What exactly is the center of rotation?

[knoisewater]

Kind of a weird question. I have a '78 Ericson 35 MKII, and I'm dinking around with making my own instruments. One of the things I have figured out is how to remove induced wind from the anemometer measurement (on a no wind day at anchor, if a wave moves under a boat, the mast will rock back and forth, registering wind... even though there is none. This system calculates and removes what that induced wind is).

The problem is that I need to know the exact center of rotation. As in, the specific point where the boat rolls, pitches, and yaws about. I suppose I could go out and give her a few hard turns in calm water to kind of see the axis is turns around, but being in the SF Bay, that doesn't seem likely.

I've kind of eyeballed it based on total anecdotal "That looks about right" knowledge to be about here (at the green dot):

I do believe this is different from the boat's center of mass, which can be shifted around and whatnot, just like an airplane's center of mass can shift but it's center of lift is based on the wing's shape.

Where do you think it is?

 

[bgary]

I don't know the answer to your question, but I have a random bit of input.

Most anemometers have some sort of damping or averaging function just so phenomena like you're describing don't provide misleading results. Averaging the measurements over (some small period of time, maybe a second or two) gives you a much more useful indication of windspeed while retaining the ability to reflects gusts and lulls.

If you're doing this for the science? Cool. But if you want to have "meaningful" windspeeds, you may want to think about just averaging out the effect of "induced wind".

$.02

 

[knoisewater]

Yeah, this is purely for "science" (as in I got bored while I'm landlocked and found a way to spend time towards my boat).

I think I might try and figure out it's location by putting the sensor near where I think and measure some stuff when I turn and... oh boy, this is getting real into the weeds.

 

[knoisewater]

Yup, I did a quick academic search for center of bouyancy, and it turns out that I am in way over my head.

 

[bgary]

Center of bouyancy probably wouldn't be that hard if you had a whole set of drawings (or access to some of the design calcs, such as prismatic coefficient)

If all that was involved was mass, that's a relatively easy problem to model - a known mass at one end of an arm, and a distance to the other end of the arm; one could calculate the center of gravity of the "system" and, in general, the system would oscillate around that point. In a simple model, knowing the righting moment might allow you to work backwards to determine the effects of mass on the movement.

The problem is that there are multiple variables, each in multiple dimensions. There is bouyancy, there is "shape" (both the shape of the bouyant body, and the shape of the foil which resists motion in one axis and is relatively unconstrained in the other), there is distribution of mass (moving an anchor from the bow to the bilge amidships can have a dramatic effect on the pitching moment).... etc, etc, etc. There's often a significant difference between center-of-gravity, center-of-effort and center-of-lateral-resistane on a boat at rest, and they all move when the boat is heeling.

It's an intriguing problem. It might be interesting to pull out a copy of Skene's "Elements of Yacht Design", or maybe Marchaj "Aerodynamics and Hydrodynamics of Sailing" to see if there is a simple way to model the axis of motion in each of three axes.

 

[bgary]

Now that I've thought about it a little more, Marchaj's more recent book, "Seaworthiness", has a section on dynamic meta centric stability, which considers stability effects from both shape and mass. Might be worth starting there.

 

[knoisewater]

Thanks -- I was just reading an ancient book from the 30's about it on Google Reader, so it'll be good to check out something a little more recent.