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Miller twist rule is a mathematical formula derived by American physical chemist and historian of science Donald G. Miller (1927-2012) to determine the rate of twist to apply to a given bullet to provide optimum stability using a rifled barrel. [1]
Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on centers of gravity, centers of buoyancy, the metacenters of vessels, and on how these interact.
The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel. Beyond that range, the stability of the vessel is dominated by what is known as a righting moment. Depending on the geometry of the hull, naval architects must iteratively calculate the center of buoyancy at increasing angles of heel.
Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
Hudson's equation, also known as Hudson formula, is an equation used by coastal engineers to calculate the minimum size of riprap (armourstone) required to provide satisfactory stability characteristics for rubble structures such as breakwaters under attack from storm wave conditions.
This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally.
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.). For a defined "trim" flight condition, changes and oscillations occur in these parameters.