Generalities about long-arms
- 1 Introduction
- 2 Types of Longarm
- 3 References
For several armies, we propose specific articles on weapons and equipment of various arms. However, there are some generic observations applying to types of weapons.
In the present article, we gathered some of these generic observations which pertained to Longarms during the war: Flintlock muskets--which were the most common class of firearm in the war; rifles, carbines, and the Indian Toradar and Afghan Jeazil (as would have been used at Plassey).
Ballistics of firearms
Any object with mass will be subjected to gravity; consequently, projectiles cannot simply go in a straight line, but must travel in an arc. This concept had been partly understood since ancient times, though it was not until the 16th century, when a more scientific approach to the matter of ballistics began to be devised. This was pioneered by one Niccolo Tartaglia, who was also the first to solve cubic equations. He observed that the greatest distance that a projectile can fly is ideally when launched at an angle of 45 degrees. He also observed that no part of a projectile's path was ever straight. However, his lack of qualifications as a gunner appears to have slowed the acceptance of his ideas by others, and for a long time, the range estimations devised by gunners tended to be inaccurate. Additionally, while it was conceded that projectiles tended to arc, it was commonly held that the initial portion of the trajectory was straight. This was to account for the mismatch between predicted ranges, and actual ranges.
It wasn't until Galileo's experiments, that it was discovered that specifically, gravity acted on the missiles, and determined that gravity caused projectiles to describe a parabola, unless acted on by air resistance. However, even this did not immediately catch on with gunners, who, whilst conceding that a projectile will travel a parabola, largely dismissed the effects of air resistance, and clung on to the above beliefs regarding trajectory.
Thus, the early study of ballistics suffered from a lack of a proper understanding of how projectiles are affected as they fly through the air, and a lack of merging of practical and theoretical experience. This was rectified by the work of Benjamin Robins, himself an artillery officer, in the 1740's. In 1742, Robins produced a treatise, simply titled The New Principles of gunnery. His work forms the basis off virtually all future developments in the science of ballistics, and contributed in no small measure to the improvement in artillery and firearm accuracy in European weapons of the future, though the full implications took time to catch on outside of Britain. Robin's insight, was to realize that, as the air itself is an object it must, according to the laws of motion devised by Isaac Newton, be acting on the projectiles as they flew. This explained the mismatch between what gunners predicted based on a parabolic model of motion (neglecting air), and actual results in practice.
Additionally, another insight was his ability to use Boyle's law of ideal gases, in order to better study the way gunpowder works. As we shall see, he put this to good effect, by devising a means to predict muzzle velocity, based on predicable factors. By using Newton's laws of motion, he was also able to devise a way to test his own predictions, via the invention of the ballistic pendulum.
Robins divided the results of his ballistic experiements into two components in his book, with a chapter dedicated to each: internal ballistics, which is the study of the behavior of the projectiles inside the firearm or artillery, and external ballistics, which considers the flight of the projectile, once it leaves the muzzle. This section of the article will discuss ballistics under these two sections, and Robin's findings regarding them--still largely applicable today--and subsequent discoveries where needed.
Internal Ballistics of Firearms
As mentioned previously, the muskets of the period fired when sparks or flame ignited the touch-hole, which then sent ignited the charge contained in the breach of the barrel. This then propelled the ball forward and out of the barrel. However, the specifics of what occurs in the barrel at the moment of ignition, and onward to when the ball leaves the muzzle, is dependent on a variety of factors. Specifically, it depends on the following:
- The quantity of the charge: Ideally, the increase in force generated by the powder is directly proportional to the quantity used. As a result, the greater the quantity of powder, the greater the resulting muzzle velocity. In practice, this is limited simply by how much of the powder could be burnt, before the ball was launched out of the muzzle; if too much powder is used, significant quantities of powder may not even be burnt, but instead are also ejected out of the barrel, to no use.
- the quality of the powder: the better the quality of the powder, the greater the muzzle velocity; this does not refer necessarily to the granulation of the powder, but simply the powder's suitability to propel the ball forward.
- the size of the bore where the charge is seated: the greater this is relative to the size of the ball, the lower the muzzle velocity. The reason is that more of the powder will not be directly behind the ball, and so will simply ignite and expel gases around the ball.
- the size of the round: the greater the round diameter, relative to the bore, the higher the muzzle velocity, as more of the powder's energy will be directed toward pushing the ball forward, rather than going around it.
- the mass of the round: the greater it is, the lower the muzzle velocity.
- the length of the barrel: up to a certain point, the greater this is, the higher the muzzle velocity. Too great a barrel length, however, will not add to the muzzle velocity, and may even reduce it via friction acting on the ball.
With regards to the powder itself, on ignition, the powder will be converted into gas. This happens at a very rapid rate,and at high temperatures, so as to cause the gunsmoke to generate enormous pressures against the projectile, and thereby launch it at great speed. This pressure, relative to atmospheric pressure, can be measured, and used to ascertain the amount of force acting against the projectile. This pressure will decline as the ball moves forward, since the volume occupied by the gas will increase, as per Boyle's law. In Robin's tests, the powder he used generated a little less than a thousand times the atmospheric pressure at the moment of ignition.
Since pressure is simply force over an area, one can relate the pressure generated by the powder to the surface area of the round (since P =F/A, where F is force, A is area), the surface area of the barrel (and by extension, the length, so that F = k/L, where k is a constant, L is barrel length), and the mass of the round (since F=ma, where m is mass, a is acceleration). These can then be integrated into a single equation, which can predict the approximate muzzle velocity.
An interactive version of the resulting equation, can be found here [here]. For a more detailed look at how this was derived, see [here]. Note that the model is still relatively simplistic, and makes the following assumptions:
- that the ball is "naked", which is to say, without the paper wrap from the cartridge. Due to the differences in types of paper, patching, or simple wads (such as grass or bits of paper), the exact "corrected" diameter, with wadding or cartridge paper, will vary, even when using the same type of cartridge. However, based on tests by [Bolasz Nemeth], as well as work conducted by David Miller, seem to point toward an increase of approximately 5%, when using the paper cartridge; this applies both to pistols and long arms.
- That the powder can be added ad infinitum; it does not account for the inefficiency resultant from adding too much powder. In practice the maximum charge is 1/2.72 of the barrel length.
- The bore at the muzzle, or any section ahead of the breach, is of similar diameter to the bore at the breech; in effect, the powder's ignition and expansion are assumed to be near-instantaneous, so that any windage would leak out ahead of the ball, and be wasted (this assumption does not apply for cannon to the same extent, and in fact, Robin's model was initially used for cannon).
- The effect of friction is not as apparent here as it should be. In this case, the contact of the barrel with the ball will generate this friction.
Aside from the process of projectile launch, other aspects exist regarding the internal ballistics of muskets. The windage--or gap between the ball and barrel--does not only sap strength from the shot, by allowing gas to escape. It also causes the ball to rattle along the course of the barrel. This will cause the ball to leave the barrel at a slight angle, and so impede accuracy.
Conversely, if the ball is placed some distance from the charge, it will be launched at a much greater velocity than if it were directly against the charge. The increase in force could (and often is), sufficient to burst the barrels of muzzle-loaders.
External Ballistics of a musket
Once the ball leaves the muzzle of the musket, external ballistics takes over: this considers not only the velocity of the ball and its flight, but also its accuracy.
In ideal circumstances (i.e., firing in a vacuum), the ball is affected by the force of gravity alone, which imparts a vertical acceleration of around -9.8 m/s; this causes the ball to drop, and give it the parabolic trajectory. When the shot is fired horizontally, the horizontal component will remain constant, but the vertical component will increase, with a vector toward the Earth's center. As the angle of the shot is raised, the vertical component of the velocity will increase, at the expense of the horizontal component; however, as the vertical component has a vector away from the Earth, it will counteract the effect of gravity. The result is that the projectile will travel further. This will continue til one reaches 45 degrees, at which point the projectile will travel the furthest possible distance. Beyond 45 degrees, range will decrease, as the horizontal component will be much reduced, and thereby allow gravity to counteract the effect of the vertical velocity.
However, the above is only an ideal behavior: the ball will be affected by interaction with the air (or any other medium). This will cause the both the vertical and horizontal velocity to quickly decrease. The vertical component was not just affected by gravity, but by the resistance of the air, which in this case serves to limit the velocity at which the ball can fall (this velocity is called "terminal velocity"). The horizontal component of the velocity is affected by the resistance of the air.
In terms of the general flight of the ball, the result is that the initial muzzle velocity will immediately begin to decrease, once the ball leaves the barrel--and decrease rapidly. Specifically, the effect of the air takes the following forms:
- Forebody drag: this is the effect of air against the front of the projectile. Below the speed of sound, this compression is minimal, as the air can simply move around and away from the all. However, if the ball travels faster than sound, the air cannot escape quickly enough, which causes the air in front of the ball to compress. This generates a conical shock-wave, which forms an angle, the sin of which is the inverse of the Mach number of the velocity (1 M = speed of sound in air). The resulting increase in drag is not infinite, but slows down as the ball moves further and further away from 1 M, and peaks at around ~450 m/s.
- Base drag: this is the drag caused by air turbulence behind the ball; this increases with velocity, till the projectile reaches the speed of sound, and then plateaus.
- Friction: air traveling alongside the projectile, will impart friction, which will increase as the velocity increases; however, this is the least important factor.
To quantify the effect of three forms of drag on the projectile, each shape for a projectile has what is known as a ballistic coefficient, a dimensionless factor which determines the efficiency of the projectile's ability to go through the air. In the case of a round ball, at low velocities the coefficient is approximately 0.47; however, in practice the ballistic coefficient at any given moment of the projectile's flight will vary, as the effect of drag on the ball increases. As a a ball approaches the speed of sound, drag will graduall rise, till once reaches the transonic zone, at which point the ballistic coefficient rises rapidly. This continues till one reaches ~450 m/s, at which point the ballistic coefficient begins to slowly decline.
However, the shape of the projectile is not the only variable that determines the loss of velocity. Other variables include:
- The density of the air: cooler air is denser; this will increase the rate at which velocity is lost. Shots fired at higher elevations will travel farther, as the air is less dense. Shots fired at an angle will also be affected by changes in air pressure, and so fly slightly further than if the ball were fired at the same angle, in a medium of constant pressure.
- The velocity of the projectile: as this changes, so will the loss of velocity as time goes on. The slower the balls gets, the lesser the loss of velocity.
- The cross-sectional area of the projectile: the greater this is, the greater the loss of velocity.
- the mass of the ball: counter-intuitively, the greater the mass (all other variables equal), the lesser the loss of velocity: this as as higher mass objects have greater inertia, so require more force to act on them.
The resulting equation, which describes the loss of velocity over a given distance, can be described as the product of the ballistic coefficient, air density, velocity, and cross-sectional area, all divided by double the mass of the projectile. Since the ballistic coefficient changes based on velocity, the coefficient must be calculated for every moment of the bullet's flight path.
The above can then be used to figure out how far a projectile be shot. The resulting equations, can be found [here], suited for muskets and cannon. Another one, more suited to muskets, may be found [here], N.B. this one lacks the ability to account for changes in air pressure due to the elevation; as a result, it underestimates the range of missiles fired at a high angle.
The effects of the above variables are as follows:
- The ball will--naturally--have a shorter range than if traveling in a vacuum; the difference can be quite dramatic, with the range in practice often as little as 5% of the range in a vacuum
- The actual optimal angle will not be at 45 degrees for most projectiles(for a 37 gram ball at 400 m/s, the optimal angle is apparently at 30 degrees, though other models state that it is at 60 degrees instead).
- since the ball will slow down through its flight, its energy will also decline quite rapidly. A shot striking a man at 400 m or more will not be as likely to inflict as one that strikes at 100 m, as the penetration possible would be lower. To illustrate this last point, here are the results of a test conducted in 1813 by Scharnhorst, cited in Duffy's Military Experience in the age of reason. Note that at each range, 200 rounds were fired:
|Hits (non penetrative)||92||64||64||42||26||19|
- As can be observed from the above, the greater arc of the trajectory will also affect the accuracy of the weapon, as aiming at distant objects will get more difficult. This will act alongside other variables, which will make muskets inaccurate at any range greater than 100 m. These factors, which affect accuracy are:
- The windage of the shot: not only does greater windage decrease velocity, but the greater the windage, the greater the instability of the ball's flight out of the barrel, which will cause the shot to veer more off-target
- The presence or absence of gyroscopic stability: unless the ball is made to spin via rifling, it will "tumble" through the air, which is to say, roll in flight; this tumbling will also affect accuracy negative.
- The interaction of the ball with the patching: while patching adds to the muzzle velocity, it can still negatively accuracy, if improperly made or used. In the case of musket cartridges, if the paper is too thick, it may not separate quickly enough from the ball (ideally as the ball exits the muzzle); the increase in drag, coupled with the asymmetry added to the shape of the projectile, can massively decrease accuracy.
- Imperfections in the ball itself: a perfectly-cast ball will fly truer than any which contain assymetry, air pockets, or still have their sprues on them. These all contribute to the tumbling of the round, and so make it even more unstable in flight (and so less accurate).
- The shape of the muzzle crown: a good muzzle crown will aid in preserving accuracy, whereas a poorly-designed one, or one which is simply damaged, will negatively affect accuracy.
Types of Longarm
European Military Muskets
Nearly all European military muskets of the period were flintlocks. Initially, these were introduced to soldiers assisting the gunners (known as fusiliers) in the 17th century, where the lack of need for an open flame from the match made it much safer to operate than the matchlocks of the day, and its cheaper cost made it preferable to the (more reliable) Wheel-lock. It was also introduced to dragoons, who simply couldn't carry lit match on their persons while on horseback. Gradually, another benefit of the mechanism was discovered: as it didn't rely on an open flame, it was suited to use in night-fighting, sentry duty, and in ambushes. These advantages led to flintlocks replacing the matchlock by c. 1700 in all major armies in Europe. Later, the simplicity of the flintlock design allowed for tighter formations to be used, as the weapon did not require the open space needed to operate the matchlock. This was combined with one other innovation, which became indispensable to European infantry and dragoons. This was the adoption of the bayonet, starting in France in the 1670's. These were initially simply knives, plugged into the muzzle of the weapon. This kept the weapon from firing, and so a better model was sought, whcih allowed for both firing and hand-to-hand combat--especially against cavalry. By 1705, this had been developed, in the shape of the socket bayonet. This became the standard form of bayonet for the next 150 years. The combined introduction of the flintlock and bayonet, rendered the pike obsolete, and allowed the armies of Europe to issue standardized weapons for their armies, while massively increasing their firepower. Standard musket patters were thus introduced in 1717 in France, 1720 in Britain, and 1722 in Prussia. This simplified the logistics of equipping an army, and so allowed for ever larger armies. The increased firepower of a battalion also demanded shallower formations, to allow as many muskets to fire at once. This led to the introduction of 2 or 3-rank linear formations, which dominate warfare in this period.
However, the old matchlock design was still used in India, and the a lesser extant, the Ottoman Empire, where its greater reliability was preferred (as noted by William Windham). All muskets of the day--regardless of mechanism--were susceptible to humidity and rain, as they relied on methods of ignition which can potentially expose the powder to the elements.
Basic Construction and operation of European military muskets
Simply put, all muskets are composed of three primary components: a lock--the device which ignites the charge; the barrel, which contains the ball and charge, and which allows for the better harnessing of the energy of the charge; and the stock, which houses the two other components, as well as the rammer. Additionally, most muskets of the period also came with leather slings, with which soldiers could carry their weapons while on the march; these were originally so that grenadiers could sling their weapons as they threw their grenades, but by 1750 they were standard issue. Rammers were originally made of wood (birch or ash) capped with brass, but starting with the Prussian Army, iron ramrods began to replace wooden version. These earliest versions were simply metal copies of the wooden version (as with the M1722/40); later models used thinner rammers, as the technology of producing metal rammers improved. Metal rammers have the advantage of durability and strength, which allowed for soldiers to increase their rate of fire, without breaking their rammers (as with wooden ones). However, if the metal rammers were not made properly, they could be too brittle (and break anyway), or too soft (and so bend). This issue was one reason Metal rammers arrived late in the British Army (1750). One other issue is that the steel can easily damage the muzzle crown, which can affect accuracy negatively. Other armies adopted the technology as its efficacy was demonstrated, over the course of the 1740's. Thus all armies by the Seven Years War used this rammer, to varying degrees.
Muskets were generally around 1.5 m long, and weight ~4-4.5 kg. Earlier flintlock models were held in place by pins and screws (Brown Bess series; M1722/40 muskets); more up-to-date muskets (the French 1728/46/54 musket, Austrian M1745 and M1754, various Russian and Spanish muskets), were held together by screws and barrel bands, which were kept in place by springs inserted into the stock; this latter arrangement proved superior in strength, reliability, and simplicity of maintenance, and would quickly catch on outside of Britain. Fittings could be brass or iron, with the former less prone to rust, though the latter was simply cheaper. Brass' resistance to corrosion made it preferable for naval service, even in countries where the muskets were generally fitted with iron (e.g. France).
Muskets stocks became less ornate over time, with earlier musket models exhibiting various decorations and extra pieces, which had things such as the monarch's cypher, or scrollwork and floral patterns. Stocks at the time generally had a relatively long grip, strong drop, and large cheek-piece. The result was that the soldier typically didn't need to tilt his head as much as with modern firearms in order to aim.
As only front sights were found on most muskets, the soldier would line up the rear of the barrel with the sight. When one considers the taper of the barrels, this causes the shots to land high. As a result, soldiers were taught to aim low at close range; experiments with the M1730 musket confirm this. However, soldiers often over-compensated and fired too low, with the situation exacerbated by the addition of the bayonet, which served to make the weapon front-heavy.
All flintlocks operate as follows: when the trigger is pulled, a spring is engaged, which releases the cock of the musket held under considerable tension. This has a piece of flint or rock quartz (typically 1-1.5" square, with a finely-knapped edge; the author cut his thumb badly from one such specimen), wrapped in leather or lead, and held in place via a vise which digs into the lead or leather. The flint strikes the hardened metal of the hammer covering the pan with force, and scrapes down along it (it also simultaneously pushes the hammer away, to expose the pan). The scraping action creates sparks (red- to orange-hot pieces of metal), which then land in the exposed pan. This then (ideally) ignites the powder in the pan, which will generate a flame, which then travels through the touch-hole, to ignite the charge in the barrel that propels the projectile. This method of ignition is safer than that of the earlier matchlock, as it does not involve an open flame. It was also faster than a matchlock. However, there is still a perceptible delay between the moment the trigger is pulled, and the launch of the projectile, which can throw off the aim--a problem universal to muskets prior to the introduction of mercury fulminate (1809). This can be mitigated by using a finer powder to prime the pan, though this was not followed by most soldiers in the war, who used cartridges to both prime and load. This delay can be exacerbated by pouring excessive quantities of powder, which could lead to a greater "hang" in the fire (it can also weaken the shot itself). Additionally, since the load used in the cartridge is used both to prime and load the weapon, the muzzle velocity also tends to be inconsistent: our tests with a replica M1730 Brown Bess gave muzzle velocities between 910 and 950 feet per second with 120 grains of black powder (the mean was 940 fps). For safe carrying of the weapons, flintlocks came with a "half-cock" mode; this mode was (theoretically) designed so that you cannot pull the trigger, or failing that, cause the cock to strike the hammer with insufficient force. However, personal experience by the author demonstrates that it is not always reliable, and premature discharges were not unheard of on the parade ground.
With regards to the ignition source, flint is better than rock quartz, as the micro-crystalline structure of the former creates a sharper edge, which is more efficient at scraping the metal of the hammer. The higher the quality of the flint, the more shots could be fired, and the more sparks are generated. A good flint will generally last 20-30 shots before it becomes too dull to generate sparks. Poor-quality flints can shatter, due to the presence of microscopic cracks. They can also contain impurities which can compromise the ability of the flint to generate sparks. The nature of the flintlock's operation means that the hardening of the hammer will eventually be scraped off or worn out. This will in turn compromise the weapon's ability to generate sparks, and with it, the reliability of the weapon. In any case, the best way to secure the flint to the cock was via a sheet of lead, which allowed the vise of the cock to grip the flint tightly, without wearing out of the sheet (as would be the case for leather). It was also more durable against the elements, and lasted longer.
Due to the need for durability, as well as the crude manufacture, the tolerances of the military muskets were such that the trigger pull was quite heavy by today's standards; for example, the Brown Bess replica used in our tests has a trigger pressure of ~12 pounds. This explains the various manuals' instructions to "pull briskly" (i.e. essentially jerking the trigger). This can also throw off aim, in this case by causing the weapon--and with it, the shot--to veer; in our tests, this was typically to the left.
Military muskets of the period exhibited considerable windage--or difference between the bore and bullet diameters; the most common bore size, for example was ~0.72 calibre, with the ball size ~0.65 calibre (e.g. Prussia, Austria). This reduced the velocity and accuracy of the musket, but was necessary to minimize the effects of fowling, and increase the rate of fire; another feature typical of musket barrels, and also meant to minimize the effect of fowling, was that they swelled toward the breech. The greater surface area which resulted would then ideally catch more of the fowling, and keep it away from the muzzle.
The windage was partly mitigated via the use of the cartridge paper--still wrapped round the ball--as a crude sabot, though accuracy still suffered, as the windage is only a secondary source of inaccuracy. As a result of the windage, the fowling – when using a military load – does not become a serious issue for several dozen shots. In our tests, we emptied all 21 rounds in our cartridge-box without experiencing any particular difficulty in ramming down the cartridge, though the fit did become tighter (the gain in accuracy was minimal). Much more dangerous was the over-heating of the barrel, which could cause the barrels to explode--particularly if the barrels were of poor quality--a common issue at the time. Additionally, though the touch-holes of the muskets during the war were too small to allow for self-priming (self-priming is another post-war invention), they were still large enough to allow excessive quantities of gas (and with it, energy) to escape from there, rather than propel the round forward.
Even firing two shots in rapid succession will result in a heat-haze around the barrel, as the outside of the barrel climbs to ~50 Celsius; this will affect the aim, as it obscures the foresight. Just ten shots are sufficient to render the barrel untouchable due to heat: rate of fire will decrease rapidly as a result. This confirms accounts by Ulrich Bräker (a soldier in Itzenplitz Infantry), who noted his barrel was hard to touch after a short time.
As mentioned previously, most military muskets of the day used cartridges: these consisted of a ball, wrapped in cartridge paper, then filled with powder. The ends were twisted or folded off, to keep the powder and ball together. Additionally, the ball itself was generally separated from the powder via a choke--usually a wetted linen or hemp cord, tied round the paper at the base of the ball; a second cord tied the ball end of the cartridge. Additional pieces of linen or hemp cord could be used to tie off the powder end. The charge used for the cartridges varied, but generally ranged from a quarter to a third of the weight of the ball itself. The cartridge paper was quite thin, often to the point of translucence. This was necessary to allow the soldier to quickly bite open the cartridge. All armies used cartridges the same way: the end containing the powder was bitten open, and part of the charge poured into the pan to prime it. The pan was then shut, and the musket was cast about. The rest of the powder would then be poured down the muzzle. The ball (still wrapped in paper), would then be inserted after the powder, and the whole rammed down.
Rate of fire, and general performance
The best rate of fire that we attained during our test was 22 seconds per shot, and most of the time it was closer to 25-30 seconds (before the barrel over-heats; afterwards, it’s closer to 1 shot per minute). This specific test has been made using the British 1757 manual exercise as loading procedure. The shortening of the rammer with the belt-buckles – universal to all manuals of the period – was initially the cause of this limitation. Removal of this step allows for 3 shots a minute (using the method prescribed in the British 1764 manual exercise), though this cannot be sustained for long. Another limiting factor is how exhausting the loading procedure is, especially with the bayonet fixed (a standard practice in war); the bayonet will cause the musket to become front-heavy, and so harder to load, as the barrel naturally tilts away from the user, when held in the loading position.
On firing, The muskets will eject pieces of paper as far as 20 yards (~18 meters); these are often still burning. This confirms other observations that the muskets can cause fires that way. Additionally, the blast of the musket will hurl sand-sized grains of unburnt powder toward the target: during the tests conducted by the author, the weapon was used on a target at a range of under 10 yards; in addition to the bullet hole, dozens of smaller holes were noted on the target, as a result of these grains; these grains also led to the chronometer being positioned at that range, as any closer and the powder would disrupt the readings. Additionally, the weapon will generate a considerable quantity of blue-gray smoke, with a sulfurous odor, which in humid, windless days could hang in the air for quite some time. The presence of thousands of these weapons on any given battlefield, all blasting off, would have quickly covered in the field in smoke, adding to the inaccuracy of the muskets. The smoke can induce coughing and vomiting, when in sufficient concentrations. The better-made the powder, the whiter-colored and cleaner the gun-smoke.
The ball itself will be hurled with considerable force, sufficient to reliably penetrate 4-6” of pine, out to combat ranges (1-200 m), as shown in our tests; muzzle velocity ranged from 250-500 m/s, depending on the quality of powder, and the model of weapon. This confirms the description of the muskets of the period by Christopher Duffy. Additionally, the musket ball, which was made of lead, tends to flatten when it strikes hard objects (e.g. bone or metal). In some cases, the rounds simply tore apart. Additionally, the recoil of a typical musket would have been heavy, though less like the snapping kick of a modern rifle, and more like a push or punch.
Regarding the accuracy of the muskets, all the weapons were able to hit a man's figure at a range of ~75 meters. Beyond that range, it was increasingly unlikely that a shot will strike an individual target if aimed at; Instead, it was better to aim at the mass of men. Beyond ~190 m, the weapons were hopelessly inaccurate, and volleys fired at that range wasted ammunition. The main source of the inaccuracy is not the windage, but rather the lack of rifling, which if present would have stabilized the shots; windage further affects the accuracy, but not to the same extent as the absence of rifling.
The accuracy of the muskets at ~80 m explains why, Tellingly, no firefight experiment from the period tested anything closer than 80 yards (see Military Experience in the Age of Reason, by Christopher Duffy). Based on the data from the range, firefights – at least typical ones described by Prussian and Austrian sources – generally didn’t seem to happen at ranges below 120 yards, and more typically at 150 yards. Anything closer would have led to heavy casualties in the space of minutes, rather than the accounts of men running out of ammunition first--which are quite common; the devastating Austrian volleys at Hochkirch were indeed likely fired at ranges under 50 yards, as Christopher Duffy suspected. This considers the effects of fear, exhaustion, and smoke: under ideal conditions, the destruction wrought in that fight could have been achieved at 100 yards (One implication of this is that the French did not fire at too far a range at Quebec: the distance they used was typical of the time. It was the British who opened fire at an unusually close range).
Toradars and Jezails
Other designs and specialty firearms
Bräker, Ulrich, Der Arme Mann im Tockenburg, 1789
By order of the Town of Boston, A short narrative of the horrid massacre in Boston: the 5th day of March, 1770, by soldiers of the 29th Regiment, with some observations on the state of things prior to the catastrophe, Edes & Gill, and T. & J. Fleet, 1770
Collins, A.R., Benjamin Robins on Ballistics, https://www.arc.id.au/RobinsOnBallistics.html . Accessed 10/04/19
Duffy, Christopher, Military Experience in the Age of Reason, Macmillan Publishing Company, New York City, NY , 1987
Miller, David P.: Ballistics of 17th Century Muskets, Cranfield University, May 2010
Scott, Douglas D.; Joel Bohy; Nathan Boor; Charles Haecker; William Rose; and Patrick Severts: Colonial Era Firearm Bullet Performance: A Live Fire Experimental Study for Archaeological Interpretation, April 2017
Roberts, N.A.; Brown, J.W.; Hammett, B.; Kingston, P.D.F, A detailed study of the effectiveness and capabilities of 18th century musketry on the battlefield, Journal of Conflict Archaeology, 2008
Robins, Benjamin: New principles of gunnery, containing, the determination of the force of gunpowder and an investigation of the difference in the resisting power of the air to swift and slow motions, 1742 
Windham, William; Townshend, George Lord Vice: A plan of DISCIPLINE for the use of THE NORFOLK MILITIA, 1759
User:Ibrahim90 and W.D.Liddell, for the initial version of this article and for ballistic tests of the M1730 Brown Bess Musket