2) Upgradability: Engines are effectively shared between tractored ships. Engine technology has a significant impact on their performance. Because speed is important, new-generation ships will often be faster than older ones, i. e. players mostly use newer engine designs to receive a boost in speed, rather than freeing up space for more weapon platforms/armour/etc. while retaining the old speed. The net effect is that older ships can not form a battle line with modern ships and have to be in separate group (unless one sacrifices many of the speed advantages of the modern ships). Therefore old engines are a serious drawback of old ships. Engines are also a big and expensive part of most ship designs, which often makes replacing old engines on old ships more expensive than building a new ship altogether.
At the same time most other things do age a bit better. A new-generation missile launcher might fire missile salvos more quickly, but that does not render the old launcher obsolete. It can still fire new model missiles, unless the size is increased. Fire controls and sensors do get better, but this is often used to save size, so that one is able to fit more things into a new ship. Given the old ship is already there, its old launchers etc. usually still provide a valuable addition to any fight – provided it could be used in the fight along with the newer ships. Many other things do not loose much or any effectiveness at all - engineer compartments, damage control, fuel space, crew quarters… It is thus somewhat wasteful to scrap these elements – if only they could be propelled to the speed of the newer ships.
So the obvious suggestion is to split ships into 2 modules: A “
Propulsion-Module” containing engines, some engineering and fuels spaces plus crew quarters, and a “
Superstructure-Module” (or however you want to call it) which contains the tractor beam, weapon stations, magazines, fire controls, sensors, etc. The superstructure-module could be retained, while the propulsion-module would be scrapped and replaced by a version using newer engines, when these become available.
The benefit is the ability to keep old ships operational at low costs. Let us assume players use a fixed proportion of their (mobile) capital combat ships’ hull space for engines, e. g. all ships are 25% engines (*1). Say we use a propulsion module of, say, 30% size (to account for fuel, crew, engineers), of a new ship. When modernizing, the old engines will yield some scrap value for the old engines (30% IIRC). Assuming the old engines had cost 20% less than the old ones, we gain the new engines for 1-0. 8*0. 3~75% percent of their actual cost. Approximating weight with costs, we can
modernize a ship in this way for 75%*30%=23% of the cost of a new ship.
After some tedious calculations I would estimate, that the “superstructure” should likely be upgraded every two to three generations as well. Yet there is a rather large number of factors influencing this and actually I am not too sure I used a sensible estimate for each. Still lets assume that the superstructure is updated every three generations, rotating, such that at each time 1/3 of the superstructures are 1st generation, 2nd generation and 3rd generation respectively.
Thus what would happen is that when a new tech generation is researched: 1) all propulsion modules are scrapped and rebuild 2) 1/3 of the superstructures are scrapped and rebuild. The first costs 23% of a new ship, while the later costs 70% (superstructure size) * (1 – 0. 3*0. 8^3 (scrap value of the old superstructure)) *1/3 (number of refits) = 20%. So overall in order to keep this fleet at that level we would require 43% of the costs of building a the same number of new ships. Scrapping and rebuilding an integrate ship of this size would have cost 1-0. 3*0. 8=75% of the costs of an entirely new ship. Put differently, in the long run the modular design allows us to have 1. 7 times as much ships, as we would have if we would scrapped and rebuild our ships every “round” of technology.
However these ships would be different. On the one hand brand new ships would all be of the latest weapon technology, while only 1/3 of the modular ones have the latest weapons, with the other 2/3 being outdated to some degree. Lets assume that each level adds about 10% to the damage dealt on the enemy. Thus the next-to-latest superstructures would deal about 91% (=1/1. 1) of the damage of the latest tech, while the 2-generation-outdates ones would deal 83% (=1/1. 1^2) of the damage of the latest tech, Or on average they would deal 91% of the damage of an equivalent number of the latest ships.
Furthermore, the modular design has some o
verhead costs compared to an “integrated” design. Notably one of the modules need to carry a tractor beam (most likely the superstructure, so to avoid rebuilding it for every new generation); both of the modules likely need a bridge; in order to achieve the same level of protection more armour must be used; shields need to be duplicated. Ignoring shields, because they might not be present at all, we can determine how much “dead” weight the modularity adds:
-The
tractor beam weighs 500t.
-The
bridge adds another 50t.
-For the
armor it is slightly more complicated. The weight needed for armour is proportional to the desired armor thickness and the “surface area” of a vessel, which are assumed to be spherical. The volume (and thus weight) of a sphere goes like V~r^3 (r=radius), while the surface are goes like A~r^2. So the surface area is proportional to A~s^(2/3) (where s is the size). Thus 2 small vessels of size 1 will have 26% more surface area than one vessel of size 2 (2*1^(2/3)-2^(2/3)=2^(1/3)=1. 26). For a 30% propulsion system- 70% superstructure split this would mean an increase in the increase in surface area is 24% compared to a big ship. If one wants to retain the same armour thickness for both modules in a modular design, then this means the weight of armour will increase by 24%. Yet it should be kept in mind that the increase in surface area is not purely a bad thing, as it also influences the probability of enemy shots hitting the same spot more than once. I haven’t yet found a nice way to quantify the value of a broader armour versus a deeper armour, but I feel the later is vastly more important, hence I will ignore that there is also a benefit here. Also it is conceivable that the two modules could be armoured differently, i. e. it could be recognized that the destruction of a superstructure module is more valuable to the enemy (because the superstructure could fight without the propulsion at reduced efficiency, but the propulsion itself can not fight at all). Therefore the superstructure should be armoured more than the engine, up to the point where the enemy is indifferent between targeting either. There is a difficulty in that heat-seeking missiles could target the engines more effectively, while radar-seeking or fire controlled missiles would be more easy to fire at the larger superstructure. We are going to ignore this benefit that the additional diversification brings, because on the other hand the two modules can not share their damage control teams or potential shields, so this might chancel somewhat.
The absolute effect for the last point (+24% in armour mass) depends on the armour that is being used in a ship, so as a totally unrepresentative example I took my 18kt Heavy Cruiser with 3 layers of composite armour, totalling around 11% of the ships mass - roughly 2kt. If I would split this into a 30%-70% modular design with the same 3 layers of armour on each, this would necessitate 24%*2,000t=500t more in weight. Together with the tractor beam we would have a total weight of 1000t that represents the “cost” for modularity. On a 18kt Cruiser this is of course quite significant. I could skim this weight of the ship by removing 4 of the 20 missile launchers, netting a drop in my broadside weight of 20% (just an approximation, ultimately it is unlikely that I would do this, the weight reduction would likely come from many sources, maybe 1-2 launchers, bits of this and that, until the marginal benefit of all component matches). For now let us assume that this nets a 20% reduction in the ability to deal damage on the enemy.
Now we can try to piece this information together. We compared two scenarios: 1) the
benchmark scenario in which every generation ships were entirely scrapped and rebuild to the latest standard and 2) a
modular design, where we separated engines and superstructures. In this scenario we replaced the engines in every generation, while only 1/3 of the superstructures were replaced every weapon generation, because weapons age better than engines do in Aurora. This allowed us to operate 1. 7 times as many ships than in scenario 1. The modular design ships were on average a bit older and thus could only deal 91% of the damage of a contemporaneous design. They could also carry 80% less main weapons as the tractor beams and lower armour efficiency took away space. In total they can thus only deal 73% (=0. 91*0.
as much damage.
Finally converting these numbers into a measure that captures the ability to win battles, lets call it “Battle Winning Ability”. Ships are both targets and shooters, so we will use the Lanchester laws(*3) and calculate BWA=N^2*Damage_dealt. The Standard (integrated) design has a BWA=1 (we normalized it this way), while the modular design has a BWA=1. 7^2*0. 73=2. 31.
In other words the modular design offers a more than twice as much higher ability to win battles.
This is derived under a large set of assumptions, maybe the most important being the ship size of 18kt. For ships of 3kt the 500t-tractor beam would present a much higher proportion of the ships weight and consequently reduce the amount of weapon space more significantly.
Still that is quite a result - Bravo, Blue Emu!
As a side issue: Modular design also reduces the capital and worker requirement for shipyards. Take a 10kt ship, which could either be built integrated, requiring a 10kt shipyard. It would be produced at a rate of 1 +0. 5*(10kt/5kt-1)=1. 5 the racial build-rate. It would thus take 10/1. 5=6. 7 generic time units. In comparison a 30%-70% modular design could be build using two shipyards, one of 7kt and one of 3kt. The 7k module would be built a speed of 1+0. 5(7/5-1)=1. 2, and take a time of 7/1. 2=5. 8 generic time units. The 3k module would be build at 0. 8 and take 3. 75 generic time units. Thus using 3 7k slipways and 2 3k slipways will generate 3 new module-ships every 5. 8 generic time units. In the same time 3 10k slipways could “only” create 2. 6 integrated ships. So modular design uses less shipyard capacity (27k of slip yards in total, instead of 30k) and still produces ships faster (3 instead of 2. 6 ships).
This also applies to the shipyard-level. To build ship+afterburner one needs two shipyards - one with size x (the size of the ship) and one at size 1000t -, while to build the bigger ship with 2 more engines, one would need a single shipyard of size (x+500t).
(*1): This might be a crude assumption, and would only constitute an optimal strategy if the marginal utility of speed is hyperbolic, or, equivalently, that the utility of speed follows a logarithmic function(*2). This is likely incorrect, but I have not been able to come up with a better approximation for the (marginal) utility of all factors yet.
(2*): This can be derived by realizing that a fleet should be built such that the marginal utility of all possible investments is equal, i. e. adding/subtracting 100t of armor (if possible) has the same use as adding/subtracting 100t of weapons, engineering compartments or any other possible (and used) ship component. If this was not the case then a better ship could be designed by adding one type of components at the expense of others. Let du/dh_e be the marginal utility with respect to engine hull space, du/dh_w be the marginal utility with respect to weapon platform hulls pace (the “d” means a derivate, so that da/db is the derivate of a with respect to b). Since all marginal utilities must be the same we know that du/dh_w = du/dh_e. We can also write du/dh_w = dv/dh_e * du/dv (i. e. use a chain rule), where v is the speed. This means we can rewrite the marginal utility with respect to engine hull space as the product of the marginal utility with respect to speed times the increase in speed that an increase in hull space offers. And now comes the trick: If we assume an increase in engine technology, the marginal utility of a missile launcher does not change, so du/dh_w is a constant. The marginal use of engine-space was equal to this constant before the new engine tech came around, and it must be equal to this constant afterwards, as otherwise we would use a different proportion of space for engines. Thus we know that the marginal utility of engine-space before and after the tech change is equal: du/dh_{e,before}= du/dh_{e,after}. Or, using the identity form above: dv/dh_{e,before} * du/dv_{before} = dv/dh_{e,after} * du/dv_{after}. A new engine tech means the speed gained for adding engines becomes larger, say by a factor x, so: dv/dh_{e,after}= x* dv/dh_{e,before}. Furthermore we know that the speed is proportional to the power of the engine. We can rearrange and find that du/dv must be proportional to 1/v – i. e. a hyperbolic function. Integrating this expression yields the claimed logarithmic utility of speed. We can thus turn the argument backwards, and interfere that if the utility of speed is not logarithmic, it is not an optimal strategy to devote a fixed amount of hull space to engines for different technology levels.
One caveat: There might well be synergy effects. For instance with beam ships the marginal utility of adding another beam weapon might well depend on the speed that this ship achieves, so the change in engine technology could have a cross-impact.
(*3): The Lanchester laws might not be entirely justified here. Not only is each ship a “shooter”, and a “target”, every ship is also a “defender” in the form of point-defence weapons, adding a third dimension. (I am making the simplifying assumption that every ship is a miniature of the fleet, which makes it more convenient to calculate. It does not matter though if separate ships are used as PD-providers or offensive-launchers, as long as they move together). Thus I would expect a larger exponent than “2”. This would increase the usefulness of the modular design.