Fyrish Artillery
Pre-pattern artillery
Before pattern artillery, no set system existed for procured artillery. Instead, armourers produced cannons using differing standards based on spherical shot weight, similar to firearms gauge measurements. For smoothbore muzzleloading small arms, the formula d = 2 3√3/4 π (1 / +n/p) describes the nominal bore diameter d with shot weight as 1/n of a 1 lb sphere of density p. Individual armouries sometimes used Anglian, Senese, or Sieuxerrian measurements, leading to differing bores using the same idea. Nevertheless, the Fyrish industrial revolution coalesced around a modified Anglian system of measurements known as Fyrish Imperial (Fyrish: Fyriscaserlic), such that early-19th century armouries generally followed C = 2 3√W. Where C is the shot calibre in inches, W is the spherical iron shot weight in pounds, and multiplicator 2 is a dimensional coefficient.
Practice
Iron shot density varies depending on the casting method, such that the multiplicator in the formula varies between 1.9 (0.2781 lbs/in^3) and 2 (.2384 lbs/in^3); therefore, 2 represents a value that is most compatible with all iron shot. As such, a mid-19th century Fyrish 2-pdr cannon fires ~2.52" (2-17/32") shot and has a ~2.65" (2-41/64") bore, whilst a 6-pdr cannon fires ~3.63" (3-41/64") shot and has a ~3.82" (3-13/16") bore. The difference between shot and bore calibre is the windage ( w), which may range from ~1/20 of the shot diameter to 1/24 on larger 18th-century artillery. Pre-pattern artillery bore diameter then roughly follows C + w = 2 3√W 1.05 in its expanded form, where 1.05 represents a windage coefficient of 1/20.
Domestic pattern artillery (1860-on)
SWEB
Fyrland increasingly looked inwards for domestic materiel from the mid-19th century, leading to the coalescence of armoury standards around an elongated solid iron shot for use in rifled muzzleloaders. The system that emerged, Shotweight System (Scotwiht Endebyrdnes — SWEB), intrinsically linked shot weight and bore diameter, shaping domestic artillery well into the 21st century. Even with the emergence of effective shells towards the end of the 19th century, SWEB calibres stuck around, designating rifles primarily meant for throwing shells by their bore diameter in inches (ynce). Table shot weight doubles up to 16 lbs, increasing from then on by ~99/70 approximating √2. Calibres did exist outside of the SWEB tables, such as export or import rifles and special order or special purpose weaponry. However, the vast majority of calibres followed the SWEB convention.
Practice
SWEB intrinsically linked shot weight and calibre through the formula W = C3/2, where W represents the greatest shot weight in pounds and C nominal calibre in inches. Divisor 2 represents a dimensional coefficient comprising projectile form factor and density, four times the weight of round shot. Calibre thusly follows C = 3√2 3√W. The greatest shot weight coefficient of 3√2 came from an elongated hemispherical flat base cast iron projectile of ~2.6 calibres with a large cylindrical midsection. However, solid shot of this L/d ratio represented a realistic maximum length, and the Short SWEB table better represented more common solid shot around ~2 calibres. Short SWEB (Scotwiht Endebyrdnes, Scort — SWEBS), otherwise known as Three-Quarter SWEB, more accurately describes solid shot weight through the formula W = 3 C3/8 and calibre as C = 2 3√W/3√3. Multiplying what was known as Long SWEB (Scotwiht Endebyrdnes, Lang — SWEBL) — Common SWEB today — shot weight by 3/4 will give you Short SWEB weights, and guns designed for Short SWEB have an s suffix following their pounder designation, whereas Long SWEB have l, e.g. 3-pds or 4-pdl — both are 2" guns.
Steel era
At the end of the 19th century, breechloaders, steel shot and guns, mass production, and finer machining tolerances coalesced into the modern Common SWEB (Scotwiht Endebyrdnes, Mæne — SWEB) table. Windage is no longer part of Common SWEB, as muzzleloaders fell from favour after introducing gas-checks, which developed into driving bands for now ubiquitous rifled cannons. In concert with modern machining, the oversized driving bands meant shell bourrelet and bore diameter at the lands are within a few thou (n/1000"), such that shell and bore calibre are essentially identical. Additionally, denser cast or later forged steel shot brought Long SWEB's dimensional coefficient of 2 back to common use as C = 3√2 W. Guns designed for Common SWEB with newer projectiles have an e, m, or r suffix following their pounder designation, e.g. 4-pde, 4-pdm, 4-pdr — all 2" guns. The last feature of Common SWEB is that all bore diameters are rounded to the nearest 1/8" working from shot weight to calibre and rounded to the nearest pound working from calibre to shot weight.
| Shot | Bore diameter @ lands | |||||
|---|---|---|---|---|---|---|
| lb | in | in-frac | mm | Lines | Use | Notes |
| 1 | 1.250 | 1-2/8" | 31.75 | 20 | */** | |
| 2 | 1.625 | 1-5/8" | 41.28 | 26 | ||
| 3 | 1.750 | 1-6/8" | 44.45 | 28 | */** | |
| 4 | 2.000 | 2-0/8" | 50.80 | 32 | ||
| 6 | 2.250 | 2-2/8" | 57.15 | 36 | * | |
| 8 | 2.500 | 2-4/8" | 63.50 | 40 | ||
| 11 | 2.875 | 2-7/8" | 73.03 | 46 | ** | |
| 16 | 3.125 | 3-1/8" | 79.38 | 50 | */** | |
| 23 | 3.625 | 3-5/8" | 92.08 | 58 | ** | |
| 32 | 4.000 | 4-0/8" | 101.60 | 64 | * | |
| 45 | 4.500 | 4-4/8" | 114.30 | 72 | */** | |
| 64 | 5.000 | 5-0/8" | 127.00 | 80 | * | |
| 91 | 5.625 | 5-5/8" | 142.88 | 90 | ** | |
| 108 | 6.000 | 6-0/16" | 152.40 | 96 | * | |
| 128 | 6.375 | 6-3/8" | 161.93 | 102 | */** | |
| 181 | 7.125 | 7-1/8" | 180.98 | 114 | ** | |
| 256 | 8.000 | 8-0/8" | 203.20 | 128 | */** | |
| 362 | 9.000 | 9-0/8" | 228.60 | 144 | ** | |
| 512 | 10.125 | 10-1/8" | 257.18 | 162 | * | |
| 724 | 11.375 | 11-3/8" | 288.93 | 182 | */** | |
| 1024 | 12.625 | 12-5/8" | 320.68 | 202 | */** | |
| 12.750 | 12-6/8" | 323.85 | 204 | |||
| 1448 | 14.250 | 14-2/8" | 361.95 | 228 | * | |
| 1680 | 15.000 | 15-0/8" | 381.00 | 240 | * | |
| 2048 | 16.000 | 16-0/8" | 406.40 | 256 | * | |
| 2896 | 18.000 | 18-0/8" | 457.20 | 288 | * | |
| 4096 | 20.125 | 20-1/8" | 511.18 | 322 | */*** | |
| All fractions expanded to 8ths. |
| 6" included as SNT example. |
| Underlined entries represent SNT calibres. |
| * Navy calibres. |
| ** Army calibres. |
| *** Largest Fyrish gun ever test fired. |
Examples
MH 2-pd FC 56: Muzzleloader 2.5" field gun of 1856 meant to shoot shot.
TM 4-pdl FC 69: Rifled muzzleloader 2" field gun of 1869 meant to shoot shot.
SF 3-pds GfC 87: Ammunition obturated 2" infantry gun of 1887 meant to shoot shot.
BC 7.1" h.GfH 98: Ammunition obturated 7.125" heavy infantry howitzer of 1898 meant to shoot shells.
128"'/45 BH Mc.I: Breech obturated 8"/45-calibre mark one naval cannon.
Glossary
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Formulae
Length/diameter ratio of hemispherical flat-base projectile assuming .258lbs/in^3 shot density and no cavity of weight W. Remove the last C divisor for shell length. Lbs, inches.
HFB L/d = W/.258 - 1/12 π C3/π (C/2)2 + C/2/C
Length/diameter ratio of calibre r-radius tangent head flat-base projectile assuming .258lbs/in^3 shot density and no cavity with weight W where k = -(r - .5) and Cv is the head volume coefficient. Remove the last C divisor for shell length. Lbs, inches.
TFB L/d = W/.258 - Cv C3/π (C/2)2 + √r2 - |k|2 C/C
Tangent ogival head volume coefficient with calibre radius r where k = -(r - .5). Multiply by calibre cubed for volume. Dimensionless calibres.
Cv = ∫√r2 - |k|2
0 π (k + √r2 - x2)2 dx