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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?

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  • $\begingroup$ Have you looked at existing designs of buoys? Why do you think they are shaped as they are? $\endgroup$
    – Solar Mike
    Commented Dec 14, 2022 at 20:11
  • $\begingroup$ 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. $\endgroup$
    – 5TableLegs
    Commented Dec 14, 2022 at 20:30
  • $\begingroup$ How do objects move in waves? $\endgroup$
    – Solar Mike
    Commented Dec 14, 2022 at 20:48
  • $\begingroup$ 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. $\endgroup$
    – DKNguyen
    Commented Dec 14, 2022 at 20:55
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    $\begingroup$ Don't forget dynamics. If waves are sufficiently violent, it will go under and resurface later. $\endgroup$
    – Abel
    Commented Dec 15, 2022 at 1:46

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