inserts each weft yarn y into a weaving machine l between the insertion system a and the winding package section b set free from the support s at one side and or in the region of the end of the support s at the other side mechanical assemblies h and g may be provided for measuring the respective correct weft yarn length for an insertion those assemblies h g are controlled in adaptation to the weaving cycles the weft yarn y withdrawn from the set free winding package section b essentially coaxial to the axis x consumes the respective first winding in withdrawal direction without any balloon formation and runs substantially radially inwards and then further axially e g such that finally all windings t 1 of the set free winding package section b may be consumed at the end of the insertion subsequently the next following winding package section for the next following insertion is set free the winding package consisting of the windings t and the winding package section b are of round or polygonal tubular configuration at least in the winding package section b the windings t 1 are more or less densely contacting each other are arranged in good order and have substantially the same form the diameter d of the winding package is selected such that the winding curvature corresponds at least approximately to the smallest natural and unforced capability of the weft yarn material to store a curvature fig2 illustrates what is meant by.