Kevin Ashton
How can deaths from mass killings be reduced? The math of mass killing is simple: the number of people killed is the number of events multiplied by the number of deaths per event. Mental health monitoring may reduce the number of events but it will not make it zero. Number of deaths per event is a crucial variable.
Firearm Physics
The physics of firearms has three main components: a weapon’s muzzle velocity, the mass of its ammunition and the rate at which ammunition can be fired.
Semi-Automatic Rifles
Semi-automatic rifles fire bullets (or rounds) between 5 and 7 mm in diameter. They have a muzzle velocity of 3200 feet per second (meaning they fire bullets at 2200 miles per hour, almost three times the speed of sound) and, in unmodified US civilian versions, the rate of fire is the same as the rate at which the trigger is pulled, up to a theoretical maximum of 800 rounds per minute, but more likely in practice to be 40 to 100 rounds per minute. Military tacticians call this high rate of fire rapid or intense. Aiming rapid fire is imprecise, even for a professional, because of the instability caused by kinetic energy imparted to the weapon by the rapid fire mechanism, and because there is no time to retarget between rounds. This is less of a problem with multiple targets grouped in a confined space – the rapid fire rate increases the probability that some proportion of rounds will hit and, at this muzzle velocity, bullets have long range and will typically penetrate beyond first targets and most solid cover.
Semi-Automatic Pistols
Semi-automatic pistols come with a broad a range of physical characteristics. To choose one example: the Sig Sauer P228 (also called the M11 in the US) fires 9mm rounds at a muzzle velocity of 1500 feet per second (1000 miles per hour), takes a 15 round magazine and can be used for rapid fire in semi-automatic mode. This empties the magazine quickly, but as pistols are generally light, mobile weapons, reloading is faster than with a semi-automatic rifle, as is retargeting after reloading.
Shotguns
Shotguns fire small multiple projectiles (“shot“) that spread out in flight (sometimes single “slugs” that do not). They have a muzzle velocity of around 1600 feet per second (1100 miles per hour) and a low rate of fire relative to a semi-automatic weapon. The low fire rate is offset in part by the spreading shot hitting multiple grouped targets, but as these projectiles are much smaller than bullets they may wound, not kill, and may not penetrate beyond initial victims or solid cover, despite their initial velocity.
Weapons Physics Most Likely To Cause Death In Mass Killings
Because of these physical characteristics, the mosts deaths in a civilian mass killing are likely to be caused by a semi-automatic rifle set to maximum fire and fitted with a high capacity magazine. This will fire 40 or more rounds a minute with high penetration and long range. A semi-automatic pistol such as a Sig Sauer P226-variant (of which the P228 described above is an example) is a good sidearm: if the semi-automatic rifle jams or empties, the pistol can be brought to bear quickly with some loss of range but little reduction in rate of fire. A shotgun (or other weapon type, such as a revolver, or bolt action rifle) is less efficient than either the semi-automatic rifle or the semi-automatic pistol. It will kill fewer people per minute because of its lower muzzle velocity and lower rate of fire.
Weapons Used In Recorded Mass Killings
This conclusion is supported by real world data. All perpetrators in the the 30 US mass shootings since 1984 used semi-automatic pistols and / or semi-automatic rifles coupled with high capacity magazines – 15 to 20 rounds in the pistols, 40 or more in the rifles. (Summary data here.)
Effective Rate Of Fire
A weapon’s effective rate of fire is the product of its rate of fire multiplied by its magazine capacity, less reload time. How does effective rate of fire impact the number of deaths in mass killings?
Effective Rate Of Fire In Recorded Mass Killings
Two extreme rates of fire in the real world data set are the Virginia Tech mass killing by Seung-Hui Cho and the Tucson mass killing by Jared Loughner. Effective rate of fire is important because most rounds fired at rapid or intense rates miss their targets. Cho used semi-automatic pistols with 15- and 10-round magazines and fired 176 rounds in 11 minutes, an effective rate of fire of 16 rounds a minute . In Tucson, Loughner used a semi-automatic pistol with a 33 round magazine, more than double the capacity of Cho’s. Loughner fired 33 rounds in 15 seconds, an effective rate of fire of 132 rounds per minute, more than 8 times faster than Cho.
The Impact of Effective Rate Of Fire On Number Of Hits
Hit efficiency is the number of unique targets wounded or killed for each round fired. Many hits on the same target are counted as one hit; hitting many targets with a single round counts as many hits. At Virgina Tech, Cho killed 32 people and wounded 17 for a hit efficiency of 28% per round discharged. In Tucson, Loughner killed 6 and wounded 13 for a hit efficiency of 58%. Loughner’s higher hit efficiency was almost certainly a result of closer range and less reaction time for his victims. Both gunmen had the same kill efficiency: the number of people they killed was 18% of the number of rounds they fired. This is typical: the average hit efficiency in mass killings is 40%; the average kill efficiency is 21%. The chart below, Shots → Hits → Kills, shows hit efficiency in the Tuscon and Virginia Tech mass killings, the average hit efficiency of all mass killings in the data set, the 5 mass killings with the highest kill efficiency and the 3 mass killings with the lowest kill efficiency.
The Impact of Effective Rate Of Fire On Number Of Deaths
This low hit efficiency is in part a result of the physics of rapid fire. (Other factors include range, how long the incident lasts and the skill and experience of the gunman.) Because such a large proportion of rounds fired miss all targets, firing more rounds per minute increases hits and kills, especially in the first minutes of an attack, when the gunman has the advantage of surprise. This is supported by the data from real incidents.
The mass killing in Tucson is an outlier which creates a stronger dependence between these variables than would exist otherwise. With the Tucson data excluded, there is a positive but less dependent relationship between rate of fire and rate of victims killed.
The Impact Of Reloading On Rate Of Fire
Because kill rates tend to be higher when more rounds are fired per minute the number of times a gunman has to reload per minute and the length of time spent on each reload is a crucial variable affecting kill rate. Time spent on each reload is relatively fixed and dependent on the gunman’s skill, experience and tactical situation. It is independent of the number of rounds in the magazine. The reload time for a skilled civilian using a semi-automatic weapon is probably between 4 to 6 seconds (measured from last bullet on target before reloading to first bullet on target after reloading), possibly longer under pressure. Two hypothetical shooters are modeled below (Magazine Capacity vs. Rounds Per Minute): a “more skilled” gunman who fires 100 rounds a minute and reloads in 5 seconds; and a “less skilled” gunman who fires 50 rounds a minute and reloads in 10 seconds. With a 10 round magazine, the more skilled gunman fires 54 rounds and spends 27 seconds reloading; the less skilled gunman fires 27 rounds and also spends 27 seconds reloading. With a 100 round magazine, the more skilled gunman fires 100 rounds and the less skilled gunman fires 50 rounds, with no time spent reloading.
The Impact Of Reloading On Victim Defense And Escape
Reloading also provides an opportunity for potential victims to escape or defend themselves. The US mass killing data set describes incidents caused by 32 shooters. 25 of these were not apprehended in the act: they either committed suicide, or surrendered or were captured after they finished killing. Two shooters were shot dead and one was wounded by police officers and one was shot dead by a military police officer. Three, including Loughner, were tackled by unarmed civilians during reloading. In summary, the same number of mass killers have been neutralized by unarmed civilians during reloading as have been shot by police. In other incidents, such as the 2008 mass killing at Northern Illinois University, potential victims escaped during reloading.
The Impact Of Carrying A Concealed Weapon (CCW) On Victim Defense And Escape
Data about the impact of legal concealed carry weapons on general crime rates has been used to show both that civilians carrying a concealed weapon, or CCW, reduces crime and that it has no impact at all. The number of homicides committed by people with concealed carry weapons, as well as the number of people whose concealed weapon has prevented a crime (know as defensive gun use, or DGU) is also a matter of debate. But, as described above, none of the incidents in the data set were ended by the use of firearms by an armed civilian. There are at least two cases where a civilian with a concealed weapon was involved in a mass killing or potential mass killing. In Tucson, CCW holder Joseph Zamudio arrived after the killing had stopped and Loughner had been disarmed and at least partially neutralized. Zamudio did not use his weapon. In another incident, not listed in the data set because it does not meet the FBI’s mass killing threshold of at least four fatalities, CCW holder Nick Meli was present during an attempted mass killing in Clackamas Town Center in Oregon. Meli says he drew his semi-automatic pistol when Jacob Tyler Roberts started firing an AR-15 semi-automatic rifle. Meli took aim but did not fire as he was concerned about the safety of people behind Roberts. Meli believes that Roberts saw him and that his presence was a factor in Roberts’ decision to flee the scene after shooting three victims, two fatally, and commit suicide. Two parts of Meli’s report are relevant here: first, reloading was significant – Meli drew his weapon and took aim while Roberts was fumbling a reload. Second, Meli was unable to fire due to the possibility that his rounds hit might other people, either because they missed the target or penetrated beyond Roberts. In Tucson, Loughner, like Roberts, fumbled his reload and created a window of opportunity for defensive intervention. 4 to 6 seconds, the fastest likely civilian reload, is a long time. A National Football League quarterback typically takes 3 seconds to pass the ball after receiving the snap.
While reloading provides the best opportunity for defensive action, it is very difficult to shoot a gunman firing at rapid to intense rates, even for professionals. Rapid fire is used by military tacticians to achieve fire superiority and is effective at doing so, even when the shooter is an amateur. This is partly because of the physics. An armed responder would almost certainly have to be in the line of sight without being in the line of fire and must be aware of the risks of rounds missing or penetrating beyond the first target, as Meli was in Clackamas. High velocity rounds also penetrate most forms of cover, so a good defensive position may be difficult to find. At the mass killing in Fort Hood, Nidal Malik Hasan discharged 214 rounds for 43 hits in 4 minutes from a twenty round pistol before being shot and wounded while he was distracted “stalking” a victim. Hasan reloaded ten times before being shot despite the presence of many armed professionals. During the mass killing at Columbine, Sheriff’s Deputy Neil Gardner exchanged fire with a gunman after 2 people had been killed and 10 wounded. Gardner fired 4 rounds with no hits. 11 more people were killed and 14 more were wounded after this exchange. During the 2012 mass killing in Wisconsin, armed police Lieutenant Brian Murphy was shot and wounded 15 times.
How To Reduce Deaths In Mass Killings
Reducing magazine capacity and therefore effective rate of fire is unlikely to have an impact on more common gun homicides, with the important exception that it may reduce the risk armed criminals pose to the police and other law enforcement officials. It is, however, a practical way to begin to reduce the number of deaths from mass killings. While it is not possible to reduce the rate of fire of weapons that already exist, it is possible to restrict the manufacture and sales of high capacity magazines so they eventually become more difficult to obtain. This will not stop mass killing but, over time, it may reduce the average number of people hit and killed in each incident, both by reducing rounds fired per minute and increasing the opportunity for potential victims to escape or defend themselves during reloading. The conclusions that being able to fire more rounds into a crowd is likely to result in more deaths and that having to reload more often provides more opportunities for escape and defense and also reduces the time a gunman spends firing may seem obvious and trivial, but it has been strongly argued that reducing magazine capacity will have no impact on mass killing. (See, for example, LaPierre, December 23, 2012: “It’s not gonna work.” ) The data suggests that these two variables are correlated and that assertions to the contrary are incorrect. According to the math, physics and evidence from actual mass killings, reducing the capacity of the magazine reduces the capability of the killer.
