CA2128333C - Methods and apparatus for determining the trajectory of a supersonic projectile - Google Patents

Abstract

Apparatus and method for determining the trajectory (86) of a supersonic projectile (87) of unknown velocity and direction having at least three spaced-apart sensors (80-82) capable of encountering a shock wave generated by a supersonic projectile (87) passing in the vicinity of the sensors (80-82) and capable of generating signals in response to the shock wave, which signals are related to an azimuth and elevation angle of a unit sighting vector from each sensor to an origin of the shock wave. Means are provided for calculating from the signals the azimuth and elevation angle of the unit sighting vector from each sensor (80-82) to the origin of the shock wave. Means are provided for calculating from the unit sighting vector of each of the three sensors (80-82), the azimuth and elevation angle of the local trajectory (86) of the projectile (87).

Description

WO 93/16395 PCr/US93/01729 2~ 2833~
I
~E:THODS ~ND APPA~ATUS FOR Dc.
TXE TR~ilECTORY OF A 8UPERSONIC PRQ~ECTI~E
The invention relates to method and apparatus for detPrm;n;n~, among others, the trajectory, miss-distance and velocity of a supersonic projectile, and to det~rm;n;ng the approximate firing position of such a projectile.
s2AcRG~OUND OF THE INV~NTION
The art has long recognized that acoustical means may be used for det~orm;ning a portion of the trajectory of a projectile, and the art, generally, has used such acoustical means for locating the point at which a projectile passes into or near a training target for scoring the accuracy of small arms fire, in lieu of the more conventional paper targets. An example of the foregoing is U. S. Patent 4,514,621. Basically, these devices operate by means of a grid of acoustical sensors in which the plane of the sensors is normal to the trajectory of the projectile, e.g. a rifle bullet. As the bullet passes through that grid of sensors, the sensors can locate the passage of the bullet through that grid of sensors by calculating the time delays of the sensors When two such grids are spaced apart, one behind the other, and the path of a bullet passes through both of the grids, a portion of the trajectory of a bullet may also be det~rm; nf~, and U. S . Patent 4,445,808 is representative thereof. That patent also points out that if a such a dual grid system is deployed cn ~ ~l itary vehicL~, ~.g ~ h Li~opter, ~nd enemy fire WO 93/16395 PCr/US93/01729 passes through the two spaced-apart grids, the general direction of the trajectory of that fire may be det~rm; necl .
Similar methods for locating the passage of a bullet may use other types of sensors, such as electricàl resistance elements, rather than acoustical transducers, and U. S. Patents 3,585,497 and 3,656,056 are representative thereof.
Rather than using a grid of acoustical sensors, curved elongated hoops with acoustical transducers at ends thereof may be used. When a bullet passes within the vicinity of the curved hoops, the position of the bullet passing such curved hoops can be calculated, and ~. S. Patent 4,351,026 is representative thereof.
Curved hoops may also be used where the target is moving within a defined field normal to the hoops, and u. S. Patent 5,025,424 is representative of that technol ogy .
Somewhat similarly, U. S. Patent 4,885,725 suggests a plurality of triangularly arrayed, mechanically connected acoustical transducers, instead of curved hoops, for detPrminin~ the point in which a bullet passes the target area and for providing some indication of the velocity of that bullet.
The foregoing patents are, primarily, directed toward training devices for scoring the accuracy of a trainee ' s f ire, although, as mentioned above, U . S .
Patent 3, 445, 808 suggests the use of double acoustical grids for ~9etPrm;n;ng the general direction of enemy fire toward a military device, such as a helicopter. . .
Further, U. S. Patent 4, 659, 034 suggests the ~se of a plurality of transducers disposed on a movable (towed)_ target and, by use of the transducers, . . . . . . _ _ _ _ _ _ _ _ _ _ _ _ ..

WO 93/l6395 PCI/I~S93/01729 dett~rm;n;ng the accuracy of fire toward that target.
That accuracy of fire includes how close the projectile comes to the towed target (referred to as the miss-distance) . ~. S . Patent 4, 323, 993 similarly dett~rm;n,o~ a miss-distance by acoustical transducers, and, particularly, in this patent the miss-distance is calculatable even though the projectile misses the towed target altogether.
U. s. Patent 4,80~,159 provides a method for estimating the miss-distance between a proj ectile and a movable training target. In making such estimation, at least a portion of the traj ectory of the pro ~ectile is also estimated. ~owever, as that ~atent points out, the estimations of at least a portion of the traj ectory of the projectile involves a number of possible estimates of the actual projectile path, and to eliminate erroneous estimates, additional transducers are used for consecutively selecting true estimates from erroneous estimates .
2 0 Thus, in general, the prior art, mainly, uses sensors, especially acoustical transducers, in various spatial arrangements for determining the miss-distance of a proj ectile passing through or near a target . 50me of these systems in the art may provide a general direction of a local trajectory of the projectile, but these systems are not capable of providing accurate information as to the entire path of the projectilet and, hence, the position of the source of that proj ectile . In addition, these prior art systems, whatever their configuration, must have pre-knowledge of the direction and/or the velocity of the proj ectile, in order to determine the local traj ectory of the pro j ectile .

WO 93/16395 ~ PCr/US93/01729 .
2128333 - 4 ~
Thus, the prior art systems are useful essentially only in training exercises where either or both of the direction or velocity of the projectile is known, and such systems have essentially only been employed in such exercises. Thus, the sy6tems are not applicable ~to battlefield conditions where it is important tD know essentially the entire direction of the trajectory of a projectile, the miss-distance of that projectile, the approximate caliber or mass of that projectile, and the approximate origin of the source of that projectile, and under conditions where the velocity and/or direction of the proj ectile is unknown. All of this information is most useful in battlefield conditions where a military unit, under attack, cannot visually or by other human senses determine the direction, miss-distance, caliber and source of enemy f ire .
This is often the case in modern warfare For example, in modern tan}c warfare, the battlefield m~y span many kilometers, and ;nrnm;n~J enemy fire, for example, shell fire, is confused with other background battle noises and noises produced by friendly fire. ~or example, a tank commander may hear the distinctive sounds of a near-miss enemy shell, but in the confusion of battle noises, the tank co~ n~l~r may not be able to determine either an approximate azimuth or elevation of the trajectory of that enemy shell. Thus, the tank cr~ nrlr~r cannot determine whether the shell is being fired from a long distance, or a very short distance, or whether the fire is coming from the front, rear or sides, or even the approximate caliber of that shell fire. Without such information, for example, the tank crm~ ntlF~r cannot quickly and positively respond to such enemy fire, and the dangers o~ a near-miss previous 2128~33 =5 shell can increase markedly with st~ ePP~l;n~ enemy shells, which makes return suppressing fire of utmost importance .
Also, the prior art devices are not capable of scoring training fire where the training fire is of unknown velocity and/or direction. This is usually the situation in maneuver training fire where, for example, moving and roving tanks are f iring on a target, e . g . an obsolete tank.
As can, therefore, be appreciated, it would be of suostantial advantage in the art to provide apparatus and methods for aetPrmin;n~ essentially the entire traj ectory of a supersonic proj ectile of unknown velocity and direction, such as shell fire, or even small arms fire. That trajectory will provide the approximate position of the origin of that incoming enemy fire. In addition, when the miss-distance of such incoming enemy fire is calculated, the 1 ;kPl ;h~7od of additional and eminent more accurate enemy fire is de~Prm;n~le. This provides an ~o~Lu~ity for immediate and effective return suppressing fire.
Further, it would be of advantage to provide such apparatus and methods which are also adaptable to maneuver training f ire .
sRIEF SUN~ARY OF ~rl}E INVENTIO~
The present invention is based on three primary and several subsidiary discoveries. Firstly, it was discovered that at least three spaced-apart sensors, which are positioned to encounter the shock wave 30 generated by a supersonic projectile, can be constructed so as to generate signals in response to the shock wave which are related to the azimuth and elevation angle of a unit sighting vector from each sensor to the origin of WO 93/16395 P(~rtUS93/01729 .
2~2~33 - 6 -the shock wave. Of course, a unit vector, while having direction, has no magnitude (distance in this case~.
Thus, the distance from each sensor to the origin of the shock wave and, hence, the trajectory remains unknown, and these unit sighting vectors could point to a large number of possible actual trajectories.
As a second and important discovery, it was found that, most surprisingly, each unit sighting vector makes the same angle with the trajectory no matter what the azimuth or elevation angle of the trajectory, so that instead of a number of possible trajectory solutions, only one actual traj ectory solution may be calculated .
As a subsidiary discovery, it was found that such a sensor may be most conveniently constructed by three spaced-apart transducers, each of which are capable of seguentially generating a signal in response to sequential pressure on each transducer, created by the shock wave as it encounters each transducer. The three transducers in each sensor, therefore, produce a signal which is related to the azimuth and elevation angle of a unit sighting vector for each sensor, and with a combination of three such sensors, three accurate unit sighting vectors to the origin of the shock wave and hence the trajectory of the projectile can be determined .
In this embodiment, the unit sighting vectors of each sensor are determined by measuring the time when the shock wave encounters each of the transducers in a sensor, and this time relationship of the three transducers provides an accurate unit sighting vector from the sensor to the trajectory of the projectile.
With the present important discovery that these unit sighting vectors form the same angle with the WO 93/1639~ PCI/US93/01729 212~333 trajectory, the magnitude (distance in this case) of the unit sighting vectors can be calculated. With the magnitude being calculated, three points in space are, therefore, defined and these three points in space will, accordingly, define the azimuth and elevation angle of the local traj ectory of the proj ectile under almost all circumstances .
As a subsidiary discovery, it was found that the portion of the shock disturbance best suited for such determinations i5 the leading edge (also called the shock front~ and the best suited shock disturbance is the first shock wave received by the sensor (also called the main shock wave).
As a further subsidiary discovery, it was found that, while three sensors are necessary for det~rm;n;ng the tr2jectory of the projectile, there are some very limited situations where three sensors cannot determine the trajectory, and for increased reliability of detc~ ning the trajectory, a plurality of more than three sensors, each projecting a like unit sighting vector from each of the plurality of sensors to the trajectory of the projectile, are used. In addition, it was found that while a plurality of such sensors may be so disposed, in certain circumstances, only selected ones of that plurality of sensors are better used for det~rm;nin~ the trajectory of the projectile, rather than using all of the plurality of sensors for any one particular traj ectory .
As a further most important primary discovery, it was found that, with the above arrangement of sensors, the velocity of the projectile may be detorminP~, and, further, by det~ining the time lapse of the passing of the main shock front and an ambient density line of the projectile over the sensors, the WO 93/16395 PCr/US93/01729 .

length of the proj ectile can also be relatively accurately calculated. Further, in this regard, it was found that the intensity of the main shock front, normalized to the miss-distance, the projectile velocity, and the length of ~he pro~ectile provide sufficient information so that, from known projectile characteristics, the likely proj ectile itself can be determined. By knowing the projectile (and hence its specific characteristics), and having determined its local velocity and the local tra~ectory, the entire traj ectory can be calculated, and this provides a close approximation of the position of the origin of that proj ectile~
Accordingly, the miss-distance of the proj ectile can be determined; the traj ectory of the projectile can be determined; the class of projectile or the projectile itself can be det~rm;n~d; and the approximate position of the origin of that projectile can be determined. With this rl~rm;n~l information, for e~ample, a tank rnmr~nder could order effective suppressive fire against the source of that projectile, even in battlefield conditions where the proj ectile of interest is of previously unknown velocity and direction .
Thus, briefly stated, the present invention provides an apparatus for det~rm;n;ng the trajectory of a supersonic projectile of unknown velocity and direction. In this apparatus, at least three spaced-apart sensors are capable of encountering a shock wave generated by a supersonic projectile passing in the vicinity of the sensors. The sensors are also capable of generating signals in response to the shock wave, which signals are related to an azimuth and elevation angle of a unit sighting vector from each sensor to the WO 93/16395 PCr/US93/01729 ~12~3~3 shock wave origin. Means are provided for calculating from those signals the azimuth and elevation angle of the unit sighting vector from each sensor to the origin of the shock wave. Means are also provided for calculating from the unit sighting vectors of each of the three sensors, the azimuth and elevation angle of the local trajectory of the projectile.
Similarly, a method for de~rm;n;n~ the traj ectory of a supersonic proj ectile of unknown velocity and direction is provided. In this method, at least three spaced-apart sensors are provided, which sensors are capable of encountering a shock wave generated by a supersonic proj ectile passing in the vicinity of the sensors. The sensors are also capable of generating signals in response to the shock wave, which signals are related to an azimuth and elevation angle of a unit sighting vector from each sensor to an origin of the shock wave. An azimuth and elevation angle of a unit sighting vector from each sensor to the origin of the shock wave is calculated from the signals.
From the unit sighting vectors of each of the three sensors, the azimuth and elevation angles of the local trajectory of the projectile are calculated.
BRIEF DESCRIPTION O~ T}~E DRAWINGS
Figure 1 is a diagrammatic illustration of the acoustical disturbances generated by a supersonic proj ectile;
Figure 2 is a diagrammatic illustration of 3 0 maj or known disturbances generated by a supersonic proj ectile;
Fig~re 3 is an illustration of an oscilloscope trace of signals generated from an acoustical transducer encountering a passing shock wave;

WO 93/16395 PCr/US93/01729 . .
212g333 - lo -Figure 4A is a diagrammatic illustration of the metbod by which the trajectory of a projectile is calculatable from the vectors generated by three spaced-apart sensors;
Figure 4B is an out take of a portion of the vectors of Figure 4A;
Figure 5 is a diagrammatic illustration of the method of calculating the vectors to the traj ectory of a passing supersonic projectile;
Figure 6 is an illustration of a suitable sensor arrangement;
Figure 7 is an illustration of a suitable apparatus arrangement;
Figure 8 is a diagrammatic illustration of a special case for calculation when the traj ectory of a proj ectile ls parallel to two of the present three sensors;
Figure g is an idealized illustration of signals produced by the present sensors during the encountering and passing of a shock wave;
Figure 10 is a diagram}ratic illustration of disposition of the present sensors on a military vehicle, with a diagrammatic illustration of a passing proj ectile;
Figure 11 is an illustration similar to Figure 10, but where the military vehicle is a helicopter;
Figure 12 illustrates the use o~ the present sensors in connection with a small arm~ i.e. a rifle;
Figure 13 shows an alternate disposition of the present sensors on a rifle; and Figure 14 shows the present sensors disposed on a portable device.

WO 93/16395 PCr/US93/Ot729 2~2~33 DE~rA~I,ED DES1'KI~llUN OF T}IE I~rENrrIoN
Before considering the details of the apparatus and method, an explanation of the believed theory by which the present invention operates is f irst provided, although it is expressly reserved herein that the applicants are not bound by this theory.
As is well known, when a supersonic projectile travels through the atmosphere, a series of shock disturbances occurs. When the projectile is a ballistic projectile, having a forward portion, e.g. tip or nose, these disturbances are well defined. The disturbance from the forward portion is the main shock wave, and the well-def ined leading edge of that main shock wave is referred to as the main shock front.
A shock wave propagates at the speed of sound normal to that shock front, as illustrated in Figure 1.
The sine e of the shock angle 1 is given by the sound velocity Vs divided ~y the projectile velocity V and is:
sin(e) = Vs/V. (1) Figure 2 is a representation of a Schlieren photograph of an actual proiectile, the shock disturbances, and the wake thereof. As can be seen, an extremely sharp boundary exists at the main shock front formed by the main shock wave emanating from the forward 2; portion, usually the nose, of the pro~ectile. The onset of this boundary is typically 1 to 10 molecular mean-~ree-paths in length, and, hence, is quite well defined. This shock front produces a very rapid rise in pressure, for e2~ample, as measured by a sensor, which rapid rise in pressure is in the order of a sub-nanosecond .
The line emanating from thQ corner of the base of tbe proj ectile and mainly parallel to the main shock front may be referred to as the ambient density ~ine, WO 93/16395 PCl/US93/01729 although it is really a cone. This line represents the position of a pressure isobar which is essentially the same as the ambient air pressure. Minor, less well-defined shock waves 20 originate along the proj ectile behind the main shock front and ahead of the ambient density line. There are also minor trailing shock waves originating behind the ambient density line and up to the relaxation shock front, at which point those waves fall back into the wake 22 of the proj ectile.
The behavior of these shock waves and their fronts can be understood from the representations of an oscillograph picture, as shown in Figure 3. The trace is a measure of pressure on a ballistic microphone due to shock waves produced by a 5 . 56 mm bullet fired from an M-16 rifle. At point A, there is a sharp pressure increase which rises from ambient pressure to a high initial value~7 indicating the passage of the shock front of the main shock wave. As the bullet passes the microphone, the pressure drops below ambient pressure at point B, indicating the ambient density line. The pressure of the relaxation shock front and the wake are indicated at point C.
The velocity of the various shock waves is a function of the density of the gas in which these waves are travelling. Since the pressure, and hence density, is higher than ambient pressure in front of the ambient density line, the shock waves in the region between the ambient density line and the main shock front (see Figure 2) travel faster than waves from the main shock front and eventually catch up with the main shock front.
On the other hand, the shock waves originating between the ambient density line and the relaxation shock front travel through lower pressure, and hence density, and, WO 93/16395 PCr/US93/01729 hence, propagate more slowly than the waves from the main shock front and, therefore, fall back into the trailing wake at point C.
In view o~ the above, it has been discovered that the ambient density line, which emanates fro~` the base of the projectile, is sufficiently defined that the proj ectile length can be estimated from the trace of Figure 3. For example, chronographic measurements indicate that the velocity of a test bullet was approximately 3,150 ft./sec. This gives a shock cone angle of sin(e) = 1,050/3,150 or e = 19.5- (see equation 1). The length LB of the bullet is approximately given by:
LB = Vst/sin(e) = Vt, (2) Nhere t is the time between point A and point B along a line perpendicular to the main shock front of Figure 2, and V is the velocity of the projectile. Since each division is 4.1 microseconds in Figure 2, this yields a time -of approximately 16.4 microseconds, and thus a length of 0 . 62 inch. The actual length of the 5 . 56 mm bullet was 0 . 678 inch.
It is the normal of the propagation of the shock front o:E the shock wave that establishes which part of the shock wave strikes an individual sensor. It is initially assumed that the portion of the conical shock wave striking an individual sensor can be considered a plane wave, and this is a reasonable assumption, if the shock wave is generated from a proj ectile passing some reasonable distance ~rom a sensor. For example, for a bullet trajectory passing only one foot from a three inch sensor, this assumption leads to a less than one degree error. -This error decreases rapidly as the distance from the sensor to the bullet is increased. E~owever, if the projectile passes WO 93/16395 PCr/US93/01729 2~2~33'~
close to a. sensor and the assumption of a plane wave introduces unacceptable error, once it is de~Prm;nP~
that the miss-distance is close to a sensor, reiteration of the calculation may be performed to correct for the shape of the shock wave.
In Figure 4, sensors S j, S2 and S3 with intraspacing vectors D12, Dz3 and D13 determine a plane.
Therefore, the vector D12 gives the distance (magnitude) and direction of sensor S2 from sensor S1, and likewise vector D13 and D23 give similar distances and directions.
Above this plane, at an unknown orientation with respect to the plane, is the trajectory of a projectile of unknown velocity. The sighting vector of each sensor is determined by each sensor, as explained in more detail below. Of course, a sighting vector has only direction and no magnitude (distance in this case) and may, therefore, be referred to as a unit sighting vector. Hence, these unit sighting vectors could establish a ~ost of different three points in space and, hence, a host of possible trajectories. Thus, without more, these unit sighting vectors would be of no usefulness .:
E~owever, as briefly set forth above, it was surprisingly discovered that each unit sighting vector forms the same angle at a given velocity of a projectile with the origin of the shock wave (and, hence, the traj ectory) . This discovery, therefore, makes .it possible to calculate the magnitude (distance) of each unit sighting vector, so that, with the magnitude rlPtPrm; ned, the unit sighting vector becomes a full sighting vector (direction and magnitude), as shown in Figure 4 as full sighting vectors I,1, L2 and L3. Without such discovery, calculation of the trajectory would have been ;Tnros~ihle. With such full sighting vector -WO 93/1639~ PCI/US93/01729 212g33~
- 15 - ;
determined, as shown in ~igure 4, each full sighting veclor will result in only one point in space, and the three points in space, one from each full sighting vector, ~ully establishes the actual traj ectory of the projectile for almost all cases.
The vector d is aefined as the local trajectory unit vector. The vector d12 (see ~igure 4B~
designates the distance and direction from the tip of L1 to the tip of L2 along the projectile. trajectory, and likewise there will be vectors d23 and d~3, which are parallel to ~!:d, as shown in ~igure 4A. The v~ectors d1z, d23 and d13 are each parallel to ~d, where d is.the local traj ectory .
The first key observation is that the vector dot-product of the traj ectory vector d with the unit sighting vectors is just cos(ai) where 1 = ~9 ~ 90- (~ is the shock cone angle). Therefore, where the unit sighting vectors are designated l1 ~ 12 and î3, then:
,o (4.3) d 11 = d îl = d î3 and s inc e (4.4) cos(~) = sin(~) these dot-products are then simply equal to V5/V. By ~5 noting from ~igure 4B that (4 5) d~ Ll + Dll + Ll, and likewise it follows that (4 . 6) dl3 = -Ll ~- Dl3 + L3 , and (4 7) d L + D + L
o Equation 4 . 3 can be used to form WO 93/l6395 PCr/US93/01729 212~333 - 16 -(4 . 8) d~ i}) = 0 (4 . 9) ~13 (~1 ~ î3) =
(4-10) c~l3~ î3) = O.
Substituting Equations 4 . 5 through 4 . 7 into :Equations 4 . 8 through 4 .10 and carrying out the dot-product distri~lltion, it is found that:
(4.11~ ~ I L1 1 + D~ + ~ -il + f Ll I i~ DL~
10(4-12) - I L1 ¦ ~- D13 11 + 1 I~3 l 11'13 ~ 1-13 - ~3_~3 - I I~3 1 =-(4-13) - I Ll I + Dl3 il ~ L3 1 il i3 + I Ll 1 i~ 13 - D~3 i? - I L3 1 or, rearrang~ng, -15(4.14) ~( I Ll I + I Li I ) + ( I Ll I + I Ll j ~ } + Dl~ ) = O
(4-15) -( ! I~ r+ ¦ L3 ~ - ( I L1 1 ~- I L3 1 )ll-i3 + Dl3 (il - î3? =
~4.16) -( 1 L~ 1 + I L3 1 ) -1- ( I ~ L3 1 )1l 13 + D~3 (il - î3) = -Through fur~her straightforward manipulations, the following set of equations are ~e~ived:
(4.17) l ~;l I + 1 ~ 1 = ~ll (ll-ïl)l(l-ll-l2)-- K,}
(4 .18) I Ll ¦ + ¦ L3 ¦ = Dl3-(1l-i3)/(1~ 3) -- Kl3 (4-19 ) 1 L~ I + ~ L3 1 = Dl3 (il-l 3)/(1-1, -i,) = I~l3 where ~ is a constant The center terms ~n Equations 4.17 through 4.19 involve quantities which are calculated ~rom the azimuthal and elevational angles of the unit sighting vectors from each sensor to the trajectory, and ~rom the ~;nown locations of the s~nsors. Thus, onc~ the sensors make a "sighting", the K-constants ~l2' K13, and ~23 are fixed. It is then a simple step to solve ~or the 5 PCr~US93/01729 212833~

magnitudes of L1, Lz, and L3 in terms of the K-~onstants.
4 - 2 0 ~ KI3-Kl3)/~
(4 2~ 2+K~3-K,3)/~
(4-22) I L3 1 = a~,3~-Kl3-K,l)/~
These equations, therefore, succeeded in de~rm;nin~ the magnitude and direction of the unit sighting vectors and result in the full sighting vectors L1~ ~2 and L3. The unit sighting vectors l1, î2 and î3 are determined from the azimuthal and elevational angles calculated from the signals of each sensor.
It wil~ be appreciated that only two of these L-vectors are needed to located the local traj ectory in most cases, but three will provide the traj ectory in almost all cases. Further, it will be noted that this traj ectory is collinear with the unit vector d. This implies that the dot-products of E~quation 4 . 3 can be constructed and thus the- quantity Vs/V can be derived.
If an assumption of the sound speed can be made or measyred, then the velocity of the projectile can be calculated .
As has been demonstrated above, given at least three sensors, each of which is capable of generating a signal related to the azimuth and elevation angle of the unit sighting vector and, hence, capable o~ det~m;ning the azimuthal and elevational angles to the normal of an incoming shock wave r a solution of the traj ectory and projectile velocity can be found.
In an example of a practical application o~
the above/ and as a preferred embodiment, the required signals can be generated by positioning three pressure sensitive transducers (three such transducers constitute a single sensor) at the apexes of a triangle, i. e an WO 93/163gS PCr/US93/01729 212~333 - 18 -equilateral triangle. These signals allow measurements which inclu~e the difference in time (tF) that the shock front encounters the first of the transducers (referred to as a hit) and the time of the hit of the second of the transducers, the time difference ~t~) between the first hit transducer and the last hit transducer, identification of the first hit transducer, and identification of the second hit transducer.
The Qriqin LS placed at transducer 3 as lo indicated in-Figure 5. The plane shock wave is assumed to hit transducer 1 first, transducer 2 second, and transducer 3 last. A change in this order will require a rotatiQn of coordinates in order to have the azimuthal and elevational angles poin~ into the correct quadran~.
If the geor~etry is "frozen~' just as th~ plane wave strikes transducer l, the time tF implies that the plane wave stands a distance Sz = tfVs frr ~ transducer 2 and a distance S3 r3 t,Vs from transducer 3. This can be accomplished by df~ ~;ning the x, y, and z coordinates at the intersection of line S3 with the incc~ming plane wave, as illustrated in ~igure 5.
Si31ce the transducers are- arranged in an equilateral triangle, a derivation of this embQdiment provides the following results:
(4 . 31~ x ==s3(s~-s3)lS
(4.32) y =--(s2s3+s32)1(S(3)h) ( 4 3 3 ) ~ = [(s3~(S2-(s3-s2)~)ls2 ~ Y ~
where S is the distance between each of the transducers.
Of course, ~when other than an equilateral triangle arrangement is used, S will not be the same for ~, y and z.

WO 93/1639~ PCr/US93/01729 - lg 212~333=
The azimuthal angle ~ and the elevational angle Sb of the normal vector to the incoming plane wave are then given by:
.

( 4 . 3 4 ) ~ (y1x) (4 35) ~ (~(X2-~y2)1~) Projectile identification, e.g. at least the approximate caliber, is also obtainable from the above.
As described above, the initial solutions of the equations give the local traj ectory and the velocity of the projectile, i.e. with the vectors described in connection with Figure 4A and Figure 4B. Also, as discussed above, a determination of the proj ectile length may be obtained, e.g. the 5.56 mm bullet, discussed above. The magnitude of the onset of the shock wave, when normalized to the miss-distance, is related to mass. These three pieces of information, i.e. the normalized magnitude, the velocity and the projectile length, are sufficient to -yield an identification of the projectile, at least within a limited class of possibilities.
In this regard, the dimensions, flight dynamics and wave generation o~ most military projectiles, ~anufactured throughout the world, are known or can be ascertaLned . When the proj ectile length is determined, this places the projectile in a defined class. The magnitude of the onset of the main shock - wave, which is related to the main shock front magnitude, defines the mass of the projectile and places the proj ectile in a subclass of that class . The velocity then classifies the pro~ectile as to a specific projec~ile or at least a subclass of projectiles. For example, the determined length of the projectile can WO 93/16395 PCr/US93/01729 ,.
212833~ - 20 -distinguish between small arms rounds and larger caliber rounds and, ~or example, place the larger caliber round within a defined group or c1ass of such rounds having that approximate length. The magnitude of the onset of the shock wave relates to the mass of the proj ectile and, with the length of the projectile, det~orm;nec the approximate caliber. The length and caliber defines a more limited group or subclass of projectiles. The velocity further defines a more limited group of projectiles and may be sufficient, with the length and caliber, to identify a specific projectile.
Such identification is not only useful for det~rmining the entire trajectory, as explained below, but is most useful for distinguishing enemy and friendly fire, so as to avoid battlei~ield accidents where friendly flre is directed toward friendly military units .
After the projectile identification has been made, the coefficient of drag and the exact mass of the projectile can be ascertained from known data and ascertained data. These two pieces of information provide enough data to back-calculate the traj ectory of the projectile to its point of origin (taking into account the proj ectile miss-distance) . This can be accomplished through standard fire control algorithms.
0_her environmental information such as temperature or windage can be used to refine that calculation, i~
desired . Fillally, even if a positive identif ication of the specific projectile is not obtainable, the class identification can yield a generic drag coefficient which will result in only small errors in the point-of-origin calculation A typical specific embodiment of the preferred sensor is shown in Figure 6, but the sensor can be of 2128~33 any desired configuration consistent with the requirements, as described above and as explained more fully below. In the example shown in Figure 6, each transducer 60, 61, 62 (three being shown in Figure 6) is mounted on a support 63 (discussed more fully hereinafter). The transducers may be any acoustical transducer capable of generating a signal in response to pressure on the transducer created by the shock wave encountering the transducer. The transducers may generate a light signal, an acoustical tone signal, an electrical signal, or others, but commercially available piezoelectric crystals are quite convenient in this regard. For example, the transducers shown in Figure 6 are such piezoelectric - crystals made by Electro-Ceramics, and are 0.125 inch thick and 1 inch in diameter, although any desired configurations thereof may be used A wire 64 is soldered to each side of the crystals after the surface of the crystal is prepared with an abrasive material, such as Scotch Brite. The polarity of each crystal is noted so that each input to the crystal has the same polarity going to the detection electronics, explained below. A positive voltage output is produced during compression of the crystal by the shock wave. The crystals may be glued to the support 63 with an adhesive, such as a silicone-based adhesive, and, preferably, the support is a conventional shock-absorbent material, e. g. Isodamp. This material has an acoustical damping property, which is useful, as - explained more fully below. Each of the transducer 3 0 crystals is positioned on support 63 in a known - geometry, for the reasons explained in connection with Figure 4~ and Figure ~B, e.g. an equilateral triangle with leg lengths of 3 inches, although any known geometry and any length of distances between the .

WO 93/1639~ PCI`/US93/01729 ~12g33~ - 22 -crystals may be used. The equilateral triangle, however, simplifies the calculations, discussed above, and for that reaso~ is the preferred embodiment.
The six wires 64, two from each of the three transducers 60, 61 and 62, are inputted to a data collection module as shown in Figure 7, with one data collection module for each transducer. These modules determine which transducer has the first hit by a main shock wave, more preferably by the main shock front, which transducer has a second hit by that shock wave, and the time between the first hit and the second hit, as well as the time between the first hit and the last hit. This information is fed to a computer for making the required calculations, as explained above, by any conventional devices, such as a parallel port multiplexer to a parallel-to-serial adapter, with associated required poWer supplies, also as shown in Figure 7. For example, this arrangement can accommodate twelve 8-bi~ parallel input ports and switch each, in turn, to a single 8-bit output parallel port. The output is fed through a parallel-to-serial adapter to the computer. All of the components of this arrangement, with the exception of the sensors, are commercially available and well known to the art.
~lence, no further description thereof is necessary.
Once in the computer, the data is used in the above-described calculations to convert that data to azimuthal and elevational information for each transducer Df a sensor. In addition, as described 3 0 above, there will be at least three sensors, and a similar arrangement as described above is used for each sensor. The computer takes the data from each sensor and makes the mathematical calculation, described above, for the azimuth and elevation of the full sighting WO 93/16395 PCr/US93~01729 212~333 -- ~ 3 --vector generated from each sensor. For example, in the arrangement shown in Figure 6, the origin of the vector will be central point 66 of the three transducers, with the full sighting vector of the transducers extending to the pro~ectile trajectory, as shown in Figure 4. That calculation, therefore, obtains the position, the azimuth and the elevation of the local trajectory of the proj ectile, in the ~vicinity of the sensors, as well as the velocity of the projectile.
While the above describes a useful embodiment of the invention, other means of measuring the time when the shock wave encounters each of the transducers of the at least three sensors may be used, and it is only necessary that some means be provided for measuring the time when the shock wave encounters each of the transducers of the sensors, since, quite obviously, it is not the particular means but the measurement of time by those means which is important to the invention.
Likewise, any means for calculating from the measured time, the a~imuth and elevation angle of the traj ectory of the proj ectile may be used . While the arrangement shown in ~igure 7 is ~uite satisfactory, and a preferred embodiment, other arrangements for making that calculation may be used.
Similarly, while a computer will be used for calculating the azimuth and elevation angle of the projectile trajectory, such calculations may be made by ordinary mathematical solving, although, for most uses, - that would be too slow, especially for battlefield conditions. Accordingly, normally, a computer will ~e used for such calculations.
It will also be appreciated, especially in battlef ield conditions, that a great number of acoustical waves may be present. It is, therefore, WO 93/16395 PCr/US93/01729 important that the apparatus be capable of discriminating between background battle noise, causing other acoustical waves, and the shock waves created by a passing proj ectile of interest . Thus, the sensors must be sensitive to a shock wave propagated by a passing projectile, and since some information, as described above, is obtained from the ambient density line, the sensors should be sensitive to the ambient density line, so as to provide means for calculating the length of the projectile. On the other hand, the sensors an~/or -associated apparatus must distinguish between the shock waves of a passing projectile and background battle noise .
Conventional means are available for producing such sensitivity. For example, either the transducers or the data collecting module or the computer may be such that signals generated by the ~ri~nC~11r r~rs will only be accepted by the computer when those signals have a rise time consistent with a shock front of a passing projectile, e.g. in the sub-nanosecond range, as opposed to the much longer rise times of background battle noise. Alternatively, a separate sensor, sensitive to the shock front of a passing proj ectile and insensitive to diffused battle background noise, may be used as a gate for delivering or interrupting transfer of signals from the sensors to t~e computer.
As will be appreciated from the above and as directly opposed to prior art discussed in the BACKGROUND OF THl~ INVENTION, herein, "cross-talk"
3 0 between transducers of a sensor or between sensors should be as little as possible. Thus, as opposed to that prior art, the present transducers/sensors should be substantially acoustically isolated from each other.
As shown in and discussed in connection with Figure 6, 7,12~333 -- 2~
the support ~or the transducers is an acoustical damping material, such as conventional Isodamp. When the support is, for example, mounted on a tank, the acoustical damping material will isolate the set of three transducers frDm each other and from the tank itself. Otherwise, "cross-talk" between transducers or- - =
sensors could not only provide acoustical shock energy from other than an incoming shock wave, but could so diffuse the pressure rise at a transducer so as to make discrimination between the shock wave and background battle noise impossible.
As illustrated irl Figure 8, at least three sensors 80, 81 and 82, e.g. arranged in a common sensor plane, are necessary for generating at least three full sighting vectors 83, 84 and 85 to the trajectory 86 of the projectile 87, which projectile 87 creates the shock wave 88. However, as shown in Figure 8, while the chances are small, it is possible for the projectile to pass two sensors on a trajectory which is parallel to the line of two sensors. In such a case, the above solution of the traj ectory will not be possible. As an illustration in the above mathematical analysis, let 12' î3 = 1. This implies that only lz and 1~ are parallel and equal, i e. sensors 81 and 82 lie in the same plane as t~e t~aj ectory but sensor 8 o is not in that plane .
E~uation 4.19, above, then becomes useless, leaving two eq~ations in two unknowns. ~owever, by using information about the difference in the initial time o-f arrival ( ~t12) at sensors 81 and 82, the following 3 0 relationship can be constructed:
(4.23) At~ /Vs + I d~l I /V ~ /Vs~
or recalling that d r î1 = Vs/~ and rearranging, WO 93tl6395 PCr/US93/01729 .
- 2~ -(4.24) I d12 I Vs/V--V~tl2 + I Ll I ~ 1 ~2 1 = dl1-11 - The conventioll that if the signal arriv~s at sensor 81 ~efore sensor 82 then ~t~3 is positive has been adopted Dotting the unit vector l1 into Equation 4 . 5:
(4.25) ~2 f, = -Ll î~ + Dl2-1l + L~ ~l Equating Equations 4 . 25 and ~ 26 and carrying out the dot products (4-26) - I Ll f + Dl2~ L~ î2) = ~5f~tl2 + I L~ L2 1, or rearranging ter~s, (4 27) ~ I Ll I = I)32 i, + L2(1 + l~ f2) - ~s~tl2 using- - I L~ L2 1 + ~12 from Equa~ion 4 17, su~sti~uting into Equation 4.27, and solving ~or ¦ L2 ¦
( 4 . 2 8 ) I L~ !K~2 - D~ ) - VS~t~2] / (~
Aga~ n using E~uation 4 .17 and Equation 4 .18, (4-29) ~ = KJ2 -(4 30) ~ L~ ¦ = K,3 - ¦ Ll I
As previously, the magnitudes of the fUll slghting vectors are ~no~r calculated from Equations 4 . 28 through 3 0 4 . 3 0, and the u~it dire~tions oî ~hese vectors are the sensor outputs This resolvable degenerate case provides the significant implication that three sensors can provide~the solutions for trajectory and velocity in WO 93/1639~ PCr/USg3/01729 all cases, except when the projectile is in the plane of all three of the sensors and outside the region bounded by the three sensors (an extremely unlikely occurrance).
It further implies that a system of four sensors, arranged non-coplanarally, can provide a solution in all cases, by using three sensors, at least one of which does not lie in the plane of the trajectory.
As can also be appreciated, the disposing of three sensors in a plane may not be practical for all military applications, and, in addition, the military application might be such that the shock wave of a pro~ ectile passing close to a piece of military equipment might be somewhat masked from one or more of the sensors by apparatus on the military eguipment, such as the turret of a tank and the like. '~herefore, in such applications, a plurality of more than three sensors are provided, and mean`s are provided for selecting at least three of the plurality of sensors for calculating the azimuth and elevation angle of the trajectory. For example, where a plurality of the sensors are used, and while the data is collected in each data collection module (see Figure 7) for each of the transducers and/or sensors, the computer may make the calculation from only three selected sensors. That selection will be made by the computer in regard to the clarity or rise time of the signal generated by the transducers and/or sensors, or other like discriminating means .
As illustrated in Figure 9, which is an idealized illustration, the discriminating means m~y rej ect any signal that does not have a f irst shock wave that rises to a peak in less than a sub-n~nnc~ n~, as illustrated at time unit 1 (an arbitrary unit shown only for illustration purposes). Or since all military WO 93/16395 PCr/US93/01729 .
2~28333 - 28 -proj ectiles will have a length within some de~ined lengths, a signal which does not have a pressure rise from and pressure fall to the ambient density line within a prescribed time ( arbitrary units 1 to 2 . 5 in Figure g) would be rejected. Or since any projectile will have a wake, any signal that does not fall below the ambient density line and then rise above the ambient density line would be rejected. Other criterion could be adopted.
Thus, the computer will canvas all sensors ~nd reject signals for calculation purposes which do not meet such established criterion. From those sensors which meet the criterion, a second or third or further set o~ criterion, along the above lines, can narrow the accepted si7nals for calculation purposes to only three or four or so sensors, e.g. such further narrowing until only three sensor signals are accepted for calculation purposes .
From the above, it will also be appreciated that the signal transmitted ~rom the sensors can be ~ny signal which is proportional to the pressure increase of the shock wave, e.g. a tone signal, a light signal, an electrical signal, etc. Similarly, the sensor is one which produces such proportional signal. However, electrical signals are more convenient to use and are pref erred .
As noted above, a preferred embodiment of the sensors is where each sensor has three spaced-apart, preferably co-planar, transducers. ~owever, the sensor, as can be ~ppreciated from the above, can take any desired form, so long as the sensor will generate the re~uired unit sighting vector or signals from which the unit sighting vector can be calculated. For example, a number of the transducers may be mounted on the surface 212833~

of a hemisphere with the center of the hemisphere being the origin of the unit sighting vector. By detecting which transducer is first hit by a shock wave, the position of that first hit transducer to the origin provides the unit sighting vector. Alternatively, crystals which internally generate a unit sighting vector may be used or other like sensors.
D~r~nrl;ng upon the military application, the sensors may be closely spaced or may be spaced apart some distance. For example, with portable units, such as might be deployed on a rifle, the sensors must be spaced apart at least l cm, but, generally, it is preferred that the sensors be spaced apart at least 3 cm, and for most applications, it is preferable that the sensors be spaced apart at least lO0 cm, or, alternately, the selected sensors, where a plurality of more than three sensors are used, are spaced apart at least lO0 cm. For a central battlefield detection unit, the sensors may be spaced apart at least 200 cm and even up to as far as 30 meters apart.
As examples of the foregoing, Figure lO shows an application of the invention where the sensors are ~nounted on a tank and a plurality of such sensors are disposed around that tank. With such disposition of a 2s plurality of such sensors, it can be seen that at least three sensors will ~e in a position for accurately determining the time and time lapses of the shock wave, no matter at what angle or orientation the projectile passes the tank. of the plurality of sensors, depending upon criterion selected, as discussed above, three, or more, of t~e sensors are selected for calculating the azimuth and elevation of the trajectory of the passing projectile. By making the above-described calculations, a tank- cnTr~n~ler can return suppressing fire. In WO 93/l6395 PCr/US93/01729 .
2128333- ~ 30_ addition, those calculations will allow the tank cnmm-n~Pr to direct detection equipment, e.g. IR
detectors ~which have a narrow field of view), toward the incoming fire and detect the position of, for example, an enemy tank.
Figure ll illustrates a different piece of military equipment where three sensors are mounted on the rear strut of a helicopter. That rear strut is in a position to, essentially, accurately determine the trajectory of a projectile, no matter at what angle or orientation the proj ectile passes the sensors .
Figure 12 shows three sensors 120, 121 and 122 mounted on a rifle, along with the appropriate data processing unit 123, re~erred to as an acoustical signal processing unit (ASPU). One of the sensors is mounted on the barrel 124 of the rifle, while two oE the sensors are mounted on retractable sensor arms 125 and 126.
~his providç!s sensors for r~ Prm;n;n~ the directiQn of projectiles, such as small arms fire, which may be incoming from an unknown direction Figure 13 shows an acceptable, but less desirable, embodiment, as opposed to Figure 12, where all three sensors 130, 131 and 132 are mounted on barrel 133 of the rifle Obviously, if a projectile comes along the line of the sensors, or very close to that line of the sensors, then the present calculations by the data processing unit 134 (ASPU) will not be possible.
Figure 14 shows another application where a portable unit is provided having sensors 140, 141 and 142 such that, for example, a squad leader may determine the directiQn of incoming fire.
~he architecture of installation of the sensors will depend upon the particular military WO 93/16395 - - PCr/US93/01729 231l2833.3 equipment upon which the sensors are placed, bearing in mind practical applications of placing such sensors.
When the sensors are mounted on a motorized vehicle, such as the tank shown in Figure 10, the sensors should be mounted on the vehicle surface and physically isolated from vehicle-induced noise, using standard high hysteresis shock insulation techniques and materials.
A wiring harness (not shown) will penetrate the tank vehicle, at some less vulnerable position of the tank, and transmit the signals produced by the sensors to an Acoustic Signal Processing Unit (ASPU) (not shown in Figure 10). The ASPU contains the necessary conventional timing circuits, discrimination circuits and computational algorithms to establish the projectile velocity, miss-distance and location of origin of the projectile, as explained above. That ASPU will also contain the ballistic data base of common friendly and hostile projectiles for comparing the information obtairLed by the present invention with those projectiles, as explained above.
The ASPU shown in Figures 12 and 13 may be.the same or abbreviated versions of an ASP~ mounted on a tank. For example, the ASPU of Figures 12 and 13 may simply be that of showing the azimuth and elevation of the projectile trajectory, and possibly an indication of only whether the proj ectile is a shell or small arms f ire . ~
Thus, the present invention provides a very accurate and easily achieved means and method of 3 o det.orm; n; ng the traj ectory of a proj ectile . The apparatus consists of components which are commercially available and can be assembled into a wide variety of configurations for a wide range of applications, as explained above. The apparatus is relatively WO 93/16395 PCr/US93/01729 212~333 - 32 -inexpensive to build and easy to operate, which is nP~Pc:~ry for battlefield conditions. Accordingly, the invention provides a considerable advance in the art.
Having thus described the invention, it will be apparent that the invention admits to many variations beyond the specific, exemplary description above, all of w~ich are intended to be embraced by the spirit and scope of the following claims.

Claims (36)

WHAT IS CLAIMED:

1. Apparatus for determining the trajectory of a supersonic projectile of unknown velocity and direction, comprising:
(1) at least three spaced-apart sensors capable of encountering a shock wave generated by a supersonic projectile passing in the vicinity of the sensors and capable of generating signals in response to the shock wave, which signals are related to an azimuth and elevation angle of a unit sighting vector from each sensor to an origin of the shock wave:
(2) means for calculating from the said signals the azimuth and elevation angle of the unit sighting vector from each sensor to the origin of the shock wave; and (3) means for calculating from the unit sighting vector of each of the three sensors, the azimuth and elevation angle of the local trajectory of the projectile.

2. The apparatus of claim 1 wherein the sensors have transducers which are sensitive to a shock wave propagated by a projectile.

3. The apparatus of claim 2 including means for measuring the time lapses of the shock wave in passing the transducers of a sensor.

4. The apparatus of claim 3 including means for measuring differences in time lapses of the shock wave in passing the transducers.

5. The apparatus of claim 4 wherein the transducers are sensitive to the shock front of the shock wave.

6. The apparatus of claim 1 wherein the sensors are sensitive to the shock wave and to an ambient density line and means are provided for calculation of the length of the projectile from the time lapse of the passing of the shock wave and the ambient density line over a sensor.

7. The apparatus of claim 2 wherein there are three transducers in each sensor.

8. The apparatus of claim 7 wherein the transducers are arranged as an equilateral triangle.

9. The apparatus of claim 1 wherein the at least three sensors are arranged so as to form a triangle.

10. The apparatus of claim 1 wherein there is a plurality of more than three sensors and means are provided for selecting at least three sensors from the plurality of sensors for calculating the azimuth and elevation angle of the local trajectory of the projectile.

11. The apparatus of claim 2 wherein the transducers of a sensor are spaced apart at least 3 cm.

12. The apparatus of claim 11 wherein the sensors are spaced apart at least 200 cm and up to 30 meters.

13. The apparatus of claim 1 wherein the sensors are substantially acoustically isolated from each other.

14. The apparatus of claim 2 wherein the transducers are substantially acoustically isolated from each other.

15. The apparatus of claim 1 wherein the sensors are mounted on a motorized vehicle, a gun, a rifle or a portable base.

16. The apparatus of claim 15 wherein the sensors are mounted on a tank.

17. The apparatus of claim 2 wherein the transducer is a piezoelectric crystal.

18. The apparatus of claim 17 wherein the crystals are mounted on an acoustic damping material.

19. A method for determining the trajectory of a supersonic projectile of unknown velocity and direction, comprising:
(1) providing at least three spaced-apart sensors capable of encountering a shock wave generated by a supersonic projectile passing in the vicinity of the sensors and capable of generating signals in response to the shock wave, which signals are related to an azimuth and elevation angle of a unit sighting vector from each sensor to an origin of the shock wave;
(2) calculating from the said signals the azimuth and elevation angle of a unit sighting vector from each sensor to the origin of the shock wave; and (3) calculating from the unit sighting vectors of each of the three sensors, the azimuth and elevation angle of the local trajectory of the projectile.

20. The method of claim 19 wherein the sensors have transducers which are sensitive to a shock wave propagated by a projectile.

21. The method of claim 20 including measuring the time lapses of the shock wave in passing the transducers of a sensor.

22. The method of claim 21 including measuring differences in time lapses of the shock wave in passing the transducer .

23. The method of claim 22 wherein the transducers are sensitive to the shock front of the shock wave.

24. The method of claim 19 wherein the sensors are sensitive to the shock wave and to an ambient density line and the length of the projectile is calculated from the time lapse of the passing of the shock wave and the ambient density line over a sensor.

25. The method of claim 20 wherein there are three transducers in each sensor.

26. The method of claim 25 wherein the transducers are arranged as an equilateral triangle.

27. The method of claim 19 wherein the at least three sensors are arranged so as to form a triangle.

28. The method of claim 19 wherein there is a plurality of more than three sensors and at least three sensors from the plurality of sensors are selected for calculating the azimuth and elevation angle of the trajectory of the projectile.

29. The method of claim 20 wherein the transducers of a sensor are spaced apart at least 3 cm.

30. The method of claim 19 wherein the sensors are substantially acoustically isolated from each other.

31. The method of claim 20 wherein the transducers are substantially acoustically isolated from each other.

32. The method of claim 29 wherein the sensors are spaced apart at least 200 cm and up to 30 meters.

33. The method of claim 19 wherein the sensors are mounted on a motorized vehicle, a gun, a rifle or a portable base.

34. The method of claim 33 wherein the sensors are mounted on a tank.

35. The method of claim 20 wherein the transducers are piezoelectric crystals.

36. The method of claim 35 wherein the crystals are mounted on an acoustic damping material.