Effect of the firing position on aiming error and probability of hit

D. Corriveau , C.A. Rabbath

a, A. Goudreau ba Defence R&D Canada, 2459 De La Bravoure Rd., Quebec, QC G3J 1X5, Canada

b Munitions Experimental Test Center, 2459 De La Bravoure Rd., Quebec, QC G3J 1X5, Canada

Keywords:Aiming error Rifle Position Range Dispersion

ABSTRACT Sources of dispersions that contribute to delivery error and reduce the soldier performance in terms of hit probability are numerous. In order to improve the warfighter performance, the source of the errors contributing to the inaccuracy and dispersion of the weapon systems must be understood.They include ammunition dispersion error,gun dispersion,aerodynamic jump and the aiming error.The aiming error or gun pointing error is defined as the angle between the gun muzzle at the instant the trigger is pulled and the line of fire that corresponds to the intendent aim point. This is a round-to-round error. In weapons systems that include the rifle, the ammunition, a sight and a gunner, the aiming error was shown to be the single most important source of dispersion for the regular infantryman.In other words,for the general purpose rifle weapon system, the weak link is often the human. In order to verify and quantify this assertion, an experimental investigation was carried out to determine the aiming error associated with general purpose rifle fired by infantryman. The aiming error was evaluated for various firing positions and scenarios using infantryman for ranges varying between 100 m and 500 m. The results show that the aiming error is the main contributor to dispersion for the general purpose rifle fired by a non-specialized infantryman. The aiming error induced dispersion for unstressed and rested gunners is shown to be at best equivalent to that of the weapon fired from a bench rest by a marksman.Crown Copyright © 2019 Production and hosting by Elsevier B.V. on behalf of China Ordnance Society.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).

1. Introduction

Aiming error which is sometimes referred to as gun pointing error or gun laying error(Strohm[1])is defined in this paper as the ability of the gunner to aim consistently at an aim point from round to round.The aim point corresponds to the gun pointing location at the trigger pull. The aiming error is a contributor to the total observed dispersion.The aiming error is the result of the inability of the gunner to aim the sight consistently at a given point on a target.The levels of combat stress,training,position and time to aim have a major effect on the aiming error, as discussed by Weaver [2].

Research aimed at quantifying the aiming error and other errors contributing to dispersion with the objective of improving soldiers performance has been going on for decades now.Over the years,a significant amount of research was performed to understand the effect of combat stress and fatigue on soldiers' performance as these two parameters have tremendous impact on the aiming error.This can be seen from Fig.1 adapted from Radcliffe[3]depicting the probability of hit as a function of range for two stress levels and for bench firings.Radcliffe[3]lists the aim point as being the number one factor affecting the performance against downrange targets,ahead of the range estimation, environmental conditions and the weapon's inherent dispersion.

The aiming error can be observed for a wide array of weapon systems going from the general-purpose rifle (Weaver [2]), to the sniper weapons (Von Wahlde and Metz [4]), manpads (Chaikin et al.[5])and tank guns(Olah and Bunn[6],Song et al.[7]).This is evidenced by the number of studies on aiming error that look specifically at these classes of weapons.Whereas the aiming error is shown to be significant in this paper when using a general-purpose rifle, it can be very small for sniper weapons. As mentioned by Weaver [2], when asked, any skilled sniper will claim that his/her aiming error is zero.Although not exactly true,it is not too far from the reality if one looks at the report referred as [8]. The author of reference [8] makes the point several times that all aiming error data he has ever seen represents rather benign, “peacetime”, conditions,i.e.,bull's-eye targets,known ranges,no combat stress,etc.He bemoans the“total absence of any test data from a test done in anything resembling an operational setting.” Nevertheless, he states that the available data “provide an adequate basis for engineers to design effective materiel.” In fact, the realization of the importance of the aiming error in the small-arms error budget has driven the development of automatic target engagement systems in the last few years.Such systems,as described by Corriveau et al.[9]have the potential to significantly reduce the aiming error.These systems control the trigger mechanism such that the weapon fires only when the fire control system detects that the weapon is properly aligned with the target to hit it.

Fig. 1. Probability of hit as a function of range for bench firings, qualification firings and combat stress firings.(adapted from Radcliffe [3]).

Torre et al.[10]evaluated the performance of soldiers under the stress induced by competition. It was found that the aiming error was greater in burst mode than in semi-automatic mode.

In this paper,a methodology is proposed to quantify the aiming error for various firing positions. Four firing positions were evaluated at three different ranges. The experimental installation and procedures are first described in the next section.The experimental results are then presented together with simulation results to demonstrate the impact of the aiming error on soldier performance. Finally, the results are discussed.

2. Experimental installation and procedures

In order to quantify the aiming error, a trial was performed indoor at DRDC's aeroballistic range. Three gunners dressed in complete tactical apparel participated in the trial.Each gunner was asked to simulate 210 engagements or 30 engagements for 7 different configurations. A simulated engagement consists of aiming at a target through a scope mounted on a rifle and pulling the trigger. No projectiles are actually fired. The process of engaging a target is carried out up to the point where the trigger is pulled in order to determine the pointing angle of the rifle at the trigger pull.The gunners were well trained snipers and marksman.

The aiming error was evaluated for four (4) firing positions:standing, kneeling, prone and trenched positions as per specific operational scenarios. The tests were performed by aiming at the center of three (3) simulated targets representing distances of 100 m,300 m and 500 m.The actual target was always located at a distance of 100 m. However, the targets were scaled down to simulate engagement distances of 300 m and 500 m. The target setup is shown in Fig.2.The relative target sizes at the three ranges can be seen in Fig. 3.

The aim point was identified using an IR (Infra-Red) aiming pointer mounted on the Elcan Specter OS3.4x (C79) sight base as shown in Fig.4.The IR aiming pointer dot is invisible to the gunner at the target. However, the IR pointer dot on the target (shown in Fig. 5) can be tracked using an SA-1 high-speed camera as seen in Fig. 2.

The high-speed camera was triggered using the actual weapon trigger and bolt mechanism sound recorded using a directional microphone connected to a trigger box. This system provided 50 frames pre and post trigger as well as the time“0”or trigger time in order to determine the aiming error.The frame rate of the camera was set at 230 fps.An Endevco microphone EM46BD mounted on a tripod was used. The trigger box was custom made in-house. A representation of the experimental setup is shown in Fig. 6.

The laser spot was about 4 cm in diameter on the target. The center of the spot was determined using proprietary software.The position of the dot center was located to within ±0.2 cm or 0.02 mils. The laser zeroing error and the sight-laser movement was limited to a maximum of 2 cm or 0.2 mils. After each simulated firing sequence, the zeroing was reconfirmed. The triggering system and the electronic have a minimum sampling rate of 1 ms.The microphone was located 2 m away from the gunner. Considering the sound propagating speed,this induced a delay of 1/100 s for the sound to reach the microphone. This is close to the time required for the projectile to reach the muzzle. The frame rate of the highspeed camera was set at 230 fps to capture any movement not exceeding 1 cm(worst case scenario:standing position).Hence,the maximum error is 0.5 cm or 0.05 mils (half the sampling time).Therefore,the estimated total error is found by computing the root sum square of the three sources of error identified. The maximum resulting error is thus 0.2 mils.

Fig. 2. Target setup at 100 m from simulated firing point with the SA-1 high-speed camera in the foreground.

Fig. 3. Target representation at 100 m, 300 m and 500 m with scope reticle superimposed.

Fig. 4. IR aiming pointer mounted on the Elcan Specter OS3.4x (C79) sight base.

Fig.5. IR laser spot as seen by the SA-1 high-speed camera(l¼830 nm)on the 500 m target.

Four (4) firing positions were tested to evaluate the magnitude of the aiming error at three(3)different ranges.The firing scenarios at 100 m involve fast pace firings to simulate advanced-to-contact engagements. At 100 m, the prone, kneeling and standing firing positions were tested. At 300 m, a normal pace firing was performed to simulate a semi-defensive scenario. The prone and kneeling positions were evaluated. Finally, at 500 m, the gunners fired at their own pace to simulate a defensive scenario.They used the prone and trenched (standing on supported wall) positions. A summary of the firing positions and ranges tested is presented in Table 1. The different firing positions used during this trial are shown in Fig. 7.

3. Results and discussion

The aiming error was evaluated using three soldiers dressed in full gear. Using the procedure described previously, the aiming error was determined for each soldier using different positions and at three different ranges. The results are presented in Fig. 8 in the form of a bar graph. The detailed results for the aiming error experiment are presented in Tables 2eTable 8. In these tables, the average aiming error and the standard deviation on the aiming error is presented for each gunner(G1,G2,and G3).At the bottom from each of these tables, the global average and standard deviation is presented for the three gunners.The aiming errors in Fig.8 were obtained by computing the radial standard deviation,sR,from the horizontal and vertical aiming error obtained experimentally.Grubbs[11]defines the radial standard deviation as the square root of the total sum of squares of the deviations in the horizontal and vertical directions from the respective sample means, divided by the number, n, of sample points. The radial standard deviation is therefore the square root of the sum of the two standard deviationsand. Thus,

According to Grubbs [11], the radial standard deviation is the most efficient estimator of dispersion.

In Fig. 8, the baseline or intrinsic dispersion for a M16A2 rifle firing M855 ball ammunition is shown using red bars. These data were obtained from Weaver[2]and are used to give the reader an idea of the relative importance of the aiming error. The aiming errors determined experimentally are presented alongside the baseline dispersion of the weapon system for the various conditions investigated.Looking at the aiming error dispersion at 100 m(Fig.8),one can readily see that it is significantly higher than that of the baseline weapon system dispersion for all firing positions tested.At 100 m,for all firing positions the firing pace was fast.This certainly contributed to increase the magnitude of the aiming error.However, a fast firing pace is more representative of a close range engagement.Firing in standing position yielded the highest aiming error followed by the kneeling position. As expected, firing in the prone position resulted in the lowest aiming error (by far) as it is the most stable posture.

For the simulated engagements at 300 m, a normal firing rate was used to simulate a typical wartime scenario.The standing and prone positions were evaluated at 300 m as these are the positions that would normally be used at that range. Again, at that range,firing in the prone position yielded the lowest aiming error compared to firing in the kneeling position.However,the measured aiming error is much lower at 300 m compared to that observed at 100 m for the same firing positions. This is explained by the firing pace which was fast at 100 m and normal at 300 m.

At 500 m, the aiming error was evaluated using a slow firing pace, leaving ample time to the gunner to properly aim at the target. At that range, two positions were evaluated for the aiming error:the prone position as done for the 100 m and 300 m ranges,and a new trenched position was introduced. At 500 m, both the prone and the trenched positions yielded similar results. The aiming error is of the order of about 0.25 mils for both of these firing positions.Furthermore,for the prone and trenched positions with a slow firing rate the aiming error falls below that of the baseline weapon dispersion.

It can also be noted that the aiming error for the prone position

Fig. 6. Complete experimental setup for determining the aiming error.

Table 1 Firing positions and ranges for which the aiming error was evaluated.

The Ground-to-Ground System Effectiveness Simulation module of PRODAS [12] was used to perform these Monte-Carlo type simulations. This is a state-of-the-art computer tool designed to facilitate tradeoffs between candidate ammunition and gun systems,burst length,targets,sensor errors and system accuracy.This program is focused on the effectiveness in hitting and killing the intended target.The simulation brings together models for the gun,ammunition, fire control system and target into a simultaneous at 300 m and 500 m are essentially the same. Therefore, this indicates that there is probably no difference in performance when engaging targets using a normal or slow firing pace.

Fig. 7. Firing positions evaluated during the trial: prone, kneeling, standing and trenched.

In order to get a better idea for the effect of the measured aiming error on the soldier performance,system performance simulations were performed. These simulations allow one to determine the probability of hit against a standard target for the conditions studied. The relative performance of a weapon system can be quantified through simulations by comparing its predicted dispersions and probabilities of hit for various scenarios. This is achieved by performing Monte-Carlo type simulations whereby the trajectories and impact points of hundreds of rounds are computed using 2 DOF trajectory fly-outs. For each of these trajectory simulations,an error is randomly applied to the parameters affecting the trajectory. The errors applied to the various parameters are specified according to the error budget.simulation. The analysis consists of a Monte-Carlo methodology with various system errors as inputs to provide standard deviations in range, cross range and height at specified ranges. The inputs to this module basically consist of an error budget that will characterize the gun-ammunition combination. It assumes that corrections for biases have been done, as for example constant wind(head/tail), non-standard atmospheric conditions, and change of muzzle velocities due to propellant temperature. It assumes that the aim point of the intended target will be at the center of the target and then system errors are added on. The trajectory fly-out routine is a 2-DOF simulation.

Fig. 8. Aiming error for various firing positions and baseline M16A2 dispersion as a function of range.

For the current study, the error budget model consisted of the gun dispersion and ammunition dispersion error lumped together as well as the aiming error.The gun dispersion and the ammunition dispersion error data are taken as being the bench rest dispersion data given by Weaver [2] for the M16A2 rifle firing M855 projectiles. These dispersion data are reproduced in Table 9 for convenience. The aiming error used for the simulations corresponds to the error in mils listed in the last row of Table 2 to Table 8.Both the errors in the vertical and horizontal directions were used.The probabilities of hit were determined from Monte-Carlo simulation. A standard Swiss target F profile was used. The dimensions of the target are shown in Fig.9.The results from the engagement simulations are presented in Fig.10.

Using the Monte-Carlo simulations described previously, the probability of hit was determined for each firing position and for three different ranges.¼The results are presented in Fig.10 in the form of a bar graph.In Fig.10,the probability of hit based solely on the baseline or intrinsic dispersion for a M16A2 rifle firing M855 ball ammunition is shown using red bars.These data were obtained from Weaver [2] and are used to give the reader an idea of the relative importance of the aiming error on the probability of hit.The probabilities of hit for the various firing positions are presented alongside that of the baseline case for the weapon system.Lookingat the probability of hit at 100 m (Fig.10), one can readily see that the probability of hit is only slightly affected by the firing position.Firing at a fast pace,standing or kneeling,reduce the probability of hit to around 0.95 from 1.0.At 100 m,for all firing position the firing pace was fast.This certainly contributed to increase the magnitude of the aiming error but not enough to impact the probability of hit significantly.However,a fast firing pace is more representative of a close range engagement. As expected firing in the prone position resulted in the highest probability of hit as it is the most stable posture.

Table 2 Aiming error results for firing in standing position at 100 m.

Table 3 Aiming error results for firing in a kneeling position at 100 m.

Table 4 Aiming error results for firing in prone position at 100 m.

Table 5 Aiming error results for firing in kneeling position at 300 m.

Table 6 Aiming error results for firing in prone position at 300 m.

Table 7 Aiming error results for firing in prone position at 500 m.

Table 8 Aiming error results for firing in trenched position at 500 m.

For the simulated engagements at 300 m, a normal firing rate was used to simulate a typical wartime scenario.The standing and prone positions were evaluated at 300 m as these are the positions that would normally be used at that range. Again, at that range,firing in the prone position yielded the highest probability of hit compared to firing in the kneeling position.The effect of the firing position start showing very much at 300 m. Shooting in the kneeling position reduces the probability of hit to 0.68 compared to 0.99 in the prone position.

Table 9 Bench rest or intrinsic round-to-round dispersion of the M16A2 rifle firing M855 ammunition.

Fig. 9. Swiss target type F: kneeling silhouette. Dimensions in cm.

Fig. 10. Probability of hit as a function of range for various firing positions and for bench rest firings of the M16A2 rifle against a Swiss target type F.

At 500 m, the aiming error was evaluated using a slow firing pace, leaving ample time to the gunner to properly aim at the target. At that range, two positions were evaluated for the aiming error: the prone position as done for the 100 m and 300 m range,and a new trenched position was introduced. At 500 m, both the prone and the trenched position yielded similar results in terms of probability of hit.The introduction of the aiming error to the bench test data reduces the probability of hit only very slightly.

Referring back to Fig.1, one can see that the predicted probability of hit obtained for this study (Fig.10) are much higher than what would be expected for soldier in qualification or under combat stress. This shows the importance of stress on the performance of soldier. Under combat stress, the aiming error is significantly larger than what was observed in this study. During this study,the soldiers were subjected to a level of stress that could be qualified as benign.

4. Conclusions

The aiming error was evaluated for various firing positions and scenarios using infantryman for ranges varying between 100 m and 500 m. The results show that the aiming error is the main contributor to dispersion for the general purpose rifle fired by welltrained infantryman. The aiming error induced dispersion for unstressed and rested gunners is shown to be at best equivalent to that of the weapon fired from a bench rest by a marksman.

The experimental results have shown that lowest aiming error is obtained when soldiers fire their weapon in the prone or trenched positions. The firing pace also has an impact on the aiming error.The fast firing rate increases the aiming error as expected.However,no significant difference was observed between the normal and the slow firing rate.

The influence of the aiming error on the probability of hit was shown to be negligible at a short range of 100 m for all firing positions. Starting at 300 m, the firing position has a significant impact on the probability of hit for the kneeling position.The firing in the prone position does not significantly reduce the probability of hit compared to bench firing.

The study was performed under benign stress condition for the soldiers involved. Combat stress would induce greater aiming errors for all firing positions. Future studies could involve the evaluation of the aiming error under simulated combat stress condition.

Acknowledgement

The authors would like to ack nowledge the soldiers that accepted to participate in this study. This study was performed under a DRDC's project called Future Small-Arms Research(FSAR).