I wanted to work out a theory of naval battles, partly to understand what is possible and partly to guide some decision making. To do this, various approximations need to be made.
- I'm going to ignore stochastic variability in hit location since warship structure generally forms a good safety and warship often have enough armor so individual hits do not destroy armor.
- I'm going to ignore discrete arc effects because in continuous space (as opposed to discrete hexes) you can always adjust orientation slightly so they do not occur. For example, let's assume that a warship that cares can always put an opponent into the fore-side, aft-side, and broad-side arcs simultaneously.
- I'm ignoring simultaneity of fire. Obviously, a unit with zero hit points but massive weapons can cause some damage but in most large scale engagements such a unit is destroyed after the first minute as a priority target.
Conversely, I'm going to consider other more continous rules like variable thresholds and individual weapon ranges. With variable thresholds, ~4 critical hit chances occur before armor is stripped from a location. Against the side arc, this usually does nothing significant to elements not in the side arc, but against the nose arc CIC, Sensors, or Crew critical hits typically make further weapons fire infeasible once armor is stripped.
Missiles, ASF, and other parasite ships are a special case that I'm not handling here (maybe at a later date).
Given the above, I see 4 primary situations that a unit can be in. Any individual battle may involve a mixture of these situations, but it's helpful to understand the situations and the strengths of units in these situations.
Execution: One side can attack when another cannot. An execution is a possibility when one side has a speed advantage, a range advantage, sufficiently good gunnery skill, and room to maneuver. Examples are of the form Warship+HNPPC vs. Jumpship or Warship+HNPPC vs. slower dropships. It's important to note that range+speed is necessary but not sufficient for an execution. For example, if a warship is deployed to protect a yard even a slow opponent can force it into a battle of another type. The duration of an execution is highly variable dependent on the scope of the range advantage. For example if the range advantage is only at extreme (+6) and the target evades (+2) while presenting a side aspect (+2) only elite naval gunners (base 2) would be able to hit, and even then only once every half hour factoring in uncertainty due to position (~= initiative) and this could easily double to an hour. On the other hand, a warship could pass near or through a constellation of jumpships and destroy them all in a minute. We haven't seen any battles of this sort yet.
Execution designs favor high speed and range above all else and marginally prefer to place weapons in the aft side arcs so they can maneuver and fire through the side arcs while keeping the range.
Low Intensity: A low intensity battle allows warships to take advantage of rolling sides. A low intensity battle is possible when there is range parity but the faster side maintains sufficient range so incoming damage/minute is low enough to respond with damage-mitigation strategies. Low intensity battles are either at long or extreme range since incoming damage is by definition occurring at a low rate. An asymmetry in gunnery skill can make a large difference in a low intensity battle. Low intensity battles eventually become infeasible as fleet sizes grow since ships can focus fire. This threshold is high though---essentially the question is: if you divide firepower by a factor of 36 can you outright kill an opposing fleet's ship? The divisor here may be even more extreme if a side has mixed gunnery skills.
A warship essentially has 3 combat sides: Left, Right, and Nose. The Left/Right sides include Fore/Aft armor and Fore/Aft/Broad weapons. The Nose side include Fore-side and Nose armor and weapons arcs, but only one fore-side weapon arc can be used in conjunction with the nose weapon arc against a single target. In a low intensity battle you always want to use the Left and Right sides before the Nose since Nose critical hits make further targeting impossible. The side aspect actually biases damage aft so effective use of low intensity typically results in the loss of all armor on the aft sides before rolling to the Nose side where nose armor and the remaining fore side armor is stripped. After that, the ship is incapable of battle but able to flee further combat if it is the faster ship. Low intensity designs favor a balance of weapons across side and nose arcs with sufficient speed to control the range and long or extreme range weapons.
High Intensity: High intensity occurs when a combatant is capable of controlling the side presented to the enemy but the enemy can destroy ships through focused fire before damage mitigation measures can be used. Most warships can control their facing in most situations while space stations and jumpships often cannot. Side choice is easier to control as the range increases. The parity point is at range/2=attacker_thrust/defender_thrust so at range 49 thrust 5 suffices to exceed the attitude control of a space station while at range 51 it does not. Ships can decide to present either the Right, Left, or Nose side as per low intensity combat, but they cannot use unpresented sides---instead they either survive fine or are destroyed outright. Most of the battles we've seen so far are examples of high intensity combat.
High intensity combat could be done with either a broadside approach or a nose approach. A nose approach creates concentration of fire and armor but cannot really benefit from structure due to nose critical hits creating a mission kill about when nose armor is removed. A broadside approach can effectively use structure to substantially improve damage capacity as broadside critical hits are rarely destabilizing. A broadside approach also imposes a to-hit penalty over a nose approach.
Backstab: An opponent can choose the side to attack against. This usually occurs with Jumpships and Space Stations although it could occur for a surprised warship in a high speed engagement. Fleet level tactics can partially mitigate the downside of a backstab. For example, 3 space stations which only fire in one arc can arrange themselves to effectively return fire in any arc. Hence, the worst case backstab fire is effectively the average of all facings while the weakest armor facing (typically aft) is presented to the enemy. Backstab avoidance designs favors uniform fire control and armor and are typically used on slow units.
Measurement: We would like a single number which allow us to estimate the outcome of any of the above forms of combat for a naval unit.
The measurement in an execution situation is based on range and speed with dominance in both being required. Together with situational tactical concerns this determines feasibility and time requirements.
The measurement in a high intensity situation assumes damage sufficient to strip fore side and aft side + 2*structure is inflicted on the sides resulting in destruction. Alternatively, damage sufficient to strip the nose armor results in a mission kill as the naval vessel will no longer be able to fire with accuracy. We use the max(sqrt(E side damage * side capital damage), sqrt(E nose damage * nose capital damage)). The square root here produces the "right" scaling so that double firepower+double armor = double value.
The measurement in a low intensity situation treats the vessel as (nearly) 3 different vessels, computing sqrt(expected {nose,side} armor * long or more {nose,side} capital damage) and then adding them up. In practice, we expect damage to hit the structure before rolling sides, but using "no armor left on aft side" as the signal to switch sides leaves a reasonable margin for avoiding accidental early destruction and a reasonable chance that fore-side weapons will remain intact for use in a nose attack.
A backstab situation is similar to high intensity but uses sqrt(average(aft,nose,side) fire * aft armor) since in a fleet situation you can disperse facings to overcome lack of facing control. Aft critical hits are debilitating through engine and thruster damage which rapidly leave a unit unable to move.
Anyways, I calculated these numbers for units in the local neighborhood of the TC just to see what the result is:
| Rapid Ventilation | Wind Spirit | Wife's Wrath | Albion | Galahad | Robinson | Crucis | Kentares IV | Northumberland | Barghest | Padfoot | Pratham | Raksha | Nova | Taurus I | Matador | Siesta | Marathon |
| Max Range | 52 | 52 | 52 | 42 | 42 | 42 | 42 | 52 | 52 | 52 | 52 | 52 | 44 | 52 | 52 | 52 | 52 | 52 |
| Max Speed | 6 | 7.5 | 4.5 | 7.5 | 6 | 6 | 4.5 | 7.5 | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 | 1 | 1 | 9 | 0.2 | 0.2 |
| Low | 411 | 413 | 555 | 317 | 504 | 181 | 851 | 195 | 467 | 36 | 72 | 278 | 333 | 195 | 80 | 78 | 68 | 175 |
| High | 539 | 184 | 325 | 154 | 474 | 188 | 601 | 94 | 173 | 37 | 74 | 104 | 124 | 203 | 84 | 67 | 26 | 181 |
| Backstab | 274 | 131 | 135 | 84 | 256 | 84 | 297 | 74 | 133 | 13 | 25 | 88 | 106 | 92 | 38 | 28 | 22 | 127 |
The executioner designs {Wind Spirit, Kentares IV, Matador} have range 52 and speed either 7.5 or 9.
The low intensity designs {Wife's Wrath, Albion, Galahad, Crucis} favor carefully metered out trading of damage.
The high intensity designs (Rapid Ventilation, Robinson, Nova} favor super destructive combat.
The Crucis in particular scores well in both low and high intensity combat although range suffers as a NAC boat.
Obviously there are limitations due to neglecting missiles and parasite ships, but other than that I'm curious if anyone sees serious flaws or gaps?
