US20180135949A1

US20180135949A1 - Methods, Systems and Devices to Shape a Pressure*Time Wave Applied to a Projectile to Modulate its Acceleration and Velocity and its Launcher/Gun's Recoil and Peak Pressure Utilizing Interior Ballistic Volume Control

Info

Publication number: US20180135949A1
Application number: US15/675,191
Authority: US
Inventors: Ronald Gene Lundgren; Kent Harvey; Kelly Dow
Original assignee: Individual
Current assignee: Individual
Priority date: 2017-08-11
Filing date: 2017-08-11
Publication date: 2018-05-17

Abstract

Methods, systems, and devices to shape a pressure*time wave applied to sniper and dangerous game rifle projectiles whereby an ammunition shell casing's volume, at release of the projectile from the casing, and rifle system impedance (Z) in conjunction with the amount of propellant are modulated to beneficially shape the wave applied to the projectile's base, and by Newton's 2^ndlaw the projectile's applied acceleration*time impulse wave, to reliably reduce the velocity of a sniper or dangerous game rifle's ammunition to a sub-Mach 1 level, preserve the projectile momentum, maintain the rifle's automatic shell casing ejection and new shell casing/projectile re-load action and maintain a projectile and rifle operation within their material's strength limits. These tools are further applied to simulate severe g acceleration environments for commercial and military weapon sub-system component's non-destructive testing and certification that are carried in a projectile and applicable to any existing propellant launcher/gun system.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to the earlier filed provisional application having Ser. No. 62/384,420 and hereby incorporates subject matter of the provisional application in its entirety.

TECHNICAL FIELD

The present specification relates to shaping an interior ballistic pressure*time wave, applied to a projectile within a projectile launcher/gun system, by control of launcher/gun system internal volume and thereby the launcher/gun system impedance to tailor a projectile's resulting base applied acceleration*time wave for the purpose of modulating the projectile's acquired velocity and beneficially controlling the projectiles applied peak acceleration, the launcher/gun system's internal peak pressure, preservation of the automatic spent projectile shell casing ejection and re-loading of new projectile and shell casing and the launcher/gun recoil.

BACKGROUND

Presently fixed impedance projectile bodies, called off-spring projectiles, are imparted a specific velocity via a launcher/gun system with an off-spring projectile barrel/guide attached to the launcher/gun system. A static, internal to the launcher/gun, fixed closed propellant chamber volume, called the off-spring projectile's parent-case, is integral to the off-spring projectile. The off-spring projectile has a specific system impedance (Z) that is equal to the ratio of the force (F) delivered to the off-spring projectile divided by the final velocity (V_f) obtained by the off-spring projectile at barrel/guide exit of the base of the off-spring projectile:
Z=F/V _f
This equation is an internal launcher/gun ballistic analog to Ohm's electrical law R=V/I; where (R) is analogous to (Z) impedance, Force (F) is analogous to Voltage (V) and Current (I) is analogous to Velocity (V_f). In English engineering units for the above equation F=#, the symbol for the physical weight of an off-spring projectile and V_fis the final velocity of the off-spring projectile's base at exit from the barrel/guide. The equation reduces to the form
Z=J;
where (Z) is the modulator that amplifies or attenuates the impulse (J) wave as it accumulates per distance of off-spring projectile travel down a barrel/guide and (J) is now the impulse per unit distance in English engineering units of g*#*seconds per foot, where * indicates multiplication as a continuum running integral during off-spring projectile travel per unit distance down the barrel/guide and until off-spring projectile base exit, and one g is the acceleration due to gravity at the Earth's surface and is the standard unitless gravity symbol g and therefore the specific system impulse force (F) term amplitude modulator. Within the parent-case solid chemical propellant grains are contained and then ignited by a primer, consisting of shock sensitive chemicals that are ignited either mechanically or electrically and that expose the contained propellant grains residing within the parent-case to the fire produced by the primer to then in turn ignite the propellant grains, and subsequently burn the propellant grains rapidly changing the solid propellant grains into a gas in the millisecond time frame. This gas produces a pressure*time wave that is applied in real time to the base of a parent case coupled off-spring projectile transferring the gas momentum to the off-spring projectile and by Newton 2^ndLaw imparts an acceleration*time (g*second) impulse (J) wave per unit travel (distance) to the off-spring projectile for the purpose of imparting a velocity (g*seconds) to the off-spring projectile thereby launching it toward a target at the acquired final velocity V_f. Currently the parent-cases, also known as propellant chambers, of a launcher/gun are fixed geometry devices with fixed initial volumes and integral to a fixed barrel/guide and the off-spring projectiles have a fixed system impedance that is a linear function of the off-spring projectile's weight. The barrel/guide's function is to drop the acceleration*time impulse wave on the base of the off-spring projectile by opening additional volume with the piston effect of an off-spring projectile traveling down the barrel/guide as the acceleration*time wave is applied and the impulse (J) accumulates. The system impedance (Z) controls the g amplitude applied to the off-spring projectile's base and the time duration that the acceleration*time impulse wave is applied to the off-spring projectile's base. System impedance (Z) control modulates the area underneath the acceleration*time curve modulating velocity V_fto newer and more beneficial levels. Present art requires new parent-cases and barrel/guides be built when the requirements of velocity, acceleration, recoil, and peak pressure change outside the very narrow design space of the material strengths of the off-spring projectiles, launcher/guns, parent-cases, or barrel/guides. The present invention is based on the very creative verified premise that the parent-case volume is nearly constant during initial momentum transfer and rise to peak pressure from the gas to the off-spring projectile providing an inflection point that is highly sensitive to off-spring projectile geometry, mass properties and parent-case volume with which to change peak applied pressure and system impedance (Z) and thereby the acceleration*time impulse wave (J); that is, peak pressure is applied to the off-spring projectile before it moves significantly down the barrel/guide and opens up additional volume. In the event off-spring projectile movement will not open significant volume during rise time to wave peak pressure amplitude and this provides a sensitive inflection point, where the g modulator can be applied by changing the system impedance or the parent-case volume during first release of the off-spring projectile from the parent-case and therefore modulate all a launcher/gun's system parameters to more beneficial values. At this inflection point the parent-case's volume can be modulated with off-spring projectile mass property and geometry changes and return a significant change in the system impedance with which to provide significant modulation of the off-spring projectile's velocity and recoil and/or dynamically reconfigure the parent-case to another geometry with a different volume in real time using a malleable formable insert material inside the parent-case. The concepts are subtle. If one is opening a large volume within the barrel/guide by off-spring projectile movement while the re-configuration of a parent-case geometry takes place or adjustment of the system impedance thru off-spring projectile mass property and geometry changes, then the effect is diminished significantly and re-shaping the pressure*time wave by adjusting the impedance or parent case volume is negated. The dynamic volume change and adjustment of the system impedance in this invention, taking place at the unique system inflection point during a state of near constant volume, thereby allows a real time change to the output pressure*time wave, which by Newton's 2^ndLaw changes the applied acceleration*time impulse (J) wave to the off-spring projectile and its impedance during transit down the barrel/guide and therefore its imparted applied acceleration, final velocity, launcher/gun recoil, and launcher/gun system peak pressure. This real-time change of the acceleration*time impulse wave to the off-spring projectile has the beneficial effect of utilizing pre-existing closed volume parent-cases and barrel/guides for a much larger design space for new system velocity, recoil, peak pressure, and peak acceleration as the barrel/guide exit off-spring projectile velocity in a modern day standard launcher/gun can be tailored to a more desired level by an a priori change to the off-spring projectile's mass properties and/or dynamically changing the geometry of existing ammunition, that is, the combination parent-case and off-spring projectile and therefore system impedance and the off-spring projectile's applied pressure*time wave upon ignition of the propellant and/or the modulation of the propellant mass. In this manner, existing ammunition parent-cases and expensive launcher/guns can be used for a much wider range of velocities and acceleration requirements and other beneficial scenarios for launcher/gun systems such as control of internal peak pressure and acceleration applied to an off-spring projectile thereby maintaining the total launcher/gun system and the off-spring projectile within their materials' strength and system operating parameters.
In addition to changing the parent-case volume and the off-spring projectile's mass properties and/or geometry to modulate the system impedance during momentum transfer at the system inflection point, the off-spring projectile can be fixed to the parent-case at the inflection point to provide a back-pressure and create a virtual mass to change the off-spring projectile's mass properties. The virtual mass method changes the system impedance but only as a partial running continuum integral, not a full barrel length continuum running integral, as a physical change in mass properties of the off-spring projectile or the dynamic re-configuration of the parent-case volume will accomplish, and the virtual mass properties method is only applied during the period that the off-spring projectile is releasing from the parent-case. This has the effect of chopping off a portion of the beginning of the pressure*time wave, reducing the area underneath the pressure*time curve thereby reducing off-spring projectile acceleration and subsequent velocity and launcher/gun recoil. The back-pressure value can be modulated by using different attachment techniques thereby further modulating the reduction of off-spring projectile velocity.
In addition to providing a larger operating space for launcher/guns and their existing parent-case chambers and their off-spring projectiles this invention reduces a launcher/gun's recoil due to a reduction in off-spring projectile final velocity V_f. This allows smaller framed and physically vulnerable individuals the ability to operate larger caliber weapons with which to afford themselves increased personnel protection.
Modern day sniper and dangerous game rifles equipped with optical scopes see further than the rifleman can accurately target an object. A sniper or dangerous game rifle's (launcher/gun) exit velocity is above Mach 1, which is the speed of sound or substantially 1100 feet/second depending on the atmospheric conditions within the barrel/guide of a rifle. There is a range to a target where the off-spring projectile slows down and passes, that is, backs thru Mach 1. When an off-spring projectile passes thru Mach 1 it experiences severe turbulence that cause the off-spring projectile to deviate severely from the path of aim and miss the acquired target. The present-day solution is to reduce the amount of propellant in the parent-case to reduce V_fto the sub-Mach 1 velocity regime at rifle (launcher/gun) barrel/guide exit. This has two undesirable effects: 1) A rifle's automatic bolt action to eject the spent parent-case and reload a new parent-case with a new off-spring projectile will not work or worse is un-reliable and 2) The momentum delivered to the target is severely reduced making the rifle unusable for dangerous game. This invention preserves automatic bolt action and momentum of the off-spring projectile.
Current art for testing the g tolerance for military weapon systems and vehicles and commercial vehicles is to destructively test the system. This invention will simulate a range of severe impact and vibration environments by tailoring the acceleration*time impulse wave applied to an off-spring projectile inside of a launcher/gun and containing within the off-spring projectile the components to be evaluated to a desired custom acceleration*time impulse (J) wave load. This permits non-destructive component testing of acceleration*time impulse wave loaded subsystems such as automobiles and military weapons and the development and certification of the sub-system components. For example, an automobile's air-bag system can be tested without undergoing an actual crash event and military weapon components such as electronic fuzes, carried explosives and structures can be tested without actual deployment of the weapon system. As another example, a military concrete penetrating projectile (off-spring projectile) weapon system will travel thru several feet of concrete after target impact. This severely g loads the weapon's internal components such as electronic fuzes. Present day methods require a massive concrete structure to be built and the weapon system deployed against it to ascertain internal component functionality. In the event the majority of the test resources are spent on concrete not the weapon system's component testing. This invention allows all the components of the system to be tested without huge expenditures of capital on items that have little to do with component testing and evaluation other than provide a venue to simulate the g environment. This invention allows the allotted test and certification resources to be directed to test and certification rather than test expedients.
Accordingly, a need exists for beneficially shaping a pressure*time wave applied to an off-spring projectile to modulate its applied acceleration, imparted velocity and its launcher/gun recoil and internal launcher/gun peak pressure.

SUMMARY

In the preferred embodiments, a parent-case's volume at release of the off-spring projectile and the system impedance (Z) in conjunction with the amount of propellant are modified to beneficially shape the output pressure*time wave applied to an off-spring projectile's base and by Newton's 2^ndlaw an off-spring projectile's base applied acceleration*time impulse wave for the purpose of reliably reducing the applied velocity of a sniper or dangerous game rifle to a sub-Mach 1 level at the barrel/guide exit, preserving the off-spring projectile momentum, maintaining the rifle's automatic parent-case ejection and new parent-case/off-spring projectile re-load action, maintaining the rifle operation within it material strength limits and applying to an off-spring projectile containing components to be tested and certified a pre-determined acceleration*time impulse wave for the purpose of non-destructively testing and certifying military weapon and commercial system components.

BRIEF DESCRIPTION OF DRAWINGS

The embodiment set forth in the drawings are illustrative and exemplary in nature and not intended to limit the subject matter defined by the claims. The following brief description of the illustrative embodiments can be understood when read in conjunction with the following drawings.

FIG. 1 schematically depicts a launcher/gun system and parent-case and off-spring projectile and the dynamic formation of a new volume within the parent-case chamber of a launcher/gun utilizing a formable material insert and dynamically hydroforming a new volume by operating the material in its forming region during propellant burn and rise to peak pressure within the parent-case and/or an a priori delta (Δ) change in the mass properties of the off-spring projectile to effect a (Δ) (Z) impedance modulation and therefore a (Δ) (J) per unit distance impulse modulation.

FIG. 2 schematically depicts on the top schematic the creation of a virtual mass and on the bottom an a priori modulation of the off-spring projectile mass properties and/or geometry to modulate system impedance (Z) and volume during dynamic propellant burn at the system inflection point negating any large initial volume expansion due to the barrel/guide piston effect and modulate the final velocity of the off-spring projectile and the recoil of a launcher/gun system.

FIG. 3 graphically depicts on the left graph the percent applied off-spring projectile base pressure versus the percent of off-spring projectile base pressure wave application time and on the right graph the percent of applied off-spring projectile base pressure versus percent of off-spring projectile barrel/guide travel during release from the parent-case and rise to the peak pressure and further identifies the system inflection point for the launcher/gun case.

FIG. 4 graphically depicts in the percent of pressure*time wave application time and per cent of peak applied pressure the applied off-spring projectile's base pressure*time wave of a parent-case chamber before and after dynamic volume control by hydro-forming a new volume within the parent-case and before and after volume reductions due to a priori mass property or geometry changes to the off-spring projectile thereby in the case shown increasing a launcher/gun system impedance (Z).

FIG. 5 graphically depicts, in percent of full applied pressure, the pressure*time wave applied to the base of an off-spring projectile by the formation of new off-spring projectile virtual mass properties by creation of these new properties by the formation of a back pressure to reduce the final velocity by reducing the area under the pressure*time curve applied to the off-spring projectile base, thereby reducing the area under the acceleration*time curve applied to the off-spring projectile in percent of wave application time.

DETAILED DESCRIPTION OF DRAWINGS

FIG. 1 depicts the forward part of a launcher/gun system 100 showing the off-spring projectile 140, parent case 150 and barrel/guide 180 with a malleable formable material insert 120 surrounded by air whose purpose is to dynamically create a new volume during rise to peak pressure at the system inflection point 152, the expansion of 120 to a new 122 geometry in the space previously occupied by air, the propellant grains 130 within the parent-case 150, the propellant changed to a gas 132 by ignition of the propellant 130 by the parent-case primer 160, the off-spring projectile 140 with a new system impedance (ΔZ) and the barrel/guide 180.
The malleable formable insert 120 fully captures the propellant grains 130 before ignition by primer 160. Fully capturing the propellant grains 130 before ignition prohibits the propellant grains 130 from repositioning in random patterns during handling and firing of the combination parent-case 150/off-spring projectile 140. This prevents variances in the barrel/guide 180 exit velocity V_fof the off-spring projectile 140 and maintains reliable ignition of the propellant 130 from shot to shot.
The insert material 120 is selected to be formable during propellant burn, that is, the material operates within its plastic regime called the hydroforming regime and defined on FIG. 1 as the forming region dotted horizontal line on the material's stress versus strain curve. During ignition of the primer 160 and burn of the solid propellant 130, changing 130 into a gas 132, the insert 122 is formed on the walls of the parent-case thereby dynamically increasing parent-case 150 volume at the system inflection point 152. This volume expansion modulates launcher/gun system parent-case 150 peak pressure, system impedance (Z), off-spring projectile velocity V_f, launcher/gun recoil and applied base off-spring projectile 140 applied pressure and acceleration.
FIG. 2 top depicts the creation of a virtual mass constituting a back pressure or null force to dynamically change the mass properties of the off-spring projectile 140 during release of the off-spring projectile 140 from the parent-case 150 at the inflection point 152. The off-spring projectile 140, normally crimped to a parent-case with only a minimal resisting back pressure force, is in order of joint 170 shear strength resistances from high to low; brazed, soldered, glued or threaded to the parent-case for the purpose of providing a resistance to movement and keeping the volume of the parent-case 150 constant until joint 170's shear resistance strength is overcome; and then permitting movement down the barrel/guide 180 of the off-spring projectile. This has the effect of nulling that portion of the pressure*time curve until the pressure rises to a value that it overcomes the shear strength of the joint 170 and the off-spring projectile 140 begins movement down the barrel/guide 180 and opens additional volume. FIG. 2 bottom shows the option of a (Δ) mass property modulation of off-spring projectile 140 linearly producing a (ΔZ) system impedance thereby reducing or increasing the percentage of barrel/guide 180 travel during rise to peak pressure thereby reducing or increasing the parent-case 150 volume at the inflection point 152 during release of the off-spring projectile 140 from the parent-case and thereby modulating system impedance (Z).
The FIG. 3 left graph is the normalized to 100% peak pressure of the pressure*time wave versus normalized to 100% percent of pressure*time wave application time of a common fixed volume and fixed system impedance parent-case 150 pressure chamber with no new volume formed dynamically by a formable material insert 120 or adjustments to the off-spring projectile 140 mass properties either virtually or physically. The right graph is the normalized to 100% off-spring projectile 140 peak pressure obtained versus normalized to 100% barrel/guide 180 off-spring projectile 140 base travel for this common case. In the event the off-spring projectile 140 piston effect of opening a new volume is substantially 6% of the off-spring projectile 140 travel as the volume remains near constant during momentum transfer from propellant gas 132 to off-spring projectile 140 and reaching maximum pressure at the inflection point 152 within the parent-case 150. This graph identifies the common case system inflection point 152 as a function of barrel/guide 180 off-spring projectile 140 travel at 100% peak applied base off-spring projectile 140 pressure.
FIG. 4 depicts the results of the real-time modulation of the parent-case 150 volume and/or an a priori physical change to the mass properties and/or geometry of the off-spring projectile 140 in normalized percent of parent-case peak pressure applied to the off-spring projectile 140 versus percent of time the pressure*time wave is applied to the off-spring projectile 140 and thereby a modulation of the system impedance (Z). The solid line is the pressure*time wave curve applied to the off-spring projectile 140 without dynamic volume expansion within the parent-case 150 or change in off-spring projectile 140 mass properties; the dotted line shows the pressure*time results due to system impedance (Z) modulation by dynamic hydroforming of a new volume within the parent-case 150 or dynamic forming of a new volume by inhibiting off-spring projectile 140 movement during release from the parent case 150 due to changes to the off spring projectile 140 mass properties or geometry. These graphs reflect a change to a higher value of system impedance (Z). The graphs would be reversed for a lower value of system impedance (Z),
FIG. 5 depicts normalized percentage results for an 80 percent pressure level that overcomes the shear strength of joint 170. The hatched area on the left graph is the area that is lost as a result of the back pressure formed by the joint 170 which nulls a portion of the acceleration*time wave area application to the off-spring projectile 140. The graph to the right is the resulting pressure*time wave applied to the off-spring projectile 140 that modulates velocity and recoil in this illustration to a higher value of system impedance (Z) due to the formation of a virtual mass, that is, back pressure.

Claims

What is claimed is:

1. A pressure*time wave, where the symbol * indicates a running continuum integral as an off-spring projectile traverses the barrel/guide of a rifle, re-shaping method to reliably obtain a sub-Mach 1 rifle barrel/guide exit velocity and preserve automatic operation of standard automatic rifles (launcher/guns) used as sniper rifles and dangerous game rifles and for stabilization of the off-spring projectile's transit to a sniper's target or dangerous game target thereby maintaining the rifle operator's aim point, where Mach 1 is the speed of sound in the atmosphere within the confines of a rifle's barrel/guide, or substantially 1100 feet/second, in which an off-spring projectile is launched by internal volume control and further applied to the base of a sniper or dangerous game rifle's off-spring projectile whereby the off-spring projectile is attached to an accompanying parent-case containing solid propellant grains by modifying the rifle system's internal volume at initial propellant ignition and thereby its impedance Z=F/V_f=J where (Z) is the rifle system's impedance in the English engineering units of g*#*seconds/foot and J in equal units is the per unit distance impulse delivered to an off-spring projectile, and further one g is the unitless acceleration due to gravity at the Earth's surface and is the standard unitless gravity symbol g, # is the symbol for the physical weight of an off-spring projectile, F is the delivered force in units of g*# to the base of the off-spring projectile and V_fis the final velocity of the off-spring projectile at the rifle barrel/guide's exit in g*seconds and further applied at the rifle system's inflection point located at the attainment of the rifle system's peak pressure occurring at the end of the time consumed by initial momentum transfer from the parent-case propellant ignition gases to off-spring projectile's base and during first release of the off-spring projectile from an attached off-spring projectile's parent-case and rise to peak pressure and peak g acceleration on the off-spring projectile's base after ignition of the rifle's propellant grains and further during the initial movement of the off-spring projectile resulting in a change in the parent-case volume, to beneficially modify the off-spring projectile's final velocity V_fat rifle barrel/guide exit and applied peak acceleration of a rifle system and peak internal pressure of the rifle system, and preserving sufficient momentum to operate the rifle's automatic ejection of the off-spring projectile's spent parent-case and reloading of a new combination parent-case and off-spring projectile, said method comprising the steps of:

Increasing the material density of the off-spring projectile thereby increasing its mass properties and lowering the system impedance (Z) to provide resistance to movement at the rifle system's inflection point thereby reducing the initial parent-case volume and occurring at first release of the off-spring projectile from the parent-case and at the system inflection point located at the first release point of the off-spring projectile from its parent-case;

Reducing the amount of propellant grains in the parent-case by an amount that will preserve off-spring projectile momentum thereby satisfying the momentum equation M_N×V_FN=M_O×V_FO, where x indicates multiplication, thereby keeping the rifle's operating conditions within the limits of the rifle's material properties and retaining proper ejection of the parent-case and re-loading of a new-parent-case with off-spring projectile and where M_Nis the new value of the off-spring projectile mass, V_FNis the desired new final velocity V_fof the off-spring projectile at the off-spring projectile's base rifle barrel/guide exit, M_Ois the former value of the off-spring projectile mass and V_FOis the former value of the velocity V_fof the off-spring projectile at off-spring projectile base rifle barrel/guide exit.

2. A method of claim 1 for simulating severe g acceleration environments for commercial or military weapon sub-system component's non-destructive testing and certification and applicable to the full suite of existing propellant launcher/guns and maintaining the launcher/gun system operation within the launcher/gun's material property limits and operating parameters by volume and off-spring projectile mass properties control and thereby system impedance (Z) control within any launcher/gun system to tailor the pressure*time wave and therefore the per distance unit impulse (J) in the equation Z=F/V_f=J applied to an off-spring projectile containing components to be tested and certified and the resulting g acceleration*time impulse wave to the desired value for application to military or commercial components during launch from a launcher/gun system containing an off-spring projectile with the components to be tested or certified therein for the purposes of testing the g tolerance of the components and/or certification of the components, said methods comprising the steps of:

Defining the required g amplitude and military or commercial component exposure time in seconds to be applied to the components to be tested and dividing this value of g*time, where the symbol * indicates a continuum running integral as an off spring projectile traverses the barrel/guide, by the length of the barrel/guide thereby forming the value of the system impedance (Z) required for the equation Z=F/V_f=J, where (Z)=(J) is the system impedance and per distance unit impulse respectively in English engineering units of g*#*seconds/foot, g*# is the delivered force (F) to an off-spring projectile and # is the symbol for the physical weight of a bullet in pounds, V_fis the final velocity of an off-spring projectile at the launcher/gun barrel/guide's exit in feet/second and one g is the acceleration due to gravity at the Earth's surface and is the standard unitless gravity symbol g:

Modifying the off-spring projectile mass thereby the off-spring projectile's mass properties and parent case initial volume and final velocity V_fat off-spring projectile base barrel/guide exit to obtain the desired characteristic impedance (Z) in the equation Z=F/V_f=J and reducing the amount of propellant in the launcher/gun system by an amount that will preserve off-spring projectile momentum that will satisfy the momentum equation M_N×V_FN=M_O×V_FOto retain the gun's operating conditions within the limits of the gun's material properties, where M_Nand V_FNare the new values of the off-spring projectile mass and final velocity of the off-spring projectile at off-spring projectile base barrel/guide exit that yield the desired system impedance (Z) and M_Oand V_FOare the former values of an off-spring projectile's mass and velocity at off-spring projectile base barrel/guide exit that were unequivocally demonstrated to maintain the gun's operating conditions within the limits of the gun's material properties and operating parameters.