Methods and apparatus provide for: conveying a glass web from a source toward a destination in a transport direction; scoring the glass web in a width direction thereof to produce a score line having a plurality of separated score segments, thereby defining a section of the glass web between the score line and a leading edge of the glass web; supporting the glass web such that an increasing portion of the section of the glass web becomes cantilevered as the glass web is conveyed such that the portion of the section of the glass web is sufficiently large to generate stress in the respective score segments and drive respective cracks through the thickness of the glass web; and permitting the section of the glass web to separate from the glass web along the score line.