Engine optimization

[bean (OP)]

I made an interesting discovery yesterday, and fleshed it out today.  It turns out that, for a given range and a fixed amount of (engine + fuel) there is an optimum that gives the maximum speed.  It occurs when the fuel is .2857 of the total tonnage, and the engine is .7143.  The engine to fuel ratio is 2.5.  I can show how I did this if anyone's interested.
Note that this ignores the gains in fuel economy for a larger engine.  I'm still working out how to include those, particularly if multiple engines are involved.
For unitary missile engines the optimum fuel fraction is .2391 and the engine is .7609 with a ratio of 3.182.  All of this assumes that you can vary the engine power modifier infinitely, so they don't translate well to very high-speed missiles (or ships).  However, it should be of some help for building slower, longer-range weapons.

[bean (OP)]

I ran the numbers for range with speed held constant, and got the same optimum values.

[deoved]

Any further success in your calculations?

[bean (OP)]

Any further success in your calculations?

No, and I'm not sure it's possible to do a general solution for ship engines.  The problem is that the fuel economy WRT size is not described by a formula that I can make independent of reference points.  With the missiles, I could set an arbitrary point as 1, and do the whole thing as a relative range/speed.  With a ship, I'd need to actually set the size I'm working with.  Also, when multiple engines get involved, things get messy.  So the best thing to do for a ship is to go for somewhere around a 2.5 engine-fuel ratio, erring towards a higher ratio.

[Cocyte]

I'll just add my grain of salt...

I made similar computations for the best range solution for a fixed allocated propulsion size : it's around 40.58% engine / 59.41% fuel.
More precisely, it's 683/1683 for engine and 1000/1683 for fuel.
This solution may be convenient for designing special purpose long range drones and the carrier stages of multi-stage missiles.

Multi-engined missiles are a waste of efficiency - 10 size 0.1 engines are exactly the same as a single size 1 engine, excepted for the fuel consumption. As the research times are not that significant, it's better to always design the best sized engine for your new missile.

[bean (OP)]

I made similar computations for the best range solution for a fixed allocated propulsion size : it's around 40.58% engine / 59.41% fuel.
More precisely, it's 683/1683 for engine and 1000/1683 for fuel.

I presume this is for missiles with a fixed power level.  If so, it makes sense, although I haven't checked the math.  I'm just not sure how often it will come up.  Fixed-range situations seem more likely IMO, as things like fire control come into play.  This solution only matters when you need absolutely the longest possible range, and don't care about speed.

Multi-engined missiles are a waste of efficiency - 10 size 0.1 engines are exactly the same as a single size 1 engine, excepted for the fuel consumption. As the research times are not that significant, it's better to always design the best sized engine for your new missile.

Totally agree.  That comment was WRT full-size ships, which often have multiple engines for various reasons.

[Jorgen_CAB]

I seldom find it possible to use the optimum engine versus fuel ratio for practical purposes because I need to consider both speed, range and the payload of my missiles at the same time.

For anti-ship missiles as an example I want to give them a speed that equals me an approximate 80% chance to hit my main target, which in turn is depending on the targets ships maximum speed. After this the amount of fuel is depending on the range versus payload, armor and sensors I wish the missiles to have. It seems impossible to put the best ratio of fuel on missiles because there are to many factors involved.

The only time when the engine to fuel ratio is practical in my opinion are when I design a multistage missile or probe.

On ships it is even less practical to match the size of the engine and size of its fuel tanks. Especially since 6.0 when fuel has become a scarcity issue in a way it was not before. Thus you need to factor in fuel efficiency into the picture as well. You also do not want engines and fuel to take up too much space on your warships. It is in general most efficient to carry most of the fuel in Tankers than in your dedicated warships.

In general I give my dedicated warships (not long range scouts and cruisers) enough fuel on the ship for battle maneuvering, that means about 15-20 billion kilometer and no more. I usually put rather fuel hungry engines on my dedicated warships and provide them with tankers when conducting open warfare. Larger ships will get towed by tugs on longer and safer journeys while smaller warships are carried inside the hangar of Escort Carriers (equipped with low powered fuel efficient engines).

In some advanced fleet compositions I even had large fleet supply vessels that carried smaller very fast ships equipped with fuel tanks who could provide battle groups with fuel at a short notice over rather great distances without endangering my larger and slower fuel ships. So, even though I'm fully aware of whats the best engine to fuel ratio I rarely find it practical to use other than on some occasions.

[sloanjh]

Well said.

John

[bean (OP)]

For anti-ship missiles as an example I want to give them a speed that equals me an approximate 80% chance to hit my main target, which in turn is depending on the targets ships maximum speed. After this the amount of fuel is depending on the range versus payload, armor and sensors I wish the missiles to have. It seems impossible to put the best ratio of fuel on missiles because there are to many factors involved.

In this case, what I'd do is select all of your various other systems (agility, warhead, sensors, etc.) and the size and speed of the missile.  This then tells you the amount of space you have for propulsion.  Take this, and apply the ratio to find how much engine you should have.  Dial the power multiplier until desired power is reached.  Simple, and it gives you the best range for the amount of propulsion space available.  And this does work in all situations.

It doesn't work quite as well on ships, as things like research start to intrude.  I do admit that, and normally skip optimization for my ship designs.

[Jorgen_CAB]

The biggest problem is that you almost never have a high enough engine multiplier to get the proper speed with an engine that small on a missile. Never managed it so far. Most of the enemies that I face are of equal or better technology so my missiles would be way to slow to do any good, even with the engine multiplier cranked up to maximum. There also is a hard cap on what multiplier you can research.

So, for me, in practical terms it is almost never possible to use the optimal ratio of engine versus fuel for missiles.

To take a practical example from my current game...

Tech levels are
Warhead Strength per MSP 4
Missile Agility per MSP 20
Fuel Consumption per EPH 0.7
Max Missile engine multiplier 3.5

Barracuda class Medium Torpedo (Size 4)
Warhead: 4 (1 MSP)
Manoeuvre Rating: 11 (0.11 MSP)
Speed: 18200 km/s (2.6 MSP x3.5)
Range: 99.1m km (0.276 MSP fuel)
Thermal Sensor & Reactor 0.014 MSP

The speed of the target ships are around 2500 km/s or more, but I put 2500 km/s as my target (both me and the enemy are mostly using Nuclear Pulse engines). The above missile has a 73% chance to hit such a ship which is about 7% lower than what I want. My target range was 100m km. My ships are fragile (don't have adequate missile defences researched yet) and I need to be able to fire them before I'm detected and we have observed that the enemy uses an active sensor where I would stay outside it at that range.

I'm not saying that the engine to fuel ratio is a bad thing to use if you can. But in real life scenarios it is hard to practice it, that's all.

[bean (OP)]

The biggest problem is that you almost never have a high enough engine multiplier to get the proper speed with an engine that small on a missile. Never managed it so far. Most of the enemies that I face are of equal or better technology so my missiles would be way to slow to do any good, even with the engine multiplier cranked up to maximum. There also is a hard cap on what multiplier you can research.

...

I'm not saying that the engine to fuel ratio is a bad thing to use if you can. But in real life scenarios it is hard to practice it, that's all.

That was one of the original caveats.  It assumes an infinitely variable power multiplier, which is not the case in reality.  I have also departed from the ratio a number of times, generally to get faster missiles than it allows.

[Jorgen_CAB]

I might have missed the part where you mentioned that it assumed an infinite multiplier.

In general I don't like to over-engineering my missile designs and therefore I usually end up trying to hit both a range and speed at the same time.
So, even if I could build a missile with a Speed X and get a range Y, that range might just be more than I need even if I get most out of the amount of fuel I put into that space on the missile. I might rather put some more armour or bigger yield on the warhead and reduce the range to a "good enough" range. No need to have a 400m km range missile if 200m km does it equally well.

When designing MIRV missiles I generally go for the efficiency but on regular missiles it almost never come in to play.

[bean (OP)]

I might have missed the part where you mentioned that it assumed an infinite multiplier.

I assumed there was no limit on how much you could vary the multiplier (up to infinity or down to 0, if necessary).  It was necessary to make that approximation, but the model fails for short-range missiles.

In general I don't like to over-engineering my missile designs and therefore I usually end up trying to hit both a range and speed at the same time.
So, even if I could build a missile with a Speed X and get a range Y, that range might just be more than I need even if I get most out of the amount of fuel I put into that space on the missile. I might rather put some more armour or bigger yield on the warhead and reduce the range to a "good enough" range. No need to have a 400m km range missile if 200m km does it equally well.

When designing MIRV missiles I generally go for the efficiency but on regular missiles it almost never come in to play.

Part of the problem is the granularity of the model.  The engine size increment is .1, so any optimization has to be approximate.  Basically, the point of the model is that if the amount of fuel that you have on the missile is more than about a third of the size of the engine, you're better off cutting the fuel and making the engine bigger with a lower power multiplier.  Conversely, if the fuel is smaller than that, and you're not at your maximum power, decreasing engine size and increasing power multiplier is the way to go.  If you're pinned by the power multiplier, then the model becomes less helpful.