1. A half-empty tire for an agricultural machine with a rotation axis (XX), containing a base (20; 42), mounted on the periphery of a rotating support (12; 52), a tread (24) of a tire opposite the base (20; 42), and two side walls (26; 44), each of which connects the base (20; 42) and the tread (24) of the tire, forming together a tire (28) forming a non-inflated chamber (30) inside the tire, characterized in that the tread (24) of the tire has a concave profile in a plane passing through the axis of rotation (XX), and the tire contains two annular edges (34), which are The extension, respectively, of two side walls (26) in the radial direction outward and connected respectively with two opposite edges (32) of the tread (24) of the tire, while the two annular edges (34) define respectively two main directions (D) intersecting at an acute angle ( A) in such a way that when the tire comes into contact with the soil, subjected to vertical loading, the two annular edges (34) locally come together, thereby creating a pinching effect on the soil, increasing the concavity of the tire tread (24) and increasing the angle (A). 2. A semi-empty tire according to claim 1, characterized in that each side wall (26; 44) and its continuing annular edge (34) are able to rotate jointly and locally under the influence of a vertical load around a point (C; C) of rotation located in the area of the lateral connection walls (26) and bases (20; 42) .3. A semi-empty tire according to claim 1 or 2, characterized in that each side wall (26) and the annular edge (34) continuing thereon have a generally convex profile in a plane passing through the axis (XX) of rotation. 4. Semi-empty tire according to claim 1, characterized in that each side wall1.Полупустая шина для сельскохозяйственной машины с осью вращения (XX), содержащая основание (20; 42), устанавливаемое на периферии вращающейся опоры (12; 52), протектор (24) шины, расположенный напротив основания (20; 42), и две боковые стенки (26; 44