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Advanced Cannon
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Advanced Cannon
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== Ballistics == === Muzzle Velocity === Let <math>n_p</math> be the number of propellant modules. Let <math>l_p</math> be the length of the gunpowder casings, <math>l_s</math> be the length of the shell without the casings and <math>l</math> be the length of the whole shell (all in metres). The muzzle velocity from propellant is: <math>v = 700 \frac{l_p}{l} s V_s^{0.03} \approx 695 \frac{l_p}{l} s l_s^{0.03} d^{0.06}</math> <math>s</math> is the speed coefficient, defined below. Projectiles inherit the velocity of the cannon they are fired from, and this affects all velocity-dependent characteristics, namely AP and kinetic damage. Once in flight, projectiles are affected by gravity and drag in water (but not air). However, this does not change AP or kinetic damage. ==== Railguns ==== For a charge expenditure of <math>q</math> and <math>n_r</math> railgun casings, the muzzle velocity is increased by <math>v_r = \frac{8^{0.5} q^{0.5}}{n_s^{0.25} \left(5d\right)^{0.75}} s \approx 0.8459 \frac{q^{0.5}}{n_s^{0.25} d^{0.75}} s </math> Railgun casings increase this by a factor <math>\left(1 + 5 \left(1 - 0.9^{n_r} \right)\right)</math> ==== Speed Coefficient ==== A factor in muzzle velocity is the speed coefficient, which is a weighted average of the speed modifiers <math>s_i</math> of the (non-casing) parts, where each component <math>i</math> starting at the head has half the weight of the previous: <math>s = \frac{\sum 0.75^i s_i}{\sum 0.75^i}</math> The head will thus always determine at least 25% of the speed coefficient. For example, suppose the shell has a Composite Head (speed modifier 1.6), a Solid Warhead Body (speed modifier 1.3), and a Supercavitation Base (speed modifier 0.9). Then we have <math>s_0 = 1.6</math> <math>s_1 = 1.3</math> <math>s_2 = 0.9</math> <math>s = \frac{0.75^0 \cdot 1.6 + 0.75^1 \cdot 1.3 + 0.75^2 \cdot 0.9}{0.75^0 + 0.75^1 + 0.75^2} \approx 1.33</math> (Since 2.3.3.1 s=s1+(0.10248*(summ(s)-s1))/(ns-1) ==== Propellant Burn ==== The length of barrel needed for optimal propellant burn is <math>\ell_{bp} = 16 n_p d</math> If the barrel is too short, muzzle velocity will be reduced proportionally. === Effective Time === The time a shell will travel before suffering drag is <math>10 s n_s</math>
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