keel bulb form factors?

does anyone know of a form factor (1+K) to apply to keel bulbs, I am aware of the hoerner k=1.5(t/c)^1.5+7(t/c)^3, but this implies a circular crossection. Are there any studies that take into account elliptical and 'drooped' crossections? or even different tail types, pin beaver etc.

also is there an xfoil equivalent for bulbs?

it would be great to make a reasonable assessment of drag if you dont have access to CFD

 

The only people who may have the resources for this are probably AC teams. Last I heard, they don't like to share data...

Considering that the bulb has to deal with an important boundary layer, angle of attack, and 3D finite wing end-effects; I would be dubious of any form factor calculation that would come from a 2D calculation.

In any case, the form factor of the overall boat should dwarf the change in form factor due to the bulb. Remember that form factor relates to viscous pressure drag - so I would doubt that even a potential flow code would work well. The only calculation which may work would have to be a RANS code.

If I were making the calculations, I would simply add the empirical drag formula for a suitable appendage. There would be a huge dependence on Reynolds number, so the Kirkman calculations may be better than Hoerner (see PNA or Kirkman 1980).

It's a big approximation, but so is naval architecture in general...
-Jon

 

A brazilian aerodynamicist, Francisco Leme Galvao, gave a speech at the OSTIV congress in Poland in 1968, where he described a method to convert 2-D foil sections into 3-D bodies with the same velocity and pressure gradients as the 2-D sections. He used this formula:

r = y**2/3 (y raised to the power of 2/3)

where
r = radius of the body at a certain x-value
y = ordinate of the section at that x-value

I know this doesn't give you a form factor, but I think it makes it possible to compare 3-D bodies using 2-D calculations (Xfoil or other) by using the formula above to convert the bodies to sections (y = r**3/2). The "best" section would then yield the best body.

This method is also only for bodies of revolution, but somewhere I've read that the important factor is the longitudinal distribution of the volume, so maybe it can be used for other cross-sections, too?

I would love to hear (or read) an experts opinion on this!

 

mcmurph1;

Use Hoerner and either calculate an equivalent hydraulic radius or and equivalent radius based upon maximum section area (provided the section is not too extreme, beavertails are a whole other animal). Either of these methods will give a reasonable answer given the vagrancies of the real world. Hoerner's work on wing tanks/tipletts is still the standard and you would do well to read that portion also. It must be remembered that form drag on a keel bulb is very small when compared to the interference drag between the bulb and the foil if the re-entrant radius is small. Design of the bulb/foil interface is the real problem that needs to be considered.