Optimal Fuel:Engine ratio

[Iranon]

Let's say we set a speed requirement and weight allowance for propulsion (i. e.  engines + fuel).

Let's standardise our weight allowance w on a weird but helpful unit: "the weight of a 1. 0-power engine needed to reach the design speed at the full design size".  Yes, it's ugly.  No, we won't have to standardise speed on "the airspeed of an unladen swallow".
Examples:
If we could reach our design speed with 1. 0 power engines but have nothing left over for fuel, w is 1
If power 1. 0 engines without fuel would require twice our weight allowance, w is 0. 5

The fuel we have available is (w-1/p), in the same awkward unit.  Because we know the efficiency modifier for a given power multiplier, our range at the desired speed and weight is proportional to (w-1/p)/p^2. 5

Now my hillbilly maths failed even harder at letting me go anywhere elegantly.  I just plugged in some values of w, differentiated the buggers with respect to p, and eyeballed the results for anything interesting.
Eureka: Maximum range at a given design speed and weight was always reached when fuel weight was 40% of engine weight.

All those long range missiles or independent (i. e.  neither tankers nor tankees) long range craft using more space for fuel than engine are wasteful.  Get close to a 2:5 ratio between fuel and engine, and adjust the power multiplier accordingly.
You may want erring slightly on the side of bigger engines: Achieving almost the same range on less fuel is an advantage, and if we're using a single big engine we get a further boost in efficiency.

[bean]

I solved this last year. http://aurora2.pentarch.org/index.php/topic,5659.0.html

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.

Your result agrees with mine for ships, but you didn't take into account the gain in efficiency from larger missile engines.  (This isn't a criticism.  I'm an engineering student, and have to do stuff like this for school.)

[Iranon]

Well, I feel a bit silly now

I deliberately mentioned engine size only as an aside, as that may not scale freely:
designing additional engines for the last few percentage points of efficiency may not be worth it, especially if larger engines cause maintenance concerns or we'd prefer slightly more redundancy over slightly more efficiency.  But in either case, relatively less fuel is preferable.

Good to have more detailed hard info than I got - I had often used 1:3 in practice.  Thanks!

[bean]

I deliberately mentioned engine size only as an aside, as that may not scale freely:
designing additional engines for the last few percentage points of efficiency may not be worth it, especially if larger engines cause maintenance concerns or we'd prefer slightly more redundancy over slightly more efficiency.  But in either case, relatively less fuel is preferable.

Depends on if we're discussing ships or missiles.  For ships, I'm in agreement with you.  Actually, I don't even pay attention to this due to research costs and other design considerations.  For missiles, this improves performance a lot.  There is one caveat, however.  The missile ratio assumes infinite scaling in the power multiplier.  That's not true in practice, so you'll often need more engine than is strictly optimal.

[Jorgen_CAB]

In my experience there is no such thing as the most efficient ration of fuel and engine. Both for ships and missiles.

The usual thing is that you want a desired speed and a desired range. It's rare you only want one thing. Then there is something called research cost, fuel production and build/maintenance cost to consider. This means you can't just make one engine for every class of ship you want to build so you normally want to keep to as few engine models as possible.

Yes there is a sweet spot between engine power level and the amount of fuel from a mathematical perspective and it can be important to understand that. But in practice it often have little relevance.

At least that is my experience playing the game...

[Iranon]

It does require some qualifiers.  The optimum holds true mostly for independent things that aren't expected to regularly transfer fuel in either direction, and even then we're constrained by tech.

For example, if we are willing to sacrifice a lot of range for a little speed (carrier-bound fighters, short-ranged missiles) we're unlikely to have researched a high enough power multiplier for the ideal setup.  Here a shotglass  of fuel and the highest-powered engines we can make will have to do.

But if you design an engine specifically for long range missiles or an independent cruiser meant to boldly go where no-one has gone before,  and you' d have to use more than 40% its weight in fuel, you should probably consider using less stressed engines.
It's also a nice guideline for larger decisions. . .  e. g.  if I want a fighter wing able to operate on its own, I'll add enough tanker versions to get the total fuel of the wing between 25 and 40%.  Less is ok (independent operations may be nice but not the top priority), but if I'd need more there is probably something wrong with my plans.

[Jorgen_CAB]

You basically need to know that the sweet spot between engine size and fuel is about 2/3 engine and 1/3 fuel if I'm not mistaken. If you bring more fuel you might rather use engines with a lower multiplier (if range and not speed is your goal)... more or less. This is if memory serves me right, have not looked up the numbers lately. Calculating the exact point is usually not very important, just knowing the roughly most optimised configuration will probably be enough.

For ships this is usually never important at all, not even commercial ships. It can be important for missiles or mostly for drones, for missiles you usually just want the highest possible multiplier that you can get so the missile is as fast as possible, unless you are designing some sort of super range missiles.

When I design a fighter for example my primary concern is to give it a certain speed and range based on doctrine, not on what is most efficient for it's maximum range. A fighter usually only need fuel for making its final run against a target, fighter-tankers take care of the longer range when needed. A fighter only need perhaps half too a billion km in range or so, perhaps slightly more the longer into a game you get. Even from a RP angle I can't really justify long range independent fighters instead of just designing a long range fighter tanker that can be attached to each wing as is needed depending on the range I want my fighters to strike at, it give me much more flexibility.
The same goes for ships, refuelling tankers is more useful than stuffing all your ships full of fuel you only need very rarely. The only ship that I can reasonably find important to apply this to would be exploration ships (as you suggested as well) that you send out for several years. But your fuel efficiency technology quickly get down to very low levels so this also become pointless as you can easily keep the ship in space way longer than their deployment time (unless you build generation ships that is) anyway.

I have seen many threads about the optimum engine/fuel ratio and they often end up talking about hypothetical cases that are not practically applicable to the game most of the time. Although, I do agree as I said above, that having the basic knowledge of the optimum weight between engine/fuel in regard to optimum range is good to know as a reference.

Perhaps you should include some real applicable examples for its use in the game would go a long way to show exactly when and why it's good to use this optimum solution. Such as presenting some hard examples of missiles, fighters and ships that use the optimum engine/fuel ratio for range and what their uses would be to capitalize on the efficiency. I think this would make the discussion a little more informative for those that are not as experienced with the game.

So, please don't look at my remarks as a negative critique, its not meant to be, but rather as an encouragement to complete your analysis with some real practical examples to show when it is smart to use it.

[bean]

In my experience there is no such thing as the most efficient ration of fuel and engine. Both for ships and missiles.

Haven't we done this before?

The usual thing is that you want a desired speed and a desired range. It's rare you only want one thing. Then there is something called research cost, fuel production and build/maintenance cost to consider. This means you can't just make one engine for every class of ship you want to build so you normally want to keep to as few engine models as possible.

This is true for ships, but not for missiles. Given the complexities of shipbuilding, I don't even consider this number when I'm doing that. 

It's also a nice guideline for larger decisions. . .  e. g.  if I want a fighter wing able to operate on its own, I'll add enough tanker versions to get the total fuel of the wing between 25 and 40%.  Less is ok (independent operations may be nice but not the top priority), but if I'd need more there is probably something wrong with my plans.

Actually, I don't think this works.  The math is based on how the engine power multiplier scales with size.  Offboard fuel will wreck that.

[Jorgen_CAB]

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.

When designing a missile with extra long range in mind we should obviously know the optimum in case we want to lower the multiplier below the maximum.

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.

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.

[bean]

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.

[Jorgen_CAB]

As I stated above, the numbers were from my memory and they were 3/4 engine and 1/4 fuel and not 2/3 engine and 1/3 fuel. I didn't really look it up I just winged it. I just know it was in that ballpark.  

[Iranon]

Regarding groups of fighters: I assumed an independent wing of uniform tonnage and speed - nothing to increase sensor footprint or slow them down.  We get an ideal of 40% of engine weight if we ignore the engine size multiplier altogether, this still works as an upper bound if fuel isn't distributed evenly. 
Usually we'll want to go slightly lower, there are fiddly details  (I listed some earlier) which preclude an absolute ideal.

Short-ranged fighters and tankers are more efficient than uniform long-range designs. : If we move most of the fuel to dedicated tankers and use the weight reductions  for more weaponry, we need fewer fire controls sets for the same firepower.  Not that this is necessarily the best use, we may prefer them smaller and faster.

[bean]

Regarding groups of fighters: I assumed an independent wing of uniform tonnage and speed - nothing to increase sensor footprint or slow them down.  We get an ideal of 40% of engine weight if we ignore the engine size multiplier altogether, this still works as an upper bound if fuel isn't distributed evenly. 
Usually we'll want to go slightly lower, there are fiddly details  (I listed some earlier) which preclude an absolute ideal.

I don't think the math on this actually works.  The 40% comes from an assumption that there is a simple tradeoff between fuel and engine, which doesn't quite hold for a tanker/fighter force.  You can't move engine from the fighters to the tankers if you decide to raise the amount of space allocated to propulsion like you could in a more conventional setup.

Short-ranged fighters and tankers are more efficient than uniform long-range designs. : If we move most of the fuel to dedicated tankers and use the weight reductions  for more weaponry, we need fewer fire controls sets for the same firepower.  Not that this is necessarily the best use, we may prefer them smaller and faster.

I will agree with this, although the math isn't quite there.  When you're tanking, fuel-efficiency becomes as important as raw range, simply to avoid placing too much of a strain on the tankers.  I've had to re-engine a bunch of survey craft because they were using too much fuel.  Their range actually went down slightly, but that was because they were carrying a lot less fuel.

[Iranon]

I don't think the math on this actually works.   The 40% comes from an assumption that there is a simple tradeoff between fuel and engine, which doesn't quite hold for a tanker/fighter force.   You can't move engine from the fighters to the tankers if you decide to raise the amount of space allocated to propulsion like you could in a more conventional setup.

I don't see the problem.  If you increase the amount of space allocated to propulsion, every fighter - refuel version or not - would get the same upgrade.  You are more limited by granularity and there's an absolute size limit, but the maths for optimum fuel:engine weights stays the same as for single craft.

I will agree with this, although the math isn't quite there.   When you're tanking, fuel-efficiency becomes as important as raw range, simply to avoid placing too much of a strain on the tankers.   I've had to re-engine a bunch of survey craft because they were using too much fuel.   Their range actually went down slightly, but that was because they were carrying a lot less fuel. 

Depends on our requirements.  If we want the  best combination of fighting ability and independent range (i. e.  just refueled by tanker-fighters  moving with us at the same speed), our maths applies.
If that independence requirement can slide and we accept the requirement to be topped up regularly by regular tankers,  "don't waste fuel schlepping fuel with fuel hogs" takes precedence over the sweet spot for independent craft/wings.

Sorry if I seem stubborn, but I'd like to see where the disagreement comes from.  If one of us is wrong with the maths or where it applies, that would be good to find out.  If we simply make different tacit assumptions, it'd be good to know them,

[bean]

I don't see the problem.  If you increase the amount of space allocated to propulsion, every fighter - refuel version or not - would get the same upgrade.  You are more limited by granularity and there's an absolute size limit, but the maths for optimum fuel:engine weights stays the same as for single craft.

No, because you're attempting to treat an entire squadron as a single craft.  While it's clever, the problem is that you are in an area where two of the underlying assumptions (free tradeoff and infinite scaling) hold very poorly.  Let's say that during design, you end up with a .5 f:e ratio, instead of the .4 you would want.  Normally, you would increase the amount of engine, and decrease the amount of fuel, but in this case, you can't increase the engine on the fighters because you don't have space, and putting the engine on the tankers won't help the fighters at all.  That, plus limited engine granularity makes working with theoretical optima here somewhat academic.

Sorry if I seem stubborn, but I'd like to see where the disagreement comes from.

Perfectly all right with that.

If one of us is wrong with the maths or where it applies, that would be good to find out.  If we simply make different tacit assumptions, it'd be good to know them,

I think it's a combination of both.  I applaud your attempt to apply the math, but I'm not sure it's either correct or relevant.