POLYMER AMMUNITION AND CARTRIDGE HAVING A CONVEX PRIMER INSERT

1 . A primer insert for a polymer ammunition cartridge comprising:

a top surface;

a bottom surface opposite the top surface;

a coupling element that extends from the bottom surface, wherein the coupling element comprises an interior surface and an exterior surface, wherein the interior surface comprises:

a convex transition region that transitions from the bottom surface to a second segment wherein the transition region has an overall convex shape;

a first segment extending from the second segment and terminates at a tip, wherein the first segment has a first segment distance from 0.02 to 0.18 inches and the second segment has a second segment distance from 0.02 to 0.18 inches, wherein the second segment has a second segment angle from +3 to −3 degrees relative to the first segment angle and the first segment has a first segment angle from +6 to −6 degrees from perpendicular to the top surface;

a primer recess in the top surface that extends toward the bottom surface;

a primer flash aperture positioned in the primer recess through the bottom surface; and

a flash aperture groove in the primer recess and positioned around the primer flash aperture and adapted to receive a polymer overmolding through the primer flash aperture.

2 . The primer insert of claim 1 , wherein the convex transition region is convex with a radius of between about 0.02 and 0.2.

3 . The primer insert of claim 1 , wherein the convex transition region comprises one or more straight segments that form a convex segment that transitions from the bottom surface to a second segment.

4 . The primer insert of claim 1 , wherein the convex transition region comprises one or more curved segments that form a convex segment that transitions from the bottom surface to a second segment.

5 . The primer insert of claim 1 , wherein the convex transition region comprises one or more straight segments and one or more curved segments that form a convex segment that transitions from the bottom surface to a second segment.

6 . The primer insert of claim 1 , wherein the first segment has a first segment distance is about 0.08 inches, the second segment has a second segment distance is about 0.08 inches and the convex transition region is convex with a radius of about 0.04.

7 . The primer insert of claim 3 , wherein the second segment has a second segment angle is about 1 degrees and the first segment has a first segment is about 3 degrees.

8 . The primer insert of claim 3 , wherein the second segment has a second segment angle is about 3 degrees and the first segment has a first segment is about 0 degrees.

9 . The primer insert of claim 3 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.34 inches.

10 . The primer insert of claim 3 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.36 inches.

11 . The primer insert of claim 3 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.38 inches.

12 . The primer insert of claim 1 , wherein the first segment has a first segment distance is about 0.079 inches, the second segment has a second segment distance is about 0.083 inches and the convex transition region is convex with a radius of about 0.04.

13 . The primer insert of claim 9 , wherein the second segment has a second segment angle is about 1 degrees and the first segment has a first segment is about 3 degrees.

14 . The primer insert of claim 9 , wherein the second segment has a second segment angle is about 3 degrees and the first segment has a first segment is about 0 degrees.

15 . The primer insert of claim 9 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.34 inches.

16 . The primer insert of claim 9 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.36 inches or an insert height that extends from the top surface to the tip, wherein the insert height is about 0.38 inches.

17 . The primer insert of claim 1 , wherein the first segment has a first segment distance is about 0.076 inches, the second segment has a second segment distance is about 0.086 inches and the convex transition region is convex with a radius of about 0.04.

18 . The primer insert of claim 15 , wherein the second segment has a second segment angle is about 1 degrees and the first segment has a first segment is about 3 degrees or wherein the second segment has a second segment angle is about 3 degrees and the first segment has a first segment is about 0 degrees.

19 . The primer insert of claim 15 , further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.36 inches or further comprising an insert height that extends from the top surface to the tip, wherein the insert height is about 0.38 inches. or

20 . The primer insert of claim 1 , wherein the first segment has a first segment distance is about 0.082 inches, the second segment has a second segment distance is about 0.08 inches and the convex transition region is convex with a radius of about 0.04.