I know next to nothing about guns (see my location 
), and generally have little interest in them either. Yet today I am unaccountably itching to know the following:
If you clamped a regular hand gun, one typical of law enforcement officers for example, in an incredibly sturdy vice so that it could be considered essentially immovable, and in completely still air, what is the likely spread of several shots over a 10 yard distance? Are there any other factors which would affect the result?
Only 10 yards? Not much spread, really. The recoil from each shot will serve to loosen the grip of the vise on the handgun, and a poorly-made or maintained handgun might not be consistent, but 10 yards is a pretty short distance.
Interesting question. What’s the spread? I don’t know. But some factors that will affect the point of impact include:
[ul][li]The Bullet. While bullets are uniform, they can’t be exactly the same. Any variation in shape or weight will affect the point of impact. [/li][li]The Charge. How uniform are the grains of powder? How are they distributed in the case? In the very short amount of time in which it burns, how uniformly does it burn based on its configuration and distribution?[/li][li]The Barrel. I think this would be the biggest factor. While residue from the bullet and charge (fouling) can affect the point of impact, I think that what is more important is that the barrel heats up as it is fired. It will expand ever so slightly.[/ul][/li]Will any of these have any noticeable effect? Over ten yards? With all components put together as well as possible to make any deviation minimal?
This is a hypothetical ultra-vice which is guaranteed never to loosen (until you want it to when it is guaranteed not to bind 
- supplementary question: where can I get one of those?). What about 20 yards? 30? (etc. etc.)
Some other factors that are small, but interesting:
The length and rigidity of the barrel: When a gun is fired and the bullet is whizzing down the barrel, the barrel, which is cantilevered on one end, vibrates. The more mass, the less variation in the vibration.
The type of hangun, revolver vs. semi-auto: The semi-auto, depending on the type, have more parts that start moving when the gun is fired. This adds to the variation.
To add an anecdote to one of Johnny L.A.'s points. I’ve a Remington 742 in 30-06 that will shoot a 1-1/2" group at 100 yards (it will probably do better, but that’s about my limit) for three shots. The fourth shot will be 3"- 4" off because the barrel is hot. Until you let it cool, it just gets worse.
Just like with rifles, there are people who’s hobby is to try and make handguns as accurate as possible. You specified a typical handgun used by law enforcement. The only change a precision enthusiasts can make their is with the bullet and cartridge that fires it. That is an almost mainstream thing to do and match quality bullets and cartridges can be bought off the shelf. The vise you are talking about is called a bench rest and you can also buy those. They are used to test the ballistics of a handgun for all kinds of reasons.
Barrel length is important here with longer generally being better. Most quality handguns can almost shoot two rounds through a single whole at 10 yards and about the same at 20 yards if the bullet and gun are good quality. After that, it is hard to say because different handguns vary a lot. Handgun accuracy generally isn’t nearly as good as rifle accuracy for longer distances and you will start to see things break down rapidly past 40 yards or so.
Some handgun accuracy testing is actually done this way, although an experienced shooter using a fixture or sandbags can obtain essentially the same accuracy. Service-grade handgun accuracy testing is typically done at 25 yards/meters, that being about the maximum distance one would or should be using a service weapon at, and 5" at 25 yards/meters is generally considered sufficiently precise for service and defense use (i.e. sufficient to be “in the black” on a B-27 silhouette target when aiming for the center of mass), although good high quality service pistols like the Sig Sauer, Heckler & Koch, Glock, et cetera typically best this by an inch or more out of the box, which equates to about 2" at 10 meters. (I’ve shot factory Sigs that came within a hair’s bredth of 3" groups at 25 meters, which would be about 1.2" @ 25m, or slightly more than double the diameter of the bullet for a .45 ACP.) With some custom-fitting work and a high precision hammer forged barrels, some pistols can pull groups in the area of 1" diameter at 25 meters.
While small, low power pistols rely on the spring force and inertia of the slide to keep the chamber closed until the bullet exits, most large bore autoloading pistols use what is called “recoil action” to control the progress of the loading action; that is, the barrel is mechanically tied to the frame by some kind of cam or linkage mechanism, and the force of the bullet in the barrel forces the mechanism to stay locked until the bullet exits the barrel. This keeps the slide closed and the gas chamber pressure contained until it is no longer needed, upon which the mechanism is unlocked, the slide is pushed back by gas pressure, and the barrel cants up (or in a few cases, rotates forward), upon which another round is stripped from the magazine and fed into the chamber, which is then closed. This necessitates a moving barrel, and the tolerance fit between parts limits repeatability. There are a handful of quality full-bore pistols that do have a fixed barrel and either use a gas retarded delayed blowback (Steyr GB, H&K P7) or roller locking (H&K P9) to lock or delay slide release. The above pistols were noted for their accuracy, but also had some other mitigating factors and were not (except arguably for the P7) particularly successful, and not pistols using these systems are currently in production, AFAIK.
Service revolvers can be even better, owing to a fixed barrel; a well-fitted revolver can pull about 2" groups at 25 yards, and I’ve seen a tuned long-barreled revolver with precision handloaded ammunition literally put one .357 Mag semi-wadcutter after another through the same hole. The problem with revolvers, however, is that the whole mechanism is very exposed and prone to contamination and damage, which is why military organizations, with spare exceptions, long ago went away from the revolver. This is ostensibly why police departments did as well, though in my opinion that had far more do to with fads than practicalities; nonetheless, a solid, well-built pistol is better suited to service use than a revovler.
The factors that control the precision and practical accuracy of a pistol are the mechanical tolerances of the moving parts (slide, frame rails, cam linkage or wedge block), the weight and evenness of trigger pull, the “tightness” and visibility of the sights, the ergonomics of the grip, and the precision of ammunition used; cheap mil-surplus ammo may have powder charges that are all over the place (sometimes even out of spec) while good target or handloaded ammo should be within 50 psi or less of nominal chamber pressure. As mentioned above, an expert gunsmith can tune many handguns to obtain a higher degree of precision, but it’s up to the shooter and his or her skill to extract the maximum accuracy that the gun can acheive. As a practical matter, as most defensive shooting scenerios occur within 7 meters, a high degree of precision isn’t really required in a duty weapon and the looser tolerances can actually make for a more reliable, contamination-tolerant weapon, but someone in IPSC or silhouette target shooting competition might strive for the upmost possible precision.
Stranger
I just thought of another barrel-caused variation that my father ran into once. The condition of the end of the barrel matters. Ideally you want the entire circumference of the base of the bullet exiting the barrel at the same time so the the pressure around the circumference will the same at any instance. If the end of the barrel is damaged, or poorly machined, it will ‘wobble’ the bullet when it exits.
He encountered this on a rifle, but I don’t see why it wouldn’t be true on a handgun on a smaller scale.
ETA: thoroughly beaten to the punch. Oh well.
I don’t have my latest issue of Guns and Ammo handy, but they do this in almost any issue where they’re proof testing a new firearm. The standard test is using a Ransom rest (not an immovable vise, but close) and usually test the firearm at 25 yards for accuracy. Most use a chronograph to measure velocity.
The tester may use up to 3 or 4 typical loads from different manufacturers, and depending on the availability, 1-3 different match grade loads. I’ve seen spreads of 3-4 inches with standard loads and 1-2 inches with match grade.
From anecdotal evidence, your standard police issue round in most countries is the 9mm Luger. In the US it varies from city to city.
Late as usual. Good dope there Stranger.
Once upon a time I used to compete in IPSC handgun matches.
The hypothetical vise you are looking for would probably be something like a Ransom Rest
Generally speaking, a decent quality stock gun out of the box will shoot tighter groups in a ransom rest than a human being is capable of. Short of a handful of people in the world your average 4" barrel handgun shot grouping are 90%+ the skill and consistency of the shooter, not the gun.
Many in shooting sports like to exaggerate the effects of slide/barrle shift, heat, inconsistently cast bullets, wind, etc. Degree of effect is usually inversely porportional to how well they shot that day.
Any decent gun shop can load your gun into a ransom rest or the like and should shoot groups deviating 1" tops at 15 yards probably more like 1/2" If a new gun is consistently throwing wild shots on brand name production ammo you probably have a warranty issue with the gun manufacturer.
One note of interest: if you clamp a handgun in a vice or Ransom Rest and squeeze the trigger, the bullet’s Point of Impact will be significantly lower that the Point of Aim. This is because a handgun pivots upward immediately after you fire a shot. While the bullet is traveling down the barrel, the barrel will pivot up (and the sights will no longer be on target) and the bullet will hit the spot you originally aimed at.
A Ransom rest has a pivot that allows the gun to recoil upward, similar to a shooter’s wrist. The weight of the clamping mechanism is more than a human hand, though, so the recoil is less. The rest is designed so that it can be reset to the same point of aim after each shot. Another nit: You don’t squeeze the trigger when using a Ransom rest. The rest has a mechanism that you work, and the rest actually operates the trigger. This is to minimize the variation between shots in how the trigger is pulled.
I don’t understand. Are people in London generally ignorant about guns?
Let’s just say that it’s easier to buy 120 year old Absynthe than legally buy a gun in the United Kingdom. A quick Google of gun ownership laws in the U.K. will prove this.
O.K., thanks, I wasn’t aware a Ransom Rest did that. But my point still stands that - if you mount a handgun in a sturdy vice - the Point of Impact will be significantly lower than the Point of Aim.
Indeed. I’ve seen that kind of performance from a standard M1911A1 .45 - after it had been tuned by a Navy gunsmith who was a true artist at that sort of thing.