An apparatus for sealing a circumferential gap between a stationary component and a rotating member of a gas turbine engine (303; 403), configured to rotate about a longitudinal axis (X-X'), the apparatus comprising: a stator configured to be disposed circumferentially about the longitudinal axis (X-X'); and a shoe (304; 404a; 404b) configured for translation in a radial direction with respect to the stator, wherein the shoe (304; 404a; 404b) includes a circumferential surface (364; 464a; 464b) and a plurality of protrusions (366; 466a; 466b) extending radially inward from the circumferential surface (364; 464a; 464b), wherein the plurality of protrusions (366; 466a; 466b) are configured to extend toward the rotating member (303; 403), the rotating member (303; 403) having a radially outer surface (368; 468) disposed at a first non-zero angle with respect to the longitudinal axis (X-X'), each one of the plurality of protrusions (366; 466a; 466b) having: a length configured to maintain a constant clearance gap (469a; 469b) with respect to the rotating member (303; 403); and a tip portion (467a; 467b) configured to be spaced a radial distance equal to the constant clearance gap (469a; 469b) from the radially outer surface (368; 468) of the rotating member (303; 403), characterised in that the constant clearance gap (469a; 469b) is the same for each of the plurality of protrusions (366; 466a; 466b); and in that the circumferential surface (364; 464a; 464b) is substantially parallel with the longitudinal axis (X-X'). a stator configured to be disposed circumferentially about the longitudinal axis (X-X'); and a shoe (304; 404a; 404b) configured for translation in a radial direction with respect to the stator, wherein the shoe (304; 404a; 404b) includes a circumferential surface (364; 464a; 464b) and a plurality of protrusions (366; 466a; 466b) extending radially inward from the circumferential surface (364; 464a; 464b), wherein the plurality of protrusions (366; 466a; 466b) are configured to extend toward the rotating member (303; 403), the rotating member (303; 403) having a radially outer surface (368; 468) disposed at a first non-zero angle with respect to the longitudinal axis (X-X'), each one of the plurality of protrusions (366; 466a; 466b) having: a length configured to maintain a constant clearance gap (469a; 469b) with respect to the rotating member (303; 403); and a tip portion (467a; 467b) configured to be spaced a radial distance equal to the constant clearance gap (469a; 469b) from the radially outer surface (368; 468) of the rotating member (303; 403), characterised in that the constant clearance gap (469a; 469b) is the same for each of the plurality of protrusions (366; 466a; 466b); and in that the circumferential surface (364; 464a; 464b) is substantially parallel with the longitudinal axis (X-X'). wherein the shoe (304; 404a; 404b) includes a circumferential surface (364; 464a; 464b) and a plurality of protrusions (366; 466a; 466b) extending radially inward from the circumferential surface (364; 464a; 464b), wherein the plurality of protrusions (366; 466a; 466b) are configured to extend toward the rotating member (303; 403), the rotating member (303; 403) having a radially outer surface (368; 468) disposed at a first non-zero angle with respect to the longitudinal axis (X-X'), each one of the plurality of protrusions (366; 466a; 466b) having: a length configured to maintain a constant clearance gap (469a; 469b) with respect to the rotating member (303; 403); and a tip portion (467a; 467b) configured to be spaced a radial distance equal to the constant clearance gap (469a; 469b) from the radially outer surface (368; 468) of the rotating member (303; 403), characterised in that the constant clearance gap (469a; 469b) is the same for each of the plurality of protrusions (366; 466a; 466b); and in that the circumferential surface (364; 464a; 464b) is substantially parallel with the longitudinal axis (X-X').