5 ms·
For many shapes, there are multiple points of stability! If you drew a cross, you'd find that it could stabilize on any two corners. Stability of a floating ob
by chrisdalke 6y ago
For many shapes, there are multiple points of stability! If you drew a cross, you'd find that it could stabilize on any two corners.
Stability of a floating object is determined by a "righting arm": A torque produced by the horizontal offset between the object's center of mass, and the center of buoyancy (The center of mass of the portion underwater).
Sometimes, that torque produces "positive stability" -- When the object tilts into the water, the center of buoyancy shifts in a direction that increases the righting arm force and pushes the object back upright.
On the other hand, other shapes produce "negative stability" -- Tilting the object shifts the center of buoyancy in a direction that reduces the righting arm force, so the object flips.
This is why ships are (roughly) square shaped when looking at a cross section: If you visualize a floating box tilting to the right, more of the right side will be underwater. This produces a righting arm force that turns the box back to the left.
The worst case for stability is a circle, since no matter what angle the shape is at, the righting moment is always zero -- There's no horizontal offset between the center of mass and center of buoyancy, so a circle never has a righting force.
- praptak 6y agoWhen it comes to stability there is a crucial handicap between ships and icebergs. The former have non-uniform mass, so it is possible for a ship's center of mass to be below its center of buoyancy. That's why ships have ballast - it lowers the center of mass relative to the center of buoyancy. An iceberg is uniform, so its center of buoyancy is always below its center of mass. This makes its stability trickier, as it relies on changes in the shape of the buoyancy to follow the center of mass when disturbed. A ship is a pendulum, an iceberg is an upright stick balanced on one's nose :)
- chrisdalke 6y agoGood point -- The way I described it really applies to _any_ object floating in water. I don't have much experience with ship design, but on small boat design you can rely mostly on the geometry of the boat to produce a sufficient righting moment even with a very high center of mass. Some off-shore speedboats have really incredible self-righting because they've been designed to always have positive stability at all angles. One of my favorite videos of this in action: https://www.youtube.com/watch?v=Y2i1fOJ-itw https://www.youtube.com/watch?v=Y2i1fOJ-itw
- sgtnoodle 6y agoIt's possible to engineer a stable boat in this simulation based on that principle for stability. https://ibb.co/T1KG5DM https://ibb.co/T1KG5DM The trick is to draw a low-mass object with high displacement, which happens to be possible because of the existence of, uh, anti-iceberg? that has negative mass.
- praptak 6y agoYes, small boats are often constrained by shallow water, so they cannot have too much ballast not to mention things like bulb-keel. This means the hull needs to be sufficiently broad and flat.