Displacement Centre of Gravity and Stability Arm in Longitudinal Tilt of a Floating Body with Circular Floats

Floating belt conveyor routes, consisting of serially arranged belt conveyors, the end parts of which are mechanically attached to floating bodies, are designed for the continuous transport of extracted granular materials from the water. The paper deals with the analytical determination of the position of the centre of gravity of the buoyancy force, the coordinates of which change depending on the longitudinal deflection of the floating body from the equilibrium state, which acts as a supporting element of individual conveyor belts. The analysis of the individual phases of deflection of the floating body, consisting of a pair of floats with a circular cross-section, shows that the complete submergence of one of the floats occurs at a higher value of the angle of inclination in the case when the floats are initially submerged under the surface to exactly half of their diameter. On the realized experimental device the buoyancy force was detected using strain gauges during the deflection of the floating body from the equilibrium position for three defined levels of immersion. The floating body of the experimental device consists of a pair of floats with a circular cross-section with a diameter of 80 mm. The output is a structured methodological procedure for determining the position of the centre of gravity of the displacement (centre of buoyancy) of a floating body when it deviates from the equilibrium position and a methodology for calculating the stability arm, which is a key parameter for assessing the buoyancy and stability of the body. On the basis of the laboratory measurements, the magnitude of the buoyancy force can be quantified as a function of the immersion depth of the floating body. It was found that the buoyancy force remains constant when the body deflects only when the immersion corresponds to half the diameter of a float with a circular cross-section. If the depth of the immersion is less than the radius of the float, the buoyancy force increases during deflection; on the contrary, if the immersion is greater than the radius of the float, the buoyancy force decreases.