CA1133138A - Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target - Google Patents
Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving targetInfo
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- CA1133138A CA1133138A CA321,028A CA321028A CA1133138A CA 1133138 A CA1133138 A CA 1133138A CA 321028 A CA321028 A CA 321028A CA 1133138 A CA1133138 A CA 1133138A
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- projectile
- pressure wave
- distance
- point
- transducers
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Abstract
ABSTRACT
Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target, compris-ing pressure-sensing transducers intended to sense the pressure wave generated by the projectile in a least four points, and means for generating corresponding electrical signals therefrom. The apparatus further comprises computer circuits, calculating the distance to the point of origin of the wave, i.e. the so-called "bang generation point", in response to the characteristics of the pressure wave. This distance has been called the "miss distance" in previously known indicator apparatus, but in accordance with the inven-tion the miss distance is defined as the shortest distance between the projectile and target, and one object of the invention is to indicate this distance and the exact position of the projectile when it is at the miss distance from the target. In the indicator apparatus in accordance with the invention, the direction of the trajectory is calculated by means of said at least four pressure transducers arranged at the corners of a polyhedron. By measuring the time dif-ferences for the passage of the pressure wave past the press-ure transducers in the transducer system, the exact position of the bang generation point can be given in relation to the pressure transducer system from these time differences and the measured distance to the point. The indicator apparatus also comprises a second transducer system which can sense either the height of the first pressure transducer system above a horizontal plane, or the passage of the pressure wave at a further instant. From these data the computer cir-cuits can give the trajectory direction which, together with the bang generation point gives the required trajectory. For shooting at fixed targets, the computer circuits give a second point on the trajectory which, together with the bang generation point, gives the trajectory perse.
Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target, compris-ing pressure-sensing transducers intended to sense the pressure wave generated by the projectile in a least four points, and means for generating corresponding electrical signals therefrom. The apparatus further comprises computer circuits, calculating the distance to the point of origin of the wave, i.e. the so-called "bang generation point", in response to the characteristics of the pressure wave. This distance has been called the "miss distance" in previously known indicator apparatus, but in accordance with the inven-tion the miss distance is defined as the shortest distance between the projectile and target, and one object of the invention is to indicate this distance and the exact position of the projectile when it is at the miss distance from the target. In the indicator apparatus in accordance with the invention, the direction of the trajectory is calculated by means of said at least four pressure transducers arranged at the corners of a polyhedron. By measuring the time dif-ferences for the passage of the pressure wave past the press-ure transducers in the transducer system, the exact position of the bang generation point can be given in relation to the pressure transducer system from these time differences and the measured distance to the point. The indicator apparatus also comprises a second transducer system which can sense either the height of the first pressure transducer system above a horizontal plane, or the passage of the pressure wave at a further instant. From these data the computer cir-cuits can give the trajectory direction which, together with the bang generation point gives the required trajectory. For shooting at fixed targets, the computer circuits give a second point on the trajectory which, together with the bang generation point, gives the trajectory perse.
Description
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Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target.
The present invention relates to an indicator appar-atus for determining the miss distance of a projectile to a fixed or moving target, comprising pressure-sensitive transducers intended to sense the pressure wave generated by a projectile at at least four points, and means for generating electrical signals there~rom, adapted for ap-plying to computer circuits which, ~rom the pressure wave characteristic, give the distance from one of the pressure transducers to the source of the pressure wave, i.e. the so-called "bang generation point".
When a projectile passes through the atmosphere at - supersonic speed, a backward pressure wave is generatçd from the tip of the projectile. The wave has the form of a conical surface with a vertex angle depending on the speed o~ the projectile in relation to the speed of sound.
In miss distance calculators known up to now, the dis-tance between the bang generation point and the point con-tacted by the pressure wave is calculated. ~his distance is ~- however not equal to the miss distance, i.e. the shortest distance between projectile and target, since the target ;~ has moved during the time the pressure wave, i.e. the coni-cal surface/ has been propagated from the bang ~eneration point to the target or a sensing point equivalent thereto.
A known miss distance calculator is taught by the 25 British Patent 902 756, and it comprises two pairs of micro-phones placed in such a way that the approximate distance to the bang generation point can be determined with the aid :;
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of one pair, and the space quadrant the target in which the pressure wave is generated by the other pair. With this system it is thus only possible to determine an ap-proximate distance to the bang generation point and to give a source area for the pressure wave. Since the point source of ~he pressure wave is not exactly known, the move-ment of the target during the time the pressure wave is propagated from the bang generation point to one of the microphones cannot be taken into consideration. Further-more, not knowing where the projectile passes through theappropriate space quadrant is extremely unsatisfactory from the point of view of miss distance calculation.
Both the United States patents 3 217 290 and 2 925 582 relate to miss distance calculators, the latter of which is 15 based on essentially the same principle of determining the -position of the bang generation point as the device accord-ing to the British patent, while the former utilizes the pressure wave attenuation from the bang generation point to the receiver for calculating the distance, since attenuation is different for different frequencies in the pressure wave frequency spectrum. However, the latter patent discloses a very accurate method of calculating the distance to the bang generation point, and this method applied in the apparatus ~` in accordance with the present invention.
The object of the present invention is to enable cal-culation of the distance between the projectile and target, even when the latter has very high speed, simultaneously as information is supplied as to the position of the projectile and target at every instant, and thus the position of the projectile in relation to the target when the projectile is at its shortest distance to the target.
; The indicator apparatus in accordance with the inven-tion is intended for use in all conceivable cases of firing at targets, i.e. firing from fixed ground weapons towards moving arial targets, from airborn movable weapons to mov-ing targets, from airborn movable weapons to fixed ground targets and finally from fixed surface weapons to fixed surface targets.
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In accordance with the invention these objects are re-alized by that at leas-t four pressure transducers are part of a first pressure transducer system, and are arranged in the corners of a polyhedron with at least four corners and computer circuits which comprise means for measuring the time differences between the passage of the pressure wave past the transducers in the first transducer system and where the computer circuits which are adapted to give the position of the bang generation point and thereby a first point on the projectile trajectory from these time differ-ences as well as the measured distance to the bang gener-ation point. The indicator apparatus also comprises a se-cond transducer system adapted either to sense the height of the first transducer system above a horizontal plane, or the passage of the pressure wave at a further instant, said circuits being adapted for giving the direction of the tra-jectory, which together with the first point gives the actual trajectory. While taking in account the positions of the tar-get and projectile, the computer circuits are adapted to give the distance between the projectile and the target at every instant. In cases where firing takes place against a fixed target, the second transducer system will sense the passage ` of the pressure wave at a further instant, the computer cir-cuits being adapted to give a second point on the trajectory which, together with the first point, gives the actual tra-jectory.
In order to execute an accurate calculation of the miss distance, it is required that the distance from a pressure transducer to the bang generation point can be calculated exactly. According to a known method, this distance can be calculated by determining when the maximum amplitude of the ~ pressure wave passes the transducer. This method is uncer--~ tain however, inter alia because of heavy background noise - being superimposed on the pressure wave, making it difficult to determine with analogue measurements when the maximum pressure wave amplitude passes the receiver. In accordance with the invention the method described in the US Patent
Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target.
The present invention relates to an indicator appar-atus for determining the miss distance of a projectile to a fixed or moving target, comprising pressure-sensitive transducers intended to sense the pressure wave generated by a projectile at at least four points, and means for generating electrical signals there~rom, adapted for ap-plying to computer circuits which, ~rom the pressure wave characteristic, give the distance from one of the pressure transducers to the source of the pressure wave, i.e. the so-called "bang generation point".
When a projectile passes through the atmosphere at - supersonic speed, a backward pressure wave is generatçd from the tip of the projectile. The wave has the form of a conical surface with a vertex angle depending on the speed o~ the projectile in relation to the speed of sound.
In miss distance calculators known up to now, the dis-tance between the bang generation point and the point con-tacted by the pressure wave is calculated. ~his distance is ~- however not equal to the miss distance, i.e. the shortest distance between projectile and target, since the target ;~ has moved during the time the pressure wave, i.e. the coni-cal surface/ has been propagated from the bang ~eneration point to the target or a sensing point equivalent thereto.
A known miss distance calculator is taught by the 25 British Patent 902 756, and it comprises two pairs of micro-phones placed in such a way that the approximate distance to the bang generation point can be determined with the aid :;
'~
, , . :
~33~
of one pair, and the space quadrant the target in which the pressure wave is generated by the other pair. With this system it is thus only possible to determine an ap-proximate distance to the bang generation point and to give a source area for the pressure wave. Since the point source of ~he pressure wave is not exactly known, the move-ment of the target during the time the pressure wave is propagated from the bang generation point to one of the microphones cannot be taken into consideration. Further-more, not knowing where the projectile passes through theappropriate space quadrant is extremely unsatisfactory from the point of view of miss distance calculation.
Both the United States patents 3 217 290 and 2 925 582 relate to miss distance calculators, the latter of which is 15 based on essentially the same principle of determining the -position of the bang generation point as the device accord-ing to the British patent, while the former utilizes the pressure wave attenuation from the bang generation point to the receiver for calculating the distance, since attenuation is different for different frequencies in the pressure wave frequency spectrum. However, the latter patent discloses a very accurate method of calculating the distance to the bang generation point, and this method applied in the apparatus ~` in accordance with the present invention.
The object of the present invention is to enable cal-culation of the distance between the projectile and target, even when the latter has very high speed, simultaneously as information is supplied as to the position of the projectile and target at every instant, and thus the position of the projectile in relation to the target when the projectile is at its shortest distance to the target.
; The indicator apparatus in accordance with the inven-tion is intended for use in all conceivable cases of firing at targets, i.e. firing from fixed ground weapons towards moving arial targets, from airborn movable weapons to mov-ing targets, from airborn movable weapons to fixed ground targets and finally from fixed surface weapons to fixed surface targets.
, 3~33ia3~
In accordance with the invention these objects are re-alized by that at leas-t four pressure transducers are part of a first pressure transducer system, and are arranged in the corners of a polyhedron with at least four corners and computer circuits which comprise means for measuring the time differences between the passage of the pressure wave past the transducers in the first transducer system and where the computer circuits which are adapted to give the position of the bang generation point and thereby a first point on the projectile trajectory from these time differ-ences as well as the measured distance to the bang gener-ation point. The indicator apparatus also comprises a se-cond transducer system adapted either to sense the height of the first transducer system above a horizontal plane, or the passage of the pressure wave at a further instant, said circuits being adapted for giving the direction of the tra-jectory, which together with the first point gives the actual trajectory. While taking in account the positions of the tar-get and projectile, the computer circuits are adapted to give the distance between the projectile and the target at every instant. In cases where firing takes place against a fixed target, the second transducer system will sense the passage ` of the pressure wave at a further instant, the computer cir-cuits being adapted to give a second point on the trajectory which, together with the first point, gives the actual tra-jectory.
In order to execute an accurate calculation of the miss distance, it is required that the distance from a pressure transducer to the bang generation point can be calculated exactly. According to a known method, this distance can be calculated by determining when the maximum amplitude of the ~ pressure wave passes the transducer. This method is uncer--~ tain however, inter alia because of heavy background noise - being superimposed on the pressure wave, making it difficult to determine with analogue measurements when the maximum pressure wave amplitude passes the receiver. In accordance with the invention the method described in the US Patent
2 925 582 is utilized, according to which any projectile moving at supersonic speed generates a ballistic pressure wave in which the air pressure increases rapidly from a sta--tic pressure P0 to an excess pressure P0 + Pl, to attenuate linearly in both time and space to a subpressure P0 - P2, subsequently to return just as quickly to the static press-ure P0. The amplitude on the leading edge and trailing edge of the wave, and the time distance between these edges de-pends on the projectile characteristics, such as caliber and speed, and on the perpendicular distance from the bang generation point to the point where the pressure wave is sensed. The apparatus in accordance with the present inven-tion also utilizes the distance in time between the leading edge and trailing edge of the wave to determine the distance to the bang generation point. The content of the abovemen-tioned patent thus constitutes documentation of the known technique utilized in the apparatus according to the inven-tion for measuring the distance to the bang generation point.
Some embodiments, selected as examples, of apparatus in accordance with the invention are described in detail below while referring to the accompanying drawings in which igure 1 shows firing from the ground to a target towed by an aeroplane, comprising an indicator apparatus with four ; pressure transducers according to the invention, Figure 2 shows an indicator apparatus according to Figure 1, and the passage of the pressure wave past the transducers, Figure 3 shows a vector diagram of the quantities measured by the transducers in Figure 2, Figure 4 shows both conceivable projec-tile trajactories ob-tained in one embodiment of the indicator apparatus in ac-cordance with the invention, Figure 5 shows the vector diagram and the quantities measured in the embodiment according to Figure 4, Figure 6 shows an alternative embodiment of the indicator apparatus with a further pressure transducer at some dis-tance from the four transducers, Figure 7 shows the vector diagram for measuring the projec-tile trajectory in the embodiment according to Figure 6, '' " , ' Figure 8 shows a vector diagram for an alternative measure ment of the projectile trajectory, Figure 9 shows a vector diagram for firing from the air towards a fixed ground target, utilizing two pressure-sensing transducer arrays in accordance with the invention,Figure 10 shows a circuit diagram for a microprocessor in a transducer array in accordance with the invention, Figure 11 shows a block diagram of an indicator apparatus according to Figure 6 with the circuit elemen-ts associated with the pressure transducers.
Figure 1 illustrates very clearly the conditions pre-vailing when firing towards targets towed by aeroplanes, moving at such high speed that the speed is not negligible in relation to the speed of sound and that of the projectile.
When a projectile is fired by a weapon towards a sleeve tar-get 2, the weapon is aimed to hit a point on the target, in this case the centre 6 of the target 2. This point of aim or sight has been calculated with reference to the distance and speed of the target in relation to the firing point. At the firing instant, the target is in a position not shown on the Figure. In the position shown in full lines on the ~ Figure, the projectile 3 is nearest to the target 2, and r~ at a distance from it denoted by dM, which is the miss dis-tance. In front of the target 2 t:here is a pressure wave -sensing transducer means 5, at a specific distance from the ~- centre 6 of the target 2. When the projectile is at the point PMp at the least distance from the target it is at the distance dMK from the transducers.
When a projectile 3 passes through the atmosphere at supersonic speed, a pressure wave 4 is generated, indicated on the figure by lines going backwards from the tip of the projectile. This pressure wave has the form of a cone with the projectile at its vertex, and moves at- the speed of sound, the wave front forming a conical surface where the cone angle is decided by the speed of the projectile in re-lation to the speed of sound. At every point on its trajec-tory the projectile will thus generate a pressure wave mov-ing at the speed of sound in a direction at right angles to ~L33~3~
the wave front. In the case shown in Figure 1, the target 2 is in a position outside the paper when the projectile was at position PB, from which a wave front 4 has been propagated in a direction parallel to the line dB. When the projectile first arrives at a pOSitiOIl 3 on the fi-gure the wave front 4 has arrived at the pressure trans-ducers 5 in front of the target, which is then in posi-tion 2 7 The point PB is thus the point at which -the wave generated mee-ts the transducers in position 5 .
If, as has been the practice up to now, it is con-sidered satisfactory to calculate the distance dB between the bang generation point PB and the transducers in posi-tion 5 , it is quite clear that this distance is in no way a measurement of the miss distance dM, i.e. the shortest distance between projectile and target, since the target has naturally moved from position 2 to position 2- during the time the conical surface has moved from position 4 to position 4 . The problems the present invention intends to solve are thus to enable calculation of the miss distance dM and also position PMp of the projectile 3 when it is nearest to the target 2.
In order to calculate the miss distance dM -the follow-ing quantities must be taken into account:
1. The distance dB between the hang generation point PB
and the posi-tion 5', of the pressure transducer array (here--~ inafter termed "array") during the passage of the pressure- wave 4 .
2. The pressure wave propagation direction from the bang generation point to the array, i.e. the vertex angle of the conical pressure wave.
Some embodiments, selected as examples, of apparatus in accordance with the invention are described in detail below while referring to the accompanying drawings in which igure 1 shows firing from the ground to a target towed by an aeroplane, comprising an indicator apparatus with four ; pressure transducers according to the invention, Figure 2 shows an indicator apparatus according to Figure 1, and the passage of the pressure wave past the transducers, Figure 3 shows a vector diagram of the quantities measured by the transducers in Figure 2, Figure 4 shows both conceivable projec-tile trajactories ob-tained in one embodiment of the indicator apparatus in ac-cordance with the invention, Figure 5 shows the vector diagram and the quantities measured in the embodiment according to Figure 4, Figure 6 shows an alternative embodiment of the indicator apparatus with a further pressure transducer at some dis-tance from the four transducers, Figure 7 shows the vector diagram for measuring the projec-tile trajectory in the embodiment according to Figure 6, '' " , ' Figure 8 shows a vector diagram for an alternative measure ment of the projectile trajectory, Figure 9 shows a vector diagram for firing from the air towards a fixed ground target, utilizing two pressure-sensing transducer arrays in accordance with the invention,Figure 10 shows a circuit diagram for a microprocessor in a transducer array in accordance with the invention, Figure 11 shows a block diagram of an indicator apparatus according to Figure 6 with the circuit elemen-ts associated with the pressure transducers.
Figure 1 illustrates very clearly the conditions pre-vailing when firing towards targets towed by aeroplanes, moving at such high speed that the speed is not negligible in relation to the speed of sound and that of the projectile.
When a projectile is fired by a weapon towards a sleeve tar-get 2, the weapon is aimed to hit a point on the target, in this case the centre 6 of the target 2. This point of aim or sight has been calculated with reference to the distance and speed of the target in relation to the firing point. At the firing instant, the target is in a position not shown on the Figure. In the position shown in full lines on the ~ Figure, the projectile 3 is nearest to the target 2, and r~ at a distance from it denoted by dM, which is the miss dis-tance. In front of the target 2 t:here is a pressure wave -sensing transducer means 5, at a specific distance from the ~- centre 6 of the target 2. When the projectile is at the point PMp at the least distance from the target it is at the distance dMK from the transducers.
When a projectile 3 passes through the atmosphere at supersonic speed, a pressure wave 4 is generated, indicated on the figure by lines going backwards from the tip of the projectile. This pressure wave has the form of a cone with the projectile at its vertex, and moves at- the speed of sound, the wave front forming a conical surface where the cone angle is decided by the speed of the projectile in re-lation to the speed of sound. At every point on its trajec-tory the projectile will thus generate a pressure wave mov-ing at the speed of sound in a direction at right angles to ~L33~3~
the wave front. In the case shown in Figure 1, the target 2 is in a position outside the paper when the projectile was at position PB, from which a wave front 4 has been propagated in a direction parallel to the line dB. When the projectile first arrives at a pOSitiOIl 3 on the fi-gure the wave front 4 has arrived at the pressure trans-ducers 5 in front of the target, which is then in posi-tion 2 7 The point PB is thus the point at which -the wave generated mee-ts the transducers in position 5 .
If, as has been the practice up to now, it is con-sidered satisfactory to calculate the distance dB between the bang generation point PB and the transducers in posi-tion 5 , it is quite clear that this distance is in no way a measurement of the miss distance dM, i.e. the shortest distance between projectile and target, since the target has naturally moved from position 2 to position 2- during the time the conical surface has moved from position 4 to position 4 . The problems the present invention intends to solve are thus to enable calculation of the miss distance dM and also position PMp of the projectile 3 when it is nearest to the target 2.
In order to calculate the miss distance dM -the follow-ing quantities must be taken into account:
1. The distance dB between the hang generation point PB
and the posi-tion 5', of the pressure transducer array (here--~ inafter termed "array") during the passage of the pressure- wave 4 .
2. The pressure wave propagation direction from the bang generation point to the array, i.e. the vertex angle of the conical pressure wave.
3. The direction of the trajectory in relation to the path of the target.
4. The projectile speed.
5. The target speed.
6. The prevailing speed of sound.
7. The distance from the array to the point on which sights are set.
' , . ~
.
7 ~
The distance dB between the bang generation point PB
and the transducer array when the pressure wave 4 passes it can be calculated, starting from the time between the front and trailing edges of the pressure wave, in accord-S ance with US Patent 2 925 582. The direction from the array to the target, and the direction of the trajectory in re-lation to a conceived coordinate system with its central point in the array can be calculated starting from the di-rection of the pressure wave in relation to the array. This distance can in turn be calculated starting from the time interval for the conical surface to pass the transducers in the array.
Figure 2 shows in detail how the conical pressure wave 4 meets two transducers M2 and Ml, in that order, the por-tion of the conical surface meeting all the transducers in ~; the array having been drawn with perspective curves in the Figure. The transducers Ml-M4 are arranged at the corners of a tetrahedron having congruent sides and moving along the x axis at a speed of VM, the transducers Ml, M2 and M3 being in the x-y plane. In the array there is a coor-dinate system with its centre at the point where the per-- pendicular from the vertex M4 meets the side surface Ml-' M2-M3- ' The coordinate system also moves at a speed of VM
along the x axis. In Figure 2 there is also plotted the point PMp, at which the projectile 3 is when the distance between the target 2 and projectile is at a minimum and which is thus the miss distance dM.
According to the invention, the direction to the bang generation point PB can be calculated with knowledge of the times for the passage of the conical surface past each of the transducers Ml M4. The curvilinear surface must thereby be approxi~ated to a flat surface as illustrated in Figure 3. In this figure, the transducer M2 is met by the conical surface first, and by the generatrix A-A which is thus common for the curvilinear conical surface and the approximated flat surface, as shown in Figure 3. The vec-tors extendirlg from the coordinate system origin to the ;' , ' ' `
', ~ .
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corner points on the tetrahedron, at which the transducers are arranged are also shown on the figure. According -to the premises, the transducers Ml, M2 and M3 are in the x-y plane and the tetrahedron moves at the speed VM along the x axis. The conical surface approximated to a flat surface moves at a speed of VK in the standardized vector direction -nk which is counter to the direction to the bang genera-tion point PB.
Since the array and the wave plane move at a certain speed in relation to each other, the total speed between the plane and array will contain a speed vector in a di-rection nk perpendicular to the plane. ~hen the array moves, the perpendicular dlrection of the plane is not affected, while the speed of the plane in relation to the array, due 15 to the movement of the latter, is given by the expression: ~:
-VM Q . nk . The speed of the plane relative to the array will thus be: -VK . nk.
For the case where the transducer M2 is in the plane, as shown in Figure 2, general expressions can be set up for the perpendicular distance from the plane to the re-maining transducers Ml, M3 and M4, these distance being : positive as seen in the direction of movement nk of the plane. The following is applicable to these distances.:
-~i = (r2 - ri) nk, where i = 1, 3, 4;
If it is assumed that the pressure wave plane meets the transducer M2 at the time t = 0, the time taken for the plane to meet the other transducers wil]. be:
~ i nk ti = V~ = (r2 ~ ri) (V )~ where i = 1, 3, 4;
The following equation system can now be set up:
(r2 ~ rl) (V ) = tl (t2 = 0) (r2 ~ r3) ~VK~ t3 nk (r2 ~ r4) ~VK~ t4 9 113313b~
If it is assumed that the side of the tetrahedron is two length units, the vectors (r2 - ri) can be written as follows:
r2 ~ r~ r, 1, O) r2 ~ r3 = (0, 2, 0) ~ r2 ~ r4 = (- 3 ~ ~ 3 ! If these expressions are introduced into the above equation system the following equation system is obtained :~ in matrix form: :
~' 10 ~- ~ 1 nxl ~tl :~ I 0 2 0 n'~ = ~ t3 ~nzJ lt4 which becomes~ n' = (nx, ny, nz) tl VK 2 ;~.
side) nK = constant nK
, 15 VK and the size of the tetrahedron are thus insignificant. .;~
ny = 12 t3 i::
. nx 2~3 t3 7~- tl 3 ~ nz ~ 6 t3 ~ 3 tl t 2 t3 - t4 nz = ~ t3 ~ t4 ~ t .~ 20 or:
x = ~ t3 - 2V~ t ny = V~ t3 nz = t3 - 3 t4 ~ tl If the array is rolled an angle ~ the following ex-pressions are obtained with respect to the flight direc-tion:
n = n' ny = nycos ~ - nzsin ,~
', :: ..
- : ' ' ~ - . :: .:... : ~ , 3~3~
n = (nx~ ny, nz) nk - :
Inl From the above equation, it is apparent that the di-rection to the bang generation point PB can unambiguously be expressed by the vector nkO
The distance dB is calculated starting from the inter~
val in time T between the leading and trailing edges of the ; pressure wave. The premise here is that the projectile has supersonic speed, i.e. it has a Mach number M > 1. If the wavelength of the pressure wave is ~, then ~ ~ k fl(M) . rnl providing that r>~L, where r is defined in Figure 2 and L is the length of the projectile. The wave length ~
- can be measured by measuring the time T between the flanks on the leading and trailing edges of the pressure wave.
Since the distance dB =cos~' the following expression on dB is obtained:
, . ~
dB = klf2 (M~ T
If supersonic streaming is generally prevalent in the vi-cinity of the projectile then we have:
f2 (M) = 3 and n = 4 M
For small values of dB and Mach number close to 1, special calibration must be done for the projectile, e.g. for M <
1,3 and dB ~ 20-39 L.
After calculating the position of the bang generation point in relation to the coordinate system in the array, the direction of the projectile trajectory can be calcu-lated in relation to the direction in which the tar~et is towed, i.e. along the x axis. Different methods can be ap-plied here, and Figure 4 illustrated one method of calcu-lating the direction of the trajectory starting from thefiring point. Apart from the transducers Ml-M4 in the array, there is a fifth pressure transducer M5 arranged at the firing point, according to this embodiment. After calcu-`: . ., :
~33~
lating the position of the bang generation point P3, thetime tB it takes for the pressure wave to go from the bang generation point PB to the transducer (in this case M2) first met by the conical surface can then be calculated.
Knowing the distance dB the time tB is obtained from:
, dB
tB = r where c is the speed of sound.
c Furthermore, the time taken from firing the projec-tile until the pressure wave hits the transducer M2 is measured. This time is denoted Q t5.
The distance from the firing point to the transducer M5 and to the bang generation point PB will then be:
db dk = Vp (~t5 c ) where Vp is the projectile speed.
Half the conical angle of the pressure wave, i.e.
the Mach angle will thus be = arc sin M
where Mp is the Mach number for the projectile.
The conceivable trajectories meeting the conditions above form the surface area of a cone, with its v~ertex at the bang generation point and a conical angle of 2 - ~.
Furthermore, the axial direction of the cone is paral-lel to the direction for the unit vector nk, and its base circle is determined by the distance dk from PB. If it is assumed that the weapon is mounted on a horizontal ground plane, then this plane intersects the base circle o~ the cone at two points coinciding on the figure with the trans-ducer points M5 and M5-. These two points thus give two con-ceivable trajectories, constituting both cone generatrices starting from the intersection points with the ground plane.
These points are also symmetrical in relation to a vertical plane through the cone axis.
The unit vector nb is directed along the path from PB
towards the weapon.
. .
~331~
n n = cos ( - - ~) = sin~
nk nb nkY by kz bz bl = 1 = > nb = ~ (n b + n b ) The distance from PB to the x-y plane is positive if PB
is under (nk ~ 0) '~ z a = -d n If nb is determined so that dk nb is the vector from the bank generation point to the firing point, then the z-com ponent of this vector is equal to -(h-a), where h is the flying altitude, i.e. dk nb = -(h-a).
h-a nb = ~
nk nb + nk nb = sin~ + nk (h-a) =~ nb ~ nb x x y y z k x y nb2 + nb2~ (h a~ 2 This equation generally gives two real solutions, cor-responding to the symmetrically situated firing points M5 and M5 , except for the case where the plan of the cone base is parallel to the hori~ontal plane, which gives an infinite number of solutions. ~owever, if corresponding 60-lutions are made for two consequent firings, one of the two conceivable solutions will be eliminated, and in the present case this means that the firing point M5 can be eliminated.
Starting from the calculations above, the miss distance ; dB kan now be calculated (the miss distance being the least ; distance between the projectile and the target) using the vectors shown in Figure 5.
The movement of the array along the x axis at the op-tional time t can be given as:
rM = VM t x At an optional time t the position of the projectile in the coordinate system with its origin in the array will ~ -- 13 ~33~3~
thus be:
r (t) = dB(nk ~ Mpnb) (vMQ p b The vector between the projectile and the array at time t = 0, i.e. when the conical surface meets the trans-ducer M2, will then be:rp(0) = dB(nk ~ Mp nb) The vector from the array to the aiming point S at which sights are set is rs and it is always on the x axis.
The vector t between the point S and the trajectory for the time t = 0 will be:
t p(0) rS dB(nk Mpnb) rS
The scalar product between the vector t and the vector g = VMQ + Vpnb then gives the angle ~ according as the fol-lowing:
. _ 1~ ~ = arccos t . ~
It~.~g!
The vector dM from the point S to the miss point PMp will then be:
dM = ! t ! . sin~
dM = t - Itlcos~ . q In accordance with an alternative embodiment of the in-vention, the direc~ion of the trajectory can be calculated using a further transducer M5, spaced from the array of four pressure transducers Ml-M4 arranged at the corner points of a tetrahedron. The mathematical model on which this calcu-lation is based is apparent from Figure 6. In this figure a coordinate system fixed in relation to the ground is used, in which the array Ml-M4 is at origin at the time t = 0, i.e. when the conical surface of the pressure wave meets the transducer M2. The position of the bang generation point P~ and the conical surface giving rise to this point is de-termined as before. The extra transducer M5 is on the x axis and at a disstance 15 in front of the array Ml-M4. The extra transducer M5 and the array Ml~M4 are moved along the x axis from the origin after the time t = 0, and at the time t = t5 the conical surface reaches the transducer M5 from a second :
. ~
~3~L38 ~
bang generation point P5 on the trajectory. The distance d5 can then be calculated, but not the position of the bang generation point P5, since the direc-tion of this point is not known. However, it is known that the point must lie on a sphere having its centre at the point M5 and radius d5, and since the projectile speed and the time t = t5 are known, the distance P5 PB between both bang generation points can be calculated. It is also known that the second bang generation point P5 must lie on the base circle of the cone, the generatrix of which corresponds to the distance between both bang generation points.
Both geometrical figures thus obtained, i.e. -the sphere with its centre in M5 and radius d5, and the base circle to a cone with its vertex at PB and cone angle = ~2 ~ ~, and the generatrix with the length from P5 to PB will intersect each other at two points, P5 and P5. Both these trajectories are symmetrical with relation to a plane through the cone axis and x axis. By making a corresponding calculation for a se-cond projectile trajectory one of both lntersection poin~s can be eliminated, and it is thus possible to determine the trajectory direction, calculation of the miss distance then taking place in the same way as that in conjunction with Fig-gures 4 and 5.
The projectile speed at the time t = 0 is obtained by placing a pressure transducer M6 at the firing point, the time dif~erence between the firing instant and the time t = 0 being thus obtained, and in turn used to obtain the projec-tile speed from firing tables. The quantities used in the mathematical treatment below are apparent from Figures 6 and 7, in which the following denotations are:
Mp - projectile Mach number c = speed of sound c . Mp = Vp= pro~ectile speed MM = Mach number for the target, i.e. VM = c . MM
distance P5 - P = ds Mp distance B B P
distance P - P - c . Mp . t5 distance M5 - M5 c . MM 5 a ~L~33~
The mathematical solution is as follows:
Projectile position at t = 0:
rp = dBnk ~ (dBMp + Vp-t)nb nb = trajectory direction, positive from PB towards the weapon . Cone along the trajectory: nb . nk = sinu; Inbl = 1 Position of transducer array:
A
rM ~- V t x The transducer M5 is assumed to lie on the x axis at a dis-tance 15 in front of the array. The position of M5 is then:
r5 = (Q5 + VM . t) x Bang generation point for M5 = P5 Registration time in M5 = t5 Distance M5 - P5 = d5 The position of M5 for the time t = t5, i.e. when the press-ure wave passes, is:
( 5 Vp ~ t5) x (= a5x) The projectile position at t = t5 is:
p( 5) dBnk ~ (dBMp + Vpt5) nb 20 The distance along the trajectory from P5 to rp (t5) = ~;
d5 . Mp The position of P5 will thus be:
P5 = rp(t5) + d5Mpnb (note that nb is positive backwards in the trajectory) The value of d5 is obtained from the following equation:
~ d = ~p5 - r5(t5)l or : d25 = (p5 - rs(ts)) ~ (P5 r5(t5)) which gives:
5) dBnk (dBMp + Vpt5)nb+ d5M nb -(15 + VMts) Q ~ dBnk b5nb 5 15 + VMt5 ; b5 = dgMp + Vpt5 - d5M
; d 2 = (dBnk - b5nb ~ a5Q) (dBnk b5nb 5 ¦ k b sin~
:. . :, :
~33~8 dB dBb5sin~ a5dBnk - dgbsSin~ ~~ b5 + a5b5nb - dBa5nk + asb5nb + a5 n = d~ - (d 2 + a52 + bs - 2a5dBdk ~ 2dBb5s ~) , nb ~ nb from !nbI = 1 ; Y Z _ _ ~two solutions for nb k b J
dM and dM are subse~uently calculated in the same manner as before.
The trajectory component nb can be alternatively cal-culated according to the following method, and with reference to Figure 8.
The position of the array at the time t = t5 is:
Mt5 Q
The position of M5 at the time t = t5 is:
r5(t5) = asx = (Q5 + VMt5) For t = t5, the vector h(t) from the projectile to M'5 is a generatrix of the Mach cone:
_ h(t5) . nb = Ih(t5)I cos~
where h(t5) = rS(t5) - rp(t5) The position of the projectile is:
r (t5) = dBnk ~ (dsMp + Vpt5) b =>quadratic equation for the x component of nb (nb ) c2nb - 2clnb + CO
c2 = Mp as , cl = - a5V t5 cO = (Mp - 1)(2dsct5 + 2a5dBnk a5 ) p 5 .:: . .. , .: . .
: ' `". ', ,' ;~ , ' - . . .
': ,., '" , ", . ~
17 ~ 31~
The advantage with this method is that the calculation of the distance d5 is not entirely necessary, although the method has the disadvantage that it gives two solutions for nb for -the above equation. Information on the distance d5 shXould therefor be used to calculate nb according to the previously described method. This value'of nb is then used for selecting the righ-t nb for -the two solut~ons in the alternative methodO
As will be apparent from the above mathematical treat-ment of the problem of determining the direction from thearray to the bang generation point, it is absolutely essen-tial to exactly determine the times at which the conical sur-face of the pressure wave arrives at -the different pressure transducers.
In the case where the indicator apparatus in accordance with the invention is to be used for firing from airborn mov-able weapons towards a fixed ground target TA, the premises are applicable which are apparent from Figure 9.
The distances dBl and dB2 are calculated in the same way 2G as previously for a certain assumed Mach number, e.y. M = 1, 5-2. The distance b between the bang generation poin-ts is sub-; sequently calculated with knowledge of the quantities dBl, dB2,/nkl~ and 12-The time ~ t for the passage of the pressure wave past both arrays K2 and Kl is meas~lred, the Mach number Mp for the projectile being subsequently calculated from the formula:
b Mp = ~ t - c - dBl ~ dB2 where c = the speed of sound.
The values of the distances dBl and dB2 are corrected with the calculated Mach number, whereafter the trajectory through the bang generation points PB1 and PB2 can be cal-culated.
As wi11 be seen from the circuit diagram according to E'igure 10, the four microphones M1, M2, M3 and M4 are con-nected to a microprocessor 10, adapted for calculating thetime interval TF between the leading and trailing edges of ~:~33~38 the pressure wave as it passes one of the microphones, and the time intervals for the passage of the wave past each of the subsequent three microphones~ Each of the microphones is connected to an amplifier 2 and a Schmitt trigger circuit 3, generating a pulse with TTL adjusted amplitide when the signal from the microphone exceeds a prede-termined limiting value. The outputs of -the Schmitt trigger circuit 3 are con- -nected to a "stop" input 4 on each o:E the connected counters 5 and to a common OR gate 6, the output of which is connected to a "start" input 7 on all the counters 5. The counters 5 are also connected to an oscillator 8, generating a pulse train with a predetermined repetition frequency. The passage times of a pressure wave past the microphones Ml, M2, M3 and M4 are determined in the following way.
When the wave passes a microphone, e.g. the microphone Ml, a pulse is generated in the Schmitt trigger circuit 3, giving a start signal via the OR gate 6 to all the counters 5. These then count the pulses generated in the oscillator 8.
The counter having its "stop" input connected to the micro-phone Ml, which is first met by the wave, is given a stop signal simultaneously as it obtains a start signal, and it thus remains zeroed. While the wave passes each of the remain-ing microphones M2, M3 and M4, a pulse is generated in the associated circuits 3 which stops the appropriate counter 5, which thus contains a count proportional to the time which has passed since it was started. When a counter has stopped, the level is also raised on an input to an AND gate 9. The counters 5 are furthermore arranged so as not to start for new pulses from the OR gate 6 before a resetting signal has been obtained from a microcomputor 11. When all the micro-phones have been passed by the pressure wave, the levels on all the inputs to the AND gate 9 are high, which means that its output is high, which in turn gives an interruption sig-nal to the microcomputer 11 which then reads off the count in each of the counters associated with the microphones, and registers these counts for transmission to the main system computer. The microcomputer 11 subsequently resets the coun-. .
: : "
,. . , -.
,. : ; :., : .
-ters 5 and the cycle can be repeated. Where there is a fifth microphone M5, this is connected to the microcomputor 11 in the same way as -the other microphones.
The -ti~e TF between the leading and trailing edges of the pressure wave is measured in a counter 12. When the lead-ing edge meets a microphone, e.g. the microphone Ml, the coun-ter 12 is started and counts pulses from the oscilla-tor 8 which is also connected to the counter. The count in the coun-ter is stored as long as pulses are obtained from the Schmitt trigger circuit 3 associated with the microphone Ml. If no pulse is detected within a certain predetermined time, which is dependent on the length of the projectile, the last re-ceived pulse is assumed to come from the trailing edge of the wave. An interruption signal is then given via the wire 13 to the microcomputer 11, which reads off the value in the counter 12. This value thus gives the time between the trailing and leading edges of the pressure wave. After read-ing it, the microcomputer 11 resets the counter 12 via the wire 14 and the cycle can be repeated.
The microcomputer 11 subsequently transmits collected data via a link 15 to the central system computer 18 where the mathematical calculations are carried ou-t. The connection to the central computer can either be done via a radio link or by a cable, in the case where the micro processor 10 is on the ground.
Figure 11 is a block diagram of an indicator apparatus in accordance with the invention, preferably of the kind shown in Figure 6, where the microcomputer 10 is connected to the central computer 18 via a radio link, comprising trans-mitter receiver units 16, 17 for two-way communication. The ground-based microphone M6 is connected to the central com-puter 18 via a wire 19 for registering the firing time. The miss distances registered during firing, and the positions of the "miss points" can be registered on different readout means 20 connected to the central computer, i.e. stylus recorders, presentation screens or magnetic tapes.
The characteristic constants for each projectile type and firing occasion, which are re~uired for calculating the position of the bang generation point and the direction of ~: :
,~
, - ~33~
the trajectory, can be obtained from tables stored in the computor.
., :' , ' ,', ' "
.
' , . ~
.
7 ~
The distance dB between the bang generation point PB
and the transducer array when the pressure wave 4 passes it can be calculated, starting from the time between the front and trailing edges of the pressure wave, in accord-S ance with US Patent 2 925 582. The direction from the array to the target, and the direction of the trajectory in re-lation to a conceived coordinate system with its central point in the array can be calculated starting from the di-rection of the pressure wave in relation to the array. This distance can in turn be calculated starting from the time interval for the conical surface to pass the transducers in the array.
Figure 2 shows in detail how the conical pressure wave 4 meets two transducers M2 and Ml, in that order, the por-tion of the conical surface meeting all the transducers in ~; the array having been drawn with perspective curves in the Figure. The transducers Ml-M4 are arranged at the corners of a tetrahedron having congruent sides and moving along the x axis at a speed of VM, the transducers Ml, M2 and M3 being in the x-y plane. In the array there is a coor-dinate system with its centre at the point where the per-- pendicular from the vertex M4 meets the side surface Ml-' M2-M3- ' The coordinate system also moves at a speed of VM
along the x axis. In Figure 2 there is also plotted the point PMp, at which the projectile 3 is when the distance between the target 2 and projectile is at a minimum and which is thus the miss distance dM.
According to the invention, the direction to the bang generation point PB can be calculated with knowledge of the times for the passage of the conical surface past each of the transducers Ml M4. The curvilinear surface must thereby be approxi~ated to a flat surface as illustrated in Figure 3. In this figure, the transducer M2 is met by the conical surface first, and by the generatrix A-A which is thus common for the curvilinear conical surface and the approximated flat surface, as shown in Figure 3. The vec-tors extendirlg from the coordinate system origin to the ;' , ' ' `
', ~ .
~ 3~
corner points on the tetrahedron, at which the transducers are arranged are also shown on the figure. According -to the premises, the transducers Ml, M2 and M3 are in the x-y plane and the tetrahedron moves at the speed VM along the x axis. The conical surface approximated to a flat surface moves at a speed of VK in the standardized vector direction -nk which is counter to the direction to the bang genera-tion point PB.
Since the array and the wave plane move at a certain speed in relation to each other, the total speed between the plane and array will contain a speed vector in a di-rection nk perpendicular to the plane. ~hen the array moves, the perpendicular dlrection of the plane is not affected, while the speed of the plane in relation to the array, due 15 to the movement of the latter, is given by the expression: ~:
-VM Q . nk . The speed of the plane relative to the array will thus be: -VK . nk.
For the case where the transducer M2 is in the plane, as shown in Figure 2, general expressions can be set up for the perpendicular distance from the plane to the re-maining transducers Ml, M3 and M4, these distance being : positive as seen in the direction of movement nk of the plane. The following is applicable to these distances.:
-~i = (r2 - ri) nk, where i = 1, 3, 4;
If it is assumed that the pressure wave plane meets the transducer M2 at the time t = 0, the time taken for the plane to meet the other transducers wil]. be:
~ i nk ti = V~ = (r2 ~ ri) (V )~ where i = 1, 3, 4;
The following equation system can now be set up:
(r2 ~ rl) (V ) = tl (t2 = 0) (r2 ~ r3) ~VK~ t3 nk (r2 ~ r4) ~VK~ t4 9 113313b~
If it is assumed that the side of the tetrahedron is two length units, the vectors (r2 - ri) can be written as follows:
r2 ~ r~ r, 1, O) r2 ~ r3 = (0, 2, 0) ~ r2 ~ r4 = (- 3 ~ ~ 3 ! If these expressions are introduced into the above equation system the following equation system is obtained :~ in matrix form: :
~' 10 ~- ~ 1 nxl ~tl :~ I 0 2 0 n'~ = ~ t3 ~nzJ lt4 which becomes~ n' = (nx, ny, nz) tl VK 2 ;~.
side) nK = constant nK
, 15 VK and the size of the tetrahedron are thus insignificant. .;~
ny = 12 t3 i::
. nx 2~3 t3 7~- tl 3 ~ nz ~ 6 t3 ~ 3 tl t 2 t3 - t4 nz = ~ t3 ~ t4 ~ t .~ 20 or:
x = ~ t3 - 2V~ t ny = V~ t3 nz = t3 - 3 t4 ~ tl If the array is rolled an angle ~ the following ex-pressions are obtained with respect to the flight direc-tion:
n = n' ny = nycos ~ - nzsin ,~
', :: ..
- : ' ' ~ - . :: .:... : ~ , 3~3~
n = (nx~ ny, nz) nk - :
Inl From the above equation, it is apparent that the di-rection to the bang generation point PB can unambiguously be expressed by the vector nkO
The distance dB is calculated starting from the inter~
val in time T between the leading and trailing edges of the ; pressure wave. The premise here is that the projectile has supersonic speed, i.e. it has a Mach number M > 1. If the wavelength of the pressure wave is ~, then ~ ~ k fl(M) . rnl providing that r>~L, where r is defined in Figure 2 and L is the length of the projectile. The wave length ~
- can be measured by measuring the time T between the flanks on the leading and trailing edges of the pressure wave.
Since the distance dB =cos~' the following expression on dB is obtained:
, . ~
dB = klf2 (M~ T
If supersonic streaming is generally prevalent in the vi-cinity of the projectile then we have:
f2 (M) = 3 and n = 4 M
For small values of dB and Mach number close to 1, special calibration must be done for the projectile, e.g. for M <
1,3 and dB ~ 20-39 L.
After calculating the position of the bang generation point in relation to the coordinate system in the array, the direction of the projectile trajectory can be calcu-lated in relation to the direction in which the tar~et is towed, i.e. along the x axis. Different methods can be ap-plied here, and Figure 4 illustrated one method of calcu-lating the direction of the trajectory starting from thefiring point. Apart from the transducers Ml-M4 in the array, there is a fifth pressure transducer M5 arranged at the firing point, according to this embodiment. After calcu-`: . ., :
~33~
lating the position of the bang generation point P3, thetime tB it takes for the pressure wave to go from the bang generation point PB to the transducer (in this case M2) first met by the conical surface can then be calculated.
Knowing the distance dB the time tB is obtained from:
, dB
tB = r where c is the speed of sound.
c Furthermore, the time taken from firing the projec-tile until the pressure wave hits the transducer M2 is measured. This time is denoted Q t5.
The distance from the firing point to the transducer M5 and to the bang generation point PB will then be:
db dk = Vp (~t5 c ) where Vp is the projectile speed.
Half the conical angle of the pressure wave, i.e.
the Mach angle will thus be = arc sin M
where Mp is the Mach number for the projectile.
The conceivable trajectories meeting the conditions above form the surface area of a cone, with its v~ertex at the bang generation point and a conical angle of 2 - ~.
Furthermore, the axial direction of the cone is paral-lel to the direction for the unit vector nk, and its base circle is determined by the distance dk from PB. If it is assumed that the weapon is mounted on a horizontal ground plane, then this plane intersects the base circle o~ the cone at two points coinciding on the figure with the trans-ducer points M5 and M5-. These two points thus give two con-ceivable trajectories, constituting both cone generatrices starting from the intersection points with the ground plane.
These points are also symmetrical in relation to a vertical plane through the cone axis.
The unit vector nb is directed along the path from PB
towards the weapon.
. .
~331~
n n = cos ( - - ~) = sin~
nk nb nkY by kz bz bl = 1 = > nb = ~ (n b + n b ) The distance from PB to the x-y plane is positive if PB
is under (nk ~ 0) '~ z a = -d n If nb is determined so that dk nb is the vector from the bank generation point to the firing point, then the z-com ponent of this vector is equal to -(h-a), where h is the flying altitude, i.e. dk nb = -(h-a).
h-a nb = ~
nk nb + nk nb = sin~ + nk (h-a) =~ nb ~ nb x x y y z k x y nb2 + nb2~ (h a~ 2 This equation generally gives two real solutions, cor-responding to the symmetrically situated firing points M5 and M5 , except for the case where the plan of the cone base is parallel to the hori~ontal plane, which gives an infinite number of solutions. ~owever, if corresponding 60-lutions are made for two consequent firings, one of the two conceivable solutions will be eliminated, and in the present case this means that the firing point M5 can be eliminated.
Starting from the calculations above, the miss distance ; dB kan now be calculated (the miss distance being the least ; distance between the projectile and the target) using the vectors shown in Figure 5.
The movement of the array along the x axis at the op-tional time t can be given as:
rM = VM t x At an optional time t the position of the projectile in the coordinate system with its origin in the array will ~ -- 13 ~33~3~
thus be:
r (t) = dB(nk ~ Mpnb) (vMQ p b The vector between the projectile and the array at time t = 0, i.e. when the conical surface meets the trans-ducer M2, will then be:rp(0) = dB(nk ~ Mp nb) The vector from the array to the aiming point S at which sights are set is rs and it is always on the x axis.
The vector t between the point S and the trajectory for the time t = 0 will be:
t p(0) rS dB(nk Mpnb) rS
The scalar product between the vector t and the vector g = VMQ + Vpnb then gives the angle ~ according as the fol-lowing:
. _ 1~ ~ = arccos t . ~
It~.~g!
The vector dM from the point S to the miss point PMp will then be:
dM = ! t ! . sin~
dM = t - Itlcos~ . q In accordance with an alternative embodiment of the in-vention, the direc~ion of the trajectory can be calculated using a further transducer M5, spaced from the array of four pressure transducers Ml-M4 arranged at the corner points of a tetrahedron. The mathematical model on which this calcu-lation is based is apparent from Figure 6. In this figure a coordinate system fixed in relation to the ground is used, in which the array Ml-M4 is at origin at the time t = 0, i.e. when the conical surface of the pressure wave meets the transducer M2. The position of the bang generation point P~ and the conical surface giving rise to this point is de-termined as before. The extra transducer M5 is on the x axis and at a disstance 15 in front of the array Ml-M4. The extra transducer M5 and the array Ml~M4 are moved along the x axis from the origin after the time t = 0, and at the time t = t5 the conical surface reaches the transducer M5 from a second :
. ~
~3~L38 ~
bang generation point P5 on the trajectory. The distance d5 can then be calculated, but not the position of the bang generation point P5, since the direc-tion of this point is not known. However, it is known that the point must lie on a sphere having its centre at the point M5 and radius d5, and since the projectile speed and the time t = t5 are known, the distance P5 PB between both bang generation points can be calculated. It is also known that the second bang generation point P5 must lie on the base circle of the cone, the generatrix of which corresponds to the distance between both bang generation points.
Both geometrical figures thus obtained, i.e. -the sphere with its centre in M5 and radius d5, and the base circle to a cone with its vertex at PB and cone angle = ~2 ~ ~, and the generatrix with the length from P5 to PB will intersect each other at two points, P5 and P5. Both these trajectories are symmetrical with relation to a plane through the cone axis and x axis. By making a corresponding calculation for a se-cond projectile trajectory one of both lntersection poin~s can be eliminated, and it is thus possible to determine the trajectory direction, calculation of the miss distance then taking place in the same way as that in conjunction with Fig-gures 4 and 5.
The projectile speed at the time t = 0 is obtained by placing a pressure transducer M6 at the firing point, the time dif~erence between the firing instant and the time t = 0 being thus obtained, and in turn used to obtain the projec-tile speed from firing tables. The quantities used in the mathematical treatment below are apparent from Figures 6 and 7, in which the following denotations are:
Mp - projectile Mach number c = speed of sound c . Mp = Vp= pro~ectile speed MM = Mach number for the target, i.e. VM = c . MM
distance P5 - P = ds Mp distance B B P
distance P - P - c . Mp . t5 distance M5 - M5 c . MM 5 a ~L~33~
The mathematical solution is as follows:
Projectile position at t = 0:
rp = dBnk ~ (dBMp + Vp-t)nb nb = trajectory direction, positive from PB towards the weapon . Cone along the trajectory: nb . nk = sinu; Inbl = 1 Position of transducer array:
A
rM ~- V t x The transducer M5 is assumed to lie on the x axis at a dis-tance 15 in front of the array. The position of M5 is then:
r5 = (Q5 + VM . t) x Bang generation point for M5 = P5 Registration time in M5 = t5 Distance M5 - P5 = d5 The position of M5 for the time t = t5, i.e. when the press-ure wave passes, is:
( 5 Vp ~ t5) x (= a5x) The projectile position at t = t5 is:
p( 5) dBnk ~ (dBMp + Vpt5) nb 20 The distance along the trajectory from P5 to rp (t5) = ~;
d5 . Mp The position of P5 will thus be:
P5 = rp(t5) + d5Mpnb (note that nb is positive backwards in the trajectory) The value of d5 is obtained from the following equation:
~ d = ~p5 - r5(t5)l or : d25 = (p5 - rs(ts)) ~ (P5 r5(t5)) which gives:
5) dBnk (dBMp + Vpt5)nb+ d5M nb -(15 + VMts) Q ~ dBnk b5nb 5 15 + VMt5 ; b5 = dgMp + Vpt5 - d5M
; d 2 = (dBnk - b5nb ~ a5Q) (dBnk b5nb 5 ¦ k b sin~
:. . :, :
~33~8 dB dBb5sin~ a5dBnk - dgbsSin~ ~~ b5 + a5b5nb - dBa5nk + asb5nb + a5 n = d~ - (d 2 + a52 + bs - 2a5dBdk ~ 2dBb5s ~) , nb ~ nb from !nbI = 1 ; Y Z _ _ ~two solutions for nb k b J
dM and dM are subse~uently calculated in the same manner as before.
The trajectory component nb can be alternatively cal-culated according to the following method, and with reference to Figure 8.
The position of the array at the time t = t5 is:
Mt5 Q
The position of M5 at the time t = t5 is:
r5(t5) = asx = (Q5 + VMt5) For t = t5, the vector h(t) from the projectile to M'5 is a generatrix of the Mach cone:
_ h(t5) . nb = Ih(t5)I cos~
where h(t5) = rS(t5) - rp(t5) The position of the projectile is:
r (t5) = dBnk ~ (dsMp + Vpt5) b =>quadratic equation for the x component of nb (nb ) c2nb - 2clnb + CO
c2 = Mp as , cl = - a5V t5 cO = (Mp - 1)(2dsct5 + 2a5dBnk a5 ) p 5 .:: . .. , .: . .
: ' `". ', ,' ;~ , ' - . . .
': ,., '" , ", . ~
17 ~ 31~
The advantage with this method is that the calculation of the distance d5 is not entirely necessary, although the method has the disadvantage that it gives two solutions for nb for -the above equation. Information on the distance d5 shXould therefor be used to calculate nb according to the previously described method. This value'of nb is then used for selecting the righ-t nb for -the two solut~ons in the alternative methodO
As will be apparent from the above mathematical treat-ment of the problem of determining the direction from thearray to the bang generation point, it is absolutely essen-tial to exactly determine the times at which the conical sur-face of the pressure wave arrives at -the different pressure transducers.
In the case where the indicator apparatus in accordance with the invention is to be used for firing from airborn mov-able weapons towards a fixed ground target TA, the premises are applicable which are apparent from Figure 9.
The distances dBl and dB2 are calculated in the same way 2G as previously for a certain assumed Mach number, e.y. M = 1, 5-2. The distance b between the bang generation poin-ts is sub-; sequently calculated with knowledge of the quantities dBl, dB2,/nkl~ and 12-The time ~ t for the passage of the pressure wave past both arrays K2 and Kl is meas~lred, the Mach number Mp for the projectile being subsequently calculated from the formula:
b Mp = ~ t - c - dBl ~ dB2 where c = the speed of sound.
The values of the distances dBl and dB2 are corrected with the calculated Mach number, whereafter the trajectory through the bang generation points PB1 and PB2 can be cal-culated.
As wi11 be seen from the circuit diagram according to E'igure 10, the four microphones M1, M2, M3 and M4 are con-nected to a microprocessor 10, adapted for calculating thetime interval TF between the leading and trailing edges of ~:~33~38 the pressure wave as it passes one of the microphones, and the time intervals for the passage of the wave past each of the subsequent three microphones~ Each of the microphones is connected to an amplifier 2 and a Schmitt trigger circuit 3, generating a pulse with TTL adjusted amplitide when the signal from the microphone exceeds a prede-termined limiting value. The outputs of -the Schmitt trigger circuit 3 are con- -nected to a "stop" input 4 on each o:E the connected counters 5 and to a common OR gate 6, the output of which is connected to a "start" input 7 on all the counters 5. The counters 5 are also connected to an oscillator 8, generating a pulse train with a predetermined repetition frequency. The passage times of a pressure wave past the microphones Ml, M2, M3 and M4 are determined in the following way.
When the wave passes a microphone, e.g. the microphone Ml, a pulse is generated in the Schmitt trigger circuit 3, giving a start signal via the OR gate 6 to all the counters 5. These then count the pulses generated in the oscillator 8.
The counter having its "stop" input connected to the micro-phone Ml, which is first met by the wave, is given a stop signal simultaneously as it obtains a start signal, and it thus remains zeroed. While the wave passes each of the remain-ing microphones M2, M3 and M4, a pulse is generated in the associated circuits 3 which stops the appropriate counter 5, which thus contains a count proportional to the time which has passed since it was started. When a counter has stopped, the level is also raised on an input to an AND gate 9. The counters 5 are furthermore arranged so as not to start for new pulses from the OR gate 6 before a resetting signal has been obtained from a microcomputor 11. When all the micro-phones have been passed by the pressure wave, the levels on all the inputs to the AND gate 9 are high, which means that its output is high, which in turn gives an interruption sig-nal to the microcomputer 11 which then reads off the count in each of the counters associated with the microphones, and registers these counts for transmission to the main system computer. The microcomputer 11 subsequently resets the coun-. .
: : "
,. . , -.
,. : ; :., : .
-ters 5 and the cycle can be repeated. Where there is a fifth microphone M5, this is connected to the microcomputor 11 in the same way as -the other microphones.
The -ti~e TF between the leading and trailing edges of the pressure wave is measured in a counter 12. When the lead-ing edge meets a microphone, e.g. the microphone Ml, the coun-ter 12 is started and counts pulses from the oscilla-tor 8 which is also connected to the counter. The count in the coun-ter is stored as long as pulses are obtained from the Schmitt trigger circuit 3 associated with the microphone Ml. If no pulse is detected within a certain predetermined time, which is dependent on the length of the projectile, the last re-ceived pulse is assumed to come from the trailing edge of the wave. An interruption signal is then given via the wire 13 to the microcomputer 11, which reads off the value in the counter 12. This value thus gives the time between the trailing and leading edges of the pressure wave. After read-ing it, the microcomputer 11 resets the counter 12 via the wire 14 and the cycle can be repeated.
The microcomputer 11 subsequently transmits collected data via a link 15 to the central system computer 18 where the mathematical calculations are carried ou-t. The connection to the central computer can either be done via a radio link or by a cable, in the case where the micro processor 10 is on the ground.
Figure 11 is a block diagram of an indicator apparatus in accordance with the invention, preferably of the kind shown in Figure 6, where the microcomputer 10 is connected to the central computer 18 via a radio link, comprising trans-mitter receiver units 16, 17 for two-way communication. The ground-based microphone M6 is connected to the central com-puter 18 via a wire 19 for registering the firing time. The miss distances registered during firing, and the positions of the "miss points" can be registered on different readout means 20 connected to the central computer, i.e. stylus recorders, presentation screens or magnetic tapes.
The characteristic constants for each projectile type and firing occasion, which are re~uired for calculating the position of the bang generation point and the direction of ~: :
,~
, - ~33~
the trajectory, can be obtained from tables stored in the computor.
., :' , ' ,', ' "
.
Claims (7)
1. An indicator apparatus for determining a distance of a supersonic projectile in relation to a target, comprising:
at least four pressure sensing transducers for sensing the conical pressure wave generated by the supersonic pro-jectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system, means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four trans-ducers in the first pressure transducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the distance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
said at least four transducers being arranged at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for sensing the firing time instant and including means for measuring the time from firing until the pressure wave is detected by said one pressure transducer in the first transducer system in order to determine the projectile speed and hence the apex angle of the conical pressure wave and thus the unit vector from the bang generation point to the firing point, said unit vector thereby defining the direction of the pro-jectile trajectory, which together with the position of the bang generation point gives the trajectory per se;
and means for computing the size and direction of the vector between said coordinate system and the projectile at an arbitrary time instant and determining this vector when it has a certain size.
at least four pressure sensing transducers for sensing the conical pressure wave generated by the supersonic pro-jectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system, means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four trans-ducers in the first pressure transducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the distance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
said at least four transducers being arranged at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for sensing the firing time instant and including means for measuring the time from firing until the pressure wave is detected by said one pressure transducer in the first transducer system in order to determine the projectile speed and hence the apex angle of the conical pressure wave and thus the unit vector from the bang generation point to the firing point, said unit vector thereby defining the direction of the pro-jectile trajectory, which together with the position of the bang generation point gives the trajectory per se;
and means for computing the size and direction of the vector between said coordinate system and the projectile at an arbitrary time instant and determining this vector when it has a certain size.
2. An indicator apparatus for determining a distance of a supersonic projectile in relation to a target, com-prising:
at least four pressure sensing transducers for sensing the conical pressure wave generated by the super-sonic projectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system, means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four transducers in the first pressure transducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the distance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
Said at least four transducers being arragned at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for detecting the passage of the conical pressure wave at a further occasion;
means for sensing the firing instant and for com-puting the projectile speed and hence the apex angle of the conical pressure wave and thus the unit vector from the bang generation point to the firing point, said unit vector thereby defining the direction of the projectile trajectory, which together with the position of the bang generation point gives the trajectory per se; and means for computing the size and direction of the vector between said coordinate system and the projectile at an arbitrary time instant and determining this vector when it has a certain size.
at least four pressure sensing transducers for sensing the conical pressure wave generated by the super-sonic projectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system, means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four transducers in the first pressure transducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the distance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
Said at least four transducers being arragned at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for detecting the passage of the conical pressure wave at a further occasion;
means for sensing the firing instant and for com-puting the projectile speed and hence the apex angle of the conical pressure wave and thus the unit vector from the bang generation point to the firing point, said unit vector thereby defining the direction of the projectile trajectory, which together with the position of the bang generation point gives the trajectory per se; and means for computing the size and direction of the vector between said coordinate system and the projectile at an arbitrary time instant and determining this vector when it has a certain size.
3. An indicator apparatus for determining a distance of a supersonic projectile in relation to a target, com-prising:
at least four pressure sensing transducers for sensing the conical pressure wave generated by the super-sonic projectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system;
means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four transducers in the first pressure trans-ducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the dis-tance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
said at least four transducers being arranged at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for detecting the passage of the conical pressure wave at a further occasion, said second transducer system having a known position relative to the target and to the first transducer system;
means for detecting the pressure wave character-istics and for calculating the distance from said second transducer system to a second bang generation point in order to determine the position of the second bang generation point;
and;
means for computing the direction of the projectile trajectory between said two bang generation points and for determining the distance between the projectile trajectory and the target in an arbitrary target plane being inter-sected by the projectile trajectory.
at least four pressure sensing transducers for sensing the conical pressure wave generated by the super-sonic projectile in at least four points, the at least four pressure transducers forming part of a first pressure transducer system;
means for measuring the time instants when the conical pressure wave is detected in the at least four transducers and for determining the time differences between the passages of the conical pressure wave past the at least four transducers in the first pressure trans-ducer system;
means for detecting the pressure wave character-istics and generating electrical signals therefrom;
computing means coupled to said detecting means for calculating based on said electrical signals the dis-tance from one pressure transducer to the point from which the conical pressure wave originated, the so-called "bang generation point";
said at least four transducers being arranged at the corners of a polyhedron, having as many corners as the number of transducers and being given fixed positions in a coordinate system with a known position relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to the target;
means for computing the direction of the speed vector of the conical pressure wave relative to said coordinate system from the determined time differences and thus the position of the bang generation point from the calculated distance to the bang generation point, thereby obtaining a first point on the projectile trajectory;
a second transducer system for detecting the passage of the conical pressure wave at a further occasion, said second transducer system having a known position relative to the target and to the first transducer system;
means for detecting the pressure wave character-istics and for calculating the distance from said second transducer system to a second bang generation point in order to determine the position of the second bang generation point;
and;
means for computing the direction of the projectile trajectory between said two bang generation points and for determining the distance between the projectile trajectory and the target in an arbitrary target plane being inter-sected by the projectile trajectory.
4. An indicator as claimed in claim 2, comprising:
means for registering the time difference between the firing instant and the time when the pressure wave is detected by a transducer in the first transducer system in order to determine the projectile speed and hence the Mach number as well as the conical angle of the pressure wave, which quantities are converted into electrical signals and supplied to the means for calculating the size and direction of the vector between the coordinate system moving with the polyhedron and the projectile.
means for registering the time difference between the firing instant and the time when the pressure wave is detected by a transducer in the first transducer system in order to determine the projectile speed and hence the Mach number as well as the conical angle of the pressure wave, which quantities are converted into electrical signals and supplied to the means for calculating the size and direction of the vector between the coordinate system moving with the polyhedron and the projectile.
5. An indicator as claimed in claim 2, wherein the second transducer system comprises:
at least one pressure transducer arranged for moving in unison with the first pressure transducer system.
at least one pressure transducer arranged for moving in unison with the first pressure transducer system.
6. An indicator according to claims 1, 2, or 4, wherein said vector size and direction computing means includes:
means for determining when the vector between said coordinate system and said projectile has a minimum size corresponding to the miss distance between the projectile and the target.
means for determining when the vector between said coordinate system and said projectile has a minimum size corresponding to the miss distance between the projectile and the target.
7. An indicator according to claim 5, wherein said vector size and direction computing means includes:
means for determining when the vector between said coordinate system and said projectile has a minimum size corresponding to the miss distance between the projectile and the target.
means for determining when the vector between said coordinate system and said projectile has a minimum size corresponding to the miss distance between the projectile and the target.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA321,028A CA1133138A (en) | 1979-02-07 | 1979-02-07 | Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA321,028A CA1133138A (en) | 1979-02-07 | 1979-02-07 | Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1133138A true CA1133138A (en) | 1982-10-05 |
Family
ID=4113485
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA321,028A Expired CA1133138A (en) | 1979-02-07 | 1979-02-07 | Indicator apparatus for determining the miss distance of a projectile in relation to a fixed or moving target |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1133138A (en) |
-
1979
- 1979-02-07 CA CA321,028A patent/CA1133138A/en not_active Expired
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