Quantitative Assessment Method of Muzzle Smoke in a Field Environment

Abstract

The muzzle of barrel weapons produces a large amount of smoke (muzzle smoke), a major source of pollution in the battlefield. Quantitative assessment of muzzle smoke is an important support for the development of advanced propellants. However, due to the lack of effective measurement methods for field experiments, most of the previous studies were based on a smoke box, and few studies have focused on muzzle smoke in the field environment. In view of the nature of the muzzle smoke and the conditions of the field environment, the characteristic quantity of muzzle smoke (CQMS) was defined based on the Beer–Lambert law in this paper. CQMS is used to characterize the danger level of muzzle smoke produced by the propellant charge, and theoretical calculations indicated that when the transmittance is e^–2, the impact of the measurement errors on CQMS can be minimized. Seven firings with the same propellant charge of a 30 mm gun were carried out in a field environment to verify the effectivity of CQMS. The measurement uncertainty analysis on the experimental results showed that the CQMS of the propellant charge used in this study was 2.35 ± 0.06 m², which indicates that CQMS can be used to quantitatively assess muzzle smoke.

1. Introduction

A large amount of smoke is usually generated at the muzzle when the barrel weapon based on chemical energy is firing, which will not only hinder their own shooting speed and accuracy¹ but also pose a risk to human health.^2,3 In addition, muzzle smoke can also be detected by an optical detection system⁴ (Zhou et al.), thereby exposing the location of the shooter. Researchers engaged in propellant research have always paid attention to this harmful phenomenon and kept seeking technical ways to reduce muzzle smoke.⁵⁻⁸ In any case, quantitative assessment of muzzle smoke is the key to guaranteeing this research.

According to the classification of the experimental environment, there are usually two methods for muzzle smoke assessment. One method is the smoke-box method, which is suitable for small arms. A measurement method for muzzle smoke was proposed and the results of the experiment were analyzed, providing the foundation for subsequent research.⁹ A pressure-removable smoke box was used to measure smoke concentration using dual optical path length measurement.¹⁰ A quantitative detection system was designed to characterize the smoke concentration of the muzzle smoke of small arms, and the system measures the photosensitive voltages of the penetrating laser through the space of the muzzle smoke box in the states with and without smoke.¹¹ The traditional method was improved to avoid the impact of the residue in the smoke box.¹² In general, researchers only focus on the smoke concentration because the smoke box has a fixed volume and a fixed optical path length. The other method is a field experiment, which is equivalent to the user’s actual environment. Steward et al.¹³ characterized and discriminated firing signatures of a large caliber gun based on two hundred and one firings of three 152 mm howitzer munitions. Zhao et al.¹⁴ took the integral of absorbance over time as characteristic smoke capacity according to the visible light transmittance of muzzle smoke in an open system.

Different from the smoke-box method, volume and optical path length are not fixed in the field environment, so it is questionable to only focus on the smoke concentration or any other single physical quantity. The purpose of this research is to provide a reliable, reproducible, and easy-to-implement method for identifying the danger level of muzzle smoke in the field environment.

2. Materials and Methods

2.1. Definition of CQMS

According to the Beer–Lambert law

1

where A is the absorbance; T_λ is the transmittance of the material; ε_λ is the absorptivity of the attenuating species; l is the optical path length; and c is the concentration of the attenuating species, and in this study

2

where m is the mass of muzzle smoke; and V is the smoke volume.

The mass of muzzle smoke increases with the discharge of smoke from the barrel in the early stage and decreases with the loss of smoke in the later stage. The moment when the mass of muzzle smoke takes the maximum is represented by t₁. Eq 1 at t₁ can be rewritten as

3

For muzzle smoke produced by the same formulation and batch of propellant charges under the same experimental conditions, maximum mass m_t1 and absorptivity ε_λ of muzzle smoke can be regarded as constant values. Namely, the left term of eq 3 is theoretically a constant value. However, it is difficult to obtain the accurate value of m_t1 and ε_λ of muzzle smoke through the existing test methods in the field environment. On the contrary, the quantity of the right term of eq 3 can be obtained relatively easily, CQMS (denoted by A_{smog, λ, t1}) is defined as

4

Similarly, the quantity of muzzle smoke (QMS, denoted by A_smog, λ) at any time is defined as

5

The muzzle smoke is axisymmetric along the central axis of the barrel, and the light source and the camera were placed on both sides of the muzzle smoke. The schematic diagram of the muzzle smoke taken by the camera is shown in Figure 1. Thus, the smoke volume can be calculated as

6

where a and b are the left and right limits of the muzzle smoke in the x-axis, respectively; f(x) is the function represented by the edge of the smoke on the upper part of the x-axis.

Figure 1.

Schematic diagram of the muzzle smoke.

Discretizing eq 6

7

where l_pixel is the actual length of a single pixel of the camera corresponding to the plane in Figure 1.

The optical path length is given by

8

where (x₀, y₀) represents the position of the light source in Figure 1.

In summary, CQMS can be specifically calculated as follows:

9

CQMS is theoretically a constant value for the muzzle smoke produced by the same propellant charge at a certain wavelength, and CQMS is proportional to the maximum mass and absorptivity of muzzle smoke. Therefore, CQMS can be used to evaluate the danger level of muzzle smoke produced by different propellant charges, and CQMS is proportional to the danger level of muzzle smoke.

2.2. Minimization of the Impact of the Experimental Errors

Both CQMS and smoke volume are fixed values at t₁. Although the experimental errors of T_λ, t1, V_t1, and l_t1 are inevitable, the impact of the experimental errors on CQMS can be minimized, that is, to find values of T_λ, t1, V_t1, and l_t1 when the partial derivative of A_{smog, λ, t1} to T_λ, t1, V_t1, and l_t1 takes the minimum

10

Eq 4 reveals the functional relationship between l_t1 and T_λ, t1

11

Substituting eq 11 into eq 10

12

Solving eq 12

13

Therefore, the experimental errors of T_λ, t1, V_t1, and l_t1 have the least impact on CQMS when T_λ, t1 is 13.53%.

2.3. Experimental Method

Seven firings with the same propellant charge of a 30 mm gun were observed in the field environment to verify the effectivity of CQMS characterizing muzzle smoke. A visible light source and the high-speed camera were placed on both sides of the muzzle, and the gun was preheated before the start timing of the experiment. Parameters of the camera and experimental conditions are shown in Table 1.

Table 1. Parameters of High-Speed Camera and Experimental Conditions.

parameter	value
high-speed camera
camera type	FASTCAM Mini UX50 type 160K-C-16G
camera lens	AF Nikkor 50 mm f/1.8D
record rate (fps)	4000
shutter speed (s)	1/256000
image width	1280
image height	512
experimental conditions
distance from the camera to muzzle (m)	15
light source location (x0, y0) (m)	(1.37, −0.143)

In this experiment, images taken by the high-speed camera were saved in the Bayer format of 16Bit, which not only guaranteed the accuracy of the data but also avoided the demosaic process inside the camera. The pixel where the light source was located belongs to the blue channel, and the corresponding center wavelength was 460 nm. Since the attenuation of the short-distance transmission of visible light in the atmosphere could be ignored, the transmittance T_λ was given by

14

where I_{λ, t = ti} indicates the intensity value of the pixel corresponding to the light source at the moment of t_i.

In order to meet the requirements of the transmittance test, the shutter speed was set to be the shortest, which makes it difficult to see the edges of the muzzle smoke in the saved original images. Therefore, gamma correction was performed on the original images first, then the position of discrete pixels on the edge of the smoke was obtained through image processing, and finally, the smoke volume V and optical path length l were calculated according to eqs 7 and 8.

3. Results and Discussion

3.1. Experimental Result Analysis

A set of the muzzle smoke images captured by the high-speed camera are shown in Figure 2, the existence time of muzzle smoke could be divided into two stages: muzzle smoke in Stage 1 appeared in the form of a whole cloud, and the edge of the smoke was clear; muzzle smoke in Stage 2 appeared in the form of two separated clouds of smoke, and the edge of the smoke was blurred.

Figure 2.

Set of muzzle smoke images captured by a high-speed camera.

Stage1 started with the moment that the projectile emerged from the barrel (denoted as t₀ = 0 ms), the smoke was then quickly expelled from the inside of the barrel, the mass of the smoke outside the muzzle increased until the smoke inside the barrel was totally discharged. With regard to the propellant charge used in this experiment, in the first half of Stage 1 (about 0–4 ms), besides the smoke, there was also muzzle flash (mainly the prime and intermediate flash with short duration and low intensity, there was no secondary flash). Thus, the absorptivity ε_λ of muzzle smoke with muzzle flash should not be calculated because the absorptivity here is not property of muzzle smoke and the existence of muzzle flash affected the measurement of transmittance T_λ.

On one hand, the blurred edge of Stage 2 indicated that there was a significant mass exchange between the smoke and the surrounding atmosphere. On the other hand, blurred edge of Stage 2 affected the measurement of smoke volume V and optical path length l, and even destroyed the theoretical premise of calculating QMS, for example, the middle section of the smoke at 14.5 ms in Figure 2 had obviously no axial symmetry. In short, there were some unfavorable factors affecting the actual measurement in the first half of Stage 1 and the second half of Stage 2, therefore, it is better to avoid calculating QMS at these moments.

As shown in Figure 3, after processing a set of high-speed images of muzzle smoke, the curves of transmittance T_λ, smoke volume V, and optical path length l with time were obtained, respectively, and then the QMS was calculated. The orange part in Figure 3 represented the stage where muzzle smoke and muzzle flash coexisted, so the time we started to collect data (i.e., 4.5 ms) was slightly later than the end time of the coexistence stage (i.e., 4 ms). The transmittance T_λ decreased slowly in the first stage of muzzle smoke until it reached a minimum value at 7.5 ms, and then rose quickly; the smoke volume V presented an upward trend in both stages; the optical path length l rose first, reached a maximum value at 6.25 ms, then decreased and reached minimum value at 10.25 ms, and then increased slowly. What needs to be reminded is that the smoke volume V has nothing to do with the selected light source position, however, the transmittance T_λ and the optical path length l will vary depending on the position of the light source.

Figure 3.

Transmittance, smoke volume, optical path length, and QMS of muzzle smoke in a field experiment.

Absorptivity of muzzle smoke could be regarded as a constant value during the time period shown in Figure 3. Considering the mass increase because of the expelled smoke in Stage 1 and the mass decrease because of the mass exchange in Stage 2, it is believed that the change in QMS was due to the change in the mass of muzzle smoke. Since the QMS reaches its maximum value at 9.5 ms, t₁ is 9.5 ms and the corresponding CQMS is 2.37 m².

3.2. Measurement Uncertainty Analysis of Experiment Results

The results of the seven sets of experiments at time t₁ are listed in Table 2.

Table 2. Experiment Results of Seven Sets of Muzzle Smoke with the Same Propellant Charge.

	1	2	3	4	5	6	7
Tλ, t1 (%)	1.982	1.978	1.897	1.941	1.876	2.160	2.000
Vt1 (m3)	1.1225	1.0503	1.0870	1.0375	1.0323	0.9676	1.0262
lt1 (m)	0.7853	0.7563	0.7479	0.7215	0.7619	0.7987	0.7340

According to “guide to the expression of uncertainty in measurement”,¹⁵ for a measurand X is measured directly, consider an input quantity X_i whose value is estimated from n independent observations X_i, k of X_i obtained under the same conditions of measurement. In this case, the input estimate x_i is usually the sample mean:

15

Type A evaluation of standard uncertainty u_A(x_i) to be associated with x_i is the estimated standard deviation of the mean:

16

As for Type B evaluation, consider an input quantity X_i whose value is estimated from an assumed rectangular probability distribution of lower limit a_– and upper limit a₊. The standard uncertainty u_B(x_i) to be associated with x_i is

17

where a = (a₊ – a_–)/2.

The combined standard uncertainty of a measurement result, suggested symbol u_c(x_i), is

18

In this study, transmittance and optical path length were measured directly, and the results based on the combined standard uncertainty are

For a measurand Y is not measured directly, Y is determined from N other quantities X₁, X₂, ···, X_N through a functional relationship f:

19

An estimate of the measurand or output quantity Y, denoted by y, is obtained from eq 19 using input estimates x₁, x₂, ···, x_N for the values of the N input quantities X₁, X₂, ···, X_N. Thus, the output estimate y, which is the result of the measurement, is given by

20

The combined standard uncertainty of the measurement result y, designated by u_c(y) and taken to represent the estimated standard deviation of the result

21

In this study, smoke volume and CQMS were not measured directly, and the results based on the law of propagation of uncertainty are

3.3. Experimental Optimization Discussion

In Section 2.2, it was deduced that the impact of the test errors of T_λ, t1, V_t1, l_t1 on A_smog, λ can be minimized when the transmittance T_λ, t1 is 13.53%. The position of the light source can be changed to meet this condition. Based on the experiment results in Section 3.2, when the optimal transmittance T_{λ, t1, opt} is 13.53%, the optimal optical path length l_t1, opt is

22

To achieve the optimal optical path length, on the premise that only the y-axis component of the light source position is changed, the y-axis component y_0, opt of the optimal position of the light source is

23

Since y₀ is −0.143 m, the light source at the position corresponding to Figure 1 in this experiment should move 0.213 m along the negative direction of y axis.

In addition, it is believed that more accurate results can be obtained using high-speed cameras with higher resolution and fps.

4. Conclusions

This research provided a quantitative assessment method of muzzle smoke, which is a major source of pollution affecting soldier’s health in a field environment. According to the nature of muzzle smoke and the conditions of the field environment, CQMS was defined based on the Beer–Lambert law to characterize the danger level of muzzle smoke, and CQMS was proportional to the danger level of muzzle smoke. Theoretical calculations indicated that when the transmittance is e^–2, the impact of the experimental errors on CQMS could be minimized. Seven firings with the same propellant charge of a 30 mm gun were observed in the field environment to verify the effectivity of CQMS. According to the measurement uncertainty analysis performed on the experiment data of seven sets of the same propellant charge, CQMS of the propellant charge used in this experiment is 2.35 ± 0.06 m². Because of the difference of mass and absorptivity of muzzle smoke produced by different propellant charges, to a certain extent, CQMS can be regarded as an inherent parameter of the propellant charge.

The authors declare no competing financial interest.