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I'm designing a weather buoy as a school project. I have read that the metacentric height is a good measurement for buoy stability and is relatively easy to calculate.

This page says the metacentric height $MG$ is given by the formula:

$$MG=\frac{I}{V}-GB$$ Where $I$ is the area of the buoys section cut by the water surface, $V$ is the submerged volume of the buoy and $GB$ is the distance between the center of gravity and the center of buoyancy.

Using this knowledge. I tried to:

  1. Keep the weight of the buoy as low down as possible.
  2. Increase the area of the buoy which is cut by the water.
  3. Keep the submerged volume as low as possible.

Here is a dirty sketch of the buoy in the water:enter image description here

The part of the buoy which lies horizontally in the water is going to have a cylindrical form with a diameter of 0,6 m. The part of the buoy which stands vertically is going to be a pipe with its weight concentrated at the bottom (as marked in the picture).

First question: What would be the optimal length of the pipe which lies under the horizontal floating element in the water? Because having a pipe going deeper into the water would keep the weight lower, but also increase the submerged volume.

Second question: Is the metacentric height the best way to determine the buoy's stability? Are there other ways of making it more stable as well?

Third question: Have I done something completely wrong?

5TableLegs
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  • Have you looked at existing designs of buoys? Why do you think they are shaped as they are? – Solar Mike Dec 14 '22 at 20:11
  • Yes, I have looked at existing designs of buoys. I was simply wondering if my thought process was right and if there are many more factors to consider. I don't know if "they are shaped the way they are" only because of metacentric height calculations. – 5TableLegs Dec 14 '22 at 20:30
  • How do objects move in waves? – Solar Mike Dec 14 '22 at 20:48
  • Increased moment of inertia would help reduce rocking. That means that if you can't cram your weight below a certain depth then you need to cram as much of it as close as possible to that maximum depth. That means that concentrating all that mass in a narrow column is not as optimal since some of it is probably sitting higher up than it needs to and you could instead spreading it thinner and wider out along the bottom. Similarly increasing the length of the horizontal arms and/or the mass at the end of them also increases moment of inertia but it's probably not the best approach here. – DKNguyen Dec 14 '22 at 20:55
  • I was thinking about using concrete at the bottom of the pipe @DKNguyen. The mass density of concrete should be high enough to get a lot of weight crammed into a small pipe. When spreading the weight along the bottom, what kind of design do you have in mind? – 5TableLegs Dec 14 '22 at 21:00
  • Instead of a column of concrete it could be a thin, wider wider disc so more concrete would sit lower without the buoy being any deeper. That might have other repercussions though. It could potentially be positive since a thin wide disc (not just a thicker column) has more drag in the water in the rocking direction than a column which could help dampen motion. There's probably also dynamic stability (damping) stuff to consider rather than just static stability but I don't know anything about that. However, you probably saw no buoy seems to be designed this way so there might be a problem. – DKNguyen Dec 14 '22 at 21:06
  • For example, perhaps a buoy that is too stable does tilt against the wind enough and presents more stress to the top parts of the buoy than it needs to. Or if a boat hits the buoy. – DKNguyen Dec 14 '22 at 21:08
  • I'm planning on putting solar panels angled about 80 degrees (from the bottom) leaning on the horizontal floating element and attaching them towards the very top of the pipe. Therefore having the horizontal floating element be somewhat tall could be an advantage since the solar panels shouldn't be too close to the water's surface. Just not sure about how much of the buoy I should have submerged in the water. – 5TableLegs Dec 14 '22 at 21:14
  • Yeah, that wind part is a problem I haven't thought of. It could especially get a lot worse because of the solar panels. – 5TableLegs Dec 14 '22 at 21:15
  • I'm thinking that to determine how much buoy you need suberged you are going to need to do a stability analysis which would involve estimating the wind force and perhaps other forces like currents (if they vary with depth). Or much more crudely, decide how much the buoy should be able to tip over under those conditions and how long it should take to reach that point. For example, a gust of a certain force and length might not be enough to tip it over, but a the same gust lasting longer could. That would be a moment of inertia (and water drag) thing. – DKNguyen Dec 14 '22 at 21:21
  • How it actually returns upright after that is the stability analysis which, as I mentioned previously, I don't know anything about. Modeled as a pendulum system with water viscosity and drag as a damper or something? – DKNguyen Dec 14 '22 at 21:23
  • Check out some examples of WW2 rescue buoys here https://www.youtube.com/watch?v=9fDnSQoneiE there are some real-world design decisions and their results mentioned. The difference is these were intended to be shelter for hours/days for downed aircrew, not just indicators. – Criggie Dec 14 '22 at 23:58
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    Don't forget dynamics. If waves are sufficiently violent, it will go under and resurface later. – Abel Dec 15 '22 at 01:46

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