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Novel Firearm Assemblies Configured To Detect Force, Suppress Rotational Recoil, And Reduce Mechanical Distortion And Methods Of Use Thereof

20220364818 · 2022-11-17

    Inventors

    Cpc classification

    International classification

    Abstract

    The present invention relates to systems, methods, and apparatus configured to supplement the functionality of firearms such as high-precision bolt action rifle. The present invention further relates to systems, methods, and apparatus configured to increase firearm accuracy and repeatability.

    Claims

    1-16. (canceled)

    17. An improved firearm assembly comprising: a firearm having one or more interfacing components wherein said interfacing components are fabricated from materials having matching coefficients of thermal expansion (CTE) forming a CTE matched firearm; and wherein said interfacing components of said CTE matched firearm undergo coordinated thermal expansion (CTX) when exposed to a thermal condition.

    18. The firearm of claim 17 wherein said matching CTE comprise interfacing components having a difference in CTE of at least 13.6 ppm or less.

    19. (canceled)

    20. The firearm of claim 17 wherein said interfacing components comprise interfacing components selected from the group consisting of: a chassis, a receiver, a stock, a scope mount, a scope tube, a barrel, a barrel guard, a trigger guard, a folding hinge, a fore-end piece, and a grip mount.

    21. The firearm of claim 17 wherein said interfacing components are fabricated from a material selected from the group consisting of: steel, steel alloy, precipitation hardened steel, 4130 steel; 4140 steel; 4150 steel, 416 steel, 17-4 steel, aluminum, aluminum alloy, 7075 aluminum, titanium, titanium grade 5, titanium Ti-6Al-4V, titanium alloy, wood, composite material, carbon fiber composite, or a combination of the same wherein the components have difference in CTE of at least 13.6 ppm or less.

    22-23. (canceled)

    24. The firearm of claim 17 wherein said firearm having undergone CTX has increased resistance to thermal-induced mechanical distortion.

    25. The firearm of claim 17 and further comprising: said CTE matched firearm is assembled at a first thermal environment forming a zero-state CTE matched firearm; and wherein said zero-state CTE matched firearm is operated at a second thermal environment, wherein said second thermal environment is the same as said first thermal environment, and wherein said CTE matched firearm resists thermal-induced mechanical distortion.

    26. The firearm of claim 25 wherein said first and said second thermal environments are selected from the group consisting of: thermal environments above room temperature, first and said second thermal environments, a thermal environment between 20° C. and 75° C., and a thermal environment between 19.9° C. and −40° C.

    27-29. (canceled)

    30. The firearm of claim 25 and further comprising wherein said zero-state CTE matched firearm is assembled at a third thermal environment forming a zero-state assembly for said firearm.

    31. The firearm of claim 30 and further comprising wherein said zero-state assembly for said firearm is operated at a fourth thermal environment, wherein said fourth thermal environment is the same as said third thermal environment.

    32. The firearm of claim 25 wherein said thermal condition comprises a thermal condition generated by firing said firearm.

    33-45. (canceled)

    46. A firearm assembly comprising: a firearm having one or more interfacing components assembled at a first thermal environment forming a zero-state assembly for said firearm, wherein said interfacing components of said firearm include matching coefficients of thermal expansion (CTE) forming a zero-state CTE matched firearm; and wherein said a zero-state CTE matched firearm is operated at a second thermal environment, wherein said second thermal environment is the same as said first thermal environment, and wherein said CTE matched firearm resists thermal-induced mechanical distortion.

    47. The firearm of claim 46 wherein said first and said second thermal environments are selected from the group consisting of: thermal environments above room temperature, first and said second thermal environments, a thermal environment between 20° C. and 75° C., and a thermal environment between 19.9° C. and −40° C.

    48-50. (canceled)

    51. The firearm of claim 46 wherein said interfacing components comprise interfacing components selected from the group consisting of: a chassis, a receiver, a stock, a scope mount, a scope tube, a barrel, a barrel guard, a trigger guard, a folding hinge, a fore-end piece, a bolt, a screw, a coupler, and a grip mount.

    52. The firearm of claim 46 wherein said interfacing components have a difference in CTE of at least 13.6 ppm or less.

    53. The firearm of claim 46 wherein said interfacing components are fabricated from a material selected from the group consisting of: steel, steel alloy, precipitation hardened steel, 4130 steel; 4140 steel; 4150 steel, 416 steel, 17-4 steel, aluminum, aluminum alloy, 7075 aluminum, titanium, titanium grade 5, titanium Ti-6Al-4V, titanium alloy, wood, composite material, carbon fiber composite, or a combination of the same wherein the components have difference in CTE of at least 13.6 ppm or less.

    54-55. (canceled)

    56. The firearm of claim 46 wherein said interfacing components are coupled with one or more thermal expansion joints.

    57. The firearm of claim 46 wherein said zero-state CTE matched firearm is reassembled at a third thermal environment forming a zero-state assembly for said firearm.

    58. The firearm of claim 57 wherein said zero-state assembly for said firearm is operated at a fourth thermal environment, wherein said fourth thermal environment is the same as said third thermal environment.

    59. The firearm of claim 46 wherein said firearm comprises a bolt-action rifle.

    60-66. (canceled)

    67. A firearm assembly comprising: a firearm having an interfacing chassis and receiver assembled at a first thermal environment forming a zero-state interfacing chassis and receiver assembly for said firearm, wherein said interfacing chassis and receiver of said firearm include matching coefficients of thermal expansion (CTE) forming a zero-state chassis and receiver assembly; and wherein said firearm having a zero-state chassis and receiver is operated at a second thermal environment, wherein said second thermal environment is the same as said first thermal environment, and wherein said zero-state chassis and receiver resists thermal-induced mechanical distortion.

    68-201. (canceled)

    Description

    BRIEF DESCRIPTION OF THE FIGURES

    [0332] The accompanying figures, which are incorporated into and form a part of the specification, illustrate one or more embodiments of the present invention and, together with the description, serve to explain certain aspects of the inventive technology. The drawings are only for the purpose of illustrating one or more preferred embodiments of the invention and are not to be construed as limiting the invention.

    [0333] FIG. 1—shows a firearm chassis and receiver assembly under a uniform thermal condition of 120° F. (48.89° C.) in one embodiment thereof;

    [0334] FIG. 2—shows mechanical distortion along a Z-axis of a firearm chassis and receiver having a different CTE in response to the application of a heat load in one embodiment thereof;

    [0335] FIG. 3—shows mechanical distortion along a Z-axis of a firearm receiver having different CTE that a corresponding chassis in response to the application of a heat load in one embodiment thereof;

    [0336] FIG. 4—shows a data set describing the thermal deformation in a firearm receiver in response to varying CTE of an Aluminum chassis in one embodiment thereof;

    [0337] FIG. 5—shows CTE/degC of commonly used exemplary material in one embodiment thereof;

    [0338] FIG. 6—shows the initial set-up to test the sensitivity of the system to the CTE of the fore-end support, trigger guard and grip mount in one embodiment thereof;

    [0339] FIG. 7—shows a side view of an improved segmented firearm chassis having a plurality of expansion joints in one embodiment thereof;

    [0340] FIG. 8—shows a rear view of an improved segmented firearm chassis having a plurality of expansion joints in one embodiment thereof;

    [0341] FIG. 9—shows a bottom perspective view of an improved segmented firearm chassis having a plurality of expansion joints in one embodiment thereof;

    [0342] FIG. 10—shows a top view of an improved segmented firearm chassis having a plurality of expansion joints in one embodiment thereof;

    [0343] FIG. 11—shows a top perspective view of an improved segmented firearm chassis having a plurality of expansion joints in one embodiment thereof;

    [0344] FIG. 12—shows a cross-sectional view of a plurality of expansion joints coupling a trigger guard to an exemplary firearm chassis in one embodiment thereof;

    [0345] FIG. 13—shows a close-up cross-sectional view of a plurality of expansion joints coupling a trigger guard to an exemplary firearm chassis in one embodiment thereof;

    [0346] FIG. 14—shows mechanical distortion along the Z-axis for a steel scope having a single piece mismatched CTE mount configuration in one embodiment thereof;

    [0347] FIG. 15—shows mechanical distortion along the Z-axis for a steel scope having a two piece mismatched CTE mount configuration in one embodiment thereof;

    [0348] FIG. 16—shows mechanical distortion along the Z-axis for an aluminum scope having a single piece mismatched CTE mount configuration in one embodiment thereof;

    [0349] FIG. 17—shows mechanical distortion along the Z-axis for an aluminum scope having a two piece mismatched CTE mount configuration in one embodiment thereof;

    [0350] FIG. 18—shows a mockup of a of a single piece mount configuration.

    [0351] FIG. 19—shows a mockup of a of a two piece mount configuration.

    [0352] FIG. 20.—shows a front view of a rotational recoil dampener having a cross-sectioned fluid track secured to an exemplary coupler in one embodiment thereof;

    [0353] FIG. 21.—shows a front view of a rotational recoil dampener having a cross-sectioned fluid track having a top and bottom spring coupled with a block in one embodiment thereof;

    [0354] FIG. 22.—shows a perspective view of a rotational recoil dampener having a cross-sectioned fluid track having a top and bottom spring coupled with a block in one embodiment thereof;

    [0355] FIG. 23.—shows a top view of a rotational recoil dampener positioned around a firearm mount in one embodiment thereof;

    [0356] FIG. 24.—shows a top view of a mass block having a block aperture in one embodiment thereof;

    [0357] FIG. 25.—shows a top view of a rotational recoil dampener with a mass block having a block aperture positioned around a firearm mount in one embodiment thereof;

    [0358] FIG. 26.—shows a top view of a rotational recoil dampener positioned around a firearm mount in one embodiment thereof;

    [0359] FIG. 27.—shows a front perspective view of a vectored muzzle brake in one embodiment thereof;

    [0360] FIG. 28.—shows a front perspective view of a vectored muzzle brake in one embodiment thereof;

    [0361] FIG. 29.—shows a front cross-sectional view of a vectored muzzle brake in one embodiment thereof;

    [0362] FIG. 30.—shows a side cross-sectional view of a vectored muzzle brake in one embodiment thereof;

    [0363] FIG. 31.—shows a front perspective view of a vectored suppressor in one alternative embodiment thereof;

    [0364] FIG. 32.—shows a side view of a vectored suppressor in one alternative embodiment thereof;

    [0365] FIG. 33.—shows a front perspective view of a vectored suppressor in one alternative embodiment thereof;

    [0366] FIG. 34.—shows a side cross-sectional view of a vectored suppressor in one embodiment thereof;

    [0367] FIG. 35.—shows a side cross-sectional view of a vectored suppressor in one embodiment thereof;

    [0368] FIG. 36.—shows a side cross-sectional line drawing view of a vectored suppressor in one embodiment thereof;

    [0369] FIG. 37.—shows a front cross-sectional view of a vectored suppressor in one embodiment thereof;

    [0370] FIG. 38.—shows a generalized schematic diagram of a firearm buttstock force detection system in one embodiment thereof;

    [0371] FIG. 39.—shows an exemplary circuit (9) that may be incorporated into a firearm buttstock force detection system in one embodiment thereof;

    [0372] FIG. 40.—shows a detailed front perspective view of a firearm buttstock force detection system in one embodiment thereof;

    [0373] FIG. 41.—shows a detailed expanded perspective view of a firearm buttstock force detection system in one embodiment thereof;

    [0374] FIG. 42.—shows a detailed top view of a firearm buttstock force detection system in one embodiment thereof;

    [0375] FIG. 43—(A,B) Numerical and graphical description of horizontal and vertical shift over time of firearm receiver and chassis at increasing temperatures. ASA description shows a CTE matched receiver and chassis while industry standard shows a mismatched CTE receiver chassis thermal-induced mechanical distortion having a difference in CTE of 13.7 ppm. The Matched CTE receiver and chassis being more resistant to thermal-induced mechanical distortion; and

    [0376] FIG. 44—(A-B) shows the comparison of the angular acceleration of a firearm with and without a rotational recoil dampener of the invention (ASA Muzzle Thruster); (C-D) shows the comparison of the angular position of a firearm with and without a rotational recoil dampener of the invention; (E-F) shows the comparison of the angular velocity of a firearm with and without a rotational recoil dampener of the invention; (G-J) shows the comparison of the overall firearm dynamics with and without a rotational recoil dampener of the invention. Data calculated according to Table 1.

    MODE(S) FOR CARRYING OUT THE INVENTION(S)

    [0377] The present invention relates to firearms and, more particularly, to the interfacing firearm components of high-precision bolt-action rifles configured to improve its shooting accuracy and to supplement its functionality. The present invention further relates to novel strategies to compensate for mechanical distortion generated when interfacing firearm components are made from a material with a mismatched CTE. The present invention further relates to novel strategies to compensate for mechanical distortion generated when interfacing firearm components that may further include the same or similar CTEs, are assembled in one thermal environment, but operated in a second, different thermal environment.

    [0378] Embodiments of the present invention relate to firearms and, more particularly, to the matching of CTEs of interfacing firearm components of high-precision bolt-action rifles configured to improve shooting accuracy and to supplement functionality. The present invention further relates to novel strategies to compensate for mechanical distortion generated when interfacing firearm components are made from materials with mismatched CTEs and then exposed to a range of different temperatures, relative to the temperature at which they were assembled. Although many firearm components are considered here and will be presented in further detail, some of the major notable components which most notably improve accuracy from being machined from matching CTEs materials include rifle chassis, stocks, scope mounts, scope tubes, etc.

    [0379] One embodiment of the present invention relates to firearms and, more particularly, to interfacing components of rifles that may or may not be the same material but such that they are configured to have matching CTEs. In a preferred embodiment, one or more interfacing firearm components may be assembled at a first thermal environment forming a zero-stress temperature state for that assembly. This first thermal environment may be customized, or manipulated to match, or approximate a second thermal environment where the rifle may be operated. For example, in one preferred embodiment, one or more interfacing firearm components that may be operated in a high-temperature environment, such as a desert or in the summertime, may be assembled in a heated first thermal environment forming a zero-stress temperature state for that assembly that may match the second thermal environment where the rifle may be operated. In another preferred embodiment, one or more interfacing firearm components that may be operated in a low-temperature environment, such as the tundra, or in the winter, may be assembled in a cooled first thermal environment forming a zero-stress temperature state for that assembly that may match the second thermal environment where the rifle may be operated.

    [0380] Another embodiment of the present invention relates to a novel CTE optimized firearm assembly. In this preferred embodiment, one or more interfacing firearm components may be formed from material having the same or similar CTE. In certain embodiments, a CTE optimized firearm assembly may include one or more directly or indirectly interfacing components. In alternative embodiments a CTE optimized firearm assembly may include one or more interfacing firearm components, where only the interfacing portion of the components may be formed from material having the same or similar CTE. Such hybrid components may be coupled with one or more expansion joints as herein described.

    [0381] In another preferred embodiment, a CTE optimized firearm assembly may include a firearm assembly incorporating two or more of the following interfacing firearm components: a chassis, a receiver, a stock, a scope mount, a scope tube, a barrel, a barrel guard, a trigger guard, a folding hinge, a fore-end piece, and grip mounts among others.

    [0382] In another embodiment, one or more interfacing firearm components having the same or similar CTE that may be operated in a low-temperature environment, such as the tundra, or in the winter, may be assembled in a cooled first thermal environment forming a zero-stress temperature state for that assembly that may match the second thermal environment where the rifle may be operated.

    [0383] Additional embodiments of the invention include novel design features for one or more thermal expansion joints that may be designed for use with a firearm, and more particularly interfacing firearm components, and even more preferably hybrid particularly interfacing firearm components. This novel technology allows hybrid interfacing firearm components to be made from a material with a mismatched CTE, for example to the receiver, stock, or chassis, and still not cause mechanical deformations to the receiver, stock, or chassis as a result of temperature changes. The inventive technology allows for an accurate precision rifle system that is insensitive to thermal excursions for a reduced price of manufacturing.

    [0384] The invention may include a novel firearm chassis or stock assembly configured to improve the accuracy of said firearm. In one preferred embodiment, the invention may include a novel firearm chassis or stock assembly configured to improve the accuracy of a precision bolt-action rifle system. This novel firearm chassis or stock assembly may thermodynamically optimize, for example a precision bolt-action rifle, or other traditional rifle configuration. Such optimization may extend across a broad range of temperatures that may be generated through operation of such a firearm. The invention's novel firearm chassis and stock assembly may be especially applicable to high-end precision rifles that are used in competitive target sports, military applications, and the like.

    [0385] Another embodiment of the present invention is to provide an improved firearm stabilization and recoil control apparatus for a firearm. In one preferred embodiment, the invention may include a firearm stabilization and recoil control apparatus configured to reduce rotational recoil generated from the operation of a firearm. Another embodiment of the invention includes a rotational recoil dampener configured to absorb rotational energy of a firearm both during the shot and until the gun has come to rest rotationally. Another embodiment of the invention includes methods of using a rotational recoil dampener configured to absorb rotational energy of a firearm both during the shot and until the gun has come to rest rotationally.

    [0386] Another embodiment of the invention includes a rotational recoil dampener configured to be rigidly secured to a firearm that may reduce rotational recoil and increase firing accuracy and repeatability. Another embodiment of the invention includes a rotational recoil dampener for a firearm which can be utilized with various sizes and styles of weapon, is easily adjustable and portable, and is simple and inexpensive to manufacture. Another embodiment of the invention includes a rotational recoil dampener configured to convert rotational energy generated from the operation of a firearm into heat that may be dissipated thereby reducing the rotational recoil generation from the operation of a firearm.

    [0387] Another embodiment of the invention includes a rotational recoil dampener having one or more fluid filled tracks having a spring supported block that allows fluid communication of a viscous fluid, such as an oil. Another embodiment of the invention includes systems and methods of coupling a rotational recoil dampener to a firearm. Another embodiment of the invention may include a novel muzzle brake configured to suppress rotational recoil of the firearm during operation. Another embodiment of the invention may include a novel muzzle brake configured to redirect exhaust gasses from the operation of the firearm such that rotational recoil is counteracted. In one preferred embodiment, the invention may include a novel muzzle brake having a plurality of vectored exhaust ports configured to redirect exhaust gasses from the operation of the firearm such that the redirected exhaust gasses are released from the muzzle brake so as to counteract the rotational recoil of the firearm during operation.

    [0388] Another embodiment of the invention may include a novel muzzle brake for a firearm which can be utilized with various sizes and styles of weapon, is easily adjustable and portable, and is simple and inexpensive to manufacture. Another embodiment of the invention may include a novel suppressor configured to incorporate embodiments of a muzzle break for linear recoil while also suppressing the noise of the firearm during operation.

    [0389] Another embodiment of the invention may include a novel suppressor configured to redirect exhaust gasses from the operation of the firearm such that rotational recoil is counteracted, while also suppressing the noise of the firearm during operation. In one preferred embodiment, the invention may include a novel suppressor having a plurality of vectored exhaust ports configured to redirect exhaust gasses from the operation of the firearm such that the redirect exhaust gasses are released from the suppressor so as to counteract the linear and rotational recoil of the firearm during operation. Another embodiment of the invention may include a novel suppressor for a firearm which can be utilized with various sizes and styles of weapon, is easily adjustable and portable, and is simple and inexpensive to manufacture.

    [0390] Another embodiment of the inventive technology includes a novel firearm buttstock force detection system. In a preferred embodiment, the inventive technology may include a system that allows measurement of force applied from the user's shoulder to the rifle's buttstock which may further be displayed to the shooter in real time. Another embodiment of the invention allows for the collection of force measurements that may be stored for later display.

    [0391] Another embodiment of the inventive technology includes a novel firearm buttstock force detection system that allows the shooter to apply a consistent amount of force to firearm, and preferably a precision rifle system like those used in competitive shooting events or military applications. This is critical since the more consistent of a force a shooter applies to the buttstock of the precision rifle system, the more consistent the velocity of the shot will be and the more consistent the shooter's recoil management will be, both of which improve accuracy. Since the ability to hit a target at long ranges depends on the shooters ability to predict the speed of the bullet and consistently manage recoil, this novel technology helps the shooter hit targets more reliably. Real time force measurements can be presented to the shooter as he takes aim or reported to the shooter after a shot to practice repeatability.

    [0392] Another embodiment of the inventive technology includes a novel firearm support force detection system that allows the shooter to apply a consistent amount of force to firearm, and preferably a precision rifle system like those used in competitive shooting events or military applications. In a preferred embodiment, a novel firearm support force detection system may be incorporated into a bipod, or other similar rifle support device. In another preferred embodiment, a novel firearm support force detection system may be configured to detachable couple a bipod, or other similar support, to a rifle' s stock. Another embodiment of the invention may include a force detection system having a spring scale instrument positioned in line with the load path. In this preferred embodiment, as force is applied, a calibrated spring scale may be actuated and provide a manual display of the force measurement.

    [0393] As used herein, the term “matching” means two interfacing components that have the same CTE, or that their CTEs are sufficiently similar to prevent thermal-induced mechanical distortion. In one preferred embodiment, a “matching” may include two interfacing components having a difference in CTE of 13.6 or less irrespective of the material used. As also used herein, the term “firearm” means any device, assembly, or apparatus that can file a projectile. Examples of a firearm can include a rifle, pistol, artillery, howitzer, mortar, cannon, shotgun, carbine, automatic rifle, bolt action rifle, and the like.

    [0394] The invention now being generally described will be more readily understood by reference to the following examples, which are included merely for the purposes of illustration of certain aspects of the embodiments of the present invention. The examples are not intended to limit the invention, as one of skill in the art would recognize from the above teachings and the following examples that other techniques and methods can satisfy the claims and can be employed without departing from the scope of the claimed invention. Indeed, while this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.

    EXAMPLES

    Example 1

    Reduction of Mechanical Distortion Resulting From Novel CTE Optimized Firearm Assembly

    [0395] One embodiment of the invention may be directed to a novel firearm chassis or stock assembly. As generally shown in FIG. 1, this embodiment may include a CTE optimized interface between the chassis (1) and the receiver (2), and preferably a rifle chassis and a rifle receiver. The CTE optimized interface of the invention may include a CTE optimized interface whereby the rifle chassis (1) and the rifle receiver (2) have the same, or approximately the same CTE. Further, in this embodiment, the CTE optimized interface between the rifle chassis (1) and the rifle receiver (2) may be configured in a first thermal environment zero-stress temperature such that the assembly is in a zero-stress state at the temperature of the first thermal environment.

    [0396] In this configuration, the receiver (2) or chassis (1) assembly may be introduced to a second thermal environment such that the temperature differential between the first and second thermal environments may cause the mechanical distortion of the receiver (2) or chassis (1), such as the physical expansion or contraction of the component along one or more axes. In this specific embodiment, both the chassis (1) and receiver (2) maintain the same, or approximately the same CTE, which may allow both the receiver (2) and chassis (1) to undergo mechanical distortion in a synchronized fashion. As a result, the CTE optimized interface eliminates any mismatched mechanical distortions between the chassis (1) and receiver (2) making the firearm insensitive to thermal excursions that may result from a mismatched CTE.

    [0397] In another embodiment, a rifle chassis (1) and the rifle receiver (2) may be configured in a first thermal environment zero-stress temperature such that the assembly is in a zero-stress state at the temperature of the first thermal environment. However, in an alternative preferred embodiment, the rifle chassis (1) and the rifle receiver (2) may be configured in a heated or cooled environment that may match or approximate a second thermal environment where the firearm may be stored or operated. In this embodiment, the rifle chassis (1) and the rifle receiver (2) may be configured in a zero-stress temperature to form a zero-stress state that corresponds to the second thermal environment. When the assembly is reintroduced to a first thermal environment, for example during the manufacture of the other components of the firearm it may undergo mechanical distortion or deviate from its zero-stress state. However, when the firearm is introduced to the second thermal environment, the receiver (1) and chassis (2) assembly may revert back to its zero-stress state formed at the time of assembly. It should be noted that the use of a receiver (2) and chassis (2) are exemplary only. In certain embodiment, the invention as described above may extend to firearm assemblies including, but not limited to: receivers (2), chassis (1), scopes (15), scope mounts (16), stocks, or any interfacing firearm component.

    [0398] Again, referring to FIG. 1, in one preferred embodiment a rifle chassis (1) may be made of a material that has the same, or approximately the same CTE to that of the rifle receiver (2) and vice versa. In one example, the entire chassis may be constructed out of materials having the same or similar CTE as the corresponding receiver and vice versa. In yet another embodiment, a firearm chassis (1) may be configured such that a portion, and preferably the portion of the firearm chassis (2) that interfaces with a receiver (2), may be constructed out of materials having the same or similar CTE as the corresponding receiver (2) and vice versa. In each of the embodiments outlined above, the CTE optimized interface may reduce stress and mechanical deformation on the receiver as a result of a mismatched CTE when the thermal environment is different than the environment at which it was assembled.

    Example 2

    Novel Firearm Chassis System

    [0399] The present inventors conducted a plurality of Finite Element Analyses (“FEA”) that compare different strategies for the design, manufacturing and assembly of a precision rifle system incorporating the inventive technology described herein. Here, the present inventors simulated the effects of the application of a thermal load mimicking the introduction of a rifle chassis and receiver assembly having a mismatched CTE to a second thermal environment. In the embodiment shown in the figures, the initial assembly includes a stainless-steel receiver, mounted to an aluminum chassis with aluminum or plastic fore-end pieces, trigger guards and grip mounts. The assembly is then modeled at a Thermal Condition (Temperature) of 120° F. (48.9° C.). A slender bar of equal length and modeled as 6061 Al supports the assembly with a fixed support at the far end from the chassis. This effectively acts as a far-field boundary condition (i.e. it allows the analysis to solve but it will not affect the results of the analysis). As commonly designed, manufactured, and assembled using traditional practices, the receiver may be modeled as 416 Stainless Steel and the chassis is made of 6061-T6 Aluminum, having different CTEs.

    [0400] As generally shown in FIGS. 1-3, mechanical deformation of the receiver and chassis assembly occurs at a modeled temperature of 120° F. (48.9° C.), which simulates a second thermal environment. Notably, the zero-stress temperature for this model assembly was assumed to be standard room temperature of 71.6° F. (22° C.). As noted above, when a firearm, assembled at room temperature, is exposed to a higher second thermal environment, the entire assembly deforms in the Z axis due to the CTE mismatch between the receiver and the chassis. The same thermal deformation occurs when a firearm, assembled at room temperature, is exposed to a lower second thermal environment, although the deformation would occur in the opposite direction.

    [0401] As further shown in FIG. 3, it is also possible to examine mechanical distortion in a receiver (shown here in isolation), since this is the component that has the greatest contribution to accuracy and point-of-aim stability. In this example, the present inventors generated a similar model as described above, however the CTE property for the aluminum chassis was varied from 0 ppm to 23.6 ppm (the actual CTE of aluminum) and the receiver deformation plotted. As shown in FIG. 4, as the chassis CTE approaches 9.9 ppm (the CTE of the receiver) the deformation of the receiver decreases.

    [0402] Notably, the present inventors have discovered empirically that the closer the CTE of the chassis is to the CTE of the receiver, the more stable over temperature the chassis and receiver may be. By more closely matching the CTE between the receiver and chassis, even as the temperature of the firearm changes, there may be less mechanical distortion induced on the receiver and thus less deformation between interfacing components. This reduced distortion equates to improved accuracy at any temperature.

    [0403] Since CTE is a functional aspect of a material, and cannot be significantly changed, other materials may be investigated that have a CTE closer ˜9.9 ppm. FIG. 5 highlights some commonly available materials and their CTEs. Several of the different stainless steels that may be used in the construction of a firearm have CTEs that are similar to 416 Stainless Steel, but raw material pricing and machinability make their practical use limited—for example, 416 Stainless Steel is prohibitively expensive to buy or to machine competitively. This is exacerbated if the other pieces to the rifle chassis system (fore-end support, trigger guard and grip mount) must also be made from a material that matches the CTE of the receiver.

    [0404] To address these limitations in traditional firearm design, an analysis was performed to determine the sensitivity of the system to the CTE of the fore-end support, trigger guard, and grip mount as shown in FIG. 6. In this embodiment, if the fore-end piece, trigger guard and grip mount are built from 416 Stainless Steel (as if to be cut out from a larger billet as one component or just as standalone parts), to match the receiver, then the predicted deformation as analyzed in the same manner as described above generally. Compared to traditional aluminum chassis, by more closely matching the assemblies CTEs, the inventive technology allows for a precision firearm system that is more than 7.38 times as accurate at 48.9° C.

    [0405] It should be noted that additional interfaces within a firearm's assembly may be configured to have matching CTEs. For example, various couplers, bolts or other interface components that join one or more firearm components together may be configured to have matching CTEs and may further be assembled at a desired or predicted second thermal environment to optimize the zero-stress state when the firearm is in actual operation by a user. For example, in one preferred embodiment, a scope (15), and scope mount (16) positioned on top of a receiver may be configured to have a matching CTE with a receiver, chassis or stock such that mechanical distortion that may occur from operation of the firearm may be substantially reduced or eliminated. In another preferred embodiment, a scope, and scope mount positioned on top of a receiver may further be assembled at a desired or predicted second thermal environment to optimize the zero-stress state of the scope (15) and scope mount (16) as generally shown in FIGS. 14-18 assembly when the firearm is in actual operation by a user.

    Example 3

    Hybrid Firearm Components and Directional Expansion Joints

    [0406] As shown in FIGS. 7-11, in one preferred embodiment only the direct chassis interface to the receiver may be made from a matching or similar CTE material, such as 416 Stainless Steel, 17-4 Steel, etc. while the secondary chassis pieces, fore-end pieces, trigger guards and grip mounts may be made from aluminum, or another less expensive material. As shown in FIGS. 7-11, in this embodiment having a hybrid CTE chassis (3) may require the use of a thermal expansion joint, and preferably a directional expansion joint (4).

    [0407] In one preferred embodiment, a firearm chassis may include a hybrid firearm chassis (3). Generally referring to FIG. 7, a hybrid component, in this embodiment a hybrid chassis (3) may include a matching CTE interface (5), shown here as the upper portion of the chassis. This matching CTE interface (5) may be configured to match the CTE of one or more corresponding assembly parts, such as a receiver, or coupler configured to secure the chassis to the receiver and the like. A hybrid chassis (3) may further include a variable CTE interface (6), preferably made from a less expensive material such as aluminum that may have a different CTE than the matching CTE interface (5). As shown in FIG. 7, a variable CTE interface (6) may include the lower portion of a chassis, as well as secondary components such as a trigger guard and the like.

    [0408] In one preferred embodiment, a hybrid chassis (3), or any hybrid firearm components such as a stock, scope mount or scope for that matter, may include one or more directional expansion joints (4). A directional expansion joint (4) may be configured to restrain mechanical distortion between portions of a hybrid chassis (3) or other components that have differential CTEs.

    [0409] Referring again to FIGS. 7-11, in one preferred embodiment, a directional expansion joint (4) may include a variable anchor (7) coupling the variable CTE interface (6) with a support (8), which in this case is shown as a linear rod positioned parallel to the hybrid chassis (3). This support (8) may be coupled with a CTE interface anchor (9) secured to the CTE interface (5) of the chassis. In this preferred embodiment, the coupling between the support (8) and CTE interface anchor (9) may be tractable, such that thermal expansion resulting from operation of the firearm is constrained and re-directed along the X axis minimizing distortion that may negatively affect accuracy and point-of-aim stability.

    [0410] In another preferred embodiment, a hybrid chassis (3), or any hybrid components for that matter, may include one or more expansion slots (10). In a preferred embodiment, an expansion slot (10) may include one or more slot position between components that may allow for expansion along a desired axis. In a preferred embodiment, as shown in FIG. 7, an expansion slot (10) may be positioned between the trigger guard and variable CTE interface (6). In this configuration, mechanical distortion, re-directed along the X axis by one or more directional expansion joints (4), may allow the different components of an assembly having differential CTEs to expand along a desired axis where the expansion slot (10) provides a voided space to accept this expansion and prevent undesired contact between assembly components.

    Example 4

    Thermal Expansion Joint Assembly

    [0411] The invention may further include one or more thermal expansion joints (11) that may be used to affix one or more secondary components, such as additional chassis pieces, fore-end pieces, trigger guards and grip mounts, to a primary rifle component such as a chassis, stock, and the like. In a preferred embodiment, one or more secondary components, such as a trigger guard shown in FIG. 12, may be coupled with a primary rifle component such as a chassis so as to be aligned with the rifle's X axis (which generally aligns with the bore of the rifle). In these configurations, the secondary component may be held rigidly in the Y- or Z-axes but may be allowed to slide along the X axis with respect to the coupled primary component such as a chassis. The thermal expansion joint allows one or more secondary components to expand or contract in response to heat generated or lost from ambient conditions or from operation of the firearm that may cause the mechanical distortion of primary components such as a chassis or receiver. In a specific embodiment, a thermal expansion joint allows a secondary component such as a fore-end piece, trigger guard or grip mount to expand or contract at different rates compared to the chassis such that no added stress is placed on the chassis system due to any mechanical distortion. The thermal expansion joint of the invention further prevents stress from being introduced to a receiver that might cause bending about the Y axis and a subsequent loss in accuracy.

    [0412] Again, referring to FIGS. 11-12, in a preferred embodiment a trigger guard, or other secondary components, may be coupled to a chassis with a plurality of thermal expansion joints (11). In this preferred embodiment, a thermal expansion joint (11) may include one or more mounting bolts (12) positioned within an aperture having a larger diameter than the mounting bolt. This configuration forms a voided space (13) as shown in the figures. The mounting bolt (12) may be further coupled with one or more washers (14), and preferably Teflon® washers that may allow sliding of the firearm components, in this case being a trigger guard within the voided space (13). In this configuration, the invention's thermal expansion joint (11) may form a secure mount for one or more secondary components, while also allowing for thermal expansion that may occur in response to the heat generated from introduction of the firearm into a thermal environment that is different than the thermal environment present during assembly of the firearm's components. Importantly, the invention's thermal expansion joint provides a sliding buffer in response to mechanical distortion such that it is not passed to the chassis or receiver which may reduce overall accuracy of the firearm during operation.

    [0413] Is should be noted that embodiments described herein may include a variety of firearm components that include one or more of the inventive features described above. For example, a chassis, receivers, scope mounts, scope tubes couplers and bolts, stocks, fore-end pieces, trigger guards and grip mounts may be configured to have matching CTEs or may further be configured as hybrid components having one or more thermal expansion joints as generally described herein.

    Example 5

    Rotational Recoil Dampener, Improved Muzzle Break, and Improved Suppressor

    [0414] The present inventors have developed a novel rotational recoil dampener (17) configured to be coupled with a firearm and counter the rotational recoil force generated through operation of said firearm. As generally shown in FIG. 20, a rotational recoil dampener (17) may include one or more fluid tracks (18) that may be mounted to a firearm. In this preferred embodiment, the fluid track (18) may be a curved fluid filled chamber that may be positioned over, for example a firearm's barrel or other component. The fluid track (18) may contain a quantity of a viscous fluid, such as oil that may be in fluid communication throughout the fluid track (18). Again, referring to FIG. 20, in a preferred embodiment, two fluid tracks (18) may be positioned in an opposing paired fashion to more effectively dampen the rotational recoil generated from operation of the firearm. Here, the rotational recoil dampener (17) may include a coupler (22) component that may be configured to allow the rotational recoil dampener (17) to be rigidly secured to a firearm. In one embodiment, one, or a plurality of rotational recoil dampeners (17) having opposing paired fluid tracks (18) may be coupled to a firearm mount (23) which may be generally described as a firearm component that may be configured to secure a rotational recoil dampener (17).

    [0415] Referring now to FIGS. 21-22, one or more block (20) components may be positioned within a fluid track (18) and further secured by one or more springs (19) coupled to the ends of the fluid track (18). In a preferred embodiment, a block (20) may have a defined mass, and one or more block apertures (21) allowing fluid communication of the fluid within the fluid track (18) across the block (20) component. In this configuration, operation of a firearm may cause a rotational recoil force that may cause the fluid, in this case a viscous oil, to pass through the block aperture (21) of the block (20) component transferring the rotational energy from the rotational recoil into heat. Notably, as rotational recoil is present in the operation of all firearms, and in particular those firing heavy bullets at high speed and/or high twist rates, the rotational recoil dampener (17) of the current invention may be configured to be adaptable to a variety of firearm types. In one embodiment each of the components of the rotational recoil dampener (17) may be adjusted to be optimized for a firearm having a known rotational recoil profile. For example, the viscosity of the fluid with the fluid track (18), the spring size and/or constants, the block (18) mass, and the size and shape of the block aperture (21) may be adjusted to be optimized for a firearm having a known rotational recoil profile.

    [0416] The invention may include a novel and improved muzzle brake (24) configured to suppress rotational recoil generated by operation of the firearm, for example as generated by a rapidly rotating a bullet traveling down a rifled barrel. In one preferred embodiment, the muzzle brake (24) of the invention may be configured redirect high-pressure, high-velocity gases exiting the barrel in a vector that is counter to the linear and rotational recoil of the firearm such that the escaping gasses provided a counter to the rotational recoil of the firearm as the bullet is ejected from the barrel.

    [0417] Generally referring to FIGS. 27-30, in one embodiment a muzzle brake (24) may include a barrel attachment (25), such as an internally threaded position that may be securely mated with the end of a barrel thereby coupling the body (26) of the muzzle brake (24) to the firearm. In this preferred embodiment, the one or more vectored discharge channels (27) may be positioned along the length of the body (26) or the muzzle brake (24). As specifically shown in FIGS. 29-30, such vectored discharge channels (27) may be configured to eject the high-pressure, high-velocity gases exiting the barrel in a vector that is counter to the rotational recoil of the firearm such that the escaping gasses provided a counter to the rotational recoil of the firearm as the bullet is ejected from the barrel. In a preferred embodiment, the escaping gasses may be directed out of the muzzle brake (24) through one or more vectored discharge channels (27) in an outward and rotational direction that is counter to the spin of the bullet leaving the barrel—which may change depending on whether the barrel of the firearm has been rifled for a right or left handed user. In this configuration, the muzzle brake (24) may reduce both the linear and rotational recoil generated by the discharge of the firearm. In another preferred embodiment, the barrel attachment (25) of the invention may be configured to position the muzzle brake (24) into a specific position such that the vectored discharge channels (27) may be orientated to eject the high-pressure, high-velocity gases exiting the barrel in a vector that is counter to the rotational recoil of the firearm such that the escaping gasses provided a counter to the rotational recoil of the firearm as the bullet is ejected from the barrel. In further embodiments, the size, and angle of the vectored discharge channels (27) may be adjusted to match the rotational recoil of a specific type of firearm, and/or type of ammunition used.

    [0418] In another embodiment of the invention, a suppressor may be configured to incorporate one or more elements of a muzzle break to reduce linear and rotational recoil. Generally referring to FIGS. 31-37, in one preferred embodiment, a suppressor (31) may include one or more vectored discharge channels (27) in fluid communication with a discharge passage (28). In this embodiment, the internal portion of a vectored suppressor (31) may include one or more discharge passages (28) formed by a concentric angled partition (29). In this configuration, a concentric angled partition (29) may be angled toward the barrel of the firearm and may further include an aperture to allow the bullet leaving the barrel to pass through the vectored suppressor (31) unimpeded. Such concentric angled partition (29) may be positioned in series and may be in fluid communication with one or more vectored discharge channels (27) through a discharge vent (30). In this preferred embodiment, the high-pressure, high-velocity gases exiting the barrel may be directed by a series of concentric angled partitions (29) to suppress noise and then through another series of discharge vents (30) and out of the vectored suppressor (31) through one or more corresponding vectored discharge channel (27) oriented to counter to the linear and rotational recoil of the firearm such that the escaping gasses provided a counter to the rotational recoil of the firearm as the bullet is ejected from the barrel and muzzle brake (24).

    [0419] In a preferred embodiment, the escaping gasses may be directed out of the vectored suppressor (31) through one or more vectored discharge channels (27) in an outward and rotational direction that is counter to the spin of the bullet leaving the barrel—which may change depending on whether the barrel of the firearm has been rifled for right twist or left twist. In this configuration, the vectored suppressor (31) may suppress not only the sound emitted from discharge of the firearm, but both the linear and rotational recoil also generated by discharge of the firearm.

    Example 6

    Force Detection System

    [0420] The present inventors have developed a novel force detection system (32) configured to detect, measure, transmit and display a force measurement applied to a component of a firearm by a user. In one preferred embodiment, the inventive technology may include a force detection system (32) configured to detect, measure, transmit, and display a force measurement applied to the rear of a buttstock by, for example a user's shoulder, as would occur when a shooter is in a standard firing position.

    [0421] Generally referring to FIG. 38, a force detection system (32) may include a force sensor positioned between a firearm's buttstock (38) and a chassis and receiver assembly (39). In this embodiment, a load may be applied to the rear of the buttstock by a shooter's shoulder which is transmitted to a force sensor coupled to the proximal end of the buttstock (38) and joined with the chassis and receiver assembly (39). The load applied to the rear or distal end of the buttstock may be detected by the force sensor and processed as generally described below. As further shown in FIGS. 40-42, in another preferred embodiment a force detection system (32) may include one or more load cells (34) configured to measure and process a force applied to a firearm's buttstock (38) by a user. As specifically shown in FIG. 3, a load cell (34) may be secured to a firearm by a mounting pad (33) positioned within a housing (42) which may further be secured to a chassis and receiver assembly (39).

    [0422] As further shown in FIG. 40, in this embodiment a buttstock (38) may be coupled with a rigidly secured outer hinge (36) component that further holds a tractable inner hinge (35) component secured to the proximal end of the buttstock (38). As highlighted in FIG. 41, the outer hinge (36) component may include an aperture position that may allow a post (41) element to pass through. In this embodiment, the post (41) may be integral with the inner hinge (35) component or may be separately secured and adjustable to allow calibration of the distance between the load cell (34) and post (41). Again, referring to FIGS. 41-42, in this embodiment the post (41) may be responsive to a force load applied to the buttstock (38) such that it may engage with the load cell (34) activating it.

    [0423] As noted above, the measurement of a shooter's force load input is complicated by the fact that it must generally be in-line with the load path, meaning the load cell (34) optimally would be measuring the entirety of the load applied to the rifle. The sensor, in this case a load cell (34), must have a path to the force load input at the buttstock that is more rigid than alternate load paths that could bypass the sensor. To overcome this limitation, as shown in FIGS. 40-42, a complaint gasket (37) may be placed between the outer hinge (36) and the chassis and receiver assembly (39) it is connected to. In this embodiment, a complaint gasket (37) may be made of a material that is less pliant than that of the load cell (34). In this configuration, the complaint gasket (37) may be axially soft and stiff in every axis such that it directs the force load to go through the rigid load cell (34) where it can accurately be measured and subsequently processed.

    [0424] In another embodiment, a force load detection system (32) may be configured to detect and display a force input from one or more firearm components. For example, in one preferred embodiment, a firearm, and preferably a rifle may be configured to be coupled with bipod, tripod or other structure design to support a rifle during operation. In certain embodiments such a bipod or other device may be coupled with the barrel of the rifle, or preferably the stock of the rifle. Similar to the force load detection system (32) described above for use with a rifle's buttstock, a force load detection system (32) may be incorporated into a bipod or other structure design to support a rifle during operation, which in other embodiments, a force load detection system (32) may include a supplementary components that may be configured to be secures to a rifle, and preferably the stock of a rifle and an exemplary support device, such as a bipod. In both of the above embodiment, a load cell (34) may be secured to a mounting pad (33) and positioned such that a load force applied to the rifle may cause a post (41) element to engage the load cell (34) and generate a display of the force measurement as generally described below.

    [0425] Similar to the embodiment shown in FIG. 40, in the force load input must generally be in-line with the load path, meaning the load cell (34) optimally would be measuring the entirety of the load applied to the rifle. The sensor, in this case a load cell (34), must have a path to the force load input interface of the bipod that is more rigid than alternate load paths that could bypass the sensor. To overcome this limitation, as described above and shown in FIGS. 40-42, a complaint gasket (37) may be placed between an outer hinge (36) or other equivalent components and the bipod assembly it is connected to. In this embodiment, a complaint gasket (37) may be made of a material that is less pliant than that of the load cell (34). In this configuration, the complaint gasket (37) may be axially soft and stiff in every axis such that it directs the force load to go through the rigid load cell (34) where it can accurately be measured and subsequently processed.

    [0426] Another embodiment of the invention may include the collection and real-time display of force measurements. In one preferred embodiment, a force measurement may be taken and transmitted to a display such as a series of LED lights, fiber optics, an LCD panel, or the like. Additional embodiments may include a modular and/or integrated system incorporated into a heads up display that may present the force measurement display through a rifle scope. In yet another preferred embodiment, a force measurement may be taken and transmitted to another device such as a cell phone or tablet for review of consistency as a training aid. Another embodiment of the invention may include a continuous force adjustment display system. In this preferred embodiment, a force measurement may be taken and transmitted to a display having a pre-configured range of optimal force. When the force measurement is within the optimal range a display feedback may be presented to a shooter to let them know that the firearm is in the optimal position to fire. If, on the other hand the force measurement is outside the pre-configured range of optimal force, a display feedback may be presented to a shooter to let them know that the firearm is not within the optimal position to fire and that the force being applied to the firearm needs to be adjusted.

    [0427] In one specific embodiment, a user may connect to the force detection system of the invention via a phone app and set a desired pressure or force to be applied to the firearm, and preferably to the buttstock. The user can then apply a load to the buttstock which is measured by the force detection system of the invention. When sufficient load has been applied a display feedback, such as a LED may light up. In this embodiment, a user can also set an over-force-limit such that if too much force is applied, a different LED will light up. Another embodiment of the invention may include a force detection system circuit having an electronic transducer that measures force, pressure or similar effect and converts the applied input into a voltage that can be processed by an electrical circuit and shown back to the user as a display feedback.

    TABLE-US-00001 TABLE 1 Evaluation of Rotational Recil Damener %Find torque and energy in bullet and gun during rotational recoil clc clear close all %% %vars barrelMass = 4;%kg barrelRadius = 0.0254;%m chassisMass = 2.4;%kg chassisRadius = .04;%m scopeMass = .4;%kg scopeOffset = .1;%m bulletMassGrains = 143;%grains powderMassGrains = 42.5;%grains startTwistRateImp = 8;%inch/rev endTwistRateImp = 8;%inch/rev bulletMomentInertia = 0.00000003;%kg*m{circumflex over ( )}2 *est bulletAccTime = 0.0015;%s est. barrelLength = 0.6;%m caliber = .00782;%m %% %Firearm Properties %gunMass = 8.6;%kg *est gunMass = barrelMass + chassisMass + scopeMass;%kg *est bulletMass = bulletMassGrains*6.47989* 10{circumflex over ( )}−5;%kg powderMass = powderMassGrains*6.47989* 10{circumflex over ( )}−5;%kg %gunMomentInertia = 0.0155;%kg*m{circumflex over ( )}2 *est gunMomentInertia = 0.5*barrelMass*barrelRadius{circumflex over ( )}2 + chassisMass*chassisRadius{circumflex over ( )}2;%+ scopeMass*scopeOffset{circumflex over ( )}2;%kg*m{circumflex over ( )}2 *est %converted vars startTwistRate = (1/startTwistRateImp) *(2*pi/0.0254);%rad/m endTwistRate = (1/endTwistRateImp) *(2*pi/0.0254);%rad/m %% %Primary Time Domain start_time = 0; time_step = 0.00001; end_time = .3; firearmTimeDomain(:, 1) = start_time:time_step:end_time; %% %Velocity Curve timeInBarrel = 0:time_step:bulletAccTime;%s velocity time domain %velocity curve derived from cubic regression of curve from quickload sim velocityCurve = [−6.490696427*10.{circumflex over ( )}11*timeInBarrel.{circumflex over ( )}3 + 1427010535*timeInBarrel.{circumflex over ( )}2 − 106836.5836*timeInBarrel + 2.1];%s:m/s %curve fit velocityCurve_Domain = 0:.0001:.0015; velocityCurve_Range = [0, 32, 97,210,419, 710, 1032,1422,1710, 2032, 2227, 2443, 2598, 2722,2814,2892]; n = 3; fitVals = polyfit(velocityCurve_Domain,velocityCurve_Range, n); velocityCurve_fit = zeros(length(firearmTimeDomain), 1); for j = 1:length(firearmTimeDomain)  for e = 2:n+1   velocityCurve_fit(j, 1) = velocityCurve_fit(j, 1) + (firearmTimeDomain(j,1){circumflex over ( )}(e− 1))*fitVals(n+2−e);  end  if(velocityCurve_fit(j, 1) < 0)   velocityCurve_fit(j, 1) = 0;  end end velocityCurve_fit(:, 1) = velocityCurve_fit(:, 1).*0.3048;%m/s [M, max_index] = max(velocityCurve_fit); timeInBarrel = 0:time_step:firearmTimeDomain(max_index);%s velocity time domain %{ figure; scatter(velocityCurve_Domain,velocityCurve_Range.*0.3048); hold on; plot(firearmTimeDomain, velocityCurve_fit); %} %% %Pressure Curve pressureCurve_Domain = 0:.0001:.0015; pressureCurve_Range = [3947, 7369, 14210,24210, 39195,51613, 57979,57979,51596, 43085, 34574, 28192, 22872, 17222,15946,13784]; n = 4; fitVals = polyfit(pressureCurve_Domain,pressureCurve_Range, n); pressureCurve_fit = zeros(length(firearmTimeDomain), 1); for j = 1:length(firearmTimeDomain)  for e = 1:n+1   pressureCurve_fit(j, 1) = pressureCurve_fit(j, 1) + (firearmTimeDomain(j,1){circumflex over ( )}(e− 1))*fitVals(n+2−e);  end end pressureCurve_fit(:, 1) = pressureCurve_fit(:, 1).*6894.76;%Pa chamber_pressure = zeros(length(firearmTimeDomain), 1); chamber_pressure(1:max_index) = pressureCurve_fit(1:max_index); chamber_pressure(max_index:end) = pressureCurve_fit(max_index); %{ figure; scatter(pressureCurve_Domain,pressureCurve_Range.*6894.76); hold on; plot(firearmTimeDomain, pressureCurve_fit); %} %% %Kinematic Calculations Bullet %Bullet Linear Velocity bullet_velocity_linear = zeros(length(firearmTimeDomain), 1); bullet_velocity_linear(1:length(timeInBarrel)) = velocityCurve_fit(1:length(timeInBarrel));%s:m/s bullet_velocity_linear(length(timeInBarrel):end) = max(velocityCurve_fit); %Bullet Linear Acceleration bullet_acceleration_linear = zeros(length(firearmTimeDomain), 1); for j = 1:length(firearmTimeDomain)−1  bullet_acceleration_linear(j) = (bullet_velocity_linear(j+1)− bullet_velocity_linear(j))/time_step;  %{  if bullet_acceleration_linear(j) < 0   bullet_acceleration_linear(j) = 0;  end  %} end %Bullet Linear Position bullet_position_linear = zeros(length(firearmTimeDomain), 1); bullet_position_linear(1) = bullet_velocity_linear(1)*time_step; for i = 2:length(firearmTimeDomain) bullet_position_linear(i) = bullet_position_linear(i−1) + bullet_velocity_linear(i)*time_step; end %Bullet Angular Velocity bullet_velocity_angular = [(((endTwistRate− startTwistRate)/max(bullet_position_linear)).*bullet_position_linear+startTwistRate).*bullet_vel ocity_linear]; %Bullet Anglular Acceleration bullet_acceleration_angular = zeros(length(firearmTimeDomain), 1); for j = 1:length(firearmTimeDomain)−1  bullet_acceleration_angular(j) = (bullet_velocity_angular(j+1)− bullet_velocity_angular(j))/time_step;  if bullet_acceleration_angular(j) < 0   bullet_acceleration_angular(j) = 0;  end end %Bullet Angular Position bullet_position_angular = zeros(length(firearmTimeDomain), 1); bullet_position_angular(1) = bullet_velocity_angular(1)*time_step; for i = 2:length(firearmTimeDomain) bullet_position_angular(i) = bullet_position_angular(i−1) + bullet_velocity_angular(i)*time_step; end %% %Thrust %with angular muzzlebreak %Constants gamma = 1.3;%specific heat ratio: estimate based on co2 and nitrogren R_gas = 8.3145;%J/mol*K P_ambient = 0;%101325;%Pa A_inlet_bore = (caliber/2){circumflex over ( )}2*pi;%m{circumflex over ( )}2 A_exit_bore = (caliber/2){circumflex over ( )}2*pi;%m{circumflex over ( )}2 mach_exit = 1; molarMass_Gas = 0.04401;%kg/mol A_inlet_tangent = (.00060){circumflex over ( )}2*pi;%(.00023){circumflex over ( )}2*pi;%m{circumflex over ( )}2 A_exit_tangent = (.00060){circumflex over ( )}2*pi;%(.00023){circumflex over ( )}2*pi;%m{circumflex over ( )}2 tangent_radius = .02;%m tangent_position = .6;%m max_volume_chamber = (caliber/2){circumflex over ( )}2*pi*barrelLength; volume_chamber = zeros(length(firearmTimeDomain), 1); volume_chamber(1:max_index) = (caliber/2){circumflex over ( )}2*pi*bullet_position_linear(1:max_index);%m{circumflex over ( )}3 volume_chamber(max_index:end) = (caliber/2){circumflex over ( )}2*pi*barrelLength;%m{circumflex over ( )}3 T_exit_initial = 2987.26;%K P_exit_initial = pressureCurve_fit(length(timeInBarrel));%Pa Mass_initial = (P_exit_initial*max_volume_chamber*molarMass_Gas)/(T_exit_initial*R_gas); m_dot = 0; mass_out = 0; P_exit = zeros(length(firearmTimeDomain), 1); gun_thrust_linear = zeros(length(firearmTimeDomain), 1); gun_thrust_angular = zeros(length(firearmTimeDomain), 1);  A_inlet_tot = A_inlet_bore + A_inlet_tangent;  A_exit_tot = A_exit_bore + A_exit_tangent; for i = 1:length(firearmTimeDomain) T_exit = T_exit_initial; P_exit(i) = 0; if(bullet_position_linear(i)>tangent_position && i>max_index)  mass_out = mass_out + time_step*m_dot;  P_exit(i) = (Mass_initial−mass_out)*T_exit*R_gas/(molarMass_Gas*volume_chamber(i));  m_dot = A_inlet_tot*P_exit(i)*sqrt(gamma/(R_gas*T_exit))*((gamma+1)/2){circumflex over ( )}(− 1*(gamma+1)/(2*gamma−2));%kg/s  V_exit = mach_exit*sqrt(gamma*R_gas*T_exit);  gun_thrust_angular(i) = ((m_dot*V_exit)*(A_inlet_tangent/A_inlet_tot)+(P_exit(i)− P_ambient)*A_exit_tangent)*tangent_radius;  gun_thrust_linear(i) = (m_dot*V_exit)*(A_inlet_bore/A_inlet_tot)+(P_exit(i)− P_ambient)*A_exit_bore; elseif(bullet_position_linear(i)>tangent_position)  mass_out = mass_out + time_step*m_dot;  P_exit(i) = (Mass_initial−mass_out)*T_exit*R_gas/(molarMass_Gas*volume_chamber(i));  m_dot = A_inlet_tangent*P_exit(i)*sqrt(gamma/(R_gas*T_exit))*((gamma+1)/2){circumflex over ( )}(− 1*(gamma+1)/(2*gamma−2));%kg/s  V_exit = mach_exit*sqrt(gamma*R_gas*T_exit);  gun_thrust_angular(i) = ((m_dot*V_exit)+(P_exit(i)− P_ambient)*A_exit_tangent)*tangent_radius; elseif(i>max_index)  mass_out = mass_out + time_step*m_dot;  P_exit(i) = (Mass_initial−mass_out)*T_exit*R_gas/(molarMass_Gas*volume_chamber(i));  m_dot = A_inlet_bore*P_exit(i)*sqrt(gamma/(R_gas*T_exit))*((gamma+1)/2){circumflex over ( )}(− 1*(gamma+1)/(2*gamma−2));%kg/s  V_exit = mach_exit*sqrt(gamma*R_gas*T_exit);  gun_thrust_linear(i) = (m_dot*V_exit)+(P_exit(i)−P_ambient)*A_exit_bore; end if P_exit(i) > 0  chamber_pressure(i) = P_exit(i); end end %{ figure; plot(firearmTimeDomain(:,1),gun_thrust_angular); %} %% %Kinematic Calculations Gun %Bullet/Gun Torque torque = bullet_acceleration_angular*bulletMomentInertia − gun_thrust_angular; %Bullet/Gun Force force = bullet_acceleration_linear*bulletMass + gun_thrust_linear; %Gun Linear Acceleration gun_acceleration_linear = force/gunMass; %Gun Linear Velocity gun_velocity_linear = zeros(length(firearmTimeDomain), 1); gun_velocity_linear(1) = gun_acceleration_linear(1)*time_step; for i = 2:length(firearmTimeDomain) gun_velocity_linear(i) = gun_velocity_linear(i−1) + gun_acceleration_linear(i)*time_step; end %Gun Linear Position gun_position_linear = zeros(length(firearmTimeDomain), 1); gun_position_linear(1) = gun_velocity_linear(1)*time_step; for i = 2:length(firearmTimeDomain) gun_position_linear(i) = gun_position_linear(i−1) + gun_velocity_linear(i)*time_step; end %Gun Angular Acceleratation gun_acceleration_angular = torque/gunMomentInertia; %Gun Angular Velocity gun_velocity_angular = zeros(length(firearmTimeDomain), 1); gun_velocity_angular(1) = gun_acceleration_angular(1)*time_step; for i = 2:length(firearmTimeDomain) gun_velocity_angular(i) = gun_velocity_angular(i−1) + gun_acceleration_angular(i)*time_step; end %Gun Angular Position gun_position_angular = zeros(length(firearmTimeDomain), 1); gun_position_angular(1) = gun_velocity_angular(1)*time_step; for i = 2:length(firearmTimeDomain) gun_position_angular(i) = gun_position_angular(i−1) + gun_velocity_angular(i)*time_step; end %% %Damping %Constants k_evironment = 3000; k_linear = 6000; damping_coeff_linear = 100; damping_coeff_angular = 18; reaction_torque_radius = 0.05; rest_angular_accel = 10;%rad/s/s angular_zero = 0; chamber_pressure_threshold = 10{circumflex over ( )}8; for i = 2:length(firearmTimeDomain)  if i > max_index && force(i) < 50  reaction_spring_force = gun_position_linear(i−1)*k_linear;  force(i) = force(i) − reaction_spring_force − damping_coeff_linear*gun_velocity_linear(i−1);  end  if i > max_index && chamber_pressure(i) < chamber_pressure_threshold && firearmTimeDomain(i) > 0.1  reaction_spring_torque = (gun_position_angular(i−1) − angular_zero)*2*reaction_torque_radius*k_evironment;  torque(i) = torque(i) − reaction_spring_torque − gun_velocity_angular(i− 1)*2*reaction_torque_radius{circumflex over ( )}2*damping_coeff_angular;  else   angular_zero = gun_position_angular(i);  end %Gun Linear Acceleration gun_acceleration_linear(i) = force(i)/gunMass; %Gun Linear Velocity gun_velocity_linear(i) = gun_velocity_linear(i−1) + gun_acceleration_linear(i)*time_step; %Gun Linear Position gun_position_linear(i) = gun_position_linear(i−1) + gun_velocity_linear(i)*time_step; %Gun Angular Acceleratation gun_acceleration_angular = torque/gunMomentInertia; %Gun Angular Velocity gun_velocity_angular(i) = gun_velocity_angular(i−1) + gun_acceleration_angular(i)*time_step; %Gun Angular Position gun_position_angular(i) = gun_position_angular(i−1) + gun_velocity_angular(i)*time_step; end %% %Plot figure; sgtitle(“Overall Firearm Dynamics (with ASA Muzzle Thruster, t = 0 − 0.3 s)”); subplot(3, 5, 1); plot(firearmTimeDomain,bullet_position_linear ); title(“Bullet Linear Position”); subplot(3, 5, 6); plot(firearmTimeDomain,bullet_velocity linear ); title(“Bullet Linear Velocity”); subplot(3, 5, 11); plot(firearmTimeDomain, bullet_acceleration_linear); title(“Bullet Linear Acceleration”); subplot(3, 5, 2); plot(firearmTimeDomain,bullet_position_angular ); title(“Bullet Angular Position”); subplot(3, 5, 7); plot(firearmTimeDomain,bullet_velocity_angular ); title(“Bullet Angular Velocity”); subplot(3, 5, 12); plot(firearmTimeDomain, bullet_acceleration_angular ); title(“Bullet Angular Acceleration”); subplot(3, 5, 3); plot(firearmTimeDomain, gun_position_linear ); title(“Gun Linear Position”); subplot(3, 5, 8); plot(firearmTimeDomain, gun_velocity_linear ); title(“Gun Linear Velocity”); subplot(3, 5, 13); plot(firearmTimeDomain, gun_acceleration_linear ); title(“Gun Linear Acceleration”); subplot(3, 5, 4); plot(firearmTimeDomain, gun_position_angular); title(“Gun Angular Position”); subplot(3, 5, 9); plot(firearmTimeDomain, gun_velocity_angular); title(“Gun Angular Velocity”); subplot(3, 5, 14); plot(firearmTimeDomain, gun_acceleration_angular); title(“Gun Angular Acceleration”); subplot(3, 5, 5); plot(firearmTimeDomain, force); title(“Force”); subplot(3, 5, 10); plot(firearmTimeDomain, torque); title(“Torque”); subplot(3, 5, 15); plot(firearmTimeDomain, chamber_pressure); title(“Pressure”);