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We know the weights of various medieval bombards and the weight of the stones they launched (such as the famous Mons Meg or Dardanelles gun). But I can't find any information about their range or how much gunpowder they required. I presume the powder was less efficient than the corned gunpowder used in the age of sail, so for the same weight shot did a bombard use more powder for the same kind of range, or was the range much less?

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    Given that early bombards varied greatly in size and design, I think it's unlikely to get a general rule for them as a whole. Lack of uniformity of both powder and shot would also make general performance difficult to judge. – Steve Bird Sep 21 '18 at 9:04
  • @SteveBird: Actually no - basic physics mandates that the range of all guns varied very little until development of the Napoleon 12-pounder (a true hybrid gun-howitzer) in the 1850;s. I'm working on an answer now. – Pieter Geerkens Sep 21 '18 at 10:46
  • @PieterGeerkens The basic physics is the same but the range of a smoothbore cannon varied depending on the gun design (materials, calibre, barrel length and amount of windage) type of shot, quantity (and quality) of powder and elevation. That's a lot of variables. – Steve Bird Sep 21 '18 at 11:00
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First, let's discuss some basic properties of guns: muzzle-loading launchers of solid shot, usually round, at sub-sonic muzzle speeds, with no internal mechanism for absorbing recoil. The absence of any recoil-absorbing mechanism dictates that launch elevations are restricted to just a few degrees, else the carriage is rapidly destroyed by shot recoil.

The solid shot being fired does damage solely by impact, unlike the explosive shells fired by howitzers and mortars at high elevations. Combined with the low muzzle velocity (typically about Mach 0.9, or ~900 fps), low firing elevations (less than 3 degrees), and high-drag of spherical shot, ranges were quite low. Further, there were two firing modes with different ranges:

  • Anti-personnel mode involved skipping the shot over the ground to sweep a path of destruction before the battery. The intent was to simultaneously attempt to keep the shot under about 5 or 6 feet of height through its entire travel, and maximize the number of skips. The shot was considered spent at a range when it began rolling and hopping instead of skipping. (However spent shot remained dangerous to the unwary for an additional few hundred yards of range - General de Division St. Hilaire and Marechal Lannes were killed and fatally wounded respectively within minutes of each other at Aspern-Essling by spent shot.)

    In this mode range is limited by the hardness and smoothness of the ground (ie by the number of skips possible). Assuming a muzzle height of 3 feet and 3 skips at 0 degrees elevation, range would be a bit less than 7 * t * 900 feet where t is the time for the shot to drop 3 feet, or sqrt(3 / 16) ~ 0.4. Then range is a bit less than 7 * 0.4 * 900 = 2520 feet = 840 yds = 750 m. This is the effective range of the gun. There is some variance on caliber due to the cube-square law, favouring heavier guns, but in effect this means that heavier guns get one or two more skips because aerodynamic drag (proportional to the square of the shot diameter) is less effective against the shot's momentum (proportional to the mass, ie the cube of the shot diameter).

    Beyond effective range the spent shot becomes dodgable (for those not in close formation) and is more likely to wound than immediately kill. There are apocryphal tales of British officers attempting to trap spent shot with their foot as they would a cricket ball - but 12 or even 8 pound iron shot is a far cry from a 5 oz cork ball, and they typically lost their leg in consequence.

    Range could be extended slightly (see hybrid mode below) by firing at slight elevation, though fewer skips would be obtained, and there would be dead ground in front of the battery where the shot was travelling above any targets.

  • Bombardment mode is the employment of elevations above level (up to about 3 degrees only) in the attempt to hit a target, undoubtedly stationary, on the fly. Here the limitation on the range is the maximum angle of elevation, about 3 degrees, at which the gun can be repeatedly fired without destroying its carriage from the recoil. For a maximum elevation angle of 3 degrees the time to land for a shot is about 2 * 900 * sin(3) / 16 =~ 6 seconds, giving a maximum range of about 6 * 900 = 5400 feet = 1800 yds = 1600 m. At these elevation angles there is no skipping of the shot as it impacts the ground with a downwards velocity component of ~48 fps.

    Here again the cube-square law advantages heavier guns relative to lighter guns, with the calculated ideal maximum range above being reduced more by drag in the case of lighter guns than for heavier guns. I have not attempted to calculate those effects in the rough calculations above. It is also possible that the heavier carriage of a heavier gun might be able to tolerate a slightly greater maximum elevation, for again a slight increase in maximum range; however I would probably only credit this to post-Gribeauval designs without hard experimental evidence.

  • Hybrid mode was sometimes attempted at very low elevation angles of about 1 degree or less, as at Waterloo by Napoleon's grand battery. Here an attempt was made to achieve one skip of the shot in order to target Wellington's troops behind the ridge; but it is uncertain how effective this was. It certainly would required very hard ground for success.

Notes

  1. I am unsure precisely why (nearly) all guns before the early-19th century are subsonic, but I suspect it is a casting limitation on the barrels. A second possibility though is that achieving higher velocities was inefficient in powder, gaining just a little in range but dramatically reducing ability to maintain fire rate and duration.

  2. Guns prior to the early 19th century absorbed recoil solely through friction of their own weight against the ground. With no internal springs, it was necessary that the gun recoil almost straight back so as to not over-stress the wooden carriage. This is the reason for the very low elevation ranges for guns. Howitzers and mortars were able to launch at higher elevation ranges by using a very much lower powder charge. This is the reason why guns and howitzers are always distinct weapons until development of the Napoleon 12-pounder (named for Napoleon III, not his more famous uncle) in the 1850's.

  3. The Napoleon 12-pounder well known through the American Civil War is a very different weapon than the Gribeauval 12-pounder so favoured by Napoleon I. The latter was a true gun designed in the late 18th century, while the former is a hybrid gun-howitzer designed for napoleon III in the 1850's.

  • sciencedirect.com/science/article/pii/S2214914715000835 is only considering the Mons Meg, but they give angles up to 45° - is the Mons Meg an exception to your 4°max-rule, or is the paper merely peddling theoretical musings? – bukwyrm Sep 21 '18 at 12:02
  • @bukwyrm: Did you read this comment: "A 45° initial inclination would mean the muzzle of the cannon would be 2.86 m off the ground which is infeasible considering the mass of the cannon. It was agreed that a 15° inclination would be used for future trajectory calculations.". Also, these are theoretical and not experimental or recorded elevations. – Pieter Geerkens Sep 21 '18 at 12:20
  • @bukwyrm: It also seems the authors have not realized the practical recoil problem in determining realistic elevation angles. The paper seems to be the first attempt of its kind to perform theoretical analysis of antique weapons, with a primary goal of verifying the barrel calculations against the actual point of failure. The rest does indeed seem to be mostly "theoretical musings". – Pieter Geerkens Sep 21 '18 at 12:26
  • I read the comment, but i did not understand the reasoning. they lugged that thing to a place of battle, and then couldn't be bothered to create earthworks to angle it however they wanted? Dig a hole, use the excavated earth to create a mound in front of it, then place the bombard into the hole, resting on the slope of the hole and the side of the mound. – bukwyrm Sep 21 '18 at 12:40
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    As far as I know, the shockwave of blackpowder is subsonic, so it is going to be difficult to obtain a supersonic shot with it. White powder has a supersonic shockwave, but it was only invented in... the 19th century (though its main immediate advantage seems to have been its smokelessness, not its speed). – Luís Henrique Sep 21 '18 at 18:54

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