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Thread: Gunnery.

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    Default Gunnery.

    Gunnery became a subject for practical mathematics in the 16th century. Printed books and new mathematical instruments dealt with the measurement of shot, the elevation of guns and mortars, and the calculation of the range of fire. Calipers and gauges were devised to measure diameters and indicate weights. Sights and levels enabled the gunner to set appropriate elevations, and there was an enormous range of forms and styles for such instruments, including exotic combinations which could never have served in warfare. More standard patterns were emerging by the 18th century when mathematical instrument makers had become regular suppliers to ordnance departments. The prediction of range in relation to the elevation of a gun was considered the pinnacle of artillery as a mathematical science, and its most difficult problem. From Galileo and Newton to the humble compilers of tables, mathematicians demonstrated the value of their art by studying the fleeting path of the shot through the air.


    To make use of range tables that related a gun's elevation to its distance fired, gunners needed an estimate or, better still, a measurement of the distance to the target. Traditional surveying techniques measured distances by making physical connections between stations, using ropes, poles, or chains; this was not, of course, an option for the gunner, who could not approach his target. Sixteenth-century geometers keen to demonstrate the practical value of their discipline were, however, developing new methods for land surveying. They offered a variety of triangulation techniques for measuring distances without moving between sites, using new instruments to establish distant positions from a single measured baseline. Contemporary illustrations often show such triangulations in a military context - either for rangefinding by the gunner, or for distant measurement by the military surveyor.


    Early mechanical gunnery aids.

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    The first recorded device to measure an elevation angle was Niccolò Tartaglia's invention of a gunners' quadrant circa 1545. This device had two arms at right angles connected by an arc marked with angular graduations. One arm was placed in the muzzle, and a plumb bob suspended against the arc showed the elevation angle. This led to many calculations relating elevation angle to range.

    The problem was that these calculations assumed what today is called an "in vacuo" trajectory – they made no allowance for air resistance against the projectile. What was needed were range and accuracy trials to determine the actual relationship between range and elevation angle. The practical approach was conducted by William Eldred, Master Gunner at Dover Castle, in gunnery trials in 1613, 1617 and 1622. He used a wide variety of guns, including the culverin, demiculverin, falconet and Saker. From the results of these trials, he produced range tables for elevations up to 10 degrees for each type with a standard propelling charge weight.

    A problem affecting gun laying, was the tapered external barrel shape. This affected elevation when the gun was aimed by sighting along the top of the barrel. In the early 17th century, 'dispart sights' compensated for this. This was a piece of metal placed on the muzzle to make the line of sight parallel to the axis of the bore. Another technique involved measuring the depth of the barrel through the touchhole and at the muzzle, the difference being the wedge size needed to compensate for the tapered barrel.

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    Ballistic pendulum, invented by Benjamin Robins to calculate muzzle velocity.
    The ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins, and published in his book New Principles of Gunnery, which revolutionized the science of ballistics, as it provided the first way to accurately measure the velocity of a bullet.
    Robins used the ballistic pendulum to measure projectile velocity in two ways. The first was to attach the gun to the pendulum, and measure the recoil. Since the momentum of the gun is equal to the momentum of the ejecta, and since the projectile was (in those experiments) the large majority of the mass of the ejecta, the velocity of the bullet could be approximated. The second, and more accurate method, was to directly measure the bullet momentum by firing it into the pendulum. Robins experimented with musket balls of around one ounce in mass (30 g), while other contemporaries used his methods with cannon shot of one to three pounds (0.45 to 1.36 kg).
    The first system to supplant ballistic pendulums with direct measures of projectile speed was invented in 1808, during the Napoleonic Wars and used a rapidly rotating shaft of known speed with two paper disks on it; the bullet was fired through the disks, parallel to the shaft, and the angular difference in the points of impact provided an elapsed time over the distance between the disks. A direct electromechanical clockwork measure appeared in 1840, with a spring-driven clock started and stopped by electromagnets, whose current was interrupted by the bullet passing through two meshes of fine wires, again providing the time to traverse the given distance.


    Tangent sights were introduced in the 19th century. These provided the rear sight used with an 'acorn' or similar foresight at the muzzle. The tangent sight was mounted in a bracket beside or behind the breech, the eyepiece (a hole or notch) was atop a vertical bar that moved up and down in the bracket. The bar was marked in yards or degrees. This direct-fire sight was aimed at the target by moving the trail horizontally and elevating or depressing the barrel. By the late 19th century the simple open tangent sights were being replaced by optical telescopes on mounts with an elevation scale and screw aligned to the axis of the bore.
    The Business of the commander-in-chief is first to bring an enemy fleet to battle on the most advantageous terms to himself, (I mean that of laying his ships close on board the enemy, as expeditiously as possible); and secondly to continue them there until the business is decided.

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    If anyone has more information which they can add to this thread please feel free to do so especially pictures and diagrams on gun ranging, and gun laying.
    Rob.
    The Business of the commander-in-chief is first to bring an enemy fleet to battle on the most advantageous terms to himself, (I mean that of laying his ships close on board the enemy, as expeditiously as possible); and secondly to continue them there until the business is decided.

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    Very interesting Rob, I shall look forward to further development.

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    Admiral of the Blue.
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    Thanks Chris. I hope we can get some feedback from the experts on this one.
    Rob.
    The Business of the commander-in-chief is first to bring an enemy fleet to battle on the most advantageous terms to himself, (I mean that of laying his ships close on board the enemy, as expeditiously as possible); and secondly to continue them there until the business is decided.

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    Mind boggling but fascinating. Do you know what additional tools or calculations were used to accommodate the effects of a rolling ship on the sea?

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    Those are the sort of things I'm hoping to get answers for.
    Rob.
    The Business of the commander-in-chief is first to bring an enemy fleet to battle on the most advantageous terms to himself, (I mean that of laying his ships close on board the enemy, as expeditiously as possible); and secondly to continue them there until the business is decided.

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    Here are a couple of references I ran across whilst looking up gunnery data. (Related to playing the Naval Action PC game).

    http://arc.id.au/CannonBallistics.html

    Warning the above abstract includes math that will make your eyes water.

    Here is a link to a period source: A Treatise on Artillery by Muller.

    https://books.google.com/books/about...d=vylEAAAAYAAJ

    The below series of articles contains a raft of information on gunnery. Now granted it is written a magazine devoted to a fictional universe "1632" , but it is non-fiction. The artivles pull together a number of period tests on accuracy and penetration for example.


    https://grantvillegazette.com/article/publish-581/

    https://grantvillegazette.com/article/publish-596/

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    Some great info there Eric.
    Thanks.
    Although a lot of the info is as you say far more detailed than we need for wargaming
    I found this almost immediately. I was particularly interested in how range was estimated on a moving ship at sea.


    Standard practice for seventeenth and eighteenth-century naval warfare was to engage at point-blank range (or less).

    Point-blank range (PBR) is the furthest that the gun can be assumed to "shoot straight," that is, the range at which the average gunner will use zero elevation. Strictly speaking, it is the range at which the "drop off" equals the height of the muzzle above the water surface, so the projectile will still hit the target. Yes, that means that PBR should vary depending on which deck the gun is mounted on!

    There is considerable disagreement as to the actual value. In 1834, Stevens (25) said from a frigate, PBR is 500 yards, and from a "battleship," 700, assuming that the guns are pointed by the "dispart sight at the hammock rails" of a frigate or larger target. In 1828, Beauchant estimated that the 18-, 24-, and 32-pounders, fired from the main deck of a frigate, had a point-blank range of 400 yards with a one-third charge, 300 with a one-quarter, and 250 with one-sixth. However, engagements were more typically at 100–200 yards.


    Range and Accuracy.

    All else being equal, if you increase the range, you decrease the accuracy. The horizontal extent of an angular error in bearing equals the range times the sine of the angle. The effect of an error in elevation is more complex, thanks to gravity, but the vertical or range error will still increase with range.



    Range Estimation.

    If the range were great enough that elevating the gun was necessary, then you had to have some way of determining what the range was so you could judge the correct elevation.
    The gun captain might, through long experience, be able to estimate visually the range to the target and know the proper elevation to strike it. This depended, of course, in the first instance on the gun captain's visual acuity.
    In the late-nineteenth century, American soldiers were required to be able to see a two-foot square black bull's eye on a white background at a distance of 600 yards. (Clowes 385). Training was also important; soldiers would pace off a distance and then study it, or estimate a range and then pace it off. Soldiers were taught that at 600 yards, a man's head was a small round ball, that at 225 yards, his face became distinguishable as a light-colored spot; the eyes can be seen at 80 yards and the proverbial whites of the eyes at 30. (Groome 151; Farrow 697). Presumably, sailors could similarly study the crew of an enemy ship, as well as the visibility of its gun ports, masts, and stays.
    In land warfare, visual estimates supposedly had an error of 12–15% at a range of 600–1200 yards. (Hopkins 196). However, at sea, there aren't a succession of fixed reference points, like trees and hills, which you can use to facilitate range estimation. In addition, weather conditions often will degrade visibility. According to Fullam (459), "it is quite impossible to estimate ranges above 2000 yards with anything like sufficient accuracy."
    Acoustics: Just as you can estimate how far off a thunderstorm is by timing the interval from lightning flash to thunder rumble, you can count the seconds between the flash and the report of the enemy's guns. This can be made somewhat more precise with an acoustic telemeter; a metal disk is caused to drop through the liquid filling a calibrated tube when the flash is seen, and stopped when the sound is heard. (Cook 593).
    Trigonometric Methods: If you know the absolute dimension of any part of the enemy ship, such as the height of its mainmast, you can measure its angular size with the sextant, and calculate the range by trigonometry (or table lookup). Douglas compiled a table of the heights of the parts of French ships of war of various classes. (Douglas 214ff). This works best if the enemy has standardized its warship classes, which unfortunately was not the case in the early-seventeenth century.
    Alternatively, as in Buckner's method, you could measure the angle between the enemy's waterline and the horizon; it requires knowledge of the viewer's height above sea level. Use of this method is expedited by what EB11 calls a "depression rangefinder."
    These methods were more likely to be used for deliberate shooting by a bow or stern gun during a chase, than for a broadside.
    Another trigonometric method is to have observers stationed at the bow and stern of your ship sight the same object and report its bearing. The accuracy of this method depends on the length of your ship, which serves as the baseline (Cook 591). It also required communication between the observers, and wouldn't work if the target were ahead or astern. (Friedman 23).

    Rob.
    The Business of the commander-in-chief is first to bring an enemy fleet to battle on the most advantageous terms to himself, (I mean that of laying his ships close on board the enemy, as expeditiously as possible); and secondly to continue them there until the business is decided.

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