Spin-stabilized non-lethal projectile with a shear-thinning fluid

Abstract

A non-lethal projectile having a shear-thinning fluid within an interior cavity. The shear-thinning fluid having a greater apparent viscosity at low shear rates to spin-stabilize the non-lethal projectile during flight and a lower apparent viscosity at a high shear rate corresponding with the shear-thinning fluid shearing against the frangible cap upon the non-lethal projectile striking the target, with the low viscosity of the shear-thinning fluid allowing proper dispersal upon impact with the target. The shear-thinning fluid can comprise a marking media and be in the form of an emulsion with less than about 50% liquid by volume to effectively disperse upon impact with the target.

Claims

1. A cartridge comprising: a cartridge casing comprising a seating portion for receiving a projectile; and the projectile received in the seating portion of the cartridge casing, the projectile comprising: a frangible shell comprising a polymeric material having an interior cavity; the frangible shell comprising a cylindrical portion, wherein the frangible shell is configured to engage rifling in a barrel so that the projectile spins when fired through the barrel; and a shear-thinning fluid within the interior cavity, the shear-thinning fluid comprising an emulsifying agent chosen from glyceryl stearate, PEG-100 stearate, petrolatum, glycol strearate, and mixtures thereof; wherein the shear-thinning fluid has a spin-stabilizing viscosity that is greater than an impact dispersing viscosity, such that the impact dispersing viscosity of the shear-thinning fluid decreases with the rate of shear at impact with a target, and the impact dispersing viscosity of the shear-thinning fluid is less than about 30 Pa.Math.s at a shear rate of about 50 Hz at about 25° C., and the impact dispersing viscosity of the shear-thinning fluid is less than about 30 Pa.Math.s at shear rates greater than about 50 Hz at about 25° C., and the spin-stabilizing viscosity of the shear-thinning fluid is greater than about 560 Pa.Math.s at shear rates less than about 2 Hz at about 25° C. in order to spin-stabilize the projectile.

2. The cartridge of claim 1, wherein the spin-stabilizing viscosity of the shear-thinning fluid is greater than about 560 Pa.Math.s at a first shear rate less than about 2 Hz at about 25° C.

3. The cartridge of claim 1, wherein the shear-thinning fluid comprises glycerin in an amount from about 50 wt % to about 70 wt %.

4. The cartridge of claim 1, wherein the shear-thinning fluid comprises water in an amount from about 12 wt % to about 20 wt %.

5. The cartridge of claim 1, wherein the shear-thinning fluid comprises an emulsifying agent in an amount from about 30 wt % to about 45 wt %.

6. The cartridge of claim 1, wherein the shear-thinning fluid comprises an acrylate crosspolymer.

7. The cartridge of claim 1, wherein the shear-thinning fluid comprises a C.sub.10-30 alkyl acrylate crosspolymer.

8. The cartridge of claim 1, wherein the shear-thinning fluid comprises an acrylate crosspolymer in an amount from about 0.4 wt % to about 0.5 wt %.

9. The cartridge of claim 1, wherein the shear-thinning fluid comprises a colorant.

10. The cartridge of claim 1, wherein the shear-thinning fluid comprises zinc oxide as a color additive.

11. The cartridge of claim 1, wherein the shear-thinning fluid comprises a shear-thinning emulsion.

12. The cartridge of claim 1, wherein the shear-thinning fluid comprises less than about 50% by volume of a liquid portion.

13. The cartridge of claim 1, wherein the shear-thinning fluid has a pH between about 7 and about 8.

14. The cartridge of claim 1 used in place of a cartridge having a conventional bullet.

15. The cartridge of claim 1 used in place of a 5.56 mm cartridge having a conventional bullet.

16. The cartridge of claim 1, used in place of a 9 mm cartridge having a conventional bullet.

17. The cartridge of claim 1, wherein the shell comprises a cup connected to a frangible cup.

18. The cartridge of claim 1, wherein the cartridge is a reduced energy cartridge adapted to propel the projectile with gases generated only by a primer.

19. A cartridge comprising: a cartridge casing comprising a seating portion for receiving a projectile; and the projectile received in the seating portion of the cartridge casing, the projectile comprising: a frangible polymeric shell having an interior cavity; the frangible shell comprising a cylindrical portion, wherein the frangible shell is configured to engage rifling in a barrel so that the projectile spins when fired through the barrel; and a shear-thinning fluid within the interior cavity; wherein the shear-thinning fluid has a spin-stabilizing viscosity that is greater than an impact dispersing viscosity, such that the impact dispersing viscosity of the shear-thinning fluid decreases with the rate of shear at impact with a target, and the impact dispersing viscosity of the shear-thinning fluid is less than about 30 Pa.Math.s at a shear rate of about 15 Hz at about 25° C., and the impact dispersing viscosity of the shear-thinning fluid is less than about 30 Pa.Math.s at shear rates greater than about 15 Hz at about 25° C., and the spin-stabilizing viscosity of the shear-thinning fluid is greater than about 130 Pa.Math.s at a first shear rate less than about 2 Hz at about 25° C. in order to spin-stabilize the projectile.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention can be completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which:

(2) FIG. 1 is a side view of a non-lethal projectile band according to an embodiment of the present invention.

(3) FIG. 2 is a cross-sectional side view of the non-lethal projectile depicted in FIG. 1.

(4) FIG. 3 is a side view of a non-lethal projectile with a driving band according to an embodiment of the present invention.

(5) FIG. 4 is a cross-sectional side view of the non-lethal projectile depicted in FIG. 3.

(6) FIG. 5 is a partial cross-sectional side view of a non-lethal cartridge for firing a non-lethal projectile having a driving band according to an embodiment of the present invention.

(7) FIG. 6 is a side view of the non-lethal cartridge depicted in FIG. 5.

(8) FIG. 7A is a graphical representation of the viscosity values of a shear-thinning exemplary embodiment of the present invention at various shear rates compared to the viscosity values of a comparative prior art marking projectile at similar shear rates.

(9) FIGS. 7B and 7C are close-up views of the graphical representation in FIG. 7A, with FIG. 7B being a close-up view at the low shear rate values less than about 4 and FIG. 7C being a close-up view at the high shear rate values greater than about 4.

(10) While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION

(11) A non-lethal projectile 2, according to certain aspects of the present invention, can comprise a shell having two or more parts that connect together to form an interior cavity 50. A shear-thinning fluid can be inserted within the interior cavity 50, the shear-thinning fluid having a greater viscosity at low shear rates to spin-stabilize the projectile during flight and a lower viscosity at higher shear rates to properly disperse the shear-thinning fluid upon impact with the target. Upon impact with the target, the shear-thinning fluid shears against pieces or shards of the shell at high shear rates such that the viscosity of the shear-thinning fluid is much lower compared to the in flight viscosity of the shear-thinning fluid. During the initial rotation of the non-lethal projectile 2, there is shear between the walls of the shell and the shear-thinning fluid, as well as between the shear-thinning fluid and itself. It is desirable that the shear-thinning fluid have enough viscosity, at the shear rate imparted by the rotation, that the rotation does not cause the shear-thinning fluid to move around inside the projectile; but instead, to properly rotate with the shell such that the non-lethal projectile is spin-stabilized and does not tumble. When the projectile strikes a target, the velocity of the projectile drops to zero immediately, leading to a high shear event. The high shear drops the viscosity of the shear-thinning fluid enough to allow the fluid to leave the projectile shell and deposit or disperse onto the target.

(12) In some aspects, the shear-thinning fluid contains a marking media, such as a colorant, a colorant with a color additive, or the like, that provides a visual marking of the projectile upon striking the target.

(13) In some aspects, in order to spin-stabilize the projectile, the shear-thinning fluid has a viscosity greater than about 560 Pa's at a shear rate less than about 2 Hz at about 25° C., and in some aspects a viscosity greater than about 560 Pa's at a shear rate less than about 3 Hz at about 25° C.

(14) In some aspects, in order to provide a proper dispersal of the shear-thinning fluid upon the target upon impact, the shear-thinning fluid has a viscosity of less than about 30 Pa's at a shear rate of about 50 Hz at about 25° C. In some aspects, the viscosity of the shear-thinning fluid is less than about 30 Pa's at shear rates greater than about 50 Hz at about 25° C.

(15) In some aspects, the shear-thinning fluid has a viscosity of about 30 Pa's or less at a shear rate of about 45 Hz or more at about 25° C., in some aspects at a shear rate of about 40 Hz or more at about 25° C., in some aspects at a shear rate of about 35 Hz or more at about 25° C., in some other aspects at a shear rate of about 30 Hz or more at about 25° C., in some other aspects at a shear rate of about 25 Hz or more at about 25° C., in some other aspects at a shear rate of about 20 Hz or more at about 25° C., and in some other aspects at a shear rate of about 15 Hz or more at about 25° C.

(16) In some aspects, the shear-thinning fluid has a viscosity of about 20 Pa's or less at a shear rates greater than about 80 Hz at about 25° C.

(17) In some aspects, the shear-thinning fluid has a viscosity of less than about 25 Pa's at a shear rate of 20 Hz or more, in some aspects at about 25 Hz or more, in some aspects at about 30 Hz or more, in some aspects at about 35 Hz or more, in some aspects at about 40 Hz or more, in some aspects at about 45 Hz or more, and in some aspects at about 50 Hz or more, at about 25° C.

(18) In some aspects, the shear-thinning fluid at a shear rate of about 2 Hz or less at about 25(' C has a viscosity greater than about 130 Pa's, in some aspects greater than about 140 Pa s, in some aspects greater than about 160 Pa's, in some aspects greater than about 180 Pa s, in some aspects greater than about 200 Pa's, in some aspects greater than about 220 Pa s, in some aspects greater than about 240 Pa's, in some aspects greater than about 260 Pa s, in some aspects greater than about 280 Pa's, in some aspects greater than about 300 Pa s, in some aspects greater than about 320 Pa's, in some aspects greater than about 340 Pa s, in some aspects greater than about 360 Pa's, in some aspects greater than about 380 Pa s, in some aspects greater than about 400 Pa's, in some aspects greater than about 420 Pa s, in some aspects greater than about 440 Pa's, in some aspects greater than about 460 Pa s, in some aspects greater than about 480 Pa's, in some aspects greater than about 500 Pa s, in some aspects greater than about 520 Pa's, in some aspects greater than about 540 Pa s, in some aspects greater than about 560 Pa's, in some aspects greater than about 580 Pa s, in some aspects greater than about 600 Pa's., in some aspects greater than about 700 Pa s, in some aspects greater than about 800 Pa's., in some aspects greater than about 900 Pa's, and in some aspects greater than about 1000 Pa's.

(19) In some aspects, the shear-thinning fluid at a shear rate of about 3 Hz or less at about 25° C. has a viscosity greater than about 130 Pa's, in some aspects greater than about 140 Pa's, in some aspects greater than about 160 Pa's, in some aspects greater than about 180 Pa's, in some aspects greater than about 200 Pa's, in some aspects greater than about 220 Pa's, in some aspects greater than about 240 Pa's, in some aspects greater than about 260 Pa's, in some aspects greater than about 280 Pa's, in some aspects greater than about 300 Pa's, in some aspects greater than about 320 Pa's, in some aspects greater than about 340 Pa's, in some aspects greater than about 360 Pa's, in some aspects greater than about 380 Pa's, in some aspects greater than about 400 Pa's, in some aspects greater than about 420 Pa's, in some aspects greater than about 440 Pa's, in some aspects greater than about 460 Pa's, in some aspects greater than about 480 Pa's, in some aspects greater than about 500 Pa's, in some aspects greater than about 520 Pa's, in some aspects greater than about 540 Pa's and in some aspects greater than about 560 Pa's, in some aspects greater than about 580 Pa's, in some aspects greater than about 600 Pa's., in some aspects greater than about 700 Pa's, in some aspects greater than about 800 Pa's., in some aspects greater than about 900 Pa's, and in some aspects greater than about 1000 Pa's.

(20) In some aspects, the shear-thinning fluid has a viscosity of about 300 Pa's to about 1000 Pa's at a shear rate less than about 1, in some aspects less than about 2 Hz, and in some aspects less than about 3 Hz, at 25° C., and wherein the shear-thinning marking fluid has a viscosity of less than about 30 Pa's at a shear rate greater than about 15 Hz, in some aspects a shear rate of about 20 Hz or more, in some aspects at about 25 Hz or more, in some aspects at about 30 Hz or more, in some aspects at about 35 Hz or more, in some aspects at about 40 Hz or more, in some aspects at about 45 Hz or more, and in some other aspects at about 50 Hz or more, at about 25° C.

(21) A marking media, according to certain aspects of the present invention, can comprise an emulsion of glycerin, water, acrylate cross-polymer and an emulsifying additive selected from the group of Glyceryl Stearate, PEG-100 Stearate, Petrolatum, Glycol Stearate and combinations thereof. Similarly, the cross-polymer can comprise, but is not limited to Carbomer ETD 2020. In one aspect, the marking media can include a colorant and a color additive such as, but not limited to, zinc oxide. In one aspect, the emulsion can comprise about or less than 50% liquid by volume. In another aspect, the marking media can further comprise a buffer including, but not limited to triethanolamine 99%.

(22) In another aspect, the emulsion can comprise about or less than 40% liquid by volume. In yet another aspect, the emulsion can comprise about or less than 25% liquid by volume. The amount of liquid in the marking media can be adjusted to provide the desired balance between dispersion of the marking media upon impact and stable shelf-life of the marking media, wherein a greater percentage of liquid improves the dispersion of the marking media upon impact and a lower percentage of liquid improves the shelf-life of the marking media. In one aspect, the marking media can have a pH 7.0 to 8.0. Similarly, the marking media can have a specific gravity of at least 0.9-1.0.

(23) A method of making the marking media, according to an embodiment of the present invention, can comprise agitating a quantity of water with the cross-polymer to hydrate the cross-polymer. In one aspect, the amount of water added corresponds to about 15 to 20 wt % of the total marking media made. Similarly, in one aspect, the amount of cross-polymer added corresponds to about 0.4 to 0.5 wt % of the total marking media made. The water and cross-polymer mixture is highly agitated until the cross-polymer is hydrated. In one aspect, the mixture is agitated for about 20 to 40 minutes. In another aspect, the mixture is agitated for about 30 minutes.

(24) After hydration of the cross-polymer, the glycerin and additives are added to the mixture and the resulting emulsion is heated to a first temperature. In one aspect, the amount of glycerin added corresponds to about 50 to 70 wt % of the total marking media made. Similarly, in one aspect, the additives added corresponds to about 30 to 45 wt % of the total marking media made. In yet another aspect, when multiple additives are used each additive is added in equal amounts such that the total amount of additives used corresponds to about 30 to 45% of the total marking media made. The first temperature can range from 65 to 85° C. in one aspect of the invention. In yet another aspect, the first temperature can be about 75° C.

(25) Once the emulsion reaches the first temperature, the buffer solution is added to the emulsion until the solution is about pH 6.0. The method is then cooled to a second temperature. In one aspect, the second temperature can be about room temperature (22° C.).

(26) In one aspect, the colorant and color additive can be added to the emulsion as the emulsion cools from the first temperature and prior to the emulsion reaching second temperature. The intermediate temperature can range from 60 to 70° C. in one aspect and can be about 65° C. in another aspect.

(27) In one aspect, after the emulsion is cooled to room temperature, the emulsion can be reheated to a third temperature until the emulsion separates into a liquid phase and a solid phase. The amount of the emulsion in the liquid phase can be about 60% by volume while the amount of the emulsion in the solid phase can be about 40% by volume in one aspect. The third temperature can be about 60 to 70° C. in one aspect and about 65° C. in another aspect. In one aspect, the emulsion can be maintained at the third temperature for about 12 to 36 hours to facilitate separation of the emulsion into liquid and solid phases.

(28) After the separation, a portion of the liquid phase can be decanted from the emulsion until the about of liquid in the emulsion is at least about or less than 50% by volume. The amount of liquid in the emulsion can be continually to at least 40% in one aspect or 25% in another aspect. Once the liquid has been decanted the emulsion can be cooled and remixed into a single phase.

(29) In one aspect, the initial amounts of water and glycerol can be lowered such that the resulting marking media is less than or about 50%. In this configuration, the reheating and decanting steps are no longer necessary.

(30) As shown in FIGS. 1 to 4, a non-lethal projectile 2, according to an embodiment of the present invention, comprises a frangible cap 4 and a projectile body 6. The frangible cap 4 can further comprise an engagement portion 8 for affixing the cap 4 to the projectile body 6. The projectile body 6 can further comprise a cup portion 10 and a base portion 12. The engagement portion 8 is receivable within the cup portion 10 to affix the cap 4 to the projectile body 6 and to define a cavity for receiving marking media. In one aspect, the projectile can further comprise a driving band 14 extending around the exterior of the projectile body 6. The driving band 14 can be positioned around the base portion 12 of the projectile body 6. A portion of the driving band 14 protrudes from outward from the projectile body 6 to engage the rifling of a barrel the projectile 2 is fired through. The projectile body 6 can further comprise a groove 16 for receiving a portion of the driving band 8 to prevent the driving band 14 from moving axially during firing.

(31) According to certain aspects, the projectile 2 can be sized to replicate the size of the bullet for 5.56×45 mm NATO (“5.56 NATO”) or 0.223 REMINGTON ammunition. The conventional bullets of 5.56 NATO cartridges and 0.223 REMINGTON have a diameter of 0.224 in (5.70 mm). In one aspect, the driving band 14 can have an outer diameter of 0.223 in (5.66 mm) and a thickness of 0.005 (0.127 mm) in such that a portion of the driving band 14 protrudes from the projectile body 6 for engaging the rifling of barrels sized for 5.56 NATO or 0.223 REMINGTON ammunition. According to an embodiment, the inner diameter of the driving band 16 can comprise 0.154 in (3.912 mm) such that a portion of the driving band 16 is seated within the projectile body 6.

(32) Although the projectile 2 is sized to approximate the conventional equivalent, the weight of the projectile 2 is less than the conventional equivalent. A conventional bullet weight for a 5.56 NATO bullet can be about 4 grams. In one embodiment, the total weight of the projectile 2 for simulating 5.56 NATO bullet and containing a payload media can weight about 0.24 grams wherein the driving band 8 comprises about 15% of the total weight of the projectile 2; in other embodiments, from 10 to 20%. In aspect, the total weight of the projectile 2 with a payload media can be about 5 to 10% of the weight of the equivalent projectile. In another aspect, the total “empty” weight of the projectile 2 without a payload media can be about 1 to 5% of the weight of an equivalent conventional projectile 2. In embodiments the total weight of the projectile is less than 5 grains. In embodiments the total weight of the projectile is less than 6 grains. In embodiments the total weight of the projectile is less than 7 grains. In embodiments the total weight of the projectile is less than 10 grains. Projectiles of less than 4.25 grains can be fired from telescoping 5.56 mm practice cartridges using only the propellant in the primer, at velocities up to about 520 fps using a metal driving band 16. With such velocities accuracy is extremely good and the kinetic energy is under 62 ft-lb/inch. This arrangement provides better accuracy and less energy than conventional 5.56 mm practice ammunition with marking projectiles. With less energy, the ammunition is safer.

(33) The projectile body 6 can comprise principally a thermoplastic polymer. Other embodiments can comprise ceramic, compressed fibrous pulp, lightweight metal or other lightweight material that can be formed to define a projectile body 6. The driving band 14 can comprise a gilding metal, a rigid polymer different from the polymer used to form the projectile body or a metal impregnated polymer. According to an embodiment, the driving band can comprise 110 Copper (99.9% copper, 0.04% oxygen). The material of the driving band 14 provides more advantageous engagement characteristics than the base material of the projectile body 6. For example, better coefficient of friction with respect to firearm barrels, less sloughing of material, easier deformation to conform to the rifling of the barrel. The frangible cap 4 can comprise a frangible material adapted to fracture upon impact with the target to release the payload within the cavity and/or reduce force with which the projectile 2 impacts the target.

(34) As shown in FIGS. 5 to 6, the non-lethal projectile 2 can be fired from a reduced energy cartridge 20 adapted to propel the projectile 2 with gases generated only by a primer 22. The cartridge 20 further comprises a cartridge casing 24, a neck portion 26 and a telescoping insert 28 adapted to telescope upon firing to trigger the cycling mechanism of the firearm. The cartridge casing 24 defines an internal cavity having a first opening 30 and a second opening 32. The neck portion 26 can comprise an insert portion 34 receivable within the first opening 30 affix the neck portion 26 to the cartridge casing 24.

(35) The neck portion 26 can also comprise a seating portion 25 for receiving the projectile 2. According to an embodiment, the neck portion 26 can be shaped to fit within the chamber of a firearm sized for 5.56 NATO cartridges. According to an embodiment, the neck portion 26 can comprise a glass filed nylon that is resistant to the temperatures associated with the hot gases.

(36) The telescoping insert 28 comprises a telescoping portion 36 and a rim 38. The telescoping portion 36 is receivable within the second opening 32 such that the rim 38 is positioned against the second opening 32. The telescoping insert 28 defines a channel 40 for receiving the primer 22 and adapted to channel gases generated by igniting the primer 22 toward the projectile 2. According to an embodiment, the telescoping portion 26 can further comprise a gasket 42 engagable to the casing 24 to prevent gases from escaping between the telescoping portion 26 and the casing 24.

(37) During firing, the projectile 2 travels through the rifled barrel of the firearm and engages the rifling of the barrel. In one aspect, the driving band 16 is engraved by the rifling of the barrel. The rifling imparts a spin to the projectile 2 such that the projectile 2 is spin stabilized once the projectile 2 leaves the barrel. The driving band 16 comprises a material of sufficient hardness that permits the driving band 16 to be etched in the same way as a conventional bullet. After the initial etching, the projectile 2 travels through the barrel with minimal friction. Upon impact with the target, the frangible cap 4 fractures dispensing the marking media contained within the cup portion 10 at the impact site.

(38) Similar projectiles directed containing marking fluid that are capable of receiving a low durometer-value core instead of marking fluid are disclosed in U.S. Pat. Nos. 7,225,741; 7,278,358; 7,621,208; 7,984,668; 8,146,505; US Patent Publication No. 2011/0252999; US Patent Publication No. 2012/0017793; US Patent Publication No. 2012/0192755; and PCT Application No. PCT/US2012/067482. The above references are herein incorporated by references in their entirety.

(39) Referring now to FIGS. 7A-7C is graphically represented the viscosity values of a shear-thinning fluid of the present invention at the various shear rates provided in the Table below. In comparison, the viscosity values at about the same shear rates of a comparative commercial non-lethal marking round are provided in FIGS. 7A-7C. The comparative commercial non-lethal marking round being a blue Simunition® 9 mm marking training ammunition. As provided in comparison to the shear-thinning fluid of the present invention, the comparative commercial round has viscosity values greater than 30 Pa's at shear rate values less than about 80 Hz, wherein the shear-thinning fluid in the non-lethal projectile of the present invention has viscosity values less than 30 Pa's at shear rate values as low as about 50 Hz.

(40) TABLE-US-00001 TABLE Shear Shear Viscosity Temperature Time (s) Stress (Pa) Rate (1/s) (Pa .Math. s) (° C.) t τ γ η T 1 0.000 0.000 0.0000 25.0 2 143.021 0.006 22711.1702 25.0 3 587.340 0.145 4055.0869 25.0 4 725.582 0.390 1858.3751 25.0 5 790.082 0.532 1484.7538 25.0 6 853.398 0.683 1248.9942 25.0 7 906.873 0.828 1095.1146 25.0 8 956.425 0.954 1002.4833 25.0 9 1,000.917 1.137 860.5613 25.0 10 1,015.976 1.244 816.8738 25.0 11 1,070.026 1.367 783.0207 25.0 12 1,125.347 1.518 741.4950 25.0 13 1,166.013 1.672 697.3931 25.0 14 1,146.835 1.795 638.9912 25.0 15 1,203.855 1.924 625.7514 25.0 16 1,226.407 2.100 583.9524 25.0 17 1,192.623 2.207 540.3233 25.0 18 1,248.494 2.355 530.0948 25.0 19 1,237.090 2.503 494.2001 25.0 20 1,277.695 2.582 494.8595 25.0 21 1,258.578 2.805 448.6122 25.0 22 1,287.828 2.856 450.9404 25.0 23 1,276.423 3.089 413.2325 25.0 24 1,308.533 3.180 411.4643 25.0 25 1,303.094 3.338 390.4259 25.0 26 1,344.823 3.416 393.6445 25.0 27 1,340.765 3.533 379.5147 25.0 28 1,366.776 3.804 359.3346 25.0 29 1,394.620 3.860 361.2718 25.0 30 1,384.890 3.930 352.4273 25.0 30 1,384.890 3.930 352.4273 25.0 31 1,380.172 4.002 344.8708 25.0 32 1,452.765 7.264 199.9937 25.0 33 1,421.682 10.702 132.8373 25.0 34 1,385.123 13.914 99.5481 25.0 35 1,317.921 17.302 76.1711 25.0 38 1,255.253 20.624 60.8638 25.0 37 1,222.459 23.914 51.1182 25.0 38 1,246.783 27.145 45.9306 25.0 39 1,259.385 30.495 41.2979 25.0 40 1,312.408 33.767 38.8670 25.0 41 1,393.886 37.092 37.5795 25.0 42 1,439.747 40.423 35.6170 25.0 43 1,398.152 43.761 31.9500 25.0 44 1,466.186 47.042 31.1679 25.0 45 1,516.251 50.326 30.1288 25.0 46 1,705.292 53.506 31.8711 25.0 47 1,768.876 56.998 31.0341 25.0 48 1,638.041 60.402 27.1192 25.0 49 1,504.419 63.654 23.6343 25.0 50 1,444.832 66.897 21.5978 25.0 51 1,495.484 70.225 21.2955 25.0 52 1,562.539 73.525 21.2517 25.0 53 1,443.451 76.857 18.7811 25.0 54 1,432.096 80.160 17.8656 25.0 55 1,401.281 83.497 16.7824 25.0 56 1,381.370 86.781 15.9178 25.0 57 1,465.122 90.037 16.2724 25.0 58 1,464.853 93.384 15.6863 25.0

(41) While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and described in detail. It is understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.