when the exponent = 0.780.

Looking at the 'Scale' sliders, you can see the middle one, where exponent=1, is set to 'Scale=1' - unmodified, original NACA foil shape. The top curve is scaled down by '0.609', reducing its maximum 'Y' value to match the original curve. The bottom curve (exponent=1.238) is scaled up by '1.714' increasing its max 'Y' value to match the original curve.

Look closely and you can see that even though the top and bottom curves are scaled to original "thickness", they differ slightly in shape from the original - more pointy for exponent values greater than one, more blunt for exponent values less than one.


Here is a quickie beaver tail solution - took ~15 minutes to get the functionality, a bit more time more time to refine and play with parameters.

It slices off the tail of the existing bulb at arbitrary 'X' value, determined by a slider, using a "YZ Plane".

A pair of sllders define the dimensions of an ellipse (width & height), a second pair of sliders positions two copies of that ellipse at arbitrary 'X' values, which affects the smoothness of the lofting that follows. The edge curve where the bulb was lopped off (blue circle) is lofted with the two ellipses to create the wide tail surface, which is joined with the forward part of the bulb, capped and passed to the bulb width scaling tool used before.

The result is an 8.92" wide bulb, 7" thick (fin shortened by 1/2"). I'm not saying it's perfect by any means, just a direction I would explore to resolve the bulb tail issue. All parameter driven, the only manual effort is knowing where and how to manipulate all the sliders that contribute to the end result.


In the final step, I'm scaling only bulb width to get the desired total weight.

A vertical beaver tail is as simple as swapping the slider inputs that define the ellipse, 'Radius 1' and 'Radius 2':

With small adjustments to ellipse dimensions and position(s):


This one uses a NACA 66-018 profile curve, 'Power=1.25'. f235_keel_bulb_2016Dec23a.3dm

Given that some of the pointy end is lopped off, I extended the axis length to 32" and adjusted the ellipse positions aft, so now the chopped tail is back to the original 30" LOA bulb instead of only 28". Bulb width is now 8.35", 7" thick. Available in horizontal of vertical tail, of course.

Sure, a longer bulb would reduce the cross section area (width and height/"thickness") but I feel constrained by the spec to not extend forward of the fin's leading edge.


Here's a trippy idea that is easy to implement. Not sure Tom would approve but he'd get a laugh out of it.

Instead of applying the same exponent value for all the NACA coordinates, how about having one 'Power' value at one end and a different value at the other end - perhaps "1", leaving one end of the curve alone?

The two 'Power' sliders define the bounds of a 'Domain' (the exponent domain), the 'ReMap' component remaps the 'X' value of each coordinate from its 0..1 domain to the exponent domain, affecting the 'Y' value passed through the 'Power' component differently for each point. The yellow curve is the result, which is scaled up by "1.323" (red curve) to approximately the original max value of 'Y', then revolved to create the raw bulb surface.


Patiently playing with parameter values makes all the difference. I spent no time at all optimizing the following, just "got 'er done". I hope it's very clear that, as a lifelong software guy, making these tools is as much or more fun for me as using them. Two different skills really... I'm not even sure this code below is done correctly yet? (In fact, I'm sure it's NOT! [now fixed?]) Most of my time goes into refining and debugging code rather than producing the ultimate shape.

Keeping the separate exponents for each end of the curve, here is what your idea looks like using two curves (in blue) as the 'Radius 1' and 'Radius 2' values for the series of ellipses, that are then scaled back to approximate the blue lines before they are lofted.


A NACA 64-012A fin with no bulb, 45" draft (span) would require a chord length of 25.12" to weigh 905 lbs. The CG (blue 'X') would be raised ~2.3" above the recent bulb efforts. Center of Area is at red 'X'.

For comparison (blue 'X' is center of volume, red 'X' is center of area):

Reducing the angle of this leading edge very slightly would make the fin tip a little longer (stronger!) and move the CG forward slightly, perhaps allowing the bulb to be a little longer too? It would be smaller too because more weight would be in the fin.


NACA 64-012A fin with no bulb, 75 degree leading edge, 45" draft, 905 lbs. Top chord is 30.9", bottom chord is 18.8". The CG (blue 'X') is raised ~6" above recent bulb efforts. Center of Area is at red 'X'.

QUESTION: Is that little flare at the top of the leading edge doing any good? It's adding weight in the wrong place. Would be easier to experiment without it. Is the 75 degree angle of the leading edge "important"?

P.S. 80 degree leading edge, 29" top chord, 21" bottom chord:


I played with this idea by scaling the foil section width alone near the fin bottom, then decided to concentrate all the flare in the bottom ~10".

Not saying this is better than a bulb, just an obvious variation on the no bulb solution. It does lower the CG, as does ignoring the flare at the top, which really doesn't add much bearing surface anyway.

Looks draggy to me - could be improved but a bulb has way more potential.


Aye, and a bulge/flare by any other name is still a bulb, eh? Plan C, A blunt faced fish, not as much weight as the bulb down low and distorts the lift from some of the foil.

V2 has a top chord of 29.29": f235_keel_bulge_2016Dec25b.3dm

Too thick with the fillets! ;-)
Back to refining Plan B - from two days ago, improved since then but not ready to show the latest:

Who else has CAD to show, specific to this project ? Did anyone get Rhino for Christmas?


Found this with image search on "Archambault a40rc sailboat keel" - well, I cropped and enhanced this enlargement from a photo I found there...


REVIEW: Remember this first one, based on the .pdf profile as drawn by Leif Beiley - CAD shows COV (VCG) just below the 24" line, which was his apparent target? So 24" or lower (deeper) is the goal, aligned vertically with his.

No way to do that without some kind of bulge/bulb shape at the bottom, less taper or not.

Will get it dialed in. Reduce leading edge angle from 15 degrees (off vertical, 75 degree slope) to 10 degrees (80 degree slope) and add five degrees to the trailing edge, gains ten degrees out of fifteen, leaving only five degrees of swept back taper, more lead at the tip, longer bulb tip flare/bulge, reduced chord.


As described, 24.9" chord, VCG on target. Same ugly bulge and want to constrain flare effect until much closer to the tip. Updated same Rhino file (see Layers panel): f235_keel_bulge_2016Dec25b.3dm

Back to the bulb! This suggests a smooth fillet-like transition might be possible though, eh?


24.8" root chord, no flare in fin thickness, bulb algorithm largely unchanged from last week. Code cleaned up and better organized. Aligning keels now using their "CG hook" (pinx 'X') at the top above the CG:

Still plenty of room for improvement and ideas to explore. Drawing a smooth rock with CAD, properly sealed ("Closed Brep"), all seams aligned, no sharp edges or dimples, can be challenging. Not too different from shaping big proa "pods" and salon/pilot houses...


Same as above - small bulb compared to original drawing, plenty of room to make it bigger, longer, heavier...


Beaver tail was chopped too short on that last one, and/or needs a better tip shape - working on that.
SO MANY subtle shape variations are easily possible with a good GH tool/algorithm that models all the parameters! Of course, the tool being software, I enhance it as necessary all the time. Love it. Cheers.

P.S. Are [sacrificial] flexible tails allowed on the keel? Class legal? Appropriate material for this? Attachment method that leaves clean trailing edge without flex tail? details... (P.S. just kidding!)

How about composite fairing for root flare, except minimal lead where needed structurally?


24" root chord, 30" bulb, "full Speer" on the 3/2 power shaping at the front of the bulb, 1.25 power at the rear. Added automatic scaling back to original 'Y' domain bounds (BIG IMPROVEMENT!), as recommended. Best yet, VCG is ~2* lower! Cheers. f235_keel_bulb_2016Dec26a.3dm


While intended to be cast as a single piece, this bulb (the slotted part) weighs 246 lbs., which is 98.2% of the 265 lbs. stated in the .pdf. The bulb is "squished" by scaling its width to 9.77" (a factor of 1.6825). The fin has a chord of 42.1", leaving 2.9" (5.8" thick) for bulb draft of 45" (.pdf notes say 47" keel draft?). By reducing the fin root chord length, avoiding the root flare and reducing the leading edge taper from 15 to five degrees (with 5 degree sweep back), more lead was moved down toward the tip, lowering VCG ~2" below the spec'd 24". Still 905 lbs. total.

Can it be engineered and work on this boat?

Has a hard spot in the chopped tail transition... will refine that. Not my invention, really, just a humble scribe following other people's notes.


4" span of root flare on the 24" root chord fin weighs ~5 lbs.

On the original fin with a base root chord length of 26.9" (not including the flare), this 6" span "collar" weighs 9.13 lbs. It adds 13.5 sq. inches of bearing surface (yellow, 19% of combined total), though ~1/3rd of the yellow area is forward of the fin's leading edge (the grid plane below), where it's mostly useless.


Explored a handful of ideas for shaping the tail on this "Speer bulb" and like this method best so far... More of a duck tail than a beaver tail?


But for a few parameter settings (and there are MANY!!!), my Grasshopper bulb model is not that different in basic shape from this one - except for the "relaxed" water balloon-like cross section:


Original fin profile (vertical trailing edge, 15.6" tip chord length) vs. swept back fin (20.27" tip chord length). CG (blue 'X') drops 0.78".

Is this thread dead? Or was it taken off line? As the only contestant to enter, do I win a prize?
It's been fun. Developed a great Grasshopper tool in the process so can now churn out custom keel fin+bulbs like these rather easily, with or without fin root flare. Bulb shape adapts well to different lengths.


I didn't invent this bulb. The bulb shape is a STRICT implementation of Tom Speer's advice on this matter, as noted earlier.
The yellow line in this image shows the original, unmodified NACA 66-018 profile.

That profile is modified by taking the 'Y' coordinate to the 3/2 power (1.5) and then scaling the resulting curve precisely back to the original profile thickness. I added the innovation of being able to apply a different exponent at each end; the bulbs I posted today use an exponent value of "1.5" on the forward end and "1.4" on the aft end, leaving it a little fuller aft, closer to the original. Every point in between uses an exponent between 1.5 and 1.4. If you want to use the original NACA profile, set the exponent value(s) to "1".

The resulting curve is revolved to make a surface/bulb, then the width is scaled to achieve the desired weight - by "1.4822" in this case:

I wrote a lot of "scaffolding" code that generates the fins, gives me the volume and weight, scales everything for this boat and generally makes all the parameter controls easier to use. The only contribution I made to this shape was the way I chopped off the tail.

"Overthinking it"? Not at all. Understanding it, yes.

I wrote a tool, not just one CAD drawing. At this point, advice to "look at some successful bulbs" is nonsense to me. Can anyone else produce a Rhino CAD file of a fin+bulb for this boat?

Top view - same as above, scaled by a factor of 1.4822 - final dimensions of blue outline: 6" X 9" X 30"

P.S. The bulb for the original fin profile is slightly shorter (28.9") and wider (9.9") than the other one... No particular reason except for time spent playing with the many parameters that affect the shape, which is an iterative process of very fine adjustments.

P.P.S. "Bulb Length Ratio" here refers to the ratio of the raw bulb length (the NACA foil chord) to the axis length, which is the fin tip chord length.


2016Dec30a, Exp 1 = 1.5, Exp 2 = 1.3
L: 30.0396
W: 9.9891 (ratio: 1.6639)
H: 6.0034

2016Dec30b, Exp 1 = 1.25, Exp 2 = 1.25
L: 30.0994
W: 9.3893 (ratio: 1.5643)
H: 6.0022

2016Dec30c, Exp 1 = 1, Exp 2 = 1 (unmodified NACA 66-018)
L: 30.0857
W: 8.7979 (ratio: 1.4658)
H: 6.0021

NOTE: 'Exp 1' is the exponent applied to 'Y' at the nose of the bulb, 'Exp 2' at the tail.

Animated comparisons (click to view?):

2016Dec30a (the most pointed one) moves the COG aft and could be longer to reduce its thickness (height) and maximum cross sectional area.
All three on separate layers: f235_keel_bulge_2016Dec30a.3dm



Mele Kalikimaka, amigo. I posted some small bits of GH earlier but not the whole thing (yet). Perhaps foolish of me to publish the Rhino files? As to the GH, I'm a little reluctant to publish all of that without password protection. It's a LOT of work over time, and still in progress (chopping the tail, adding root flare). GH is well suited to many things! Super powerful.

Last one for today - very low CG, thanks to extra weight in the bottom of the fin. Added layers to the Rhino file: f235_keel_bulge_2016Dec30a.3dm

Root chord: 22", Leading edge: 10 degrees, Trailing edge: 5 degrees

2016Dec30e, Exp 1 = 1.2, Exp 2 = 1 (slightly longer tail than 2016Dec30d...)
L: 32.2272"
W: 11.6374" (ratio: 1.9357)
H: 6.012"


As to placement of the keel, on Dec. 26th I started aligning all my keels by their CG (center of volume) to match the bull's-eye target shown on the MK III design (blue 'X' of CG aligned with fixed pinx 'X' at the top). You can see them jumping fore and aft in some of the animations - that's not an accident, the CG's are aligned regardless of fin leading edge. Some may not be practical in terms of mounting hardware?

More grist for the mill... same leading edge angle as the MK III design (15 degrees) but with ten degrees sweep on the trailing edge, resulting in surface area and CG similar to yesterday's version 2016Dec30e. The bulb on 2016Dec31b (below) is 1/2" thicker (6.5" vs. 6") than 2016Dec31a, yielding a narrower bulb with a sharper entry:

Part 1: Shaping the Keel/Bulb (this page) - Part 2: Attaching the Keel/Bulb