The metacenter is the point that affects the transverse stability of a symmetrical body.
Crossing of axis and line
The idea of metacenter is used in nautical science to name the place where the vertical axis of the hull of a boat intersects (when it is in its equilibrium position) and the vertical line that crosses the position reached by the hull center when heeling. the helmet.
As you can see, to understand the definition you have to have several ideas clear. To begin, it must be said that the hull is the body of the boat without the equipment, masts or machines. When a hull lists , it leans to one side with respect to its vertical , something that can be caused by waves or wind, for example.
The hull , on the other hand, is the sector of the hull that extends from the keel (the piece that goes from the bow to the stern, being the most important longitudinal reinforcement) to the waterline . The center of the submerged volume, where the thrust force acts to keep the boat afloat, is called the center of the hull (or hull volume ).
With all this clear, we can return to the notion of metacenter . This is the point where the vertical axis of the hull in balance and the vertical line that crosses the center of the hull when heeling intersect. The balance will be stable as long as the metacenter is higher than the center of gravity .
Fundamental concepts
The point at which the vertical that crosses the centers of mass and initial hull, and the projection of the thrust point, are called the initial metacenter . This applies to an infinitesimal inclination with respect to the stable equilibrium condition. In cases where the metacenter refers only to a well-defined area in the middle of a pair of parallel floating planes, it is called a zone metacenter , to distinguish it from that which encompasses the box and the center.
The prometacenter is the point at which the vertical that crosses the hull center and the thrust point meet in an inclination where the metacenter is no longer found on the initial line. The metacentric involute is the set of all points described by the metacenter along a finite variation of inclination. The evolution of the metacenter usually gives rise to the emergence of branches symmetrical to the potential axes of symmetry of the floating body.
The metacentric radius is the distance between the center of the ship and the metacenter, and is equivalent to the radius of curvature seen when projecting the trajectory of the center. Its proportion is given based on the relationship between the volume of the body and the moment of inertia. This tells us that there are maximum and minimum points on the principal axes of inertia.
Archimedes was the first to define the metacenter.
Origin
The origin of the concept of metacenter goes back to ancient Greece , since it was the polymath Archimedes of Syracuse who defined it. Note that it was not he who coined this term, but rather the one who recorded this and other phenomena that he observed of floating bodies.
It was only in the 18th century that the French mathematician and astronomer Pierre Bouguer , considered by many the "father of naval architecture," came up with this name to refer to the physical concept in question. To complete the study of the metacenter, Newton 's second law and Euler 's first were essential.