Aircraft tyre comprising: - a working reinforcement radially on the inside of a tread and radially on the outside of a carcass reinforcement, - the working reinforcement comprising at least one working bi-ply made at least in part of two radially superposed working layers (211, 212), - each working layer (211, 212) being made up of a juxtaposition of portions (51, 52, 53) of a strip of width W, - the strip being wound in a zigzag, in the circumferential direction (XX') of the tyre, onto a cylindrical laying surface of radius R, having as its axis of revolution the axis of rotation (YY') of the tyre, and with a periodic curve, - the periodic curve corresponding to the mid-line of the strip and forming, with the circumferential direction (XX') of the tyre and in the equatorial plane of the tyre, a non-zero angle A, - two consecutive strip portions (51, 52, 53), each having respective mid-lines comprising extrema (S 51, S 52, S 53), - the circumferential distance (c) between the extrema (S 51, S 52, S 53) of the respective mid-lines of two consecutive strip portions (51, 52, 53) is equal to the ratio W/sinA between the width W of the strip and the sine of the angle A, - for any set of three consecutive strip portions (51, 52, 53), made up of a first, a second and a third portion having respective mid-lines comprising extrema (S 51, S 52, S 53), the respective mid-lines of the first and third strip portions (51, 53) intersect at an intersection point, axially aligned with the extremum (S 52) of the mid-line of the second strip portion and axially on the inside of said extremum (S 52) at an axial distance (a) at least equal to the width W of the strip, characterized in that any portion of the periodic curve, extending axially inwards from one extremum of the periodic curve to a point on the equatorial plane of the tyre, comprises a first, concave circular portion of radius R 1, extending axially inwards from the extremum to a second, convex circular portion of radius R 2, the second, convex circular portion of radius R 2 extending axially inwards to a third, rectilinear portion forming an angle A with the circumferential direction (XX'), the third, rectilinear portion extending axially inwards to the point on the equatorial plane of the tyre. - a working reinforcement radially on the inside of a tread and radially on the outside of a carcass reinforcement, - the working reinforcement comprising at least one working bi-ply made at least in part of two radially superposed working layers (211, 212), - each working layer (211, 212) being made up of a juxtaposition of portions (51, 52, 53) of a strip of width W, - the strip being wound in a zigzag, in the circumferential direction (XX') of the tyre, onto a cylindrical laying surface of radius R, having as its axis of revolution the axis of rotation (YY') of the tyre, and with a periodic curve, - the periodic curve corresponding to the mid-line of the strip and forming, with the circumferential direction (XX') of the tyre and in the equatorial plane of the tyre, a non-zero angle A, - two consecutive strip portions (51, 52, 53), each having respective mid-lines comprising extrema (S 51, S 52, S 53), - the circumferential distance (c) between the extrema (S 51, S 52, S 53) of the respective mid-lines of two consecutive strip portions (51, 52, 53) is equal to the ratio W/sinA between the width W of the strip and the sine of the angle A, - for any set of three consecutive strip portions (51, 52, 53), made up of a first, a second and a third portion having respective mid-lines comprising extrema (S 51, S 52, S 53), the respective mid-lines of the first and third strip portions (51, 53) intersect at an intersection point, axially aligned with the extremum (S 52) of the mid-line of the second strip portion and axially on the inside of said extremum (S 52) at an axial distance (a) at least equal to the width W of the strip,