Abstract:
A projectile and a method of launching a projectile from a barrel. The projectile of the present invention may be matched to a pre-selected barrel rifling to produce a controlled spin rate. Controlled spin rate is characterized by substantially balanced forward and axial deceleration. Substantially balanced forward and axial deceleration is characterized by an axial speed that decreases in relationship to the decrease in forward speed. Substantially balanced forward and axial deceleration produces a trajectory that is characterized by a gyroscopic stability factor that remains highly stable over a given distance of a trajectory. Gyroscopic stability is controlled during the projectile&#39;s flight by controlling the spin damping moment as a design element. Control of the spin damping moment may be achieved by incorporating physical features in the projectile&#39;s design and manufacture and/or may result from the incorporation of physical features imparted upon the projectile during launch.

Description:
BACKGROUND OF THE INVENTION 
     1. Technical Field 
     This invention relates generally to projectiles and more specifically to a projectile and a method of launching a projectile from a barrel to produce a controlled spin rate. 
     2. Background Art 
     Where the gyroscopic stability factor, S g , of a projectile in flight exceeds one, a gyroscopic stability condition is present. The gyroscopic stability factor may be defined as follows: 
     
       
           S   g =( I   x   /I   y )×( pd/V   w )×(2 I   x   /ρπd   5 )  
       
     
     where: 
     I x =axial moment of inertia of the projectile 
     I y =forward moment of inertia of the projectile 
     V w =velocity 
     d=projectile diameter 
     p=spin rate of the projectile 
     ρ=air density 
     Alternately, the gyroscopic stability factor may be defined as follows: 
     
       
           S   g   =P   2 /4 M=I   x   2   p   2 /2 pI   y   SdV   2   C   Mα   
       
     
     where, 
     P=the sum of epicyclic turning rates 
     M=mach number 
     I x =axial moment of inertia of the projectile 
     p=projectile axial spin in radians/second 
     I y =forward moment of inertia of the projectile 
     S=projectile reference area S=d 2 /4 
     d=projectile diameter 
     V=velocity 
     C Mα =pitching moment coefficient 
     The relationship between the axial moment of inertia I x  and the forward moment of inertia of the projectile I y  is readily observed. Additionally the above expressions attempt to characterize the relationship between a projectile&#39;s forward velocity, spin rate and geometry and the effect that these variables may have on gyroscopic stability. 
     It is generally believed that a projectile may be made gyroscopically stable by increasing the spin rate of the projectile. It is also widely believed that if a projectile is gyroscopically stable at the muzzle, it will be gyroscopically stable throughout its flight. 
     Practically speaking, however, the spin rate p decreases more slowly than the forward velocity, and therefore, the gyroscopic stability factor S g , continues to increase throughout the flight of the projectile. Designers usually prefer a gyroscopic stability factor S g &gt;1.2 to 1.5 at departure from the muzzle, but because spin rate decreases more slowly than the forward velocity it is also possible to introduce too much spin to a projectile. This condition is commonly characterized as “over-stabilization”. It has been observed that a projectile may become unstable by being “over-stabilized”, however, most designers and commentators have not been terribly concerned with this aspect of flight as it is also commonly held that small arm fire is ineffective past the range where instability due to “over-stabilization” may occur, for instance, in the range of 2000 to 4000 yards. 
     “Over-stabilization” is a popular mischaracterization used to describe a phenomenon wherein the axial speed of the projectile continues to increase in proportion to the forward speed. As a result, the projectile becomes incapable of following the bending trajectory and the longitudinal axis of the projectile continues to nose up in relation to the bending trajectory. This effect may be referred to as a decrease in tractability. The relationship between excess gyroscopic stability and lack of stability in flight has been previously observed. FIG. 11 is a schematic representation depicting the relationship between gyroscopic stability GS and distance D in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be readily seen, in each case the value for gyroscopic stability GS effectively continues to increase from the muzzle until termination of flight at T in the range of 2300 to 2500 yards. As will be seen, the relationship between a maximum GS value and a starting GS value produces the following ratios: 7.62 mm—approximately 9.50:2.20 or 4.32:1 and 50 caliber—approximately 5.60:1.60 or 3.50:1. 
     Skin friction at the surface of the projectile has a direct effect on the axial velocity of a projectile. A spin damping coefficient M S  may be defined as follows: 
     
       
           M   S =−(ρ/2)× A×C   spin ( B×Ma×Re )× V   w   2   ×d ( pd/V   w )× e   c    
       
     
     where: 
     ρ=air density 
     A=projectile cross section area 
     C spin =the spin damping moment coefficient 
     B=projectile geometry 
     Ma=mach number 
     Re=Reynolds number 
     V W =velocity 
     d=projectile diameter 
     p=spin rate of the projectile 
     e c =unit vector in the direction of the projectile&#39;s longitudinal axis 
     A spin damping moment may be defined as follows: 
     
       
         ½ρV 2 Sd(pd/V)C spin    
       
     
     where: 
     ρ=air density 
     V=projectile velocity 
     S=projectile reference area 
     d=projectile diameter 
     p=spin rate of the projectile 
     C spin =the spin damping moment coefficient 
     The relationship between the spin damping moment coefficient and the spin damping moment may be observed in the above formulas. Particularly, the greater the spin damping moment coefficient for any given atmospheric condition, projectile geometry, projectile velocity, both axial and forward and the ratio of axial spin to forward velocity, the greater the spin damping moment. The relationship between spin damping moment coefficient and forward velocity has likewise been observed. 
     FIGS. 12A and 12B are schematic representations depicting generally the relationship between axial deceleration, forward deceleration and distance in two projectiles of the prior art, a 7.62 mm and a 50 caliber. As can be seen in either case, the rate of decrease in forward deceleration exceeds the rate of decrease in axial deceleration in both cases and as a result, there is an increased probability of the occurrence of “over-stabilization” and as a result, instability in flight. 
     FIG. 13 is a schematic representation depicting the relationship between spin damping moment coefficient, SDMC, and forward velocity, MACH, in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be seen, in each case the spin damping moment coefficient in either case remains in the range of approximately −0.018 to −0.027 regardless of forward velocity. 
     The relationship characterized by the expression pd/V, projectile diameter times the spin rate of the projectile divided by the velocity, expressed in spin per caliber of travel, has also been previously observed. FIG. 14 is a schematic representation depicting the relationship between projectile diameter times the spin rate of the projectile divided by the velocity, pd/V, and distance D in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be readily seen, in each case the spin per caliber of travel effectively continues to increase from the muzzle until termination of flight at T in the range of 1300 to 2500 yards. Additionally, the relationship between a maximum pd/V value and a starting pd/V value produces the following ratios: 7.62 mm—approximately 4.22:1.94 or 2.17 and 50 caliber—approximately 5.07:2.35 or 2.15. In each instance, it should be noted that the value for pd/V, at termination of flight, may be characterized as increasing. 
     It may be advantageous to the efficiency of a projectile&#39;s flight to control the spin damping moment coefficient of the projectile by controlling various parameters of projectile design including projectile aerodynamics, projectile surface area and projectile surface features and finish. By controlling the spin damping moment coefficient the gyroscopic stability factor may be maintained within a predetermined desirable range and overall ballistic efficiency maybe improved. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a projectile and a method of launching a projectile from a barrel, the projectile having an axial velocity upon launching. The projectile of the present invention may be matched to a pre-selected barrel rifling to produce a controlled spin rate. “Controlled spin rate”, as used herein, is characterized by substantially balanced forward and axial deceleration. “Substantially balanced forward and axial deceleration”, as used herein, is characterized by an axial speed that decreases in relationship to the decrease in forward speed. Substantially balanced forward and axial deceleration produces a trajectory that may be depicted by a curve exhibiting a relatively narrow band of values for the gyroscopic stability factor over a given distance of a trajectory. 
     Gyroscopic stability is controlled during the projectile&#39;s flight by controlling the spin damping moment as a design element. More particularly, control of the spin damping moment may result from a projectile design that incorporates a relatively low aerodynamic drag value with physical features incorporated in the projectile&#39;s design and manufacture, or produced during launch, that increase the skin friction at the surface of the projectile. Alternately, the projectile may include both physical features incorporated in the projectile&#39;s during manufacture and physical features which are imparted upon the projectile during launch. 
     In one preferred embodiment of the invention, a projectile is provided having a relatively low density and a relatively low drag coefficient. A projectile manufactured and launched according to the present invention exhibits a drag coefficient in the range of 0.100 to 0.250. A physical feature is then identified and selected that will produce a pre-selected projectile surface area and/or surface relief that produces a calculated spin damping moment. For instance a projectile may be matched to a barrel including riflings that produce physical scoring on the exterior surface of the projectile which cover a predetermined percentage of the exterior surface of the projectile to produced a controlled effect on the spin damping moment resulting in a controlled deceleration of axial velocity of the projectile during flight. 
     In one preferred embodiment of the invention, the spin stabilized projectile is manufactured having sufficiently low aerodynamic drag so that upon launching, the ensuing axial drag, as increased by designed physical features, will cause the projectile to exhibit a controlled spin rate and controlled axial deceleration. The trajectory of such a projectile is characterized by substantially balanced forward and axial deceleration. The result is a projectile which is aerodynamically stable while not being overspun to the point of induced instability. The lower aerodynamic drag and the increased axial drag are substantially balanced throughout the projectile&#39;s flight to produce a controlled spin and increase in the spin damping moment. During flight, the gyroscopic stability of the projectile is not increasing or decreasing dramatically. 
     The gyroscopic stability factor of a projectile of the present invention, a projectile exhibiting substantially balanced forward and axial deceleration, should remain in the range of greater than or equal to 1.0 to less than or equal 3.0. Alternately, the gyroscopic stability factor of a projectile of the present invention, a projectile exhibiting substantially balanced forward and axial deceleration, should remain in the range of greater than or equal to 1.0 through and including three times the initial value at the muzzle. A projectile manufactured and launched according to the present invention, should exhibit increased tractability and stability particularly down range. Balancing forward and axial deceleration should produce a trajectory that is characterized by a nose that maintains a near direct into oncoming air orientation throughout its trajectory. The gyroscopic stability factor of the projectile increases or decreases only within a relatively narrow range. 
     Physical features which may contribute to a calculated control of a projectile&#39;s spin damping moment include but are not limited to the total surface area of the projectile, the length of the projectile, the length, depth and number of lands and grooves engraved by barrel riflings on launch, surface roughness and material density of the projectile. Controlled axial drag imparts a controlled axial deceleration. Physical features which may be calculated to affect the spin damping moment include but are not limited to the following: 
     a. control of projectile total surface area and total axial surface friction; 
     b. decrease in the density of constituent materials; 
     c. control of the number of lands and grooves in the rifle bore from which the projectile is shot and engraved, thereby controlling the number of engraved grooves on the projectile; 
     d. control of the length of engraving to control axial deceleration; 
     e. control of the depth of engraving to control axial deceleration; 
     f. control of the forms of engraving using trigonal, polygonal, and multi-cornered shapes to increase axial drag to control axial deceleration; 
     g. incorporation of fins, canards, wings, deflectors, and protrusions to control axial deceleration; 
     h. control of the surface roughness of the projectile to control axial deceleration; 
     i. any other feature manufactured into the projectile or caused by the engraving process which by effect controls the spin dampening moment and causes a gyroscopic balance the projectile&#39;s trajectory. 
     It is believed that the control of spin damping moment by the control and specification of physical features provides a projectile which in flight maintains gyroscopic stability within a specified range preventing increased yaw, increased precession, increased inaccuracy and projectile instability. 
     Historically, designers of projectiles for small arms have not been concerned with ballistic efficiency or the effects of “over-stabilization”, primarily instability, at ranges beyond 2000 yards as it is commonly held that small arm fire is ineffective past this range. A projectile engraved and launched according to the teachings of the present invention, however, is designed to decelerate from supersonic flight through transonic to subsonic in a stable and predictable manner effective in a range beyond 3000 yards. 
     The present invention consists of the combination and arrangement of parts hereinafter more fully described, illustrated in the accompanying drawings and more particularly pointed out in the appended claims, it being understood that changes may be made in the form, size, proportions and minor details of construction without departing from the spirit or sacrificing any of the advantages of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a representative side view of a projectile according to the invention; 
     FIG. 2 is a representative side view of a projectile according to the invention; 
     FIG. 3 is a representative side view of a projectile according to the invention; 
     FIG. 4 is a representative side view of a projectile according to the invention; 
     FIG. 5 is a representative side view of a projectile according to the invention; 
     FIG. 6 a cross-sectional cutaway of a projectile according to the invention; 
     FIG. 7 is a schematic representation depicting the relationship between distance and gyroscopic stability in a projectile of the present invention; 
     FIG. 8 is a schematic representation depicting generally the relationship between axial deceleration, forward deceleration and distance in a projectile of the present invention; 
     FIG. 9 is a schematic representation depicting generally the relationship between the spin damping moment coefficient and forward velocity in a projectile of the present invention; 
     FIG. 10 is a schematic representation depicting generally the relationship between the spin rate of the projectile divided by the velocity, pd/V, and distance in a projectile of the present invention; 
     FIG. 11 is a schematic representation depicting generally the relationship between gyroscopic stability and distance in two projectiles manufactured and launched according to the prior art; 
     FIG. 12A is a schematic representation depicting generally the relationship between axial deceleration, forward deceleration and distance in a projectile of the prior art; 
     FIG. 12B is a schematic representation depicting generally the relationship between axial deceleration, forward deceleration and distance in a projectile of the prior art; 
     FIG. 13 is a schematic representation depicting generally the relationship between spin damping moment coefficient and forward velocity in two projectiles manufactured and launched according to the prior art; and 
     FIG. 14 is a schematic representation depicting generally the relationship between projectile diameter times the spin rate of the projectile divided by the velocity and distance in two projectiles manufactured and launched according to the prior art. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIGS. 1 through 5, projectile  10  is shown including body  11  having bearing surface  12  and ogive  15  which is continuous to and extends forward from bearing surface  12 . Projectile  10  includes boattail  14  continuous to and extending rearward from bearing surface  12 . Boattail  14  terminates at tail end  16 . Ogive  15  is formed including relatively long radius R converging at méplate  17 . Alternately, as shown in FIG. 2, ogive  15  may be formed including pointed tip  18 . FIG. 1 is a representative side view of projectile  10  according to the invention having a low aerodynamic drag factor. FIG. 1 is a representative side view of projectile  10  prior to launching and engraving of physical features. 
     FIG. 2 is a representative side view of one embodiment of projectile  10  according to the invention including a pattern of alternating lands  20  and grooves  21  forming a physical feature which is imparted on the surface of bearing surface  12  of projectile  10  upon launching. 
     FIG. 3 is a representative side view of projectile  10  according to the invention including a pattern of alternating lands  22  and grooves  23  forming a physical feature which is imparted on the surface of bearing surface  12  of projectile  10  during a manufacturing process. 
     FIG. 4 is a representative side view of projectile  10  according to the invention including a pattern of dimples  24  forming a physical feature which is imparted on the surface of bearing surface  12  of projectile  10  during a manufacturing process. Additional physical features may be added to the pattern of alternating lands  22  and grooves  23  shown in FIG. 3 or the pattern of dimples  24  shown in FIG. 4 during launch to achieve a desired ratio of surface area of projectile  10  including physical features to the total surface area of projectile  10  such that a substantially balanced forward and axial deceleration is achieved. 
     FIG. 5 is a representative side view of projectile  10  according to the invention including a pattern of alternating lands  20  and grooves  21  forming a physical feature which is imparted on the surface of bearing surface  12  of projectile  10  upon launching. In the embodiment of the invention shown at FIG. 5, alternating lands  20  and grooves  21  include angle of attack  19  substantially equal to 5°±1°. 
     In the embodiment of the invention shown at FIG. 5, projectile  10  includes overall length L. Bearing surface  12  includes length L 1  and diameter D 1 . Ogive  15  includes effective length L 2  and is formed having a radius R. Tip  17  is configured as a flat having a diameter D 3 . Boattail  14  includes length L 3  and diameter D 2  at tail end  16 . Grooves  21  include length L 4  and, as shown in FIG. 6, width W and depth E. 
     According to one aspect of the invention, length L of projectile  10  equals 5.25 to 5.50 times diameter D 1 , length L 1  of bearing surface  12  equals 1.25 to 1.50 times diameter D 1  and length L 2  of ogive  15  equals 3.10 to 3.25 times diameter D 1 . The length L 3  of boattail  14  may equal 0.10 to 1.1 times diameter D 1 . 
     In the embodiment of the invention shown at FIG. 5, projectile  10  is shown in a .408 caliber. In this embodiment of the invention, projectile  10  is formed by machining a solid copper nickel alloy, for instance C-145, a Tellurium copper-alloy containing less than 1% Tellurium. C-145 has a density on the order of 0.322 lb./in. 3 . Projectile  10 , as shown in FIG. 5 will have a mass in the range of 400 grains to 430, depending upon nose configuration and length of boattail  14 . Projectile  10 , as shown at FIG. 5 includes an overall length L substantially equal to 2.217 inches. Bearing surface  12  has a length L 1  substantially equal to 0.580 inches and diameter D 1  substantially equal to 0.408 inches. Ogive  15  has length L 2  substantially equal to 1.300 inches and is formed on a 7.00 inch radius. Tip  17  is configured as a flat having a diameter D 3  equal to 0.020 inches. Boattail  14  includes length L 3  substantially equal to 0.337 inches and diameter D 2  at tail end  16  substantially equal to 0.340 inches resulting in a taper from bearing surface  12  to tail segment  14  substantially equal to 6.00 degrees. A projectile manufactured and launched according to the present invention exhibits a drag coefficient in the range of 0.100 to 0.250. Projectile  10  shown at FIG. 5 exhibits an drag coefficient substantially equal to 0.211. 
     The configuration shown in FIG. 5 results in projectile  10  having a ratio of length L 1  over L substantially equal to 0.262, a ratio of length L 2  over L substantially equal to 0.586 and a ratio of length L 3  over L substantially equal to 0.158. Length L 4  of grooves  21  is substantially equal to 0.686 in. As shown in FIG. 6, width W of grooves  21  is substantially equal to 0.100 in. and depth E is substantially equal to 0.004 in. The configuration shown in FIG. 5 results in projectile  10  having a ratio of depth E of groove  21  to diameter D 1  approximately equal to 0.001. Otherwise stated, grooves  21  may be of virtually any depth, however, a depth E substantially equal to 1% of the projectile body diameter D 1  is preferred. 
     The total surface area of projectile  10  as shown at FIG. 5 is substantially equal to 1.923 in. 2 . The total surface area of bearing surface  12  as shown at FIG. 5 is substantially equal to 0.744 in. 2 . The total aggregate area of grooves  20  as shown at FIG. 5 is substantially equal to 0.550 in. 2 . The ratio of the aggregate areas of all groves  21  to total surface area of bearing surface  12  is substantially equal to 0.739. The ratio of the aggregate areas of all groves  21  to total surface area of projectile  10  is substantially equal to 0.285. The ratio of the total surface area of projectile  10  to the total surface of the physical feature as shown at FIG. 5 is substantially equal to 3.40:1. A projectile manufactured and launched according to the present invention includes a ratio of the total surface area of projectile  10  to the total surface of the physical feature as shown at FIG. 5 in the range of to 3.00:1 to 4.00:1. 
     FIG. 6 a cross-sectional cutaway taken through bearing surface  12  of projectile  10 . Projectile  10  includes a plurality of alternating lands  20  and grooves  21 . In this case, there are a total of eight lands  20  and  8  alternating grooves  21 . Each groove  21  includes a depth E and a width W. 
     FIG. 7 is a schematic representation depicting the relationship between gyroscopic stability GS and distance D in a projectile manufactured and launched according to the present invention. As can be readily seen, the value for gyroscopic stability GS remains in the range of 1.0 to 2.0 from the muzzle until termination of flight at T in the range of 3500 yards. As will be seen, the relationship between a maximum GS value and a starting GS value produces the following ratio: approximately 1.88:1.42 or 1.32:1. It should also be noted that the value for GS, at termination of flight, may be characterized as decreasing. Projectile  10 , as shown at FIG. 5, exhibits a gyroscopic stability in the range of greater than or equal to 1.0 to less than or equal 3.0 for any given distance from the muzzle. In an alternate embodiment of the invention, the trajectory of projectile  10  is characterized by a gyroscopic stability greater than or equal to 1.0 through to three times the gyroscopic stability at the muzzle for any given distance from the muzzle. 
     FIG. 8 is a schematic representation depicting the relationship between axial deceleration, forward deceleration and distance in a projectile of the present invention. As can be seen, the slope of both curves remains substantially equal from the muzzle until termination of flight at T in the range of 3500 yards. A projectile manufactured and launched according to the present invention includes a trajectory characterized by a rate of axial deceleration that is continuously decreasing throughout flight. 
     FIG. 9 is a schematic representation depicting the relationship between the spin damping moment coefficient and forward velocity in a projectile of the present invention. Projectile  10 , as shown at FIG. 5, exhibits a spin damping moment coefficient in the range of −0.035 to −0.045. It will be noted that the spin damping moment coefficient remains effectively in the range of approximately −0.035 to −0.045 throughout flight regardless of the forward velocity of the projectile. This represents a substantial increase in the spin damping moment coefficient over the prior art. As previously noted, the spin damping moment coefficient for projectiles representative of the prior art, remains effectively in the range of approximately −0.018 to −0.027 regardless of forward velocity. In one preferred embodiment of the invention, projectile  10  exhibits a ratio of a high spin damping moment coefficient to a low spin damping moment coefficient in the range of 1.25:1 to 1.45:1. 
     Projectile  10  exhibits a ratio of total projectile surface area to spin damping moment coefficient in the range of 45 to 50 during flight. Projectile  10  exhibits a ratio of density of the projectile to spin damping moment coefficient of the projectile in the range of 7.0 to 9.0 
     FIG. 10 is a schematic representation depicting the relationship between the spin rate of the projectile divided by the velocity as expressed in spin per caliber of travel, pd/V, and distance in a projectile of the present invention. As will be seen, the relationship between a maximum pd/V value and a starting pd/V value produces the following ratio: approximately 3.11:2.35 or 1.32:1. It should also be noted that the value for pd/V, at termination of flight, may be characterized as decreasing. 
     Without limiting the invention, it is believed that the negative increase in the spin damping moment coefficient, over projectile design for spin stabilized projectile of the prior art may be due the spin/forward movement stabilizing effect of the air flow passing through grooves  21 , (shown in FIG.  5 ). The value for spin per caliber of travel, pd/V, for projectile  10  remains fairly constant and the spin damping moment coefficient decreases from the point of exit from the muzzle. Grooves  21  may act effectively as fins to control spin per caliber of travel, pd/V, to match the speed of oncoming air. It is believed that projectiles of the prior art are not capable of acting in this manner for the reasons previously discussed. Without limiting the invention, it is believed that because the value for spin per caliber of travel, pd/V, remains fairly constant, a more laminar flow of air about projectile  10  results preventing heat transfer that is associated with a more turbulent air flow that results from the effects of “over-stabilization”. The heat transfer that is associated with a more turbulent air flow results in a decrease in the friction coefficient allowing an associated increase in the spin per caliber of travel, pd/V. As the spin rate, pd/V, increases the engravings of a projectile of the prior art spin past the flow of oncoming air and, rather than channeling the air through the grooves, the air about the projectile increases in temperature and becomes more turbulent. 
     While this invention has been described with reference to the detailed embodiments, this is not meant to be construed in a limiting sense. Various modifications to the described embodiments, as well as additional embodiments of the invention, will be apparent to persons skilled in the art upon reference to this description. It is therefore contemplated that the appended claims will cover any such modifications or embodiments as fall within the true scope of the invention.