NON-CONTACT SEAL FOR ROTATIONAL EQUIPMENT WITH AXIALLY EXTENDED SEAL SHOES

An assembly (20) is provided for rotational equipment. This rotational equipment assembly (20) includes a plurality of seal shoes (53), a seal base (52), a plurality of spring elements (54) and a secondary seal assembly (44). The seal shoes (53) are arranged circumferentially about an axial centerline (22) in an annular array. The seal shoes (52) include a first seal shoe (53). The seal base (52) circumscribes the annular array. The spring elements (54) include a first spring element (54). The first spring element (54) connects and extends between the first seal shoe (53) and the seal base (52). The secondary seal assembly (44) is configured to seal a gap between the seal base (52) and the seal shoes (53). An axial end portion (102) of the first seal shoe (53) projects axially along the axial centerline (22), in a direction away from the first spring element (54), beyond the secondary seal assembly (44).