i spend too much non-recreational time staring at a screen these days to try to parse through the formulae you posted, even though that is the kind of thing that generally appeals to me.  i suspect the optimization criterion i mooted doesn't admit a closed analytical form.

you're absolutely right about cost not being squared; i merged a condition from another type of game into the idea i was trying to express (where speed is essentially fixed, as in aurora's forerunner starfire, you want to optimize offense*defense/cost^2 so as to not want to duct tape two small ships together in order to improve them).

as well, using "mission tonnage" was not just vague but misleading.  it's value of the mission package, not the tonnage.  generally to simplify analysis i will design a ship, and look at only the hull, engineering, quarters, and propulsion in terms of "cost per (free tonnage*kkps)" and then hash out the mission package in a subsequent step.

obviously im putting forward a plan that is highly sensitive to subjective inputs.
 what can i say?  the entire field of finance operates the same way.  the alternative is "a solution that is neat, simple, and wrong."

mission tonnage times speed / (weighted cost)^2 is the way to go imo

msrp beeps don't really cut it as a measure of cost; corbomite is a whole lot less valuable than gallicite.  if you're such a horrible penny-pincher that you are generally zero slack in your build capacity some overhead needs to be applied too- which can *really* change your optimum!  of course, if you're NOT constrained by capacity forget about optimizing your ships, you've got bigger inefficiencies to worry about.

For the upcoming C# version, we can incorporate fuel efficiency by engine size since that now scales consistently. The first graph (and performance-optimal fuel-to-engine ratio of 2:5) still stands if size of an individual engine remains fixed; if the number of engines remains fixed we get

(((x(1-x)^2.5)/(10/(1-x)^0.5))^0.4)/(72804525*(1.5)^0.2/487671196)

with a performance-optimal ratio of 1:3; this also applies to missiles.

I have some questions about ~10,000 ton parasite craft with boosted engines:

It seems to me that operating large craft with boosted engines runs the risk of golden BBs blowing the engines up, with secondary explosions potentially taking out the whole ship.

With fighters and LACs, that isn't as much of a concern, since any destroyed system is likely to be a mission kill, but losing a 10,000 ton craft because of a lucky meson hit would cause some questions for the design staff, I would think.

Having used boosted pocket battleships, or parasite battleships or whatever you call them, how often do you lose them to engine explosions?

Yes I agree with the math and the principle that bigger more fuel efficient engines is generally cheaper and better from a cost perspective. Compact engines with a high power setting is only useful in short ranged ships. I think this should be common sense.

I often use power settings lower than one for reducing the fuel costs and increase the range of the ships with less space for fuel.

Although when doing your overall calculations you need to include the size the engine and fuel take up since the engine increase in size more than fuel due to maintenance and crew requirements.

One point on the ships above, they do severly lack in maintenance facilities, not that it is important for this comparison though. In general you need at least twice the amount of MSP (military ships) on ships than the most expensive component, one reason I stay away from big engines in the early game not withstanding research cost.

Also, overall fuel efficency of engines change the ratio of engine and fuel. If you have an overall fuel efficency of 50% the ratio of engine to fuel change accordingly for any given range. So as fuel efficency get better and your range requirement stay mostly the same these constraint with engine versus fuel ratio get less and less of an issue.

What I mean to say is that the engine to fuel weight are mainly important on really fast ships where you also want relatively long range. I think that those restrictions are probably not that common in general ship design.

I do however think it is very informative to explain that if you want to give ships exceptional range requirements you need to consider more fuel efficient engines when fuel exceeded a certain weight ratio of the ships engines, anything else is a waste of resources.

In basic terms it comes down to what resources you are willing to make a sacrifice on; build cost, range, fuel consumption, research cost, speed, mission tonnage, uppgrade/refitt issues and so on.

If we take Magneto Plasma tech as an example my military ships would likely have speeds varying from 2500-5000 km/s depending on role in the fleet. I would deem 4000km/s as a fast ship the likes of a Destroyer. Engines would range from 1.25 down to perhaps 0.75 in power efficiency depending on my needs, fuel consumption is allways an important issue, especially when you have lots of fighters and other parasite ships that have extreme fuel usage during operations.

I also invest as much research into fuel efficiency as I can, that is generally more efficient the first four or five engine generations than building big research costly engines. In principal my ship engines up until Magneto Plasma are size five, just don't like size one engines on real ships, not a rational thing though..

In general I have no problem sacrificing speed for fuel efficiency, mission tonnage capacity and retrofit expediency on some types of military ships, generally the really big ships such as carriers. Ships wich are not suppose to be even remotely close with the enemy, or in ships that need both mission space and range, such as long range cruisers who operate alone or in small packs far from friendly bases. I often also try to target ships to a certain fuel efficiency, lower and it is OK with a more powerful engine and either I get more speed or more mission tonnage but also need extra fuel, but no point if it does not give me anything in return. The list goes on and on about what sacrifices I need to do in every design.

Engine to fuel efficency IS an important part of this process. It is certainly good to know when your designs start to waste resources.

That was why I asked for some practical example ships to see when this is actually super relevant...

I looked at a game I had played for a short while with magneto plasma drives and an overall fuel efficiency of 0.7. I had a standard engine for fast ships at x1 power with a 0.63 fuel efficiency.

One ship I just quickly glanced at was a fast armored invasion ship (troop transport), 10000t and 4000km/s speed, same speed as my 12000t destroyers.

The ship had my standard 20 billion km range which is the standard range for a destroyer type military ship. 18 month deployment and 2.5 years on the maintenance cycle.

The engine made up 25% of the size of the ship but adding crew, maintenance and armor the engine displaced about 29% of the ship total size. The fuel was 5% but with maintenance and armor (no crew) it displaced 5.35%.

My larger ships and such as cruisers and carriers usually use 0.8 to 0.9 multiplier on the engine. This decrease research and fuel cost considerably and the engines are usually a bit bigger to reduce fuel consumption even more. I rarely research 50HS engines until later in the game when such engines are cheap in comparison with fuel efficiency technologies.

Another thing, in most of my military designs from destroyer and up they all have hangars and recon or strike crafts of some kind, this also mean I need extra large fuel reserves for those crafts... fuel I can use for traveling further if I have to. This also put a huge kink into the engine versus fuel ratio relationship a ship might need.

If I replace the above engine with a 0.9 efficient engine the speed dropped to 3600km/s and fuel efficiency was 0.48 instead of 0.63. With everything else the same I could add an additional 200t of mission tonnage.

I really appreciate your dedication to engine versus fuel efficiency. But when do you actually have engine to fuel ratio as the primary objective of any ship design?

I find that design constraints are rather what speed and range I desire in contrast with other things that never make me able to produce a ship with a ratio of engine to fuel efficiency for range. Different ships with the same engine might have different constraint on their design concept.

I usually just have a operational range as one parameter and engine size as another, they rarely coincide with each other very well. The rest is just a measure of how much speed I will sacrifice for fuel efficiency. One engine might also often be used in multiple ship types and sizes and make up different weight ratios in different ships.

In general smaller ships tend to have more powerful engines and larger ships less powerfully engines for fuel efficiency. Mainly to reduce the necessary logistical and infrastructure investment in fuel production as well as upgrading, retrofitting and maintenance of my ships. It is a fairly straightforward process to calculate the optimal fuel to engine ratio for best range, but that seem rarely to be important when designing the concept of your fleet objectives.

But I might just be wrong and missing the overall picture. Some practical examples would be nice...

You should move to less than 2/7 fuel, and constant range is assumed.
For ships that aren't meant to refuel others, you can ignore anything to the right of 2/7, as that'd use more fuel while being slower.

Performance-optimal would be ~0.286, or 40% of engine tonnage, for 100% of achievable speed and 100% fuel we can use without wasting any.
At  0.2, or 25% of engine tonnage, we achieve 97% of our maximum speed but only use 0.2/(2/7)=70% as much fuel.
At ~0.167, or 20% of engine tonnage, we achieve 94% of our maximum speed using (1/6)/(2/7)=58% as much fuel.
At ~0.091, or 10% of engine tonnage, we achieve about 80% of our maximum speed using (1/11)/(2/7)=32% as much fuel.
At ~0.048, or  5% of engine tonnage, we achieve about 65% of our maximum speed using (1/21)/(2/7)=17% as much fuel.
At ~0.010, or  1% of engine tonnage, we achieve about 36% of our maximum speed using (1/101)/(2/7)= 3% as much fuel.

Wow, the 94% speed for 58% as much fuel is very dramatic. It looks like 1:4 is a pretty good balance for most uses. Very helpful. Thanks for explaining this Iranon.