A hydrostatic air-riding seal system for use within a gas turbine engine comprising: (a) a primary seal assembly movable between a seal runner extending from a rotatable shaft and a housing structure, said primary seal assembly including: (i) an annular seal ring having a cross section that is substantially L-shaped and a surface with a step face including a circumferential dam thereon, said surface disposed opposite of a sealing surface along said seal runner; and (ii) an arcuate support arm attached at one end to said annular seal ring and having a tooth at one end adjacent to an outermost circumferential surface along said seal runner, said tooth and said outermost circumferential surface separated by a gap; (b) a secondary seal ring disposed between and contacting said primary seal assembly and said housing structure so as to form a bore seal and a face seal therewith; and (c) a structure along said surface which increases the stiffness of a thin film between said surface and said sealing surface, said structure having a plurality of radial dams disposed along said surface in an outward radial arrangement with respect to said circumferential dam; characterised in that: a radial width (W R) of each said radial dam is approximately as wide as a circumferential width (W C) of said circumferential dam, a height (H R) of each said radial dam is at least as high as that of said circumferential dam, said height of each said radial dam being nominally 0.0762-mm and said radial width of each said radial dam being nominally 1.6002-mm so as to significantly stiffen said thin film with a thickness between 0.0254-mm and 0.0762-mm. (a) a primary seal assembly movable between a seal runner extending from a rotatable shaft and a housing structure, said primary seal assembly including: (i) an annular seal ring having a cross section that is substantially L-shaped and a surface with a step face including a circumferential dam thereon, said surface disposed opposite of a sealing surface along said seal runner; and (ii) an arcuate support arm attached at one end to said annular seal ring and having a tooth at one end adjacent to an outermost circumferential surface along said seal runner, said tooth and said outermost circumferential surface separated by a gap; (i) an annular seal ring having a cross section that is substantially L-shaped and a surface with a step face including a circumferential dam thereon, said surface disposed opposite of a sealing surface along said seal runner; and (ii) an arcuate support arm attached at one end to said annular seal ring and having a tooth at one end adjacent to an outermost circumferential surface along said seal runner, said tooth and said outermost circumferential surface separated by a gap; (b) a secondary seal ring disposed between and contacting said primary seal assembly and said housing structure so as to form a bore seal and a face seal therewith; and (c) a structure along said surface which increases the stiffness of a thin film between said surface and said sealing surface, said structure having a plurality of radial dams disposed along said surface in an outward radial arrangement with respect to said circumferential dam; characterised in that: a radial width (W R) of each said radial dam is approximately as wide as a circumferential width (W C) of said circumferential dam, a height (H R) of each said radial dam is at least as high as that of said circumferential dam, said height of each said radial dam being nominally 0.0762-mm and said radial width of each said radial dam being nominally 1.6002-mm so as to significantly stiffen said thin film with a thickness between 0.0254-mm and 0.0762-mm. a radial width (W R) of each said radial dam is approximately as wide as a circumferential width (W C) of said circumferential dam, a height (H R) of each said radial dam is at least as high as that of said circumferential dam, said height of each said radial dam being nominally 0.0762-mm and said radial width of each said radial dam being nominally 1.6002-mm so as to significantly stiffen said thin film with a thickness between 0.0254-mm and 0.0762-mm.