Vessel for operating on a body of water comprising: a non-planing hull having a waterline and a longitudinal direction with a forward portion, an aft portion, and a central portion, the hull being configured to have the aft portion with a smaller water displacement relative to a water displacement at the central portion; and an aft foil affixed to the aft hull portion with one or more connecting members, and below the surface of the water, and spaced from the hull, the aft foil having a span (ba), a chord (ca), and a leading edge and a trailing edge relative to a forward direction, wherein the leading edge of the aft foil is aligned with the horizontal or tilted at an upward or downward angle (α) relative to the horizontal, wherein the aft foil has a chord and profile in longitudinal cross section, with a configuration to provide a lifting force (La), the tilt angle of the chord of the aft foil being measured with respect to the horizontal, and wherein the aft foil is oriented to provide a continuous, upward, forwardly directed component of the lifting force (La), wherein, during use, in the longitudinal direction the central portion of the hull displays a pressure transition region, wherein the pressure force on the hull changes from increasing drag forward of this region, to reducing drag aft of this region, characterized in that a forward foil is positioned in front of the pressure transition region and the aft foil is positioned aft of the pressure transition region, the forward foil being arranged at a distance not greater than one chord length from the hull, whereby the low pressure on the upper side of the forward foil is continued on the hull above, wherein the aft and forward foils are configured to keep at least 50% to 70% of the submerged volume of the vessel, when stationary, below the waterline, the forward foil preventing the vessel to adopt a bow-down trim condition. a non-planing hull having a waterline and a longitudinal direction with a forward portion, an aft portion, and a central portion, the hull being configured to have the aft portion with a smaller water displacement relative to a water displacement at the central portion; and an aft foil affixed to the aft hull portion with one or more connecting members, and below the surface of the water, and spaced from the hull, the aft foil having a span (ba), a chord (ca), and a leading edge and a trailing edge relative to a forward direction, wherein the leading edge of the aft foil is aligned with the horizontal or tilted at an upward or downward angle (α) relative to the horizontal, wherein the aft foil has a chord and profile in longitudinal cross section, with a configuration to provide a lifting force (La), the tilt angle of the chord of the aft foil being measured with respect to the horizontal, and wherein the aft foil is oriented to provide a continuous, upward, forwardly directed component of the lifting force (La), a forward foil is positioned in front of the pressure transition region and the aft foil is positioned aft of the pressure transition region, the forward foil being arranged at a distance not greater than one chord length from the hull, whereby the low pressure on the upper side of the forward foil is continued on the hull above, wherein the aft and forward foils are configured to keep at least 50% to 70% of the submerged volume of the vessel, when stationary, below the waterline, the forward foil preventing the vessel to adopt a bow-down trim condition.