keel bulb design - help

we are trying to design a bulb for a keel - we have about 1700lbs of lead and if our calculations are correct that translates into about 2.4 cubic feet - we are looking for the shape/dimensions of the bulb, we know it to be 2.4 cubic feet and 48 inches long (with the front of the bulb attaching to the leading edge of the fin) - can anyone have or tell me of a program to design this or give me the critical dimensions of the bulb - your assistance is appreciated - thank you...jim

 

Jim,

There are drafting programs and 3-D shaping programs in which you can develop the shape (you have to manipulate the computer to get what you want, it won't do it for you), but you may need a designer or engineer to specify the attachment of the bulb to the keel, to figure out how the modified keel should be built. I just finished a new keel design for Bagatelle, my 44' lightweight racer, for the owner in Niantic, CT. The bulb will be cast by I. Broomfield and Son. in Providence, RI.

You can look at my website, www.sponbergyachtdesign.com for details on Bagatelle and her keel (Boat Designs--Sailboats--Bagatelle), and you can see the keel modifications to the Cambria 44, Magic, on the site in Boat Repairs and Modifications.

If you think you would like some professional help, let me know.

Eric

 

You may want to look carefully at the hydrodynamics of the bulb and its effect on the effective aspect ratio to determine the cross section shape and the tail design. A round cross section bulb acts to reduce effective aspect ration as well as raisoing the KG of the lead, but has lowest downwind drag. This is a CDF / VPP exercise, the former generally using some form of VSAERO, and the latter any VPP.

 

You can download a program that might come in handy here:

http://www.onemetre.net/Download/Bulbcalc/Bulbcalc.htm

Be aware that the program is meant for designing bulbs for RC sailing models, so you'll have to scale your dimensions. Another thing is that it doesn't tell you the location of the center of gravity, so you'll have to work that out too.

 

The shapes used by Bulbcalc appear to be two-dimensional airfoil sections. There's a difference between the flow around a two-dimensional cylinder and the flow around an axisymmetric bulb. The whole point of shaping an airfoil or a bulb is to manipulate the boundary layer through the pressure distribution along each surface streamline. Using an airfoil section for a bulb profile will not give you the design pressures or the desired boundary layer development.

Alex Strojnick, in his book, "Laminar Aircraft Technologies" (published by the author, now deceased), recommends taking airfoil coordinates to the 3/2 power (and scaling to the original thickness) to use them as templates for bodies of revolution. The result will be a more pointed shape than the corresponding 2D airfoil profile. For example, the figure below shows the NACA 66-021 section converted to an axisymmetric profile using Strojnick's technique. This resembles a Parson's low drag body shape, although Parson designed his bodies using a CFD analysis code and an optimization technique (Parson, J. S, Godson, R. E, Goldschmied, F.R., "Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow", Journal of Hydronautics, July 1967.)

The finest source of info on body shaping that I've seen is Bruce Carmichael's "Personal Aircraft Drag Reduction" (published by the author, 1995, mailto:brucecar1@juno.com; reviewed at http://www89.pair.com/techinfo/Books/bookrev.htm). Carmichael did pioneering research on low-drag bodies in water and came up with the Dolphin and SHAMU vehicle shapes. These bodies were designed in the 1960's for high speed towed sonar systems. It's possible to have quite low drag with bodies that have a fineness ratio as low as 3. There is extensive theoretical and experimental data on low drag bodies of several kinds presented in his book.

The strategy for designing low drag bodies is the same as the strategy for designing low drag airfoils: use a flat rooftop or favorable pressure gradient for as long as you can, transition the boundary layer from laminar to turbulent, then use a concave Stratford-like pressure recovery to the end. The result is a tadpole-like shape.

I think it also makes sense to place the maximum thickness near the trailng edge of the keel, if you can stand to do that from a structural standpoint. In the junction between keel and bulb, the fluid velocity tends to be something like the sum of the bulb and keel velocities. So the flow is accelerated there, and if it has to slow down to near freestream velocity, the boundary layer tends to separate. This causes extra drag at the junction. By placing the trailing edge of the keel near the maximum thickness of the bulb, you've placed the keel trailing edge near the maximum velocity on the bulb. So the boundary layer on the keel doesn't have to slow down all the way to freestream - it only has to slow down enough to match the bulb velocity there. And you have a more favorable pressure gradient all along the junction. This will help to keep the boundary layer attached.

Carmichael's book also has information on wing/body junction drag that would be applicable to keel bulbs. However, you have to use some caution when interpreting the results of sailplane wing/body junction studies. This is because the wing on a sailplane is typically placed behind the maximum thickness of the fuselage, not in front as is the case for your proposed keel bulb. This places the junction in the region where the body flow is decelerating strongly, which has an adverse effect on the boundary layer in the junction. This is why Carmichael advises against strongly contracted fuselages for this application. But a strongly contracted bulb may be just what you need to keep the c.g. of the bulb as forward as possible and minimize the wetted area for a given bulb volume.

 

Bulbcalc indeed uses two-dimensional NACA sections. I was under the impression that Jim's project isn't a racer, and therefore (some of) these sections would be OK. If I'm wrong, then Bulbcalc is not the way to go.

I've read about this technique in Sailing Yacht Design by Claughton et al. and I've also got a copy of Galvao's A Note on Low Drag Bodies, and I have a question: I often use Young's Laminar Bodies for keel bulbs, but maybe something better can be found. If one transforms the coordinates of YLBs "backwards" by taking them to the 2/3 power and scale them, would it be possible to compare this new section with others (using Xfoil or Profili) to find a better alternative (which is then transformed to a axisymmetric section)? The comparison doesn't need to be accurate and/or precise - qualitative answers are quite OK!

 

Bearing in mind that the local flow on a keel bulb wil rarely be perfect, or even close to it, all the theoretical "perfect" sections in the world will not do you much good. I have always used a 2D foil rotated, and sometimes "squished" here and there , and have not noticed much ill effect.

Steve "Empirical, baby...."

 

Doesn't the bulb also act as an end cap on the keel?

 

I've not heard of Young's laminar bodies, so don't know what they look like.

Instead of transforming an axisymmetric shape to 2D for analysis, I'd be inclined to use something like CMARC to analyze it as is. With keel, too. CMARC can do a pseudo-2D boundary layer analysis along a streamline. It doesn't handle crossflow boundary layer profiles, etc., but it's probably at least as good as trying to use an airfoil analysis code.

 

Young's Laminar Bodies look like the one in your previous post (at least one of them does). They can be found in Model Aircraft Aerodynamics by Martin Simons, Argus Books 1991.

Yes of course, but I don't have access to CMARC (or any three-dimensional code), so I was just wondering if doing it like I described could give at least an idea about which sections might be better choices - I'm not looking for absolute numbers, ballpark figures are fine with me!

 

Remember (as indicated above, by "SailDesign"), laminar flow may occur if the bulb is very smoth, like perfect gelcoat, and the water is undisturbed. Very often a lead bulb will not be smooth enough to make a (theoretically) "laminar" shape/profile work. In that case a standard naca 6500xx or 6400xx may be better.

However I agree that a professional designer with experience from bulb design should be consulted. Then you can get an IGES file that can be sent to a cnc shop to make 3D template in wood or foam that you can bring to you foundry or use to make a concrete mold.

 

It's true that the bulb may not have much laminar flow. However, even with a fully turbulent boundary layer, the same sort of pressure distribution would be beneficial. A long stretch of favorable pressure gradient will minimize the growth of the boundary layer and help damp out any local disturbances. The concave pressure recovery results in low skin friction because the velocity profile there has low shear stress at the surface.

The whole point of taking the coordinates to the 3/2 power is to use a NACA section, but in a way that is appropriate for the axisymmetric flow instead of the flow about an infinite cylinder for which the sections were designed. Naturally, the further aft the rooftop extends (the second digit in the NACA 6-series sections), the more severe the pressure recovery is going to be and the greater the risk of separation there.

Here's what several NACA-derived axisymmetric shapes look like. All have been scaled to produce a 5:1 fineness ratio. The two 6-series shapes show the effect of changing the length of the 2D rooftop from 30% chord (blue) to 60% chord (magenta). The green line is the axisymmetric shape you'd get from a NACA 4-digit section like the 0012; it's a lot blunter in the nose but has a similar tail to the 63-based shape. But not as blunt as the 2D shape of the NACA 0020, shown as the thin red line.

The tail of the 2D profile is also a lot fuller than for the axisymmetric profiles. I think the more contracted tails are the way to go. I think they are more likely to have lower drag for the same diameter, and their center of gravity is farther forward. However, for the same volume in the bulb and the same length, it will be possible to give the bulb a smaller diameter using the 2D profile. Of course, there's no real reason to limit the length, so you can get the volume back by going to a little higher length and fineness ratio.

So I think it makes sense to use the 3/2 power modification no matter which 2D profile you use.

 

What about the rule of thump saying that the optimum length/diameter-ratio for an axisymmetric body with a given volume is somewhere around 4.5?
I've seen it published in a number of different texts and books, but is it true?

 

On my final year project (volvo 70), i have a part on bulb design (see pdf). I used common aerodynamic theory, xfoil and a VPP together to optimize performance.
I used the 2/3 power law to design my bulb section in Xfoil.
It deals with optimized length, diameter to length ratio and height to breadth ratio.

 

I don't think there's a given optimum fineness ratio. Just look at the bulbs in the last America's Cup so see the difference of opinion among those designers! It's going to depend on the design Reynolds number, how much laminar flow you think you can maintain, and how aggressively you want to push the boundary layer toward separation.

Don't forget that the bulb is operating at an angle to the flow, too, so designing for purely axisymmetric flow is not appropriate. We have a similar problem with designing fairings for landyachts. The apparent wind is 15 degrees to the centerline. So one technique that I've used is to shape the body so it has a teardrop shape in the streamwise direction for both tacks. Then fair in around those two skeletons. The result is a fat delta-wing-like body with a horizontal trailing edge, shown below. Panel code analysis showed that I could cut down the corners and save some wetted area because of the bending of the streamlines at the surface.

For a boat you wouldn't want a shape as extreme as this because the leeway angles are much smaller. But the idea is to consider the lines taken in the streamwise direction, as below, including the heel angle.