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I have found a fascinating study. This is a long story, and a precise one, and worse one that mixes Imperial and Metric units. I'm sorry.
It ends with the study's fundamentals falling apart. One of the co-authors driving the study has used it to make claims he knew or should have known were false, misleading multiple federal courts, while receiving public funding for that advocacy. One particular false claim has been cited by appeals court judges in two separate federal circuits.
Study Design
The investigators took ballistic gel blocks, put a high-speed camera pointed at the side, slap pressure transducers in the front and back. Shoot the gel from three meters. Know the mass of the bullet, use the camera to measure speed of the bullet and size of cavity, do math. 21 shots, across 17 firearms. One gel block was specially manufactured with a pig femur in it, to examine the impact of a bullet that passes, but not hits, bone. It's not exactly a LuckyGunner comparison deck, but it's a first step.
And while the investigator's efforts were clearly not informed by the decades of experience that the gunnie community has built up since the FBI Miami Report got a lot of neurotic people very interested, they are also genuinely working on a different task. People interested in self-defense care a lot about downing an opponent quickly, or what thick clothing might do to a hollow-point. There genuinely is little ballistics gel work thinking ten or fifteen minutes after a shooting, rather than five seconds into a gunfight, and the investigators here cared about that.
Even among gunnies, the data has never been great. Hydrostatic shock has been a massive source of infighting and controversy among gun owners, and the experimental evidence is primarily deer carcass and tales about the one that got away. Depth-of-penetration testing is so dependent on experimental setup that replication was found hard and mostly not attempted. The FBI Miami Report is treated as a bible, but its foundations are little deeper than gut checks by professionals extrapolating from a tiny number of events. The end result is that there's a ton of spreadsheets that look more like marketing material, and serious advice that says little more than "a handgun's a good tool to get to a rifle".
And there are some innovations in this approach. Most gunnie work is in traditional organic 10% ordnance gel, with minimal calibration, validation, and a temperature control of 'the weather'. Here, the investigators used a 20% synthetic gel, which is more expensive but probably a better simulation of muscle tissue, and followed the manufacturer's calibration tests and temperature constraints to the letter. They're not the first to use high-speed cameras, but very few hobbyists could get their hands on a 50k frame-per-second camera, and fewer still actually did it. The use of animal bones inside a test sample has been done by Mythbusters, but it's not a part of the FBI Standard, and has meaningful impact for medical practitioners.
The most interesting decision is to completely reverse the conventional wisdom on overpenetration. Where self-defense testing tries to measure how far a round can penetrate before stopping, this study selected a ballistics gel block specifically such that every round penetrated all the way through, allowing them to measure how much energy bleeds off inside what the investigators considered a standard limb or torso. That's a decision with some serious tradeoffs, because round behavior changes dramatically as it bleeds of speed and fragments, and to allow low-power rounds to penetrate completely, they're going with a shallow enough sample that there's a lot of overpenetration at the high end.
Also, it's all FMJ for this round of testing. To be fair, there's not much public information on FMJ vs hollow-point when it comes to homicide or assault stats.
Results
Because the PDF is not especially navigable, I've transcribed the results into a single unified table, available here. Note that there's a few variables I can't properly place: I'll give points for a paper actually publishing so much of its data, but splitting input and output variables into two separate tables is painful. In particular, there is strong photographic evidence that a fragmenting 5.56 NATO round went into a 15x15x25cm target, but the numbers from that trial are only close, not the same or so close as to be a pure rounding error, so it could plausibly be a separate event.
I've triple-checked my version, but I can't guarantee I've avoided misunderstanding or transcription error, and it's more likely than not I've screwed up sigfigs or rounding or units somewhere. If anyone wants to prove me wrong, please do so.
Nitpicks
There are other aspects to the experiment that I'll just mark as not just inexperienced, but odd.
The methods say that they picked a 15x15x25cm gelatin target, or a 25x25x25cm cube, based on expected muzzle velocity. Sub-600m/s gets the smaller target, greater than 600 m/s gets the cube. That's a reasonable decision when measuring cavitation effects, since ballistics gelatin is expensive and annoying to work with.
But they didn't actually do it. At least two shots from 800+ m/s rounds were fired into the small block. And one of them is 30-06, a round that's very rare to find in subsonic ammo, and this specific shot very clearly wasn't, so either someone didn't read the packaging or they were using whatever blocks were available. A "rifle versus pistol" rule would have made more sense to start with, or if they wrote-up the procedure post-hoc after winging it, the methods section should have matched what they actually did.
As noted, this synthetic ballistics gel is new, and somewhat controversial. LuckyGunner just started moving to it for their last pistol trials, but had a lot of uncertainty for rifle ammo. The lead investigator here did lead a study to validate it against porcine and post-mortem human flesh... and as far as I can tell from the abstract, did so in a low-velocity (181 meter/sec), low-mass protocol. The slowest pistol round here is bigger, heavier, and faster. Most of the study result is dominated by supersonic and high-energy rounds, where this gel formulation is least-supported.
Looks nice, though, and that's a genuine compliment.
They've mixed mostly-fresh ballistics gelatin and remelted gelatin for a handful of tests, and the comparison is weakly supported by one paired shot, in a handgun round. Probably not a big impact on the final numbers, even if the remelted material isn't perfect, but it makes the small sample size even more frustrating, and the use of remelted material for one of the hottest cartridges counterproductive.
For repeatability, the study says "the AR-15 5.56 NATO projectiles, excluding the fragmented trial, produced low coefficients of variation in impact velocity (0.035), energy transfer (0.079) and maximum temporary cavity diameter (0.032)". That's mathematically correct, but only if you accept 'repetition' to includes different behaviors (a 12-inch barrel and a 20-inch barrel), while excluding an identical experimental setup that behaved differently (the fragmenting round). It's also not mathematically correct in a coherent single set: the impact velocity and energy transfer works for four AR-15 tests, excluding only the fragmentation example, but the cavity diameter only works with three, dropping both the fragmentation and bone test.
The one round that fragmented was also was the slowest round from an AR-15, and slower than the shot from a 12" barrel. Fragmentation in AR-15 FMJ is an artifact of both yaw and velocity, and this was at the lower range at time of impact. More critically, it's also massive variation from every other round. This could indicate they used a different cartridge and didn't document it, or got a bad powder load, but it could also be a sign their speed measurement wasn't up to par. A 80-dollar chronograph would have cost less than a single block of this ballistic gel, and would have validated the camera measurements.
There's some annoying summary stuff that's technically wrong, even if it probably wasn't intentional. "[B]ullets from handgun and sub-machine gun cartridges transferred only about half of the initial kinetic energy to the gelatin, except the 25 caliber round" kinda needs to expand that caveat to 'except the 9mm and .40 and .45 Auto and basically it only applies to the .32', presumably .32 ACP. They probably meant to say the smaller, weaker rounds didn't dump much of their energy into the gel, but 25% is not "almost half".
The Remington Bolt Action numbers don't match up at a basics physics level: they give a 150 grain (9.7 gram) bullet at 812 m/s and 247.6 m/s as having 2777 J and 258 J energy, respectively. If the energy measurements are right, that has to be a 130 grain bullet. If the weight is correct, the energies were 3204 J and 297 J. My guess is the weight is correct and some typo happened during a table format: 30-06 in 130 grain exists, but it's usually a higher-speed round. That said, it's shown up in other places.
It's just a typo, though, not a big mistake.
The Big Mistakes
There's the gelatin sizes, not as a procedure-following nitpick but what it does to the measure. The Remington Bolt Action shot produced a 20-cm diameter temporary cavity in a 15-cm cross-section. At least one of the AR-15 16" shots produced a greater than 17.1-cm temporary cavity in a 15-cm cross-section. Ballistic gel is elastic, so that's not physically impossible, but boundary effects almost certainly inflate the cavity size as the cavity gets close to an edge, since there's less force pushing back against the expansion. Since that's going against the experiment methods to start with, it's a bizzare decision.
Multiple sample measurements are just extrapolated. Literally "maximum temporary cavity extended beyond the camera view and was assumed as double the cavity diameter from the path of the bullet to the bottom edge of the cavity". Once is an accident, but it happened in fresh and remelted 30-06. Probably also means free boundary effects dominated there.
One take-away from the study is a massive correlation between velocity and how much energy is transferred : "impact velocity and energy transfer expressed a linear correlation (R2 = 0.71). However, the relationship between impact velocity and energy transfer displayed much stronger linearity when excluding the 30 − 06 caliber rounds from bolt action rifles (R2 = 0.94)". For a given caliber round that makes a ton of sense: drag is a velocity squared thing. But it's also a cross-section thing. Excluding the 30-06 rounds is plausibly defensible if you wanted to just compare the same round at different velocities, but if you're trying to validate how much effect impact velocity has across ammunition in general, excluding bigger rounds to improve the model is just ignoring that your model doesn't fit.
That's a philosophical problem, though. Worse, the math doesn't math.
I can reproduce the R2 = 0.94 number easily. I can't make the R2 = 0.71 one, at all. Just throwing the full dataset in gives 0.57. Correcting the Remington numbers to assume a 150 grain bullet just makes the relationship worse, to 0.51. Selective deletion of one example doesn't get you there. Adding a zero-origin point is incoherent for velocity to energy transfer, and it also gets you R2 = 0.75.
I'm not great at statistics, so maybe I'm missing something or messing up the formula. If I'm not, it's a big difference. It also highlights the philosophical problem and makes it into a genuine study design problem.
Remember how I talked about gunnies have spent a lot of time, money, and ammo to figure out a handgun is a good tool to get you to your rifle? Well, we've got two distinct groups, and a lot of intragroup variables. Removing the 30-06 rounds is the single strongest way to improve R2, and the study's cited reasons to exclude it are just examples of the paper's velocity-driven model not working. Worst, most other decisions hit the correlation hard. Never enough to make the correlation outright flip, so it's not a full Simpson's Paradox, but enough to start needing those other variables more and more.
Exclude all the handgun rounds and the submachinegun, because they penetrate poorly and low exit velocities have bigger impact on measurement errors? R2 = 0.224. Look at just the handguns, no rifles or submachine guns? R2 = 0.45. Dial down the comparison to just the 5.56 NATO rounds? R2 = 0.79, which isn't great since it should beactually removing all the other variables. Pull out the fragmenting round, too, and you get R2 = 0.325, which is worse than I would have expected.
That's a major point of the discussion, and it's near-certainly vastly overstated, and it's not the only relationship that falls apart on inspection. The paper says outright in its discussion that "Maximum pressure from non-fragmenting rounds was significantly influenced by bullet exit velocity ( p < 0.001), which was mainly driven by large maximum pressures paired with low exit velocities from 30 − 06 caliber rounds. Bullet caliber (p = 0.20), bullet mass (p = 0.087), and impact velocity (p = 0.072) did not significantly influence maximum pressure." That is a great p-value, but it's also a small relationship (r = -0.15) that flips back and forth depending on what rounds you look at, including the 30-06 rounds that the paper excludes elsewhere (r = + 0.14). Since impact velocity and bullet mass are two-thirds of the energy relationship, these non-significant relationships are a red flag.
Bizarrely, they don't actually write up that energy test number despite putting it in the conclusions, and it gives a R = 0.6 to 0.9 depending on whether you trust the small-block-rifle pressure data, with a p < 0.001. It's a bivariate predictor so it's defensible to focus on single variables first, but it's a glaring omission. If it's not so obvious that you want to put it in the conclusion, it's worth actually formalizing. It also holds up for all of the data no matter what outliers you decide to trim, no surprise.
Some of that mess is probably small sample size, measurement limits, high variablity. Two rounds from the same box and the same gun might have 1-2% muzzle velocity difference or one bullet might yaw and burn another 5% of its energy off, the fragmenting bullet is a genuine and targeted behavior. But the underlying measures here are weak enough, and the sample size small enough, that the analysis has lost most of its meaningful predictive power, even before getting to the actual design problems.
The Core
That pressure transducer implementation here is fundamentally flawed.
Pressure is a distance phenomena, falling off at roughly 1/√radius for cylindrical spread like this, with an emphasize on roughly. Depending on gel block size, the transducers were either 6.5cm or 10.5cm from the ideal bullet pathway. The optimistic math gives that a 25% difference reduction in pressure at a sensor head, going from the small gel brick to the large one, just because of transducer distance.
That distance varies with the bullet path. They tried to use a laser sight to assist with aim, and at three meters it's hard to miss, but even small errors compound a ton, here, and zeroing a laser sight perfectly is harder than you'd think: a 0.1 degree difference is aim is 0.5 centimeters at the front of the gel. Once the bullet actually hits, tumbling, yaw, and random behaviors in the gel dominate, and whether the bullet walks closer or further from the transducer effects the exit pressure dramatically. Again, a small difference here should have a big difference in measured pressure.
Which doesn't show up in the data, in the two cases where the same caliber was used in a small gel and the large gel. One is almost certainly the fragmented AR-15 round, which had over three times higher rear-pressure than its large-block equivalents, and with a front pressure sitting just over the center of the 200-650 kPa band large-block 5.56 NATO rounds gave. The other is the 30-06 Remington Bolt Action round, which gets less than 70% the front pressure of the large-block 30-06 rounds, and less than a sixth of the rear pressure. That's not a sign they avoided the falloff problem; it's a sign other, much larger unintended effects dominated their data.
The first is pretty likely boundary conditions, either a ton of pressure bulging or completely venting from the smaller block, or the temporary cavity nearing or encroaching on the transducer, or a combination of both. The videos and slide decks show clear free body behavior, along with the entire block recoiling and shifting, and while that's hard to avoid at the powers involved, it's also a nontrivial error source.
The 2500hz filter is extremely aggressive for this environment, both because the incoming pressure spikes from the bullet are fast, and because the wall reflections at 10cm are well under (<20 microseconds) the rise time for the filter (400 microseconds). Whether boundary effects add or subtract when merged depends a ton on the specific experiment setup, but at the higher energy states you can get large portions of pressure waves reflected or interference dropping the measurement dramatically. This probably understates the rifle max pressures, badly, but I can't write this in-depth of a criticism and only complain about the mistakes that hurt my side.
Distance from the cavity center might matter for some pressure measurements, where the max pressure wave comes from the energy dump rather than from the bullet's travel itself. This actually surfaces other data oddities, since the Polymer80 PMF's max cavity depth doesn't match the transducer behavior or expected 9mm round characteristics. That might be another typo or limit to the measurement tools. But the data (and reporting on the data) sometimes uses the phrase "first peak", which would point to the bullet's shockwave, and then uses data from the maximum peak, which is cavitation effects. From a biomedical perspective, both should cause damage, but the entire hydrostatic shock theory depends on them causing different types of damage; that's why the investigators are using the high-speed camera.
In at least a few cases, the cavity either got very close to, or swallowed entirely, the sensor. This doesn't clearly match the study trials, but it's the same test layout, and it shows everything from cavitation non-circularity to sensors at the cavitation edge to clear pressure venting.
Add all these things together, and it's no surprise that the coefficients of variation for the pressure ratings were left uncalculated. It's more surprising that they're 'only' 0.29 (5.56 excluding fragment) to 0.8 (including fragment) for the 5.56 NATO. Comparing the handgun rounds to the rifle rounds used here is probably directionally correct, but you're getting that more from first principles and intuition than from the data. And any numbers comparing magnitude within small variations of cartridge are barely better than random chance.
I'm not claiming intent or misconduct. Even the embarassing math problems here are just math problems, and the experimental design issues sounds like what someone trying to build a protocol from scratch, unfamiliar with gunnie past efforts, might do. This is not some high Impact Factor or H-Index publication, and it's far from the worst academic paper I've seen. The studies actually did happen, the measurements about cavity size are probably directionally correct, and to the extent they're contaminated by boundary effects, there's a fair argument that the human body has a lot of boundary effects going on, too. There's a real relationship between projectile velocity and pressure generated on impact.
But the study doesn't really illuminate what that relationship is, or what it means. The paper openly positions itself as triage and forensic science tool, and I really hope no one involved has to make a triage decision involving a 357 Magnum injury or any big, heavy rifle round.
Everything above is a hope for future papers to be stronger. I'm not sure what the fix for the pressure measurements could be, or even if one exists. Maybe much larger gel samples using multiple surfaces with transducer arrays? Or measuring the cavity path and correcting for distance? Using the transducers as a crude spatial probe?
But the first step to improving experimental design is recognizing the limits, so I do have to thank them for publishing the paper with this level of detail. This is important stuff, and the first step to doing something at all is often doing it kinda wrong.
It's not like anyone submitting clearly incorrect to a court as an expert witness statement, with either clear disregard for their factual basis or intentional effort to mislead judges.
Someone Submits A Sworn Statement
The published paper lists six co-authors: five academics from the Wisconsin College of Medicine, and one member of the Wisconsin Department of Justice's Division of Forensic Sciences. The last man on the list is Professor Stephen Hargarten, Wisconsin College of Medicine, MD, MPH.
Hargarten's staff page describes him as a professor at the Wisconsin College of Medicine, founding director of the Comprehensive Injury Center, and a Senior Science and Policy Advisor. He performed as an emergency physician until 2018, and left that field after a long term of difficult and appreciated service. Caps off to the men and women of emergency surgery.
He's also a political advocate, and has been since the 1990s, promoting a wide array of gun control. Not an unusual matter, for physicians in general, nor those with emergency room experience. See Firearms as a Market-Driven Epidemic or "The Bullets He Carried" as examples. He has served as the Chair of the Network to Prevent Gun Violence in the Americas since 2020.
Some of these past claims have been somewhat more based in current events and advocacy than theory. I'll give his publication and public commentary on the then-breaking news of the 'Black Talon' hollow-point bullets as an example. Hargarten's theory that the jagged edges of an expanding bullet might increase the risk of HIV or hepatitis transmission to surgeons never panned out, despite the round (renamed to Ranger SXT) remaining popular among law enforcement and self-defense users in the intervening three decades.
As far as I can tell, his state had invented forceps and tweezers by the 1990s. That's mean, and not deserved. Yet.
He has presented expert testimony in at least two cases I've been able to track down, focused on this particular test rig: Rocky Mountain Gun Owners v. Superior and _Barnett v. Raoul. His declarations also include past expert witness work in Viramontes v. Cook County, National Association of Gun Rights v. Highland Park, and Association of New Jersey Rifle and Pistol Clubs v Grewel (paragraph 9 here). I've not been able to track down those particular declarations, but given the timeline, they're likely to include similar claims.
Note that I say "focus on the test rig". Not the paper. Because his testimony has a different format, focusing on a smaller subset of trials, which line up mostly-ish to the study data, so long as you have a thick sharpie.
It also includes one new data point: a "musket". I've highlighted the data, here. The declarations only give energy lost and percent energy lost, so I've back-calculated those to estimate a 285 m/s impact velocity, and 136 m/s exit velocity. A little low by historical standards, but the velocity isn't insanely wrong.
The mass is, though.
For those unfamiliar with firearms, a 'musket' ball weighing 3.5 grams would be a lead sphere 0.32 inches in diameter, or a steel sphere 0.37 inches in diameter. Those do exist in the modern day: the lead version is even fairly common. It's known as OO Buckshot. Not the shotgun cartridge, the individual lead balls that go into the the 12-gauge shotgun cartridge nine at a time. My bet is the steel, but that's mostly hanging on deformation properties and environmental safety rather than a mathematical proof or trusting the clip art from a slide deck posted on his school's web site.
That's mean, and not yet earned. That's a mistake, and one that's hard to justify, but it's still remotely plausible someone who hates guns is just going to average names and not think it matters.
But it is a mistake that's hard to justify: neither formulation is compatible with an actual musket, and that's not just the trivial 'historical lead shot used soft tin-lead or pure lead, that would have definitely deformed under these pressures and velocities, causing drastically higher drag and energy transfer' sense.
For those who've never been to a Revolutionary War historical site, the typical rounds of the era were the British 0.71 lead shot for the Brown Bess (gun bore 0.75-0.8 inch) or the French 0.65 lead shot Charleville (gun bore 0.7 inch). Larger options were more common than smaller, and small cuts off around a half-inch diameter.
They do not weigh 3.5 grams. They have heft. Manufacturing limits of the time means they weren't perfect spheres, but 25-48 grams is the traditional range. By the Civil War, advances had lead to a slight decrease in ammunition sizes, but they were still large by modern standards. Even Revolutionary War military sidearms would not have been in 0.32 or 0.37. Mass increases with the cube of a sphere's radius.
That's not a surprise to anyone remotely familiar with guns. As anyone who's been to a range where some jerk is citing in their 'historically accurate' muzzleloader, they've got some boom to them. Whatever Hargarten's "musket" is, it's not one of them. Real muskets would have had an expected impact kinetic energy of 1000-1500 J, several times what was present here, with corresponding downstream impacts increasing drag, deformation, and kinetic energy transfer.
My first thought is that he, or his armorer, had gotten a squirrel gun and just not known any better. But Dr. Hargarten has multiple declarations. And his claims have only gotten more specific over time.
There's even a helpful footnote, in that very paragraph, explaining that "The size of the bullet can affect wound severity. In general, holding all else equal, larger caliber rounds are more likely to cause more severe injuries because they increase the surface area of affected tissue."
That's not a claim about his experiment setup. That's a claim about the world, and it's wrong.
He knew this mattered.
The data from a paper he co-authored, even if only as an editor, demonstrates clearly the relevance of bullet mass for the very transmission of energy and cavitation effects he focuses on, and his own expert witness declaration highlights the relevance of bullet diameter in the very same paragraph.
And this claim is not some number constrained to a PDF only two people on the planet ever read. He's not named when Judge St. Eve wrote that AR-15s “can discharge thirty rounds—each of which travels five football fields in half-a-second and releases ten times the energy of a musket ball upon impact—as quickly as he can pull the trigger”" in Barnett v Raoul, nor where Judge Krause cited it approvingly in ANJRPC. But he's the source, and it's a unique claim because it's not real.
Expert declarations are sworn statements before the court, and intentional and material false claims are thus perjury, so I am going to be very careful to say that I do not know whether Hargarten made every or any decision here with intent. It is, after all, still possible that he's completely ignorant of a topic he has selected to be an example of his expertise.
It also doesn't matter if he did. All that perjury stuff is theory; while prosecution has gone after expert witnesses, it's for stuff like falsifying credentials in medical malpractice civil suits or crime lab technicians committing forgery or tampering with evidence. In an adversarial system the responsibility of fighting false claims from an expert is to bring an expert of your own, and Hargarten has been opposed by a James Buford Boone, who is reasonably focused more presenting correct data than fighting incorrect methods. Daubert focuses more on whether the expert's methods are genuinely recognized in their field and testable, than whether the factual claims are true, and Hargarten has a paper immunizing him on that matter. Professional certification services are supposed to come down like a bag of rocks on men and women who use their expertise to wrongly steer a court, but Hargarten is no longer a practicing physician, so it's not even a remotely possible threat, and it wouldn't be a credible one even were he still working the emergency room.
I'd like to think that his academic environment might tut-tut and say not to do it again. He's a professor and "senior science and policy advisor" working at a medical school, proud to say he's a Founding Director of the Comprehensive Injury Center that promotes their very research. I might try to set up a PubPeer account to at least fix the math problems, and I'll be lucky to get anything on that.
Instead, I am going to say something more damning.
Dr. Hargarten is a professor, medical professional, and expert witness. He was paid 30,000 USD by Illinois alone in 2023-2024 for consulting and expert witness services related to this specific litigation. I don't know how many of his co-authors were involved in actually performing the 'musket' experiment -- his witness declaration just says "science leaders, and a technician and a doctoral student" and "the Wisconsin Crime Lab personnel" were involved -- but they include a published expert in and pioneer ballistics gel and a firearms-and-tool-mark examiner, each and every one from a career where precision, honesty, and consideration matter. I would hope he has their phone numbers.
And he is sloppy. Careless. Loose with the numbers, and the facts. Has been since he proposed surgeons were likely to cut themselves on Black Talon ammo, as if they were shoving their fingers into bullet wounds; in when he's signing on to co-author a paper or promote a slide deck with typos for several years; and he's just gotten more easily caught, now.
This is all theatre. The studies are made up to support the claims the state is making, the state knows this, and the courts know this -- but the courts (being part of the state, after all) want to find for the state, so they accept them. No different than courts which accept "the dog barked so the search was OK" when everyone knows you can train a dog to bark on surreptitious command.
"All the world's a stage, And all the men and women merely players; They have their exits and their entrances; And one man in his time plays many parts,"
-Leonard Nemoy, Civ IV, Once you get the Drama tech and ideally first thus spawning a great Artist for you to engage in some extreme culture war by flipping cities or getting the ball rolling on culture victory.
More seriously, no, firearms serious fucking business, so are court decisions, especially broad reach court decisions about firearms, thus expert witnesses being stupid and/or liars actually does matter.
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