Rewriting the Propulsion Equation in this form gives a useful insight: ship propulsion performance tends to improve as ship size increases. In practice, if V and R are fixed as design criteria by the player, this means that the propulsion fraction decreases slowly as the ship size increases. In terms of ship design, this means that larger ships can dedicate a larger fraction of their mass to mission payload e.g. weapons, hangars, sensor suites, etc.
Why is that exactly? Only if you increase the ship mass in relation to it's number of engines, meaning having larger and more efficient engines on a ship instead of more small ones? Or is there something else making larger ships more efficient irrespective of size/number of engines?
Because a larger engine is more efficient than a smaller engine with the same EP modifier, purely due to increased efficiency from engine size (see Eq. 6c). Because of this, you would get more range out of the same amount of fuel (assuming 3:1 ratio). If you do not need so much range, it becomes possible to use a smaller engine with a larger boost modifier to get the same speed while bringing the range back down to the desired value.
For example: suppose I want to have 5,000-ton frigate and 10,000-ton cruiser designs for a INPE fleet with speed 4000 km/s and range 20 billion km, using two engines per ship for redundancy in case of battle damage. For the frigate, this can be accomplished using two size-16.8 HS engines with a 1.20x EP modifier along with 10.84 HS of fuel, so the total propulsion size is 44.44 HS. For the cruiser, using the same relative proportion would give me two size-33.6 engines and 21.68 HS of fuel for a propulsion size of 88.88, however this would have a range of 28.3 billion km which is much more than we need. Instead, we can push the EP modifier up to 1.30x and build size-31 HS engines along with only 19.46 HS of fuel - a total propulsion size of only 81.46 HS. That gives an extra 373 tons (3.7% of total mass) for weapons, armor, shields, etc. while giving the same speed and range as the smaller frigate.
To sum up: because larger engines are more fuel-efficient, you can get the same performance as a smaller engine using a higher EP modifier and lower mass fraction. It's a bit unintuitive but it works.
In either case, the application of that knowledge for warships will likely remain limited as restraining engine size has benefits in HTK and maintenance.
Certainly this gets into the questions of fleet doctrine which are beyond the scope of my post. However, it is worth noting that the benefits in HTK and maintenance are offset at least in part by the ability to mount extra weapons, armor, etc. not to mention fuel use as you mentioned later.
I'd also like to explore the limits of the usage of the the 3:1 fuel ratio from a practical standpoint. As this is a very theoretical approach it does not factor in fuel as a limited resource, which may cause somebody to want to include less fuel than the ratio suggests. For instance in freighters using such ratios would be absurd.
If an empire finds itself generally low on fuel/with bad access to it and therfore prefers ships with higher efficiency, how does the situation change when you set a specific fuel amount (or an amount per tonnage) as a design parameter?
It's actually not hard to modify the Propulsion Equation to use a fixed engine:fuel ratio. If we let, say, G be the engine:fuel ratio so that G*Mf=Ne*Me, then the Propulsion Equation becomes:
If we increase engine-to-fuel ratio G, the result is a larger engine is needed to achieve the same performance (and per Eq. 4c it will have a lower EP modifier). The consequence of course is that your overall propulsion size will be larger, thus your warship may be more fuel-efficient but also less capable in combat. This again gets into the realm of doctrinal choice which is more art than science.
With regards to freighters and other commercial ships, this is indeed absurd and I would not suggest using this method to design those ships. The "optimal" design for a freighter engine would usually end up requiring an EP modifier greater than 0.5 which is not even possible on a commercial ship, and I mentioned as much in my OP.
There's another factor that may be worth looking at: fuel time. How long does a tank last? Assuming that you always want to have at least as much deployment time on a ship as it takes to run the tank dry (eventually plus some certain percentage of that or a fixed amount of time), does a given propulsion configuration reduce it's own efficiency by requiring a larger deployment time, meaning more crew? I'm imagining this may be an interesting thing to know for designing survey ships and serve as a reason to reduce deployment times and increase the boost factor.
In theory, yes. However, the deployment time usually accounts for more than just the fuel endurance time as it also counts time when the ship is not moving while doing its job. A survey ship for example splits time between moving around and sitting still running surveys - thus the optimal deployment time depends on how long it takes to survey a body or location as well as on the average distance between those bodies or locations. Similarly, a warship fleet may spend large parts of its deployment time "on station" away from maintenance facilities, not moving and thus not using fuel but still running up the deployment clock. Thus once again deployment time becomes more of an art than a science. Personally, I try to choose deployment times so that my ships come back to the overhaul docks having just ticked past their clocks, since I'd rather deal with tired crewmen than a ship dead in space due to no fuel.
A question: The crew requirement of engines is proportional to the increase in engine power in an engine, right? There is no reason to say many small, heavily boosted engines require a significantly larger amount of crew than fewer, slightly more efficient and therefore less boosted engines?
This is true. While in my OP I expressed it in terms of base quantities, conceptually the crew requirement is proportional to the EP divided by your drive tech (EP per HS), which essentially means your crew quarters requirement is determined only by your design speed. Because of that, it is perfectly reasonable to
not consider the crew requirement as part of the propulsion mass, and in fact I do not do this when I design my own engines. Ultimately it is a philosophical distinction; either approach is equally "optimal", it's all a question of bookkeeping.
Some impressive math! My ship design bureaus are currently hiring :-)
My people will be in touch with your people.
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