SSS.6.40 - Research Supplement: The PEW Science Omega Back Pressure Metric (Public Article)

A Novel Methodology for Quantifying Relative Flow Restriction (Back Pressure) of Firearm Silencers using External Measurement

Firearm silencers reduce muzzle blast sound signature by restricting the rate at which combustion products exit the weapon system and are exposed to atmospheric conditions. Various silencer designs exhibit different flow rate restriction, dependent upon initial combustion product flow rate and amplitude, internal geometry, and even mounting characteristics that influence entrance aperture into the silencer assembly and flow interaction with internal geometry.

Quantifying the influence of different silencer designs on internal weapon system combustion dynamics is relatively straight forward, experimentally. For example, one may instrument the initial pressure vessel (firearm barrel or chamber) with dynamic pressure transducers and thereby measure the internal pressure history of the suppressed weapon system. One may then compare that history to that from an unsuppressed system, and other suppressed systems, to develop parametric relations quantifying silencer flow restriction. The subject of this publication is to present a less-intrusive method of flow restriction quantification, using existing externally measured data. A preliminary research quantity is presented: The PEW Science Back Pressure Metric, Omega (Ω) [Pa^-1].

Article Summary and Notes:

1. The PEW Science Back Pressure Metric, Ω [Pa^-1], may be generated for any silencer and suppressed weapon system using any suitable raw external overpressure signature data acquired 1.0 m left of the silencer endcap. PEW Science highly recommends data acquisition in accordance with The Silencer Sound Standard.

2. Omega Zones are presented, which are intended to provide guidance to weapons developers, silencer designers, and end-users, with regard to flow restriction characteristics of different silencer designs. It is very important to note that silencers possessing a relatively high Ω can still provide functional use on weapon systems. Some weapon systems are more sensitive to Ω than others.

3. It is important to note that a silencer’s Omega Zone can shift when using a mounting scheme that differs from that used in the testing referenced in the published PEW Science Sound Signature Reviews. This phenomenon occurs due to some silencer mounting schemes significantly influencing flow restriction with some silencer designs.

4. The theoretical lower limit of flow restriction, or so-called "zero back pressure" is presented mathematically with empirical parameters.

5. PEW Science acknowledges that other dynamic events occur within a suppressed weapon system that can also influence weapon function. Therefore, PEW Science acknowledges that Ω is not the sole parameter one must consider for total supppressed weapon system operation. However, PEW Science postulates that the Ω metric influence can be significant. Note that weapon system influence is also a function of early-time wave propagation factors which may be measured inside the system, in close proximity to the muzzle orifice. These factors include the so-called PEW Science Alpha parameter; a subject of future research.

6. The author has chosen to name the PEW Science flow restriction parameter "Omega," after the Omega Firearms Suppressor design by J.D. Gaddini, United States Patent US6575074B1. This nomenclature is intended to honor the legacy of one of the most prolific and duplicated modern firearm silencer baffle design refinements, originally named by the late John R. Weaver of JRW Sports in Edgewater, Florida. Many high-performance designs share characteristics with this technology. The Greek letter Ω is also fitting to represent a flow restriction in a weapon system.

This Research Supplement is funded by PEW Science Members and is provided as a public article to further the industry state of practice and suppressed small arm weapon system research. PEW Science thanks you for your interest and support.

6.40.1 Goal and Impetus of Maximizing Data Utility: From Rev.1 to the Rev.2 Metric

Through the development of The Silencer Sound Standard and the publication of Sound Signature Reviews, PEW Science has collected a significant amount of externally measured high fidelity sound signature data. The dataset contains waveforms measured in a consistent way, in accordance with the Standard. As the analysis of the measured test data has progressed, various characteristics of waveform parameters have been observed that correlate to suppressed small arm weapon system function. Two parameters of interest are the rise-time to initial maximum positive phase impulse accumulation measured 1.0 m left of the silencer endcap, t_m,s [ms] and the linear approximation of the rate of rise to peak impulse amplitude, ρ_i,s [Pa-ms / ms] from time of initial accumulation, t_0,s [ms]. These quantities are illustrated in Figure 1 with the Shot 2 impulse waveform signature from the PEW Science test of the Dead Air Sandman-K (Sound Signature Review 6.15). Click or tap the figure to enlarge. Note that first-round-pop (FRP) waveforms are always excluded from impulse rise-time analyses due to ancillary combustion. For a discussion of the difference between sound signature pressure [Pa] and sound signature impulse [Pa-ms], the reader may refer to Section 2 of the Silencer Sound Standard.

Early in the examination of the positive phase impulse rise-time parameter correlation with semiautomatic and automatic suppressed small arm weapon systems, an initial postulation was made by PEW Science, that the shorter the time it takes to reach maximum initial positive phase impulse accumulation, the higher the flow rate through the suppressed weapon system. This initial hypothesis was tested semi-quantitatively using adjustable gas blocks on the gas-operated AR-15 and AR-308 suppressed small arm weapon systems by noting the function of the reciprocating system(s) and the influence various silencers had on the system dynamics such as function and case ejection patterns with various gas port orifice sizes. Anecdotal reports from PEW Science members and other third parties were also used as preliminary tests for the hypothesis. Correlation was noted.

As more testing was performed and further analyses progressed, it was noted that the relative behavior of suppressed weapon systems with certain silencer designs correlated well with the rise-time parameter (represented by t_m,s [ms], Back Pressure Metric Rev.1) but the behavior of some weapon systems with some other silencer designs had less robust correlation. PEW Science further postulated that the rate of initial positive phase impulse accumulation, not only the rise-time, was a more robust parameter to correlate to weapon function (represented by ρ_i,s [Pa-ms / ms], Back Pressure Metric Rev.2).

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Fig 1. Positive Phase Impulse Waveform Parameters (Dead Air Sandman-K, 1.0 M left of Silencer Endcap, Shot 2, 09-MAY-2020)

The metric update to Rev.2 was first presented in Section 6.36.3 of the Sound Signature Review of the Griffin Armament Explorr EX3. The following is a more formal presentation of the Rev.2 metric, using existing nomenclature from the Silencer Sound Standard and new nomenclature from PEW Science.

6.40.2 Using Empirical Relations to Quantify Back Pressure (Flow Restriction)

PEW Science has developed an empirical relation to quantify the back pressure (flow restriction) of silencers. Preliminary metric information and silencer metrics are provided below. Note that although the metric is based on empirical data, the relationship between the metric, silencer flow restriction, and the function of various suppressed small arm weapon systems, is under continuous validation by PEW Science and third parties.

At the time of initial maximum peak impulse, t_m, rarefaction begins to overwhelm the net positive phase impulse accumulation from the muzzle blast overpressure P(t), external to the weapon system, as measured 1.0 m left of the bare weapon muzzle or silencer endcap, if equipped. It is postulated that t_m is proportional to the time at which there is a significant reduction in flow rate from an unsuppressed or suppressed weapon system. The rate of impulse accumulation prior to t_m is shown for suppressed and unsuppressed weapons, in Equation 1 and Equation 2, respectively.

Equation 1. Initial Impulse Accumulation Rate for a Suppressed Weapon System

Equation 2. Initial Impulse Accumulation Rate for an Unsuppressed Weapon System

The above quantities ρ_i,s and ρ_i,u are the early-time suppressed and unsuppressed sound signature impulse accumulation rates from a small arm weapon system, respectively, in units of [Pa-ms / ms]. Let ρ_i,r represent the relative impulse accumulation rate, in Equation 3.

Equation 3. Initial Relative Impulse Accumulation Rate of a Suppressed to Unsuppressed Weapon System

The relative impulse accumulation rate, ρ_i,r, also has the units [Pa-ms / ms]. For silencers with relatively high flow restriction (back pressure), the rate of impulse accumulation, ρ_i,s is low. The rate of impulse accumulation for unsuppressed weapons, ρ_i,u is always high. Therefore, for small values of ρ_i,s (low flow rates; high back pressure silencers), the relative impulse accumulation rate, ρ_i,r approaches that of ρ_i,s. As the silencer flow rate increases, the relative flow rate also increases. This minimizes the reciprocal of the relative impulse accumulation, representing a drop in back pressure.

The relationship between the silencer characteristic of relative impulse accumulation, and its reciprocal (back pressure), for various designs, is nonlinear. Let ω_cal represent the back pressure for a silencer design, in units of [Pa^-1] in Equation 4:

Equation 4. PEW Science Silencer Back Pressure Parameter

and let Ω_cal represent the relative back pressure of a silencer to the unsuppressed weapon system, also in units of [Pa^-1] in Equation 5:

Equation 5. PEW Science Silencer Relative Back Pressure Metric

It then follows that the theoretical lower limit of silencer back pressure is as shown in Equation 6, which would theoretically represent the threshold reached by a so-called zero back pressure silencer.

Equation 6. The Theoretical Lower Limit of Silencer Back Pressure (Omega Metric = 0)

Each value of ω _cal is valid for a respective constant ρ _i,u for a particular cartridge load and barrel length. As ρ _i,u is tied to input and output combustion product flowrate, it may be empirically derived and cataloged as presented in the example Table 1, for use in computing ω _cal,u for each unsuppressed weapon system.

Table 1. Examples of Unsuppressed Impulse Accumulation Rate Constants

For each respective cartridge, ρ_i,s is computed and cataloged as presented in example Table 2, for use in computing ω_cal,s for each silencer.

Table 2. Examples of Silencer Impulse Accumulation Rate Constants

6.40.3 The PEW Science Back Pressure Metric, Omega, and the Ω Relationship

The silencer back pressure metric, for each cartridge, is now represented by Ω_cal in units of [Pa^-1]. The Ω₇₆₂ relationship between many .30 silencers on the market is relatively linear on a semi log scale, as plotted in Figure 2. Note the data is multiplied by a factor of 10, as shown in the horizontal axis label, to facilitate a more user-friendly view of the data.

Figure 2. PEW Science Silencer Relative Back Pressure Metric, Omega, for 30 Caliber Rifle Silencers

Seven (7) so-called Omega Zones are deliniated in Figure 2. These zones are preliminary. It is proposed that these zones be used to classify the degree to which a semi-automatic or fully-automatic small arm weapon system's function may be influenced by a silencer design. The influence of a silencer design's Omega Zone on weapon function depends upon:

1. The cartridge of interest.
2. The weapon operating system.
3. Weapon system parameters, including but not limited to, recoiling mass, recoil operation, and gas system parameters.

Table 3 presents qualitative descriptions of potential silencer influence on weapon system function, for each Omega Zone.

Table 3. PEW Science Back Pressure Metric Omega Zones and Suppressed Weapon System Functional Descriptions

Omega characterizes silencer back pressure. It is important to note that back pressure is not blow back. The back pressure of a silencer is the flow restriction it introduces to a suppressed weapon system. The blow back phenomenon that can occur during the use of a suppressed weapon system is caused by the reciprocating system actuating too early relative to overpressure decay within the weapon system, resulting in exposure of excessive internal system overpressure to atmosphere. Some weapons may be tuned to function well with silencers in a high Omega Zone. Some weapons may require low-Omega silencers due to constraints in their operating system(s).

Omega Zone Anecdotal Example: Anecdotal reports from users operating gas sensitive semi-automatic and automatic weapons often reference silencers such as the SilencerCo Omega and the Rugged Surge as possessing “high back pressure” resulting in “blow back.” Those silencers reside in Omega Zones 5 and 6, respectively. Similarly, anecdotal reports from users operating the same weapon systems with the Dead Air Sandman-K and the OSS Helix HX-QD 762 report these silencers to possess “low back pressure,” resulting in little to no “blow back.” Those two silencers reside in Omega Zones 1 and 2, respectively. All four silencers may function with little to no blow back on a weapon system, depending on system parameters. Back pressure is a function of the silencer. Blow back is a function of the entire suppressed weapon system.

PEW Science Research Note: It is important to note that a silencer’s Omega Zone can shift when using a mounting scheme that differs from that used in the testing referenced in the published PEW Science Sound Signature Reviews. This phenomenon occurs due to some silencer mounting schemes significantly influencing flow restriction with some silencer designs.

PEW Science Research Note (03-APR-2023): Further field research has been conducted since the original publication of this article. Some potential outliers have been noted in the dataset, with regard to their computed Omega Metric and Zone, and their functional influence on weapon systems. One such potential outlier is the CGS Hyperion (Sound Signature Review 6.27). Field research indicates this silencer may induce weapon function similar to silencers in a lower zone (Zone 6, instead of Zone 7, shown in Figure 2). PEW Science postulates that early-time flow rate, unable to be fully characterized by external waveform measurement, is responsible for this deviation. Research is ongoing.

6.40.4 Research Supplement Summary

A novel methodology for quantifying relative flow restriction (back pressure) of firearm silencers using external measurement is presented in this article.

1. The PEW Science Back Pressure Metric, Ω [Pa^-1], may be generated for any silencer and suppressed weapon system using any suitable raw external overpressure signature data acquired 1.0 m left of the silencer endcap. PEW Science highly recommends data acquisition in accordance with The Silencer Sound Standard.

2. Omega Zones are intended to provide guidance to weapons developers, silencer designers, and end-users, with regard to flow restriction characteristics of different silencer designs. It is very important to note that silencers possessing a relatively high Ω can still provide functional use on weapon systems. Some weapon systems are more sensitive to Ω than others.

3. It is important to note that a silencer’s Omega Zone can shift when using a mounting scheme that differs from that used in the testing referenced in the published PEW Science Sound Signature Reviews. This phenomenon occurs due to some silencer mounting schemes significantly influencing flow restriction with some silencer designs.

4. The theoretical lower limit of flow restriction, or so-called "zero back pressure" is now presented mathematically with empirical parameters. The efficacy of designs claiming this trait can now be evaluated.

5. PEW Science acknowledges that other dynamic events occur within a suppressed weapon system that can also influence weapon function. Therefore, PEW Science acknowledges that Ω is not the sole parameter one must consider for total supppressed weapon system operation. However, PEW Science postulates that the Ω metric influence can be significant. Note that weapon system influence is also a function of early-time wave propagation factors which may be measured inside the system, in close proximity to the muzzle orifice. These factors include the so-called PEW Science Alpha parameter; a subject of future research.

6. The author has chosen to name the PEW Science flow restriction parameter "Omega," after the Omega Firearms Suppressor design by J.D. Gaddini, United States Patent US6575074B1. This nomenclature is intended to honor the legacy of one of the most prolific and duplicated modern firearm silencer baffle design refinements, originally named by the late John R. Weaver of JRW Sports in Edgewater, Florida. Many high-performance designs share characteristics with this technology. The Greek letter Ω is also fitting to represent a flow restriction in a weapon system.

This article is part of ongoing PEW Science suppressed small arm weapon system research. This research is funded by PEW Science Members. PEW Science thanks you for your support.