Aeronautics and astronautics – Missile stabilization or trajectory control – Stabilized by rotation
Reexamination Certificate
2001-06-14
2003-10-07
Barefoot, Galen L. (Department: 3641)
Aeronautics and astronautics
Missile stabilization or trajectory control
Stabilized by rotation
C102S529000
Reexamination Certificate
active
06629669
ABSTRACT:
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
/&rgr;&pgr;d
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
&rgr;=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
M&agr;
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
M&agr;
=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'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
>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
=−(&rgr;/2)×
A×C
spin
(
B×Ma×Re
)×
V
w
2
×d
(
pd/V
w
)×
e
c
where:
&rgr;=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's longitudinal axis
A spin damping moment may be defined as follows:
½&rgr;V
2
Sd(pd/V)C
spin
where:
&rgr;=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'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 balan
Barefoot Galen L.
Holland Joseph W.
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