Apparatus and methods for aimpoint correction

In order to determine crosswind effects between a weapon and its intended target (204) a crosswind gradient measuring apparatus (600) directs a first pulsed coherent light beam (646) and a second pulsed coherent light beam (648) to the target (204). Light of both beams scattered back by aerosols in the air is measured by using a detector (652) thus generating a beat frequency in the detector signal. The beat frequency indicates a Doppler-shift due to crosswind as a function of range between weapon and target wherein the range is determined by the time of flight. The information determined by such a Doppler differential interferometer, DDI, is utilized by a signal processor (608) to calculate the bullet's crosswind offset which enables manual of automatic adjustment of an aiming mechanism.

TECHNICAL FIELD

The present invention relates generally to correcting the aimpoint of a direct fire projectile weapon. More particularly, the present invention relates to aimpoint correction based on measurement of downrange wind gradients.

BACKGROUND

Cross-range wind (crosswind) compensation is part of most precision long-range gunnery. Snipers do it by estimation, training and experience. It is done in tank gunnery, using only the locally measured crosswind speed at the tank. Artillery may use meteorological data for the high altitude winds between battery and target. Crosswind measurement is applicable to any direct-fire projectile and to many indirect-fire weapons as well. The most challenging of these crosswind compensations is the long range sniper scenario. The sniper fires a small projectile (bullet) a long distance through unknown and varied low-level winds. Thus, the sniper scenario is one of the more sensitive cases of cross-range compensation.

Traditionally snipers estimate crosswind based on environmental cues such as grass movements or visible “mirage.” These methods rely partially upon instincts and are imprecise and difficult to master. Nevertheless, highly trained snipers use these methods to achieve astonishingly accurate results at times. For instance, in 2004 a world record was set in which six sets of five shots each landed inside a 16 cm circle at 1000 yards. During the afternoon event that same day, however, the same shooter entirely missed the 6′ square target 7 of 10 shots before being eliminated from contention.

It is known that the path of a projectile fired from a sniper's rifle (e.g., a bullet fired from a rifle) will be adversely affected by any crosswinds existing between the firearm and the desired target. For example, a crosswind having a horizontal component orthogonal to the line of sight between the weapon and the target will deflect the projectile to the left or right of the target. Depending on such factors as the magnitude of the horizontal (or vertical) crosswind component, the distance between the firearm and the target, and the size of the target, mass of the projectile, a crosswind may result in an otherwise properly aimed projectile missing the target entirely. Hence, crosswinds present a significant challenge in situations calling for precise targeting, particularly over long distances.

Indirect methods such as Doppler triangulation or dynamic speckle statistics have operational drawbacks due to large footprints, large apparatuses, or long data collection times. Moreover, such conventional methods are not able to adequately account for a non-homogeneous crosswind, i.e., a crosswind having a magnitude that varies along the distance between the firearm and the target. In addition, conventional methods are prone to inaccuracies occasioned by motion and/or vibration of the measuring device. Some examples of approaches that attempt to gauge cross-range wind include: eye-balling a target with instincts and training102,FIG. 1; laser Doppler velocimeter (LDV) that only measures tailwinds104,FIG. 1; LDV parallax that is able to determine cross-range wind compensation, but is restricted to wide-open spaces and requires cumbersome equipment106,FIG. 1; scintillation correction may work in homogeneous wind applications, but is less efficient in non-homogeneous wind108,FIG. 1; and instrumented range which is impractical in real world applications because anemometers are placed at multiple points (i.e. every 50 meters) between the weapon and the target110,FIG. 1.

None of these approaches solves the problems of cross-range wind compensation. It would be therefore be advantageous to be able to easily measure the crosswind between a weapon and its intended target and then be able to adjust the aimpoint of the weapon by an offset amount that accounts for the measured crosswind.

In view of the foregoing, the present disclosure provides a novel approach to determining the crosswind as a function of downrange distance that does not have the drawbacks of previous attempts.

SUMMARY

To address the foregoing problems, in whole or in part, and/or other problems that may have been observed by persons skilled in the art, the present disclosure provides methods, processes, systems, apparatus, instruments, and/or devices, as described by way of example in implementations set forth below.

According to one implementation, systems, apparatuses, devices, instruments, and/or methods are provided for determining crosswind (either horizontal or vertical) from measurements of downrange wind gradients.

In some examples, an interferometric device may be provided. According to another implementation, systems, apparatuses, devices, instruments, and/or methods are provided for executing an algorithm that computes bullet path offset due to potentially non-homogeneous crosswinds.

According to another implementation, systems, apparatuses, devices, instruments, and/or methods are provided for manually or automatically adjusting a shooter's aiming reticle to display or otherwise indicate a compensated impact point.

DETAILED DESCRIPTION

InFIG. 2, a diagram200illustrating the positional relation between a direct fire weapon (for example, a rifle, cannon, or tank) and an intended target T is depicted. For purposes of illustration, the shooter S202(i.e. location of the direct fire weapon) is placed at the origin of a Cartesian coordinate system in which the y-axis is collinear with the direct line of sight between the shooter S and the target T204, the x-axis is the horizontal direction orthogonal to the line of sight, and the z-axis (not shown) is the vertical direction relative to ground. The line-of-sight distance between the shooter S (y=0) and the target T may be given by D206(a value for the y-coordinate at the target T204). A typical sniper rifle (not shown) to which the present teachings may be applied will be equipped with a telescopic sight (e.g., a scope) that includes a reticle, which aids the shooter S202of the weapon in finding, viewing and aiming at the target T204. A scope of any suitable design may be utilized.

According to the present teachings described herein, the aimpoint of the sniper rifle is corrected to compensate for the effect of a spatially-varying horizontal crosswind (i.e., a crosswind having an x-component) on the impact point of the projectile (e.g., bullet). In the absence of such a correction, the crosswind in the x-direction (Wx208) would steer the bullet away from a straight downrange (y-direction) path. The correction may be implemented by finding a value for the horizontal offset, d210, due to the crosswind existing at the target T204, and then correlating this offset with an adjustment to be made (manually or automatically) to the rifle's scope, thereby enabling the shooter S202to accurately and consistently hit the target T204.

For convenience, the following description will focus on correcting for the presence of a horizontal crosswind. It will be appreciated by persons skilled in the art, however, that the present teachings may be applied analogously to a crosswind described by a vertical component (i.e., in the z-direction). This description will not discuss correction in the z-direction caused by gravity acting on the mass of the projectile, as approaches for gravity corrections are known.

In the case of constant or homogeneous winds, the determination of the horizontal offset d210may be derived from the Didion Equation that was put forth in 1858 by French engineer/mathematician Isadore Didion:

d=Wx⁡(t-DVo),(1)
where:D is the distance to the Target (downrange),Vois the muzzle velocity,t is the time of flight to the target,Wx is the cross-range wind speed, andd is the cross-range offset (drift) at the target.

In the present context, the Didion Equation may be considered as being applicable to finding the horizontal offset d210that would be due to a spatially constant crosswind, by considering Wx208as representing the horizontal crosswind as a function of distance (y) downrange, t as the time of flight of the bullet from the rifle's muzzle (i.e., shooter S202) to the target T204, D206as the distance along the y-axis from the shooter S202to the target T204, and Voas the muzzle velocity.

The time-to-impact (t) is not easy to establish in combat conditions so Didion also derived t as a function of bullet parameters:

where k=ρCdA/2M with A=bullet cross sectional area, M=bullet mass, ρ=air density, and Cd=coefficient of drag. Cdaccounts for bullet shape and is, in general, a function of velocity. Cdis tabulated for each bullet by manufacturers and is available on the internet. For historical reasons manufacturers list Cdas a multiple (fraction) of a “standard” bullet's drag. (Care must be exercised in converting the manufacturer's values to the physical coefficient of drag since the properties of the “standard” bullet are not necessarily consistent across manufacturers.) For simplicity the value k=0.001/m will be used for the remainder of this example implementation as it is consistent with a 0.30 caliber SIERRA MATCHKING bullet, a favorite among long-range shooters.

What Didion was unable to determine was down-range crosswind as a function of down-range position. For use with remote measurement techniques that will be explained in more detail later, the Didion equation may be generalized for non-constant crosswinds:

d=kVo⁢∫0D⁢∫0y⁢Wx⁡(y′)⁢eky′⁢ⅆy′⁢ⅆy.(3)
Thus, to calculate the offset for non-constant crosswinds one must know the value of the crosswind as a function of the downrange coordinate: Wx(y). Equation (3) may be integrated by parts to yield:

Derivation of the Generalized Didion Equation (3) is not shown, but it may be derived by following Didion's original derivation but without extracting Wx from the integrals, where Equation (4) governs the bullet offset due to non-homogeneous crosswinds.

The example of determining the crosswind and a function of downrange distance that overcomes the drawbacks of previous approaches is shown inFIG. 3. Considering the conceptual diagram300ofFIG. 3, the diverging laser beams302and304may function as individual Doppler wind sensors and return a measurement of the projection of the wind field onto the laser direction at any point. We specify the unknown wind velocity field by:
{right arrow over (W)}(x,y)=Wx(x,y){circumflex over (x)}+Wy(x,y)ŷ,(5)

a vector function of x and y. The wind sensors return a speed measurement at downrange coordinate y given by:
m1(y)={right arrow over (W)}(−ytan α,y)·{circumflex over (k)}1=−Wx(−ytan α,y)sin α+Wy(−ytan α,y)cos α
m2(y)={right arrow over (W)}(ytan α,y)·{circumflex over (k)}21=Wx(ytan α,y)sin α+Wy(ytan α,y)cos α.  (6)

Subtracting the two measurements, and a little algebra results in the following expression:

We recognize the first term in the curly braces as the mean crosswind at a distance y. The second term in curly braces is likewise recognizable as the gradient of Wy in the x direction. Thus, we make the following substitutions:

Then the expression can be simplified:

It is recalled from fluid mechanics that the respective x- and y-components of a wind field W may be described as gradients of a scalar potential function φ (phi). Thus,

The value dWx/dy may be further manipulated by the following set of identities:

Substituting into equation (11) into equation (9) and integrating over y gives:

Solving for the crosswind:

Equation (13) is the desired expression for the crosswind at a distance y from the shooter based on measurements that are easily made with existing devices. While it is reasonable to make the desired wind speed measurements using a pair of Doppler wind sensors a solution that reduces complexity and is substantially self-calibrating is described in this section.

Turning toFIG. 4, a diagram illustrating a crosswind gradient measuring device that employs the concepts ofFIG. 3in accordance with an example implementation of the invention is depicted. In the preferred approach one may use a “Doppler differential interferometer” (DDI) sensor400that employs both free legs that are used as symmetric probe beams (unlike a traditional Michelson interferometer). The geometry of the self-aligning interferometer may be seen inFIG. 4. The angle α is set by the angle of the final mirrors402and404on each leg and will be selected based on the application but will always be small.

The distance downrange (y) is parameterized by the time (t) between the observation and the pulse leaving the laser:

where c, as usual, is the speed of light. The pulse from the laser406must be long enough to resolve the desired beat frequencies. For example a 0.5 micron laser wavelength and a 2 MHz frequency resolution results in a 0.5 m/s velocity sensitivity every 70 meters down-range with a 500 nsec laser pulse.

The photo-detector (photodiode408) senses a beat frequency that indicates the difference in the individual Doppler-shifted frequencies of each beam. Fourier analysis will extract the beat frequency which, for typical terrestrial wind conditions will be less than a few MHz. The Doppler shifted frequency of each beam is given by:

where we have used equation (6) to replace the vector dot product. The beat frequency is the difference between the Doppler frequencies:

Equation (13) may be re-written in terms of the measurements made by the DDI thusly:

Computing the Bullet Drift:

The bullet drift may be expressed in terms of the measured beat frequencies by combining equations (17) and (4):

Equation (18) may be integrated by parts to cast the formula into a more favorable format:

Equation (19) is more favorable in that the integral inside the curly braces may be considered a weighting factor that depends only upon the distance downrange and static parameters of the rifle, bullet and atmosphere. We name this the “K-factor” and define it as:

Since the integrand has a pole at z=0 the K-factor is defined only over intervals that do not include zero. For all cases of interest for shooters, both ky and kD are positive.FIG. 5shows a graph500of K-factors for a representative range of values. For a given rifle-bullet (i.e. weapon-shell) combination the K-factor may be pre-computed for easy application in the field.

The bullet offset is determined by:

in which the values of Δf(y) are measureable with the DDI instrument described and the values of K, V0, λ and α can be determined a priori.

Turning toFIG. 6, a block diagram600of a crosswind gradient measuring apparatus (or device, system, etc.) ofFIG. 4in accordance with an example implementation is depicted. The crosswind gradient measuring apparatus600generally includes an optics device604and a signal processing device (or signal processor)608. The optics device604and the signal processor608may be enclosed in any suitable housing (not shown), may be carried by the shooter S202,FIG. 2and/or mounted to or on the shooter's weapon or in a vehicle, and may be self-powered such as via an internal power source (e.g., battery). In the illustrated example, the optics device604,FIG. 6is configured as an interferometer in a novel manner that is herein termed a Doppler differential interferometer (DDI).

The optics device604may include any suitable source of coherent light such as a laser612of any suitable type, a beam splitter626of any suitable type (e.g., grating, half-mirror, etc.) for splitting the laser beam into two probe beams622,624, and one or more mirrors628,632,636as necessary for directing the two probe beams622,624toward the downrange target T at a horizontal spacing Δx on either side of the line-of-sight y-axis with a predetermined angle α (or vertical spacing Δz with a predetermined angle α in the case of vertical correction). The optics device604may further include separate collection/transmission optics (lenses, etc.)642,644for each probe leg for respectively transmitting collimated probe beams646,648toward the target T and receiving backscattered light. The optics device604further includes a photodetector652of any suitable type (e.g., a photodiode) for receiving and measuring backscattered light. By measuring the intensity of the backscattered light as a function of time, the photodetector652shows a Doppler frequency beat resulting from the difference in the respective velocities of the winds encountered by the two probe beams646,648propagating through the air.

In use, the shooter aims the crosswind gradient measuring apparatus600toward the target T and activates the laser612. The laser beam is split into the two probe beams622,624, as directed by the mirrors628,632and636downrange (y-direction) and at an angular separation of α. A fraction of the laser light originating from each of the probe beams622,624is scattered back toward the crosswind gradient measuring apparatus600by aerosols in the air and directed by the mirrors628,632and636to the beam splitter626, where the backscattered light rays are combined and transmitted along a path656to the photodetector652. As noted above, the photodetector652senses a beat frequency that indicates the difference in speed between the two legs of the interferometer. Stated differently, the beat frequency at the photodetector652indicates the difference in downrange wind speed at conjugate points. It can be seen that this new technique is both motion and vibration tolerant.

It will also be noted that the laser612is pulsed to provide range by time of flight. The pulse must be long enough to resolve the desired beat frequencies. For example, a 0.5 micron laser wavelength and a 2 MHz frequency resolution results in a 0.5 m/s velocity sensitivity every 70 meters down-range with a 500 nsec laser pulse.

From the measurements made by the photodetector652, equations (11), (4) and (3) above may be utilized to calculate the bullet's crosswind offset, d. In the present example, the photodetector652transmits electrical signals corresponding to the incident light detected to the signal processor608and the signal processor608performs the necessary calculations. As appreciated by persons skilled in the art, the signal processor608may be configured in a wide variety of different ways readily apparent and implementable without undue experimentation, and thus the signal processor608requires only a brief description herein. Generally, the signal processor608may be any microprocessor-based device that may include various hardware attributes (e.g., a central-processing unit, system memory, busses for communicating signals to or from various components, input and/or output interfaces, a display or readout, etc.). The calculations performed to obtain the crosswind offset d may be implemented by the signal processor608as an algorithm, which may be executed by hardware or firmware of the signal processor608such as a digital signal processor (DSP), application-specific integrated circuit (ASIC) or other type of processing unit. Additionally or alternatively, all or part of the calculations may be performed by software executed by the signal processor608, i.e., a set of computer-executable instructions.

Once the crosswind offset d is calculated, the shooter's telescopic sight or scope may then be adjusted, by any means either manual or automated, to indicate the calculated hit point. The signal processor608may be configured to correlate the calculated value for the crosswind offset “d” to an adjustment level that will depend on the type and design of the telescopic sight being utilized. As an example, in the case of manual adjustment and for a scope that implements offset adjustments by the shooter incrementally rotating a part of the telescopic sight, the signal processor608may cause an output to be displayed (or otherwise communicated) to the shooter that indicates “four clicks counterclockwise”. As an example in which adjustment is automated, the calculated crosswind offset d may be correlated to a control signal generated by the signal processor608that actuates an adjustment mechanism mechanically linked to the telescopic sight.

The automated approach is diagrammatically illustrated inFIG. 6, which shows the signal processor608in signal communication with an adjustment mechanism662and the adjustment mechanism662communicating with (e.g., mechanically linked to) a telescopic sight666. The adjustment mechanism662and corresponding telescopic sight666may be implemented in any suitable manner. For example, the adjustment mechanism662may include one or more servo motors, solenoids or similar mechanisms that communicate with an appropriate adjustable portion of the telescopic sight666via suitable linkages. In other examples, whether manual or automated, the adjustment may be only partially mechanical or not mechanical at all. For instance, the adjustment may entail projecting information in the shooter's scope666, such as a lighted dot that the shooter must align with the reticle to effect the offset adjustment.

As noted above, the crosswind gradient measuring apparatus600may be adapted for use in providing an offset adjustment that accounts for a vertically directed crosswind gradient. In one example, this is accomplished by rotating the crosswind gradient measuring apparatus600ninety degrees about the y-axis relative to the firearm, by any suitable manual or automated means. In this manner, the two diverging probe beams622,624are positioned above and below the y-axis by the predetermined angle instead on either side of the y-axis. In still other implementations, two crosswind gradient measuring apparatuses may be provided, either as separate modules or integrated together, with one apparatus configured for measuring horizontal crosswind gradients and the other apparatus configured for measuring vertical crosswind gradients. The respective offsets dxand dzmeasured by the apparatuses may then be utilized by the signal processor608to generate an adjustment solution that accounts for crosswinds in both dimensions.

In another implementation, a crosswind gradient measuring apparatus may be provided in the form of two Doppler velocimeters mounted and oriented so as to direct respective probe beams in a manner similar to that shown inFIG. 4. In this case, each velocimeter would measure the downrange wind speed as a function of range and the two measurements may then be subtracted through performing an algorithm to give the same result as described above for the DDI described above. At the present time, however, it is believed that the DDI is less subject to detector noise and round-off errors.

Discrete measurements that may be applied are described in detail below. Such measurements may be performed by hardware and/or software as noted above. Briefly here, it is noted that the Doppler shift for backscatter is Δf=2V/λ. As an example, for a wind change of V=1 m/s and a wavelength of λ=1 μm, the beat frequency is 2 MHz. To resolve a 2-MHz beat frequency, the laser pulse must be at least 500 ns in duration. A 500-ns, 1-micron pulse results in a range resolution (Δy) of about 70 or 75 m. Hence, for example, a 1000-m sniper shot yields N=14 measurements of wind change, where N=D/Δy, D is the range to target (e.g., 1000 m) and Δy is the range resolution (e.g., 70 m). The set of N measurements, Mi, is proportional to the relative Doppler shift between the two legs of the interferometer, Δf. The integrals in the generalized Didion Equation given above may be approximated by summing over the measurement set Miand noting that:

and further noting that the apparatus described above measures:

which is true for incompressible flow.

A recursion relation for Wx(y) may be expressed as follows:

Further evaluation yields the following expression for horizontal offset, or windage, d:

Wind Compensator Sensitivity

The sensitivity of the measurements described herein may be determined through appropriate experimentation. Generally, from various experiments it has been found that the use of shorter wavelengths results in increased sensitivity.

The parallel coherent light beam case and divergent coherent light beam case share the same key physical insight in their derivation as taught herein. It is therefore apparent to those skilled in the art that crosswind may similarly be measured using parallel coherent light beams situated a small distance apart. In the parallel coherent light beam embodiment, the divergent angle of the beams Δα shown inFIG. 6is changed to a predetermined separation Δx of the parallel beams. To calculate the offset for non-constant crosswinds one must know the value of the crosswind as a function of the downrange coordinate: Wx(y).

The crosswind field Wx(y) may be expressed as:

where Wx(0) is the crosswind at the shooter S (y=0) (which may be measured by any number of handheld devices such as, for example, an anemometer) and dWx/dy is the gradient of the crosswind in the downrange direction. According to the present teachings, the crosswind gradient dWx/dy may be directly and remotely measured by a crosswind gradient measuring device. Thus, as taught herein it can be seen that the crosswind field Wx(y) may be determined from parameters (Wx(0) and dWx/dy) that are now both measurable.

To measure the crosswind gradient dWx/dy, it is recalled from fluid mechanics that the respective x- and y-components of a wind field W can be described as gradients of a scalar potential function φ (phi). Thus,

The value dWx/dy may be further manipulated by the following set of identities:

The value dWy/dx may be measured in a number of ways, including with a crosswind gradient measuring apparatus. Such an apparatus may be configured similar to the crosswind gradient measuring apparatus600described above in conjunction withFIG. 6. In this case, the optics device604may be configured for directing the two probe beams622,624toward the downrange target T204at a predetermined horizontal spacing Δx (instead of the Δα shown inFIG. 6) on either side of the line-of-sight y-axis (or vertical spacing Δz in the case of vertical correction).

InFIGS. 7 and 8a front view700and rear view800drawing of an aimpoint corrector (crosswind gradient measuring device) ofFIG. 4in a rifle-mounted configuration is shown. The front view700(FIG. 7) shows a main scope aperture702and two laser apertures704and706. The rear view800(FIG. 8) shows an eye cup802, control buttons804,806and battery compartments808and810. The divergence between the two laser beams is too slight to be noticeable in the drawing.

Turning toFIG. 9, a flow diagram900for the steps for aimpoint correction is depicted in accordance with an example implementation. A coherent light source, such as a laser, is activated and at least two probe beams of coherent light are projected at predetermined angles relative to a target902. A photodetector detects and measures the intensity of backscattered light as a function of time904. The Doppler frequency beat resulting from the difference in the respective velocities of the winds encountered by the at least two beams of coherent light906is identified. The crosswind offset “d” (e.g., the projectile impact point offset) using the identified Doppler frequency beat908is calculated. The targeting may then be adjusted by “d”910.

It will be understood, and is appreciated by persons skilled in the art, that one or more processes, sub-processes, or process steps or modules described in connection withFIG. 9may be performed by hardware and/or software. If the process is performed by software, the software may reside in software memory in a suitable electronic processing component or system inFIG. 6. The software in software memory may include an ordered listing of executable instructions for implementing logical functions (that is, “logic” that may be implemented either in digital form such as digital circuitry or source code), and may selectively be embodied in any tangible non-transitory computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that may selectively fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. In the context of this disclosure, a “computer-readable medium” is any tangible means that may contain or store the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium may selectively be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device. More specific examples, but nonetheless a non-exhaustive list, of computer-readable media would include the following: a portable computer diskette (magnetic), a RAM (electronic), a read-only memory “ROM” (electronic), an erasable programmable read-only memory (EPROM or Flash memory) (electronic) and a portable compact disc read-only memory “CDROM” (optical). Note that the computer-readable medium may even be paper (such as punch cards) or another suitable medium upon which the program is printed and captured from and then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.

In general, terms such as “communicate” and “in . . . communication with” (for example, a first component “communicates with” or “is in communication with” a second component) are used herein to indicate a structural, functional, mechanical, electrical, signal, optical, magnetic, electromagnetic, ionic or fluidic relationship between two or more components or elements. As such, the fact that one component is said to communicate with a second component is not intended to exclude the possibility that additional components may be present between, and/or operatively associated or engaged with, the first and second components.