For missiles I guess this can get sort of useful. But in practical terms I think we mostly pick whatever the highest multiplier there is and then slap on fuel to give it a desired range, the rest goes into warhead and agility depending on the need. Of course using more than half the engine size in fuel will not be optimal. But I think that many missile designs use much less fuel than what is optimal in favour of high speed (or bigger yield) since high speed means the missile is more likely to hit something and evade enemy AMM/PD. It obviously depend on what maximum multiplier you have, but we can't just assume that every missile design uses very high multipliers.
I'm well aware of this, and as I said earlier, we've been over this before. The fact that a piece of math is not useful in all cases does not mean we shouldn't share it.
An optimised missile design would in this case be 50% engine, 25% fuel and 25% warhead. But I often find this to make missiles with too much range at lower multipliers, such as x4 or something for that technology level and thus either increasing the size of the warhead or engine is preferable over that much fuel. At x5-6 multiplier then 25% fuel might be a good choice.
Umm, that's not the optimum. The optimum is to have fuel equal to 31% of the engine. A Fuel/Engine ratio of .5 is always too high, unless you've bottomed out your power multiple.
Perhaps the best way to state the optimum missile engine rule is as follows:
The missile's fuel should always be as close as possible to 31% of the engine size, unless you are operating at either the maximum (lower percentage) or minimum (higher percentage) values for the power multiplier. This will always give you the best possible combination of speed and range.
This is a fact, and takes your objections into account. The only other marginal case to mention is when multiple missile engines are involved. That's rare, but it does happen. For example, two size 3 engines would have .9x the fuel consumption of a single size 5 engine of the same power. If the optimum is technically a size 6 (fuel is 1.86 in that case), the size 5 will have 38% more range.
As en example with ION tech engines and maximum x4 multiplier and a size four missile and 0.7 fuel efficiency a missile with 50% engine, 25% fuel would have 24000km/s speed and a range of slightly over 200 million km. I think that such a range might many times be a little too much, it does not have to be but it depends on the size and quality of fire-controls and other sensor systems in use.
Actually, this is an instructive case of how optimization can help. An actual optimum missile would have 57% engine, 18% fuel, and 25% warhead. There are three ways that the engine can be optimized, and I will illustrate all three of them. (I did this numerically, not experimentally, so I had to assume perfect scaling of the power multiplier. Implementing this will give slightly different values due to granularity. Also, I assumed starting range was exactly 200 mkm, so there will be some error there.)
1. Keep the power multiplier at x4. Range will drop to 157.5 mkm, but speed will increase to 27630 km/s.
2. Keep speed at 24000 km/s. Range will increase by 9.3%, to 218.5 mkm.
3. Keep range at 200 mkm. Speed will increase by 3.6%, to 24865 km/s.
While the last two may not look like much, consider that you've gotten (in the case of #2) over half the benefit of the next tech level at no additional missile cost. When you do this when you first build the missile, it can help a lot.